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diff --git a/0NE0T4oBgHgl3EQfuAEL/content/tmp_files/2301.02598v1.pdf.txt b/0NE0T4oBgHgl3EQfuAEL/content/tmp_files/2301.02598v1.pdf.txt
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+1
+Online Fusion of Multi-resolution Multispectral Images with Weakly
+Supervised Temporal Dynamics
+Haoqing Lia, Bhavya Duvvuria, Ricardo Borsoib, Tales Imbiribaa, Edward Beighleya,
+Deniz Erdo˘gmu¸sa, Pau Closasa
+aNortheastern University, Boston, 02215, MA, USA
+bUniversity of Lorraine, CNRS, CRAN, Nancy, F-54000, France
+Abstract
+Real-time satellite imaging has a central role in monitoring, detecting and estimating the
+intensity of key natural phenomena such as floods, earthquakes, etc. One important con-
+straint of satellite imaging is the trade-off between spatial/spectral resolution and their
+revisiting time, a consequence of design and physical constraints imposed by satellite or-
+bit among other technical limitations. In this paper, we focus on fusing multi-temporal,
+multi-spectral images where data acquired from different instruments with different spatial
+resolutions is used. We leverage the spatial relationship between images at multiple modal-
+ities to generate high-resolution image sequences at higher revisiting rates. To achieve this
+goal, we formulate the fusion method as a recursive state estimation problem and study
+its performance in filtering and smoothing contexts. Furthermore, a calibration strategy is
+proposed to estimate the time-varying temporal dynamics of the image sequence using only
+a small amount of historical image data. Differently from the training process in traditional
+machine learning algorithms, which usually require large datasets and computation times,
+the parameters of the temporal dynamical model are calibrated based on an analytical ex-
+pression that uses only two of the images in the historical dataset. A distributed version
+of the Bayesian filtering and smoothing strategies is also proposed to reduce its compu-
+tational complexity. To evaluate the proposed methodology we consider a water mapping
+task where real data acquired by the Landsat and MODIS instruments are fused generating
+high spatial-temporal resolution image estimates. Our experiments show that the proposed
+methodology outperforms the competing methods in both estimation accuracy and water
+mapping tasks.
+Keywords:
+Multimodal image fusion, Online Fusion, Bayesian Filtering, Water mapping,
+Super-resolution
+1. Introduction
+High spatial resolution satellite image data is a fundamental tool for remote sensing
+applications such as the monitoring of land cover changes [1, 2], deforestation [3, 4] or wa-
+ter mapping [5, 6] and water quality [7]. Moreover, to adequately deal with the variability
+Preprint submitted to ISPRS Journal of Photogrammetry and Remote Sensing
+June 2022
+arXiv:2301.02598v1  [eess.IV]  6 Jan 2023
+
+of such events over time it is important to have short time spans between different image
+acquisitions of the same scene (i.e., a high temporal resolution, or low revisit times). How-
+ever, fundamental limitations of multiband imaging instruments and large sensor-to-target
+distances impose a trade-off between spatial and temporal resolutions of satellite image
+sequences.
+This means that instruments providing high spatial resolution have long revisit times,
+while the converse holds for instruments with short revisit times. This can be illustrated, for
+instance, by considering Landsat 8 and MODIS instruments (with 30 and 250/500 meters
+spatial resolution, respectively). While MODIS is able to provide daily images at coarse
+resolution, Landsat-8 only revisits the same site once every 16 days [8].
+Considering these limitations, many works proposed multimodal image fusion techniques
+to generate high (spatial, spectral or temporal) resolution remote sensing images. Multi-
+modal image fusion aims to combine multiple observed images, each of which having high
+resolution in a given dimension – spatial, temporal, or spectral – to generate high reso-
+lution image sequences.
+Several instances of image fusion have been considered, some
+works aim to directly supply classification maps from multiple satellite image and surface
+elevation data at each time instant [9], integrating optical and radar data for time-series
+crop classification [10, 11], or fusing spatio-temporal optical and elevation data to obtain
+high-resolution land temperature maps [12].
+In particular, classification or mapping tasks based on time-series remote sensing data
+is receiving increasing interest in the literature [13, 14, 10, 11]. Thus, to overcome the limi-
+tations of existing instruments, fusing images with different spectral and spatial resolutions
+has been extensively studied to generate images with high spatial and spectral resolutions,
+which are critical for accurately distinguishing different materials in a pixel [15, 16, 17].
+Recently, an increasing interest has been observed in applying multimodal image fusion to
+generate image sequences with high spatial and temporal resolutions [18], with particular
+interest dedicated to fusing data from multiple satellites to obtain daily images with high
+(e.g., 30 m) resolution [19].
+This has already had an important impact in applications
+such as the generation of daily snow cover maps [20] and the study of drought-induced
+tree mortality [21]. Existing spatiotemporal image fusion methods are usually divided in
+weighted fusion, umixing-based, learning-based and Bayesian approaches [22]. There also
+exist hybrid techniques, which leverage ideas from more than one family of approaches.
+Weighted fusion methods assume that the temporal changes occurring between two time
+instants are consistent between the high and low spatial resolution images for low resolution
+pixels which are composed of only a single material [23]. However, coarse resolution pixels
+are often mixtures of different materials.
+The predicted high resolution pixels are then
+computed as a weighted linear combination of the previous high resolution pixels and of
+the changes occurring at low resolution pixels in a given neighborhood [24, 25]. Different
+works have designed various weighting functions, which aim to select neighboring pixels
+that are homogeneous and spatially/spectrally similar to the pixel whose change is being
+predicted [24, 22, 26].
+Other works have extended such framework account for sudden
+changes [27] or to use different weighting functions [25].
+2
+
+Figure 1: Overview of the proposed method. Multimodal (e.g., Landsat and MODIS over time) images time
+series are fused by the Distributed Multimodal Bayesian Fusion algorithm resulting in a high spatial-temporal
+resolution estimated sequence. Covariance estimates for the dynamical model are estimated through a weakly
+supervised strategy based on local high-resolution historical data. We highlight that the Bayesian fusion
+methodology employed here is agnostic to the multimodal measurement model making the strategy easily
+generalizable to different data scenarios.
+Unmixing-based methods make use of the linear mixing model (LMM), which assumes
+that each pixel in the low resolution image can be represented as a convex combination of the
+reflectance of a small number of pure spectral signatures, called endmembers [28, 29]. The
+LMM has been used for multimodal image fusion by assuming the proportions of each mate-
+rial in a low resolution pixel to be stable/constant over time [30, 31, 32]. This way, spectral
+unmixing [28] is used to estimate the endmembers at different time instants from low reso-
+lution images, while using different strategies to mitigate the spectral variability of a single
+material [30, 33, 34]. However, abrupt abundance variations (originating from, e.g., land
+cover changes) are commonly found in multitemporal image streams [35, 36, 37, 38], which
+may negatively impact the performance of such methods and can be particularly challeng-
+ing to address when occurring jointly with finer endmember variations [35]. Thus, special
+care is required when fusing images which are temporally distant from one another [39],
+motivating the development of strategies using, e.g., spatially adaptive quantification of the
+reliability of the input images to guide unmixing based image fusion strategies [40].
+Learning-based approaches leverage training data and different machine learning al-
+gorithms in order to perform image fusion.
+Those approaches are varied, ranging from
+approaches such as dictionary learning [41], which are based on a sparse representation
+of image pixels and have a strong connection to the LMM, to convolutional neural net-
+works [42], which are flexible function approximations which are typically used to learn a
+mapping from the low-resolution to high resolution data.
+Bayesian methods are flexible alternatives to the previous approaches that take into ac-
+count the uncertainty present both in the imaging model and in the estimated images. The
+3
+
+Bayesian framework is based on the definition of probabilistic models to describe the rela-
+tionship between images of different spatial, spectral and temporal resolutions acquired by
+different instruments. This allows image fusion to be formulated as a maximum a posteriori
+estimation problem [43]. Although Bayesian methods usually consider Gaussian distribu-
+tions for mathematical tractability, different variations have been proposed depending on
+how the image acquisition process is modelled and on how the mean and covariance matri-
+ces are estimated. This included assuming them diagonal [44], estimating image covariance
+matrices based on an initial estimate of the high resolution image [43], or based on the low
+resolution image pixels [45].
+A recent work considered a Kalman filter-based approach to estimate a high resolution
+image sequence based on mixed resolution observations from the Landsat and MODIS in-
+struments [46]. However, to define the model for the Kalman filter, two Landsat+MODIS
+image pairs at times t0 and tN are considered, as well as a time series of MODIS images
+at instants tk P rt0, tNs, making it unsuitable for online operation. Moreover, changes be-
+tween each pair of images were assumed to be constant/uniform over predefined groups of
+high resolution image pixels, which can be restrictive (due to the large resolution difference
+between the measured images, the groups must contain many pixels in order to make the
+model well-posed). It also does not benefit from auxiliary information that could aid the
+estimation of the high resolution images. Another work used the Kalman filter to esti-
+mate normalized difference vegetation indices (NDVI) time series images from Landsat and
+MODIS observations, using an affine model for the dynamics of the states whose coeffi-
+cients are selected based on the seasonality, and another affine model to relate the NVDI
+estimate obtained from MODIS and Landsat measurements [47]. The Kalman filter was
+also recently applied to estimate land surface temperature by fusing thermal infrared and
+microwave data [48].
+In this paper, we propose a weakly supervised Kalman filter and smoother framework
+for spatio-temporal fusion of multispectral images. The proposed framework relies on ex-
+plicit modeling assumptions about the image acquisition and temporal evolution processes,
+under which the proposed solution is statistically optimal. The Kalman filter-based meth-
+ods can operate in a fully online setting, where high-resolution images are only available
+as past data. We also develop a smoother-based method to optimally exploit information
+contained in future high-resolution observed images when processing images in a time win-
+dow. However, the quality of the reconstruction of Kalman filter and smoother strategies
+depend directly on the quality of the dynamical image evolution model. Thus, to overcome
+this limitation, a weakly supervised strategy is proposed to learn the temporal dynamics
+of the high-resolution images from a small amount of past data. More precisely, instead of
+considering the changes to be constant over areas comprising large amounts of image pixels,
+we propose an analytical calibration strategy to estimate a more informative time-varying
+dynamical image model by leveraging historical data. This allows for a better localiza-
+tion of changes in the high resolution image even in intervals where only coarse resolution
+observations (e.g., MODIS) are available. Moreover, to mitigate the high computational
+complexity of the Kalman filter and smoother, we propose a distributed implementation
+4
+
+by exploiting different independence assumptions about the high-resolution state space,
+allowing the proposed methods to be applied to large datasets and geographical areas. Fig-
+ure 1 depicts the proposed methodology where high-resolution (spatially and temporally)
+estimates are generated by fusing different data modalities. We illustrate the application
+of the proposed framework by fusing images from the Landsat and MODIS instruments.
+Experimental results indicate that the proposed method can lead to considerable improve-
+ments compared to using a non-informative dynamical model and to widely used image
+fusion algorithms, both in image reconstruction and in downstream water classification
+and hydrograph estimation tasks. A software package containing an implementation of the
+proposed method and the image dataset is available at https://github.com/HaoqingLi/
+Multi-resolution-Multispectral-image-fusion-based-weakly-supervised-constrained-Kalman-filter.
+This paper is organized as follows. In Section 2, we present the paper notation and the
+proposed imaging model. Section 3 presents the Kalman filter and smoother approaches
+for multimodal image fusion. Section 5 contains simulation experiments that illustrate the
+performance of the proposed method. Finally, Section 6 concludes the paper.
+2. Dynamical Imaging Model
+2.1. Definitions and notation
+Let us denote the the ℓ-th band of the k-th acquired image reflectances from modality
+m P Ω by ym
+k,ℓ P RNm,ℓ, with Nm,ℓ pixels for each of the bands ℓ “ 1, . . . , Lm, and Ω denoting
+the set of image modalities. As a practical example, we consider Ω “ tL, Mu to contain
+the Landsat-8, and MODIS image modalities, without loss of generality. We also denote by
+ΩH the highest resolution image modality, e.g., ΩH “ tLu. We denote the corresponding
+high resolution latent reflectances by Sk P RNHˆLH, with NH pixels and LH bands, with
+LH ě Lm and NH ě Nm,ℓ, @ℓ, m. Subindex k P N˚ denotes the acquisition time index. We
+also denote by vecp¨q, colt¨u, diagt¨u and by blkdiagt¨u the vectorization, vector stacking,
+diagonal and block diagonal matrix operators, respectively. The notation xa:b for a, b P N˚
+represents the set txa, xa`1, . . . , xbu. We use Npµ, Σq to denote a Gaussian distribution
+with mean µ and covariance matrix Σ.
+2.2. Measurement model
+To formulate our measurement model we assume that the acquired image at time index
+k, for any imaging modality, is a spatially degraded and spectrally transformed version of
+the high resolution latent reflectance image Sk. Following this assumption our measurement
+model for the m-th modality becomes:
+ym
+k,ℓ “ Hm
+ℓ pSkqcm
+ℓ ` rm
+k,ℓ ,
+ℓ “ 1, . . . , Lm ,
+(1)
+where cm
+ℓ P RLH denotes a spectral transformation vector, mapping all bands in Sk to the
+ℓ-th measured band at modality m; Hm
+ℓ
+is a linear operator representing the band-wise
+spatial degradation, modeling blurring and downsampling effects of each high resolution
+band, and rm
+k,ℓ represents the measurement noise. Note that, while we consider the spatial
+5
+
+resolution of the high resolution bands in Sk to be the same, different bands from the
+same modality can have different resolutions. We also assume the measurement noise to
+be Gaussian and uncorrelated among bands, that is, rm
+k,ℓ „ Np0, Rm
+ℓ q with time-invariant
+covariance matrix given by Rm
+ℓ P RNm,ℓˆNm,ℓ, and covprm
+k,j, rm
+k,ℓq “ 0 for all j ‰ ℓ.
+Note that satellite images may be corrupted by several effects, including dead pixels
+in the sensor, incorrect atmospheric compensation, and the presence of heavy cloud cover.
+Such pixels cannot be reliably used in the image fusion process as they may degrade the
+performance of the method.
+Directly addressing these effects using a statistical model
+would require the choice of a non-Gaussian distribution for the noise vector rm
+k,ℓ, which
+could make the computational complexity of the fusion procedure prohibitive. Thus, we
+consider a matrix Dm
+k P R r
+NmˆNm, which eliminates outlier pixels from the image, leading
+to the following transformed measurement model:
+rym
+k,ℓ “ Dm
+k Hm
+ℓ pSkqcm
+ℓ ` rrm
+k,ℓ ,
+(2)
+where rym
+k,ℓ “ Dm
+k ym
+k,ℓ and rrm
+k,ℓ “ Dm
+k rm
+k,ℓ denotes the measured image band and the mea-
+surement noise in which the outlier values have been removed.
+Using (2) and the properties of the vectorization operator, we can write this model
+equivalently as
+rym
+k,ℓ “
+“
+pcm
+ℓ qJ b Dm
+k
+‰
+vec
+`
+Hm
+ℓ pSkq
+˘
+` rrm
+k,ℓ
+“
+“
+pcm
+ℓ qJ b Dm
+k
+‰
+Hm
+ℓ sk ` rrm
+k,ℓ
+(3)
+where b denotes the Kronecker product.
+The variable sk P RLHNH denotes a vector-
+ordering of the high-resolution image Sk which is obtained by grouping all pixels such that
+the bands of a single HR pixel are adjacent to each other, and the pixels that are contained
+within a single “lowest-resolution” pixel are also adjacent to each other, that is:
+sk “
+»
+—————————–
+»
+————————–
+sk,1,ιp1,1q
+...
+sk,LH,ιp1,1q
+sk,1,ιp2,1q
+...
+sk,LH,ιpd,1q
+fi
+ffiffiffiffiffiffiffiffifl
+J
+, . . . ,
+»
+—————————–
+sk,1,ιp1,Nm1,ℓ1q
+...
+sk,LH,ιp1,Nm1,ℓ1q
+sk,1,ιp2,Nm1,ℓ1q
+...
+sk,LH,ιpd,Nm1,ℓ1q
+fi
+ffiffiffiffiffiffiffiffiffifl
+Jfi
+ffiffiffiffiffiffiffiffiffifl
+J
+,
+(4)
+where sk,i,j is the pi, jq-th position of Sk, m1 and ℓ1 are the modality and spectral band with
+the lowest spatial resolution (i.e., for which Nm,ℓ is smallest), d “ NH{Nm1,ℓ1 is the number of
+HR pixels inside each low resolution pixel of band ℓ1 and modality m1, and ι : N˚ ˆN˚ Ñ N˚
+is a function such that ιpi, jq returns the index (in Sk) of the of the i-th HR pixel contained
+inside the j-th low resolution pixel (where i P t1, . . . , du) for modality m1 and band ℓ1. Hm
+ℓ
+is a matrix form representation of the operator Hm
+ℓ , such that vecpHm
+ℓ pSkqq “ Hm
+ℓ sk.
+6
+
+We can now represent all bands from each modality in the form of a single vector
+rym
+k P R r
+NmLm as
+rym
+k “
+¨
+˚
+˝
+“
+pcm
+1 qJ b Dm
+k
+‰
+Hm
+1
+...
+“
+pcm
+LmqJ b Dm
+k
+‰
+Hm
+Lm
+˛
+‹‚
+looooooooooooooomooooooooooooooon
+Ă
+H
+m
+k
+sk ` rrm
+k ,
+(5)
+where rrm
+k „ Np0, rR
+m
+k q, and
+rym
+k “ col
+␣
+rym
+k,1, . . . , rym
+k,Lm
+(
+,
+(6)
+rrm
+k “ col
+␣
+rrm
+k,1, . . . , rrm
+k,Lm
+(
+,
+(7)
+rR
+m
+k “ blkdiag
+␣
+Dm
+k Rm
+1 pDm
+k qJ, . . . , Dm
+k Rm
+LmpDm
+k qJ(
+(8)
+Note that at most time instants k, one or more of the modalities m P Ω is not observed. In
+this case, we set the matrix Dm
+k as an empty (zero-dimensional) matrix, which simplifies
+the problem and avoids introducing additional notation.
+2.3. Dynamical evolution model
+Defining reasonable dynamical models for image fusion requires detailed knowledge re-
+garding the scene evolution over time, which is often unattainable. In this contribution, we
+aim at a complete data driven strategy assuming very little knowledge regarding the scene
+evolution except for past data coming from the imaging modalities being used. To match
+such lack of prior knowledge we consider a simple random-walk process to model the latent
+state dynamics as:
+sk`1 “ F ksk ` qk ,
+(9)
+where F k P RLHNHˆLHNH is the state transition matrix, which is assumed to satisfy
+}F k}2 ď 1, and qk „ Np0, Qkq with Qk P RLHNHˆLHNH being the state process noise
+covariance matrix. Note that the above model plays a crucial role in the estimation results,
+as it describes both the distribution of the changes occurring in the image at time k, as well
+as the marginal distribution of the states. This means that more sophisticated dynamics
+can be introduced in the problem through the appropriate design of the process noise co-
+variance matrix Qk. Although expectation maximization (EM) can be used to estimate Qk
+in time invariant models [49], the problem becomes extremely ill-posed in the time-varying
+setting. Another issue relates to the computational complexity of EM-based strategies re-
+quiring the solution of the Kalman filter and smoother systems multiple times, becoming
+unfeasible when dealing with large images. For these reasons, we propose an alternative
+route to estimate Qk.
+7
+
+2.4. A weakly supervised approach for estimating Qk
+We consider QkpDkq as a function of the set Dk “ t˜ymPΩH
+ℓ
+uℓăk of past high resolution
+images. The set Dk represents historical data and images currently being fused up the the
+time step k. Although many strategies could be leveraged to find suitable past time windows
+to account for more relevant covariance estimation and consider full covariance matrices,
+in this preliminary work we choose a simple route to validate this type of approach. For
+this, let ymPΩH
+k´τ
+be the the most recently observed high resolution image1. We compute Qk
+by finding in our historical data the most similar image to ymPΩH
+k´τ
+and then computing the
+pixelwise variance across the following n P N˚ images in our historical data. That is, we
+compute Qk executing the following three steps for every time step k:
+1. Identify the most similar state over Dk, that is, the image that is most similar, ac-
+cording to a metric L
+ℓ˚ “ arg min
+ℓPIDk
+L
+`
+ymPΩH
+k´τ
+, rDksℓ
+˘
+,
+(10)
+with rDksℓ being the ℓ-th image in the historical set Dk, and IDk Ď Z is the set
+containing the time index of each image in Dk.
+2. select a time window rDksℓ˚:ℓ˚`n.
+3. compute the diagonal process noise covariance matrix, i.e., Qk “ diagtq2
+k,1, . . . , q2
+k,LHNHu,
+as
+q2
+k,j “ max
+ˆvar
+`
+rDkspjq
+ℓ˚:ℓ˚`n
+˘
+∆ℓ˚
+Dk
+, ε2
+˙
+ˆ ∆k ,
+(11)
+where rDkspjq
+ℓ˚:ℓ˚`n “ r˜ymPΩH
+ℓ˚,j
+, . . . , ˜ymPΩH
+ℓ˚`n,js, ε ą 0 is a small scalar allowing for changes on the
+scene that were unseen on the historical data window rDksℓ˚:ℓ˚`n, ∆k is the time interval
+(in days) between ymPΩH
+k
+and ymPΩH
+k`1
+, and ∆ℓ˚
+Dk is the time interval (in days) between rDksℓ˚
+and rDksℓ˚`n. As similarity metric we used the cosine similarity Lpy, zq “ cospy, zq.
+3. Multimodal image fusion using a weakly supervised constrained Kalman fil-
+ter
+Considering models (5) and (9), the online multimodal image fusion problem can be
+formulated as the problem of computing the posterior distribution of the high resolution
+image given all previous measurements available, i.e.,
+p
+`
+sk
+ˇˇtrym
+1:kumPΩ
+˘
+“ N
+`
+sk|k, P k|k
+˘
+.
+(12)
+Due to the choice of a linear Gaussian model, this distribution is also Gaussian. Moreover,
+its mean vector sk|k and covariance matrix P k|k can be computed recursively using the
+standard Kalman filter with a prediction and update steps [50].
+1That is, τ P Z` is the smallest integer such that a high resolution image was observed at time instant
+k ´ τ.
+8
+
+More precisely, the prediction step of the Kalman filter computes the first and second
+order moments of p
+`
+sk
+ˇˇtrym
+1:k´1umPΩ
+˘
+as:
+sk|k´1 “ F k´1sk´1|k´1
+(13)
+P k|k´1 “ F k´1P k´1|k´1F J
+k´1 ` Qk´1
+(14)
+The update step computes then computes of (12).
+Note that the update step can be
+simplified and implemented separately for each data modality by using the Markov property
+of the model and the independence between noise vectors of different modelities:
+p
+`
+sk
+ˇˇtrym
+1:kumPΩ
+˘
+9p
+`
+trym
+k umPΩ
+ˇˇsk
+˘
+p
+`
+sk
+ˇˇtrym
+1:k´1umPΩ
+˘
+“ p
+`
+sk
+ˇˇtryu
+1:k´1uuPΩ
+˘ ź
+mPΩ
+p
+`
+rym
+k
+ˇˇsk
+˘
+.
+(15)
+By computing the first product in the right hand side as:
+p
+`
+sk
+ˇˇtryu
+1:k´1uuPΩ
+˘
+p
+`
+rym
+k
+ˇˇsk
+˘
+9p
+`
+sk
+ˇˇtryu
+1:k´1uuPΩ, rym
+k
+˘
+,
+(16)
+which is an update step of the Kalman filter with image modality m to yield a new posterior
+in the r.h.s. of (16). This can be computed as:
+vm
+k “ rym
+k ´ Ă
+H
+m
+k sk|k´1
+(17)
+T m
+k “ Ă
+H
+m
+k P k|k´1
+`Ă
+H
+m
+k
+˘J ` rR
+m
+k
+(18)
+Km
+k “ P k|k´1
+`Ă
+H
+m
+k
+˘J`
+T m
+k
+˘´1
+(19)
+sk|k “ sk|k´1 ` Km
+k vm
+k
+(20)
+P k|k “ P k|k´1 ´ Km
+k T m
+k
+`
+Km
+k
+˘J
+(21)
+for m P Ω.
+By proceeding with the computation of the product in the r.h.s.
+of (15)
+recursively, the Kalman update can then be performed separately for each of the modalities
+observed at time instant k. Note that after the first modality is processed, the update
+equations above are used again for the subsequent modalities by setting sk`1|k and P k`1|k
+as equal to the posterior estimates from the previously processed modality.
+3.1. The Linear Smoother
+Given a window of K image samples, the Bayesian smoothing problem consists of com-
+puting the posterior distribution of the high resolution image given all available measure-
+ments available, i.e.,
+p
+`
+sk
+ˇˇtrym
+1:KumPΩ
+˘
+“ N
+`
+sk|K, P k|K
+˘
+,
+(22)
+9
+
+which is also a Gaussian. Just like in the filtering problem, the linear and Gaussian model
+allows this solution to be computed efficiently using the Rauch-Tung-Striebel (RTS) smooth-
+ing equations [50], which consist of a forward pass of the Kalman filter (as described before),
+followed by a backwards recursion that updates the previously computed mean and covari-
+ances matrices of the state with information from future time instants.
+We note that the smoothing can also be performed efficiently for the case when multiple
+image modalities are available. Let us consider the Bayesian smoothing equations as defined
+in [51, 50], which is performed in two steps. Starting from the Kalman state estimate at
+time K, given by p
+`
+sK
+ˇˇtrym
+1:KumPΩ
+˘
+, the smoothing distribution is computed recursively for
+k “ k ´ 1, . . . , 1, according to the following relation:
+p
+`
+sk
+ˇˇtrym
+1:KumPΩ
+˘
+“ p
+`
+sk
+ˇˇtrym
+1:kumPΩ
+˘
+ˆ
+ż ppsk`1|skqp
+`
+sk`1
+ˇˇtrym
+1:KumPΩ
+˘
+p
+`
+sk`1
+ˇˇtrym
+1:kumPΩ
+˘
+dsk`1 ,
+(23)
+where p
+`
+sk
+ˇˇtrym
+1:kumPΩ
+˘
+“ Npsk|k, P k|kq is the Kalman estimate of the state PDF at time k,
+ppsk`1|skqq is the state transition PDF, computed according to (9), p
+`
+sk`1
+ˇˇtrym
+1:KumPΩ
+˘
+“
+Npsk`1|K, P k`1|Kq is the smoothing distribution obtained at the previous iteration, and
+p
+`
+sk`1
+ˇˇtrym
+1:kumPΩ
+˘
+is the predictive state distribution, which is computed exactly as in the
+prediction step of the Kalman filter.
+In the linear and Gaussian case this translates into the following closed form solution [50],
+with
+sk`1|k “ F ksk|k
+(24)
+P k`1|k “ F kP k|kF J
+k ` Qk
+(25)
+being used to compute the predictive state distribution, and
+Gk “ P k|kF J
+k P ´1
+k`1|k
+(26)
+sk|K “ sk|k ` Gkpsk`1|K ´ sk`1|kq
+(27)
+P k|K “ P k ` GkpP k`1|K ´ P k`1|kqGJ
+k
+(28)
+to update the covariances. It should be noted that the mean and covariance sk|k and P k|k
+used in the Smoothing equations are the final result obtained from the Kalman update after
+processing all image modalities that were available at instant k.
+Thus, while in the Kalman filtering the update equations must be computed sequentially
+at each time step w.r.t. the different image modalities, smoothing only needs only the final
+state estimates at each instant, no matter how many modalities are present.
+3.2. Constraining the estimates
+Although the Kalman filter provides closed-form solutions to the estimation of the high-
+resolution image sequence, it relies on a Gaussian assumption on the states and observations
+10
+
+which does not correspond to the physics of the problem. In fact, represented in reflectance
+values, each pixel and band of a high-resolution images sk is actually constrained to an
+interval sk,i,j P r0, smaxs, where smax is the maximum reflectance values of the scene. Since
+this information can potentially improve the accuracy of the estimated states, we propose
+to incorporate this information by considering the linearly constrained Kalman filter [52],
+in which the final constrained state s`
+k|k is obtained as the solution to a constrained opti-
+mization problem:
+s`
+k|k “ arg min
+s
+`
+s ´ sk|k
+˘JP ´1
+k|k
+`
+s ´ sk|k
+˘
+subject to s P r0, smaxsNHLH
+.
+(29)
+Problem (29) consists in a constrained quadratic program, which can be costly to solve due
+to the high dimensionality of the variables. Thus, we propose a simple solution consisting
+of truncating the result of the traditional Kalman update:
+s`
+k|k “ max
+`
+min
+`
+sk|k, smax
+˘
+, 0
+˘
+,
+(30)
+where functions maxp¨, ¨q and minp¨, ¨q compute the elementwise maximum and minimum
+value between a vector and a scalar. Note that this truncation provides the exact solution
+when P k|k is diagonal. The same truncation strategy was also applied to the results of the
+linear smoother sk|K. We generally observed that this gave good results in practice. smax
+can be estimated as the maximum value of the observed images in a time window, or from
+the historical data.
+4. A distributed implementation
+A problem with the Kalman filter is the need to compute and store the state covariance
+matrix, P k|k. This incurs in storage and operations asymptotic complexity in the order of
+OpN2
+HL2
+Hq and OpN3
+HL3
+Hq, respectively. This can make the method intractable for images
+with a large number of pixels.
+Thus, to reduce the complexity of the filter and of the
+smoother, we consider splitting the pixels in the estimated state sk into multiple groups
+which are assumed to be statistically independent [53, 54, 55]. To this end, we divide the
+state space into G groups as:
+sk “ vec
+`
+rsp1q
+k , . . . , spGq
+k
+s
+˘
+,
+(31)
+where the variables within each block spgq
+k
+are correlated, but different blocks spg1q
+k
+and spg2q
+k
+are assumed to be independent for g1 ‰ g2. This leads to the following approximation for
+the predictive and posterior covariance matrices P k|k´1 and P k|k as block diagonal matrices:
+P k|k´1 “ blkdiag
+!
+P p1q
+k|k´1, . . . , P pGq
+k|k´1
+)
+(32)
+P k|k “ blkdiag
+!
+P p1q
+k|k, . . . , P pGq
+k|k
+)
+(33)
+We consider different splitting possibilities, with different trade-offs between approxi-
+mation accuracy with respect to the full-state-covariance Kalman filter and complexity:
+11
+
+iq A fully diagonal model (with G “ NHLH blocks).
+iiq A block diagonal model where each block consists of all bands of one single high-
+resolution pixel (with G “ NH blocks).
+iiiq A block diagonal model, with blocks corresponding to the high-resolution pixels which
+reside inside a single MODIS pixel (with G “ NHLH{NMODIS blocks).
+Following [54], the Kalman equations for the prediction step (13)–(14) can be written
+for each block as:
+spgq
+k`1|k “
+“
+F k
+‰
+pgq,:sk
+(34)
+P pgq
+k`1|k “
+“
+F k
+‰
+pgq,:P k
+`“
+F k
+‰
+pgq,:
+˘J ` Qpgq
+k
+(35)
+where
+“
+F k
+‰
+pgq,: means the matrix formed by taking from F k the rows which correspond to
+the indices in the group of states g, and all columns. Matrices Qpgq
+k
+are defined as:
+Qk “ blkdiag
+␣
+Qp1q
+k , . . . , QpGq
+k
+(
+.
+(36)
+Similarly, the Kalman update equations (17)–(21) are performed separately for each block
+of variables, and are given by:
+spgq
+k
+“ spgq
+k|k´1 ` Kpgq
+k vm
+k
+(37)
+P pgq
+k
+“ P pgq
+k|k´1 ´ Kpgq
+k T m
+k
+`
+Kpgq
+k
+˘J
+(38)
+with:
+Kpgq
+k
+“ Σpgq
+xy,k|k´1
+`
+T m
+k
+˘´1
+(39)
+vm
+k “ rym
+k ´ Ă
+H
+m
+k sk|k´1
+(40)
+T m
+k “ Ă
+H
+m
+k P k|k´1
+`Ă
+H
+m
+k
+˘J ` rR
+m
+k
+(41)
+Σpgq
+xy,k|k´1 “
+“
+P k|k´1
+`Ă
+H
+m
+k
+˘J‰
+pgq,:
+“
+“
+P k|k´1
+‰
+pgq,:
+`Ă
+H
+m
+k
+˘J
+(42)
+where
+“
+P k|k´1
+‰
+pgq,: means the matrix formed by taking from P k|k´1 the rows which corre-
+spond to the indices in the group of states g, and all columns. Note that the block diagonal
+structure of P k|k´1 and P k|k can be explored to perform the above operations efficiently,
+since these matrices are very sparse.
+Following the same approach, the linear smoother can also be approximated in blockwise
+fashion as in [55], for the predictive equations (24)–(25):
+spgq
+k`1|k “
+“
+F k
+‰
+pgq,:sk
+(43)
+P pgq
+k`1|k “
+“
+F k
+‰
+pgq,:P k
+`“
+F k
+‰
+pgq,:
+˘J ` Qpgq
+k
+(44)
+12
+
+and for the smoothing equations (26)–(28):
+Gpgq
+k
+“
+“
+P kF J
+k
+‰
+pgq,pgq
+`
+P pgq
+k`1|k
+˘´1
+“ rP kspgq,pgq
+`“
+F k
+‰
+pgq,pgq
+˘J`
+P pgq
+k`1|k
+˘´1
+(45)
+spgq
+k|K “ spgq
+k
+` Gpgq
+k
+`
+spgq
+k`1|K ´ spgq
+k`1|k
+˘
+(46)
+P pgq
+k|K “ P pgq
+k
+` Gpgq
+k pP pgq
+k`1|K ´ P pgq
+k`1|kqpGpgq
+k qJ
+(47)
+where
+Gk “ blkdiag
+␣
+Gp1q
+k , . . . , GpGq
+k
+(
+.
+(48)
+One last issue is that the innovation covariance matrix T m
+k can also be large for big
+images (e.g., Landsat measurements), as it has pLm
+śLm
+ℓ“1 Nm,ℓq2 elements. Fortunately, the
+model implicitly imposes a simple structure for this matrix. To show this, let us consider a
+permutation of the pixels Πm, such that Πmrym
+k reorders rym
+k by making different bands of
+each LR pixel contiguous:
+Πmrym
+k “
+»
+—–
+»
+—–
+rym
+k,1,1
+...
+rym
+k,Lm,1
+fi
+ffifl
+J
+, . . . ,
+»
+—–
+rym
+k,1,Nm
+...
+rym
+k,Lm,Nm
+fi
+ffifl
+Jfi
+ffifl
+J
+,
+(49)
+where rym
+k,ℓ,n is the n-th pixel of the ℓ-th band of ryk.
+If we assume that Hm
+ℓ
+is a local filter, i.e., each pixel in the low-resolution image is
+generated according to a fixed linear combination of a distinct subset of HR pixels, this
+allows us to express the row-permuted version of Ă
+H
+m
+k equivalently as:
+ΠmĂ
+H
+m
+k “ blkdiag
+␣
+H, H, . . . , H
+looooooomooooooon
+Nm times
+(
+,
+(50)
+where matrix H P RLmˆd2LH is given by:
+H “ hm b Cm ,
+(51)
+where Cm “
+“
+pcm
+1 qJ, . . . , pcm
+LmqJ‰J is the spectral response function for all bands, hm P
+R1ˆd is the local spatial response filter, which defined how the HI pixels inside each LR
+pixels are combined, and d is the number of HR pixel in each LR pixel.
+Using this permutation, the innovation covariance matrix can be written as:
+ΠmT m
+k ΠJ
+m “ ΠmĂ
+H
+m
+k P k|k´1
+`Ă
+H
+m
+k
+˘JΠJ
+m ` Πm rR
+m
+k ΠJ
+m
+“ blkdiagtH, . . . , HuP k|k´1 blkdiagtHJ, . . . , HJu
+` Πm rR
+m
+k ΠJ
+m
+“ blkdiagtHP p1q
+k|k´1HJ, . . . , HP pGq
+k|k´1HJu
+` Πm rR
+m
+k ΠJ
+m .
+(52)
+13
+
+Algorithm 1: Weakly supervised online image fusion
+Input
+: Measured multimodal images ym
+k , for all time instants k “ 1, . . . , K and
+modalities m, historical datasets of high-resolution images Dk, parameters smax.
+Output: Estimated image sequence sk|K
+1 Initialize P 0|0 and s0|0;
+2 // Filter ;
+3 for k “ 1, 2, . . . , K do
+4
+Compute innovation covariance matrix Qk using sk´1 and Dk according to Section 2.4 ;
+5
+Compute sk|k´1 and P k|k´1 using equations (31), (32), (34) and (35) ; // Prediction
+6
+Compute sk|k and P k|k using equation (33) and equations (37)–(42) ;
+// Update
+7
+Constrain sk|k using (30) ;
+8 end
+9 // Smoother ;
+10 for k “ K, K ´ 1, . . . , 1 do
+11
+Compute sk`1|k and P k`1|k using equations (31), (32), (43) and (44) ; // Prediction
+12
+Compute sk|K and P k|K using equations (45)–(47) and equation (48) ;
+// Backwards
+update
+13 end
+14 return Estimated images sk|K
+Thus, as long as the noise is independent among different pixels (i.e., rR
+m
+k is block diago-
+nal), it is possible to express the innovation covariance matrix in block diagonal form by
+adequately permuting the LR image pixels. This shows that each pixel from the lowest
+resolution image modality can be processed independently when Qk and P 0|0 also have a
+block diagonal structure. The proposed image fusion method is summarized in Algorithm 1.
+5. Experiments
+In this section, we use the proposed methodology to fuse Landsat and MODIS image
+over time. The Kalman filter and smoother are built under the three different assumptions
+for the state covariance matrices regarding the distributed implementation discussed in
+Section 4: iq diagonal state covariance (denoted by KF-D and SM-D); iiq block-diagonal
+state covariance with one block per Landsat multispectral pixel (denoted by KF-B and SM-
+B); and iiiq block-diagonal with blocks for all Landsat multispectral pixels corresponding to
+the same coarse pixel in a MODIS image being correlated (denoted by KF-F and SM-F). A
+filter in which Landsat multispectral pixels corresponding to more than one coarse pixel in
+a MODIS image being all correlated could not be implemented due to computational and
+memory limitations.
+Although in our experiments we consider only two modalities the proposed methodology
+admits multiple different modalities provided that enough computational power is available.
+As benchmark, we compare the performance of Kalman filter and smoother under all three
+assumptions to that of the Enhanced Spatial and Temporal Adaptive ReFlectancefusion
+Model (ESTARFM) algorithm [25], and the Prediction Smooth Reflectance Fusion Model
+14
+
+(PSRFM) algorithm [56, 57]. The ESTARFM algorithm requires two high-resolution (e.g.,
+Landsat) images at the beginning of the image sequence, and can generate high-resolution
+reconstructions at later time instants based on MODIS measurements. Thus, it is a good
+candidate for comparison with the Kalman filtering based strategies, which also do not
+require future data. The PSRFM method, on the other hand, uses two high-resolution (e.g.,
+Landsat) images (one at the beginning and one at the end of the sequence), and provides
+high-resolution reconstruction for the intermediate MODIS images. Thus, it consists in an
+adequate comparison to the smoother algorithms, which also require future high-resolution
+images. In the following, we describe the data and simulation setup, followed by the results
+and the discussions.
+5.1. Study region
+For the experiments, we consider two sites. The first is the Oroville dam (Figure 2, left
+panel), located on the Feather River, in the Sierra Nevada Foothills (38° 35.3’ North and
+122° 27.8’ W) is the tallest dam in USA and is major water storage facility in California
+State Water Project.
+The reservoir has a maximum storage capacity of 1.54 ˆ 1011 ft3
+or 4.36 ˆ 109 m3, which fills during heavy rains or large spring snow melts and water is
+carefully released to prevent flooding in downstream areas, mainly to prevent large flooding
+in Butte County and area along the Feather River. The reservoir water storage change in
+between 07/03 and 09/21 of 2018 is as shown as the hydrograph curve in Figure 8. Another
+unique characteristic is that it has three power plants at this reservoir. The water released
+downstream is used to maintain the Feather and Sacramento Rivers and the San Francisco-
+San Joaquin delta. Lake Oroville is at an elevation of 935 feet (285 meters) above sea level.
+We focus at a particular area of the Oroville dam delimited by the red box in Figure 2.
+The second site is the Elephant Butte reservoir (Figure 2, right panel), located in the
+southern part of the Rio Grande river, in New Maxico, USA (33° 19.4’ N and 107° 26.2’ W).
+It is the largest reservoir in New Mexico, providing power and irrigation to southern New
+Mexico and Texas. Elephant Butte reservoir is at an elevation of 4,414 ft (1,345 meters),
+and has a surface area of 36,500 acres (14,800 ha).
+Table 1: Spectral angle mapper between the estimated high-resolution image and the Landsat measurement
+for the Oroville Dam example (note that the Landsat images at dates 07/19, 08/20, and 09/05 were not
+supplied to the algorithms and only used for evaluation purposes). However, the Landsat image at 09/21
+was available to all algorithms. Note that the spectral angle is not reported for PSRFM at 09/21. This is so
+since PSRFM uses the last pair (MODIS-Landsat) of images and directly sets its estimations at this dates
+to the ground-truth.
+Method
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+PSRFM
+Image (07/19)
+7.1240
+10.8537
+4.2356
+6.1515
+4.9304
+5.9064
+6.0810
+6.8837
+Image (08/20)
+27.6343
+26.2786
+26.1229
+25.1520
+27.1928
+26.1758
+29.0892
+27.7802
+Image (09/05)
+8.5741
+6.0366
+6.6246
+3.6838
+7.4482
+4.4135
+11.4553
+6.0354
+Image (09/21)
+8.0588
+3.6385
+6.4042
+0.5471
+6.9754
+0.6960
+11.9584
+–
+Average
+12.8478
+11.7019
+10.8468
+8.8836
+11.6367
+9.2979
+14.6460
+10.1748
+15
+
+National Geographic, Esri, Garmin, HERE, UNEP-WCMC, USGS, NASA,
+ESA, METI, NRCAN, GEBCO, NOAA, increment P Corp.
+0
+0.55
+1.1
+0.28
+mi
+0
+0.9
+1.8
+0.45
+km
+1:44,418
+National Geographic, Esri, Garmin, HERE, UNEP-WCMC, USGS, NASA,
+ESA, METI, NRCAN, GEBCO, NOAA, increment P Corp.
+0
+5
+10
+2.5
+mi
+0
+8.5
+17
+4.25
+km
+1:368,824
+Figure 2: (Left) Oroville dam site. (Right) Elephant Butte site. The red boxes delimit the specific study
+areas used in our experiments.
+Table 2: Percentage of misclassified pixels for the Oroville Dam example (the Landsat image at 09/21 was
+available to all algorithms). Note that the misclassification percentage is not reported for PSRFM at 09/21.
+This is so since PSRFM uses the last pair (MODIS-Landsat) of images and directly sets its estimations at
+this dates to the ground-truth.
+Method
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+PSRFM
+Image (07/19)
+9.5412
+7.6360
+6.4472
+8.2914
+6.1119
+8.0171
+5.4870
+5.2431
+Image (08/20)
+14.9215
+10.4405
+7.8647
+4.1000
+7.2245
+3.7799
+18.2899
+17.9851
+Image (09/05)
+13.4888
+8.2152
+9.6632
+4.7859
+9.4345
+4.5877
+22.7404
+20.8962
+Image (09/21)
+11.7360
+3.8409
+9.3583
+0.2439
+9.2974
+0.2591
+26.3374
+–
+Average
+12.4219
+7.5332
+8.3333
+4.3553
+8.0171
+4.1610
+18.2137
+11.0311
+5.2. Remote Sensed data
+For our simulations with the Oroville Dam site, we collected MODIS and Landsat data
+acquired from the region marked with a red square on Figure 2, and on a interval ranging
+from 2018{07{03 to 2018{09{21. This interval was selected since the hydrograph analysis
+indicates high variation in the water level of the reservoir, see, the hydrograph curve in
+Figure 8. Such variation in the water levels result in large changes in the acquired images,
+exposing flooded areas. In this experiment we will focus on the red and near-infrared (NIR)
+bands since they are often used to distinguish water from other landcover elements in the
+image [58]. We also collected 5 Landsat data from 2017{08{01 to 2017{12{07 to serve as a
+past historical dataset Dk.
+The study region marked in the left panel of Figure 2 corresponds to Landsat and
+MODIS images with 81 ˆ 81 and 9 ˆ 9 pixels, respectively2. After filtering for heavy cloud
+cover during the designated time periods, a set of 6 Landsat and 16 MODIS images were
+obtained. We used the first MODIS and Landsat images for initialization of all methods
+leading to 5 and 15 images used in the remaining fusion process.
+2The Landsat images were also upsampled to a spatial resolution of 27.77 meters to make its resolution
+exactly 9 times that of MODIS.
+16
+
+Lake Oroville
+Lake Oroville
+State
+Recreation AreaNOSA
+SPRINGDRAW
+Elephant
+Butte
+Reservoi
+R
+52
+M
+Conseqgences
+Truhort
+MuniAirport
+V
+A
+1991m
+GARCIA
+PEAKS
+TruthOr
+Z
+Consequences.
+R
+o-Grande
+JOHNSON
+IEMESA
+MCCLENFrom the set of 5 Landsat images of the Oroville Dam site that were available for
+testing, three of them were set aside and not processed by any of the the algorithms.
+These images were acquired at dates 07/19, 08/20 and 09/05, when MODIS observations
+were also available, and will be used in the form of a reference for the evaluation of the
+algorithms’ capability of estimating the high resolution images at these dates solely from
+the low resolution MODIS measurements.
+For the simulations with the Elephant Butte site, shown in the right panel of Figure 2, we
+aim to evaluate the performance of the algorithms when processing a larger geographical
+area, with an area of approximately 9km ˆ 9km.
+The setup is similar to the Oroville
+Dam example. We focus on the red and near-infrared bands of the Landsat and MODIS
+instruments, and collect 47 Landsat images from 2014/01/16 to 2017/11/24 to serve as the
+past historical dataset Dk.
+The study region corresponds to Landsat and MODIS images with 324ˆ324 and 36ˆ36
+pixels, respectively. After removing images with significant cloud cover, we obtained a set
+of 5 Landsat and 7 MODIS images to process. We used the first MODIS and Landsat
+image pair to initialize the algorithms, leading to 4 Landsat and 6 MODIS images to be
+used in the remaining fusion process. From the set of 4 Landsat images that were available
+for testing, 2 of them were set aside as ground truth to evaluate the algorithms. Theses
+images are acquired at dates 06/07 and 06/23. However, the MODIS measurements at those
+dates contained significant cloud cover, and had to be discarded. Therefore, we evaluate
+the performance of the algorithms through the estimation results obtained dates 06/14 and
+06/27 (in which the MODIS observations were available).
+5.3. Algorithm setup
+We initialized the proposed Kalman filter and smoother using a high resolution Landsat
+observation as the state, i.e., s0|0 “ ryL
+0, and set P 0|0 “ 10´10P 0. The structure of P 0
+varies with different assumptions: iq P 0 “ I if the state covariance is diagonal; iiq P 0 “
+blkdiagtP 0,1, P 0,2, ¨ ¨ ¨ , P 0,NHu, where P 0,i “ 1
+21 ` 1
+2I, with 1 being an all ones matrix,
+if the state covariance matrix has a block-diagonal structure with one block per Landsat
+multispectral pixel; iiiq P 0 “ blkdiagtP 0,1, P 0,2, ¨ ¨ ¨ , P 0, ˜
+NmˆLmu, where P 0,i “ 1
+21 ` 1
+2I if
+the state covariance matrix has a block-diagonal structure with each block containing all
+Landsat multispectral pixels corresponding to the same coarse pixel in a MODIS image.
+Figure 7 shows an example of the final P k|k, k “ 13, obtained with the KF under all the
+assumptions discussed in Section 4. The noise covariance matrices were set as RL
+ℓ “ 10´10I
+and RM
+ℓ “ 10´4I, for all ℓ. The blurring and downsampling matrices were set as HL
+ℓ “ I
+for Landsat, while for MODIS HM
+ℓ consisted of a convolution by an uniform 9 ˆ 9 filter,
+defined by h “
+1
+8119ˆ9 (where 19ˆ9 is a 9 ˆ 9 matrix of ones), followed by decimation by
+a factor of 9, which represents the degradation occurring at the sensor (see, e.g., [44]). We
+also set F k “ I for all k. The vectors cm
+ℓ
+contained a positive gain in the ℓ-th position
+which compensated for scaling differences between Landsat and MODIS sensors, and zeros
+elsewhere.
+The matrices DM
+k were constructed based on the quality codes (i.e., the QA bits) released
+17
+
+by MODIS for each image pixel [59]. QA bits provides information regarding pixel quality
+and cloud cover for all pixels and all bands. In our experiments we dropped any pixel not
+classified as corrected product produced at ideal quality in the QA bits [59] by adding zeros
+at corresponding positions in DM
+k . Matrices Qk were computed following our data-driven
+strategy described in Section 2.4 where ε2 “ 10´5 and n “ 1.
+The ESTARFM algorithm was parametrized as follows [25], w “ 14 as half of the window
+size, the number of classes was set to 4, and the pixels range was set to r0, 0.5s. The PSRFM
+algorithm was parametrized as follows, CLUSTER METHOD “ KMEAN, and CLUSTER DATA “
+fine`coarse. We highlight that all methods have access only to the first (07/03) and last
+(09/21) Landsat images, which allows the algorithms to produce estimates for the MODIS
+images observed from the second (07/09, k “ 2) up to the last date (09/21, k “ 16).
+However, PSRFM uses the the last pair (MODIS-Landsat) during its inference process. For
+this reason, error metrics computed for PSRFM on (09/21) should be disregarded as the
+estimate is directly the ground-truth (i.e., the Landsat image) and, thus, are not reported
+in the experimental results.
+All algorithms are evaluated using three metrics, which are computed taking as reference
+the Landsat images, three of which are not observed by the algorithms. The first metric
+is the Spectral Angle Mapper (SAM), which attempts to measure the estimation accuracy
+directly:
+SAMpS, pSq “
+1
+NH
+NH
+ÿ
+r“1
+arccos
+´
+sJ
+r psr
+}sr}}psr}
+¯
+,
+(53)
+where S and pS denote the true and the estimated images, respectively. sr and psr denote
+the r-th pixels of different bands in S and pS, respectively. The two remaining metrics are
+related to downstream tasks of water classification and water level monitoring, which are
+performed on the reconstructed image sequence.
+We evaluate the direct benefit of the different fusion strategies in classifying water pixels
+from the estimated images. To classify water pixels we resorted to a KNN classifier whose
+centroids of water and non-water 2-band pixels were computed using K-Means algorithm.
+Finally, we evaluate the performance of the algorithms for hydrograph estimation by plot-
+ting the proportion of pixels in the image classified as water over time against the true
+hydrograph for the period, for all algorithms.
+5.4. Results for the Oroville Dam site
+As discussed, we fused the red and NIR reflectance bands of MODIS and Landsat for
+the selected study region. In Figure 3, we show the fused red (Figure 3a) and NIR (Fig-
+ure 3b) reflectances as well as the acquired red and NIR reflectance values from MODIS and
+Landsat. Acquisition dates are displayed in the top labels at each column with a character,
+M for MODIS and L for Landsat, indicating the image used in the fusion algorithms. We
+recall that only the first and last Landsat images were used in the fusion process, keep-
+ing the remaining three images as ground-truth for evaluation purposes. Analyzing the
+18
+
+results we can see that the images estimated by the proposed Kalman filter and smoother
+methods, under different assumptions, produce better visual similarity with the Landsat
+(ground-truth) images for both bands. For instance, the increase in the island and the
+expansion of other land parts are clearly visible for the proposed methods. In contrast,
+analyzing ESTARFM results we note that land parts remain mainly constant through time
+until a new Landsat image is observed. Although lighter areas on the water portions can
+be noticed, specially for k ą 8, its distribution does not resemble the ground-truth. This
+is expected since ESTARFM is not designed to acknowledge prior information or historical
+data. PSRFM results show an improvement compared with ESTARFM results, since it
+uses both the first and the last Landsat images. However, the PSRFM results does not
+resemble the ground-truth very closely, and significant blurring occurs around the edge of
+the island when k ă 8. The blurring results in PSRFM are caused by the fact that the
+reconstructions provided by this algorithm are based on a form of interpolation which does
+not consider any information about the transition of the pixel reflectance values, whereas
+in our proposed methods we use the historical data to calibrate the time-varying dynamical
+model by means of matrix Qk, which can increase the accuracy of the estimations.
+Note that the images estimated by KF-F and SM-F (which used a full state covariance
+matrix) contained more artifacts when compared to the ones obtained by KF-B, SM-B,
+KF-D and SM-D (which constrained the state covariance matrix to be diagonal or block
+diagonal). This occurs due to the high-dimensionality of the state vector (i.e., equivalent
+to a vectorized Landsat image) when compared to the MODIS measurements, as this leads
+to the amount of measurements not being sufficient to provide an accurate estimate of the
+full state vector and its covariance matrix, as shown in [60]. Thus, the extra degrees of
+freedom of KF-F and SM-F end up impacting their performance negatively. By setting the
+covariance matrix of the Kalman filter and smoother to be block diagonal or fully diagonal,
+the amount of parameters to be estimated is greatly reduced in KF-B, SM-B, KF-D and
+SM-D, leading to better results.
+The results discussed above are corroborated by the absolute error maps displayed in
+Figure 4, and SAM results shown in Table 1 for dates in which ground-truth is available.
+Analyzing Figure 4 we highlight that SM-B and SM-D clearly present the smallest errors
+(i.e., overall darker pixels) for both bands and all dates. KF-B also presents low absolute
+error except for contour regions. PSRFM is the third overall darker image, followed by
+KF-B, KF-D, SM-F, KF-F and ESTARFM with exception of the results on 07/19 (first col-
+umn), where ESTARFM is close to the ground-truth. Similar conclusions can be achieved
+by analyzing Table 1. The difference between the images estimated by the Kalman filter
+and smoother under the different approximations for the state covariance matrices (which
+are discussed in Section 4 and illustrated for this example in Figure 7) is shown in Figure 5.
+It can be seen that the approximations had a more pronounced effect on the Kalman filter
+compared to the smoother. Moreover, the differences between the filter with a diagonal
+(assumption i) and block diagonal state covariance with one block per Landsat pixel (as-
+sumption ii) was relatively small. Taking in to consideration the quantitative metrics in
+Table 1, this indicates that using a diagonal or block diagonal assumption on the state
+19
+
+covariance matrix with small blocks has a positive effect on the estimation performance,
+which likely occurs since it drastically reduces the amount of unknowns in the model that
+have to be estimated by the methods.
+The left panel in Figure 6 presents the water maps for the ground-truth (first row) and
+all studied algorithms obtained using K-means clustering, while the right panel in Figure 6
+shows the misclassification maps (i.e., the absolute error between the water maps obtained
+by each algorithm and the ground-truth). When comparing the resulting classification maps
+and the misclassification error with the ground-truth, the proposed methods present classi-
+fication maps that are semantically better than the competing methods. This conclusion is
+also reached by considering the quantitative misclassification results presented in Table 2,
+in which the Kalman filter- and smoother-based methods led to smaller misclassification
+rates for all images except the ones on 07/19 and 09/21. A closer analysis reveals that the
+SM-D and SM-B methods hold the first and second best performance on average, followed
+by SM-F, KF-D, KF-B, PSRFM, KF-F and ESTARFM. Note that the PSRFM method
+requires access to the ground-truth (Landsat image) on 09/21 in order to produce an esti-
+mation for the MODIS image observed in this same date (i.e., measurement k “ 16), which
+is why the corresponding misclassification percentage is not reported. We also remark that
+KF-D and KF-B also obtained competitive misclassification performance (i.e., better than
+PSRFM), despite using no knowledge of the Landsat image at 09/21. Moreover, comparing
+the results in Table 1 and 2, it can be seen that the higher SAM results observed for all
+methods at date 08/20 does not translates into a worse classification performance. This
+indicates that the SAM results at this date were influenced by the acquisition conditions of
+the Landsat image which was used for ground truth, making the classification performance
+more straightforward to interpret.
+Finally, we plotted the percentage of pixels classified as water over the time index k in
+Figure 8, as well as a hydrograph which serves as an indicative of the dynamical evolution
+of the true level of the reservoir over time. It can be seen that ESTARFM was not able to
+properly identify the dynamical evolution of the reservoir level, leading to an estimation that
+was almost constant for all k ă 17 and very different from the hydrograph curve. PSRFM
+led to results that, although showing relatively high day-to-day variations, were closer to
+the hydrograph curve. The Kalman filter and smoother-based algorithms, particularly those
+with the diagonal and block diagonal state covariance assumption (KF-D, KF-B, SM-B and
+SM-D) led to curves that were very close to the hydrograph.
+Thus, the Kalman filter
+methods captured the general trends of the hydrograph curves, even without having access
+to information from the Landsat image at the end of the sequence (like the smoothers and
+PSRFM). We note, however, that the connection between the hydrograph and the water
+surface area is indirect; thus, small differences between the algorithms have to be interpreted
+with proper care.
+5.5. Contribution of the temporal dynamics calibration strategy
+This subsection aims to show the impact of the proposed calibration strategy, which
+learns the temporal dynamical model parameters Qk using historical data, on the perfor-
+mance of the proposed KF and SM algorithms. To this end, we compared the proposed
+20
+
+KF-D and SM-D (which estimate Qk and use a diagonal assumption on the state covari-
+ance matrix), to a Kalman filter and smoother with a fixed Qk “ 10´2I, which we denote
+by KF-I and SM-I, respectively. In Figure 9, we show the fused red (Figure 9a) and NIR
+(Figure 9b) reflectance images, as well as the acquired red and NIR reflectance values from
+MODIS and Landsat. Acquisition dates are displayed in the top labels at each column with
+a character, M for MODIS and L for Landsat indicating the image used in the fusion algo-
+rithms. We recall that only the first and last Landsat images were used in the fusion process,
+keeping the remaining three images as ground-truth for evaluation purposes. Analyzing the
+results, we can see that the images estimated by the proposed KF-D and SM-D methods
+produce significantly better visual similarity with the Landsat (ground-truth) images for
+both bands. For instance, the increase in the island and the expansion of other land parts
+at date 08/20 are clearly visible for the proposed methods. On the other hand, analyzing
+the results of the KF-I and SM-I methods, where the temporal dynamics matrix Qk was
+kept constant and independent of past data, we observe that the results appear very blurry,
+with a resolution that is comparable to that of the MODIS images. This shows that the
+proposed weakly supervised calibration strategy is key in order for the KF- and SM-based
+strategies to obtain high quality reconstructions.
+5.6. Results for larger scale Elephant Butte site
+In this subsection, we compare the proposed strategies to ESTARFM and PSRFM in
+the Elephant Butte example, which comprises a larger geographical area. For simplicity
+and to reduce the use of space, we compare only proposed Kalman filter and smoother
+methods with the block diagonal assumption on the state covariance matrices (i.e., KF-B
+and SM-B).
+The fusion results for both bands and all algorithms are shown in Figure 10, while
+Figure 11 shows the corresponding water mapping results. To measure the performances
+of different methods in this large area, the Landsat images at dates 06/07 and 06/23 were
+chosen as a ground truth to evaluate the quality of the reconstructed images at dates 06/14
+and 06/27 (we remark that the MODIS images at dates 06/07 and 06/23 were not available
+due to the presence of cloud cover). It can be seen that the proposed KF-B, SM-B and the
+PSRFM methods provide estimates that are close to the ground truth images, whereas the
+ESTARFM method shows an inferior performance. This can be seen more clearly for the
+image at date 06/14 (k “ 5), in which the smoother method better captured the increase in
+the area of the reservoir. To evaluate the performances of different methods more clearly,
+Figure 12 shows the absolute error of water maps of images compared with the ground
+truth, and Figures 13 and 14 show a zoomed-in area of the image of the fused image and
+water mapping result, respectively. It can be seen from Figure 12 that the misclassification
+errors are concentrated at the borders of the reservoir, which is the area that undergoes the
+largest amounts of changes over time, and consequently the hardest to classify correctly.
+The SM-B algorithm shows the best results, followed by KF-B, PSRFM and ESTARFM.
+Nevertheless, PSRFM provides results that contain less artifacts compared to KF-B, despite
+the lower classification accuracy. The superior visual quality of the results of SM-B and
+21
+
+PSRFM is explained by their use of Landsat images both at the beginning and at the end of
+the image sequence, whereas KF-B and ESTARFM do not have access to the last Landsat
+image.
+Table 3 presents the SAM results, and Table 4 shows the corresponding percentage of
+misclassified pixels for the different methods. It can be seen that in terms of SAM, the SM-B
+method obtained the best results for both dates, followed by PSRFM and ESTARFM. How-
+ever, the KF-B strategy was able to obtain a better water mapping performance compared
+to PSRFM. This indicates that the artifacts seen in the (comparatively noisier) reconstruc-
+tions of KF-B impact the the classification performance in a less substantial way compared
+to the SAM. This shows that the proposed Kalman-filter based strategy can provide mean-
+ingful water mapping results in a real-time setting, in which we do not have access to future
+Landsat images, precluding smoothing-based algorithms (such as SM-B and PSRFM) to be
+used.
+Table 3: Spectral angle mapper between the estimated high-resolution image and the Land- sat measurement
+for the Elephant Butte example (note that the Landsat images at dates 06/07 and 06/23 were not supplied
+to the algorithms and only used for evaluation purposes).
+Method
+KF-B
+SM-B
+ESTARFM
+PSRFM
+Image (06/07)
+5.5416
+2.9993
+9.2678
+4.2698
+Image (06/23)
+5.7514
+1.9923
+6.2158
+4.8719
+Average
+5.6465
+2.4958
+7.7418
+4.5709
+Table 4: Percentage of misclassified pixels for the Elephant Butte example (note that the Landsat images
+at dates 06/07 and 06/23 were not supplied to the algorithms and only used for evaluation purposes).
+Method
+KF-B
+SM-B
+ESTARFM
+PSRFM
+Image (06/07)
+5.3593
+1.4289
+9.2678
+6.6606
+Image (06/23)
+5.9233
+0.8250
+10.8330
+7.8675
+Average
+5.6413
+1.1269
+10.0504
+7.2640
+5.7. Discussion
+The results presented above clearly indicate that the proposed weakly supervised smoother-
+based image fusion strategy outperforms the ESTARFM and PSRFM algorithms in terms of
+image reconstruction when an appropriate covariance structure is selected (SM-D and SM-
+B). This highlights that having less model parameters to estimate (i.e., a more constrained
+state covariance model) can lead to better results. Moreover, even the Kalman filter strate-
+gies (particularly KF-B and KF-D), which estimate high-resolution images from MODIS
+without having access to any future data, have shown very competitive performance, with
+great potential for tasks in which high-resolution estimates are required online and one can-
+not wait for another Landsat image to be available before computing the high-resolution
+reconstructions.
+The advantage of the proposed filter and smoother strategies is more clear when eval-
+uated semantically by means of the water classification performance.
+For instance, the
+22
+
+growth of the island portion over time in regions that are semantically meaningful leads
+to more meaningful results that cannot be entirely captured by one standard metric such
+as the SAM. This can be observed more clearly through the spatial distribution of the
+misclassification error maps in Figure 6, which for ESTARFM and PSRFM are signifi-
+cantly more concentrated on the borders between land and water. In general, the proposed
+filtering-based strategies clearly outperformed both the ESTARFM and PSRFM algorithms,
+a standard and a state of the art remote sensing image fusion algorithms. Moreover, the
+proposed distributed implementation, described in Section 4, is able to reduce the com-
+putational power and memory demand of the standard Kalman filter and smoother when
+applied for large images.
+6. Conclusions
+In this paper, an online Bayesian approach for fusing multi-resolution space-borne mul-
+tispectral images was proposed. By formulating the image acquisition process as a linear
+and Gaussian measurement model, the proposed method leveraged the Kalman filter and
+smoother to perform image fusion by estimating the latent high resolution image from the
+different observed modalities. Moreover, a weakly supervised strategy is also proposed to
+define an informative time-varying dynamical image model by leveraging historical data,
+which leads to a better localization of changes occurring in the high-resolution image even
+in intervals where only coarse resolution observations are available. Experimental results
+indicate that the proposed strategy can lead to considerable improvements compared to
+both classical and state-of-the-art image fusion algorithms.
+7. Acknowledgments
+The authors would like to thank the support of the National Geographic Society under
+Grant NGS-86713T-21, the National Science Foundation under Award ECCS-1845833, and
+NASA – GRACE–FO Science Team (80NSSC20K0742).
+23
+
+Landsat
+07/03L
+07/09M
+07/14M
+07/19M
+07/26M
+08/01M
+08/03M
+08/08M
+08/13M
+08/20M
+08/24M
+08/29M
+09/05M
+09/11M
+09/16M
+09/21M
+09/21L
+MODIS
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+k = 1
+PSRFM
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+k = 9
+k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17
+0.00
+0.05
+0.10
+0.15
+0.20
+(a) Fused images in band 1 (MODIS) and band 4 (LandSat)
+Landsat
+07/03L
+07/09M
+07/14M
+07/19M
+07/26M
+08/01M
+08/03M
+08/08M
+08/13M
+08/20M
+08/24M
+08/29M
+09/05M
+09/11M
+09/16M
+09/21M
+09/21L
+MODIS
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+k = 1
+PSRFM
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+k = 9
+k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+(b) Fused images in band 2 (MODIS) and band 5 (LandSat)
+Figure 3: Fused bands from MODIS and Landsat for the Oroville Dam example using different strategies over
+time. The first two rows of each subfigure depict MODIS and Landsat bands acquired at dates displayed on
+top labels. At each time index estimation with KF and SM under different model assumptions, ESTARFM
+and PSRFM are presented. Some Landsat images were omitted from the estimation process and used solely
+as ground-truth. Images used at each update step are indicated on top labels where “M” stands for MODIS
+and “L” for Landsat.
+24
+
+KF-F
+07/19
+08/20
+09/05
+09/21
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+k = 4
+PSRFM
+k = 10
+k = 13
+k = 16
+0.00
+0.05
+0.10
+0.15
+0.20
+KF-F
+07/19
+08/20
+09/05
+09/21
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+k = 4
+PSRFM
+k = 10
+k = 13
+k = 16
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+Figure 4: Absolute difference between the estimated and ground truth (Landsat) images for the Oroville
+Dam example in the red (upper panel) and NIR (lower panel) bands.
+25
+
+--Landsat
+07/03L
+07/09M
+07/14M
+07/19M
+07/26M
+08/01M
+08/03M
+08/08M
+08/13M
+08/20M
+08/24M
+08/29M
+09/05M
+09/11M
+09/16M
+09/21M
+09/21L
+MODIS
+KF-BF
+KF-DF
+KF-DB
+SM-BF
+SM-DF
+k = 1
+SM-DB
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+k = 9
+k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Landsat
+07/03L
+07/09M
+07/14M
+07/19M
+07/26M
+08/01M
+08/03M
+08/08M
+08/13M
+08/20M
+08/24M
+08/29M
+09/05M
+09/11M
+09/16M
+09/21M
+09/21L
+MODIS
+KF-BF
+KF-DF
+KF-DB
+SM-BF
+SM-DF
+k = 1
+SM-DB
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+k = 9
+k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Figure 5: Absolute differences between the images estimated by the KF and Smoother under different model
+assumptions for red (upper panel) and NIR (lower panel) bands, for the Oroville Dam example. KF-BF:
+difference between the estimates of KF-B and KF-F. KF-DF: difference between the estimates of KF-D and
+KF-F. KF-DB: difference between the estimates of KF-D and KF-B. An analogous notation holds for the
+smoother (SM) estimates.
+26
+
+Landsat
+07/19
+08/20
+09/05
+09/21
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+k = 4
+PSRFM
+k = 10
+k = 13
+k = 16
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Landsat
+08/07
+08/23
+09/08
+09/24
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM_D
+ESTARFM
+k = 4
+PSRFM
+k = 7
+k = 11
+k = 14
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Figure 6: (Upper Panel) Water map of the reconstructed images of the Oroville Dam example based
+on K-means clustering strategy, where 1 indicates land and 0 indicates water pixels. Classification maps
+obtained from Landsat images not observed by the image fusion algorithms establish the ground-truth (first
+row). (Lower Panel) Absolute error of Water map of images based on K-means clustering strategy, where
+0 indicates correctly classified pixels and 1 indicates misclassifications. The ground-truth is shown in the
+first row.
+27
+
+-:-
+L.
+1二
+.--12
+-10
+-8
+-6
+-4
+-14
+-12
+-10
+-8
+-6
+-4
+-20
+-15
+-10
+-5
+-7
+-6
+-5
+-4
+-3
+-7
+-6
+-5
+-4
+-3
+-15
+-10
+-5
+Modis Observation in Band 1
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+Modis Observation in Band 2
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+Landsat Observation in Band 4
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+Landsat Observation in Band 5
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+Figure 7: (Top Colored Panel) Estimated state covariance structure of the Kalman filter under model
+assumptions i, ii and iii for a small image area in the Oroville Dam example and k “ 13. Top row depicts
+the whole covariance matrix with a red square indicating the zoomed part displayed on the bottom row. The
+plots indicate that correlations are present when assuming block diagonal covariance matrices. (Bottom
+Panel) Zoom of the MODIS image for bands 1 and 2 (left), and the corresponding Landsat observations for
+bands 4 and 5 (right) corresponding to the covariance matrices plotted in the right panels.
+28
+
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+Image Indices (k)
+45
+50
+55
+60
+65
+70
+75
+80
+Water pixel percentage
+1.6
+1.8
+2
+2.2
+2.4
+2.6
+2.8
+Volume [m3]
+109
+KF-F
+SM-F
+KF-B
+SM-B
+KF-D
+SM-D
+ESTARFM
+PSRFM
+Hydrograph
+Figure 8: Percentage of water pixels in the estimated images over image index (time) and the reservoir
+volume in m3 (hydrograph) for the Oroville Dam example. Classification of water was done by performing
+clustering on the estimated bands for each method and time index. High resolution Landsat images were
+observed at indices k P t1, 17u.
+29
+
+Landsat
+07/03L
+07/09M
+07/14M
+07/19M
+07/26M
+08/01M
+08/03M
+08/08M
+08/13M
+08/20M
+08/24M
+08/29M
+09/05M
+09/11M
+09/16M
+09/21M
+09/21L
+MODIS
+KF-D
+SM-D
+KF-I
+k = 1
+SM-I
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+k = 9
+k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17
+0.00
+0.05
+0.10
+0.15
+0.20
+(a) Fused images in band 1 (MODIS) and band 4 (LandSat)
+Landsat
+07/03L
+07/09M
+07/14M
+07/19M
+07/26M
+08/01M
+08/03M
+08/08M
+08/13M
+08/20M
+08/24M
+08/29M
+09/05M
+09/11M
+09/16M
+09/21M
+09/21L
+MODIS
+KF-D
+SM-D
+KF-I
+k = 1
+SM-I
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+k = 9
+k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+(b) Fused images in band 2 (MODIS) and band 5 (LandSat)
+Figure 9: Fused bands from MODIS and Landsat for the Oroville Dam example using different strategies
+over time. The first two rows of each subfigure depict MODIS and Landsat bands acquired at dates displayed
+on top labels. At each time index estimation results of the diagonal Kalman filter and smoother with the
+proposed weakly supervised calibration strategy (KF-D and SM-D) are compared to the result of a Kalman
+filter and smoother with Qk being proportional to the identity (denoted by KF-I and SM-I). Landsat images
+at dates 07/19, 08/20 and 08/29 were omitted from the estimation process and used solely as ground-truth.
+Images used at each update step are indicated on top labels where “M” stands for MODIS and “L” for
+Landsat.
+30
+
+Landsat
+03/19M
+03/19L
+04/18M
+05/18M
+06/07
+06/14M
+06/23
+06/27M
+07/09M
+07/09L
+MODIS
+KF-B
+SM-B
+ESTARFM
+k = 1
+PSRFM
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+(a) Fused images in band 1 (MODIS) and band 4 (LandSat)
+Landsat
+03/19M
+03/19L
+04/18M
+05/18M
+06/07
+06/14M
+06/23
+06/27M
+07/09M
+07/09L
+MODIS
+KF-B
+SM-B
+ESTARFM
+k = 1
+PSRFM
+k = 2
+k = 3
+k = 4
+k = 5
+k = 6
+k = 7
+k = 8
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+(b) Fused images in band 2 (MODIS) and band 5 (LandSat)
+Figure 10: Fused bands from MODIS and Landsat for the Elephant Butte example using different strategies
+over time. The first two rows of each subfigure depict MODIS and Landsat bands acquired at dates displayed
+on top labels. At each time index estimation with KF and SM under block diagonal model assumptions,
+ESTARFM and PSRFM are presented. Some Landsat images were omitted from the estimation process and
+used solely as ground-truth. Images used at each update step are indicated on top labels where “M” stands
+for MODIS and “L” for Landsat.
+31
+
+06/14
+Landsat
+KF-B
+SM-B
+ESTARFM
+k = 5
+PSRFM
+06/27
+k = 6
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Figure 11: Water map of images for the Elephant Butte example based on K-means clustering strategy where
+1 indicates land and 0 indicates water pixels. Unused Landsat classification maps establish the ground-truth
+(first column).
+06/14
+Landsat
+KF-B
+SM-B
+ESTARFM
+k = 5
+PSRFM
+06/27
+k = 6
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Figure 12: Absolute error of Water map of images for the Elephant Butte example based on K-means
+clustering strategy. Unused Landsat classification maps establish the ground-truth (first column).
+06/27
+Landsat
+KF-B
+SM-B
+ESTARFM
+k = 6
+PSRFM
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Figure 13: Zoomed-in water map of images for the Elephant Butte example based on K-means clustering
+strategy where 1 indicates land and 0 indicates water pixels. Unused Landsat classification map at date
+06/23 establish the ground-truth (first column).
+32
+
+7.4B4
+Landsat
+KF-B
+SM-B
+ESTARFM
+k = 6
+PSRFM
+B5
+k = 6
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+Figure 14: Zoomed-in version of the fused bands from MODIS and Landsat for the Elephant Butte example
+using different strategies at date 06/27 (ground-truth at 06/23 is shown in the first column).
+33
+
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diff --git a/0NE0T4oBgHgl3EQfuAEL/content/tmp_files/load_file.txt b/0NE0T4oBgHgl3EQfuAEL/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf,len=1375
+page_content='1  Online Fusion of Multi-resolution Multispectral Images with Weakly  Supervised Temporal Dynamics  Haoqing Lia, Bhavya Duvvuria, Ricardo Borsoib, Tales Imbiribaa, Edward Beighleya,  Deniz Erdo˘gmu¸sa, Pau Closasa  aNortheastern University, Boston, 02215, MA, USA  bUniversity of Lorraine, CNRS, CRAN, Nancy, F-54000, France  Abstract  Real-time satellite imaging has a central role in monitoring, detecting and estimating the  intensity of key natural phenomena such as floods, earthquakes, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' One important con-  straint of satellite imaging is the trade-off between spatial/spectral resolution and their  revisiting time, a consequence of design and physical constraints imposed by satellite or-  bit among other technical limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In this paper, we focus on fusing multi-temporal,  multi-spectral images where data acquired from different instruments with different spatial  resolutions is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We leverage the spatial relationship between images at multiple modal-  ities to generate high-resolution image sequences at higher revisiting rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To achieve this  goal, we formulate the fusion method as a recursive state estimation problem and study  its performance in filtering and smoothing contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Furthermore, a calibration strategy is  proposed to estimate the time-varying temporal dynamics of the image sequence using only  a small amount of historical image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Differently from the training process in traditional  machine learning algorithms, which usually require large datasets and computation times,  the parameters of the temporal dynamical model are calibrated based on an analytical ex-  pression that uses only two of the images in the historical dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' A distributed version  of the Bayesian filtering and smoothing strategies is also proposed to reduce its compu-  tational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To evaluate the proposed methodology we consider a water mapping  task where real data acquired by the Landsat and MODIS instruments are fused generating  high spatial-temporal resolution image estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Our experiments show that the proposed  methodology outperforms the competing methods in both estimation accuracy and water  mapping tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Keywords:  Multimodal image fusion, Online Fusion, Bayesian Filtering, Water mapping,  Super-resolution  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Introduction  High spatial resolution satellite image data is a fundamental tool for remote sensing  applications such as the monitoring of land cover changes [1, 2], deforestation [3, 4] or wa-  ter mapping [5, 6] and water quality [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, to adequately deal with the variability  Preprint submitted to ISPRS Journal of Photogrammetry and Remote Sensing  June 2022  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='02598v1  [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='IV]  6 Jan 2023  of such events over time it is important to have short time spans between different image  acquisitions of the same scene (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', a high temporal resolution, or low revisit times).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' How-  ever, fundamental limitations of multiband imaging instruments and large sensor-to-target  distances impose a trade-off between spatial and temporal resolutions of satellite image  sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  This means that instruments providing high spatial resolution have long revisit times,  while the converse holds for instruments with short revisit times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This can be illustrated, for  instance, by considering Landsat 8 and MODIS instruments (with 30 and 250/500 meters  spatial resolution, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' While MODIS is able to provide daily images at coarse  resolution, Landsat-8 only revisits the same site once every 16 days [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Considering these limitations, many works proposed multimodal image fusion techniques  to generate high (spatial, spectral or temporal) resolution remote sensing images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Multi-  modal image fusion aims to combine multiple observed images, each of which having high  resolution in a given dimension – spatial, temporal, or spectral – to generate high reso-  lution image sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Several instances of image fusion have been considered, some  works aim to directly supply classification maps from multiple satellite image and surface  elevation data at each time instant [9], integrating optical and radar data for time-series  crop classification [10, 11], or fusing spatio-temporal optical and elevation data to obtain  high-resolution land temperature maps [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  In particular, classification or mapping tasks based on time-series remote sensing data  is receiving increasing interest in the literature [13, 14, 10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, to overcome the limi-  tations of existing instruments, fusing images with different spectral and spatial resolutions  has been extensively studied to generate images with high spatial and spectral resolutions,  which are critical for accurately distinguishing different materials in a pixel [15, 16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Recently, an increasing interest has been observed in applying multimodal image fusion to  generate image sequences with high spatial and temporal resolutions [18], with particular  interest dedicated to fusing data from multiple satellites to obtain daily images with high  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', 30 m) resolution [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  This has already had an important impact in applications  such as the generation of daily snow cover maps [20] and the study of drought-induced  tree mortality [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Existing spatiotemporal image fusion methods are usually divided in  weighted fusion, umixing-based, learning-based and Bayesian approaches [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' There also  exist hybrid techniques, which leverage ideas from more than one family of approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Weighted fusion methods assume that the temporal changes occurring between two time  instants are consistent between the high and low spatial resolution images for low resolution  pixels which are composed of only a single material [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, coarse resolution pixels  are often mixtures of different materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The predicted high resolution pixels are then  computed as a weighted linear combination of the previous high resolution pixels and of  the changes occurring at low resolution pixels in a given neighborhood [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Different  works have designed various weighting functions, which aim to select neighboring pixels  that are homogeneous and spatially/spectrally similar to the pixel whose change is being  predicted [24, 22, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Other works have extended such framework account for sudden  changes [27] or to use different weighting functions [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2  Figure 1: Overview of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Multimodal (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', Landsat and MODIS over time) images time  series are fused by the Distributed Multimodal Bayesian Fusion algorithm resulting in a high spatial-temporal  resolution estimated sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Covariance estimates for the dynamical model are estimated through a weakly  supervised strategy based on local high-resolution historical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We highlight that the Bayesian fusion  methodology employed here is agnostic to the multimodal measurement model making the strategy easily  generalizable to different data scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Unmixing-based methods make use of the linear mixing model (LMM), which assumes  that each pixel in the low resolution image can be represented as a convex combination of the  reflectance of a small number of pure spectral signatures, called endmembers [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The  LMM has been used for multimodal image fusion by assuming the proportions of each mate-  rial in a low resolution pixel to be stable/constant over time [30, 31, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This way, spectral  unmixing [28] is used to estimate the endmembers at different time instants from low reso-  lution images, while using different strategies to mitigate the spectral variability of a single  material [30, 33, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, abrupt abundance variations (originating from, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', land  cover changes) are commonly found in multitemporal image streams [35, 36, 37, 38], which  may negatively impact the performance of such methods and can be particularly challeng-  ing to address when occurring jointly with finer endmember variations [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, special  care is required when fusing images which are temporally distant from one another [39],  motivating the development of strategies using, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', spatially adaptive quantification of the  reliability of the input images to guide unmixing based image fusion strategies [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Learning-based approaches leverage training data and different machine learning al-  gorithms in order to perform image fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Those approaches are varied, ranging from  approaches such as dictionary learning [41], which are based on a sparse representation  of image pixels and have a strong connection to the LMM, to convolutional neural net-  works [42], which are flexible function approximations which are typically used to learn a  mapping from the low-resolution to high resolution data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Bayesian methods are flexible alternatives to the previous approaches that take into ac-  count the uncertainty present both in the imaging model and in the estimated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The  3  Bayesian framework is based on the definition of probabilistic models to describe the rela-  tionship between images of different spatial, spectral and temporal resolutions acquired by  different instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This allows image fusion to be formulated as a maximum a posteriori  estimation problem [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Although Bayesian methods usually consider Gaussian distribu-  tions for mathematical tractability, different variations have been proposed depending on  how the image acquisition process is modelled and on how the mean and covariance matri-  ces are estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This included assuming them diagonal [44], estimating image covariance  matrices based on an initial estimate of the high resolution image [43], or based on the low  resolution image pixels [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  A recent work considered a Kalman filter-based approach to estimate a high resolution  image sequence based on mixed resolution observations from the Landsat and MODIS in-  struments [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, to define the model for the Kalman filter, two Landsat+MODIS  image pairs at times t0 and tN are considered, as well as a time series of MODIS images  at instants tk P rt0, tNs, making it unsuitable for online operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, changes be-  tween each pair of images were assumed to be constant/uniform over predefined groups of  high resolution image pixels, which can be restrictive (due to the large resolution difference  between the measured images, the groups must contain many pixels in order to make the  model well-posed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' It also does not benefit from auxiliary information that could aid the  estimation of the high resolution images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Another work used the Kalman filter to esti-  mate normalized difference vegetation indices (NDVI) time series images from Landsat and  MODIS observations, using an affine model for the dynamics of the states whose coeffi-  cients are selected based on the seasonality, and another affine model to relate the NVDI  estimate obtained from MODIS and Landsat measurements [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The Kalman filter was  also recently applied to estimate land surface temperature by fusing thermal infrared and  microwave data [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  In this paper, we propose a weakly supervised Kalman filter and smoother framework  for spatio-temporal fusion of multispectral images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The proposed framework relies on ex-  plicit modeling assumptions about the image acquisition and temporal evolution processes,  under which the proposed solution is statistically optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The Kalman filter-based meth-  ods can operate in a fully online setting, where high-resolution images are only available  as past data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We also develop a smoother-based method to optimally exploit information  contained in future high-resolution observed images when processing images in a time win-  dow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, the quality of the reconstruction of Kalman filter and smoother strategies  depend directly on the quality of the dynamical image evolution model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, to overcome  this limitation, a weakly supervised strategy is proposed to learn the temporal dynamics  of the high-resolution images from a small amount of past data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' More precisely, instead of  considering the changes to be constant over areas comprising large amounts of image pixels,  we propose an analytical calibration strategy to estimate a more informative time-varying  dynamical image model by leveraging historical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This allows for a better localiza-  tion of changes in the high resolution image even in intervals where only coarse resolution  observations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', MODIS) are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, to mitigate the high computational  complexity of the Kalman filter and smoother, we propose a distributed implementation  4  by exploiting different independence assumptions about the high-resolution state space,  allowing the proposed methods to be applied to large datasets and geographical areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Fig-  ure 1 depicts the proposed methodology where high-resolution (spatially and temporally)  estimates are generated by fusing different data modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We illustrate the application  of the proposed framework by fusing images from the Landsat and MODIS instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Experimental results indicate that the proposed method can lead to considerable improve-  ments compared to using a non-informative dynamical model and to widely used image  fusion algorithms, both in image reconstruction and in downstream water classification  and hydrograph estimation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' A software package containing an implementation of the  proposed method and the image dataset is available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='com/HaoqingLi/  Multi-resolution-Multispectral-image-fusion-based-weakly-supervised-constrained-Kalman-filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In Section 2, we present the paper notation and the  proposed imaging model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Section 3 presents the Kalman filter and smoother approaches  for multimodal image fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Section 5 contains simulation experiments that illustrate the  performance of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Finally, Section 6 concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Dynamical Imaging Model  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Definitions and notation  Let us denote the the ℓ-th band of the k-th acquired image reflectances from modality  m P Ω by ym  k,ℓ P RNm,ℓ, with Nm,ℓ pixels for each of the bands ℓ “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , Lm, and Ω denoting  the set of image modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' As a practical example, we consider Ω “ tL, Mu to contain  the Landsat-8, and MODIS image modalities, without loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We also denote by  ΩH the highest resolution image modality, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', ΩH “ tLu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We denote the corresponding  high resolution latent reflectances by Sk P RNHˆLH, with NH pixels and LH bands, with  LH ě Lm and NH ě Nm,ℓ, @ℓ, m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Subindex k P N˚ denotes the acquisition time index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We  also denote by vecp¨q, colt¨u, diagt¨u and by blkdiagt¨u the vectorization, vector stacking,  diagonal and block diagonal matrix operators, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The notation xa:b for a, b P N˚  represents the set txa, xa`1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , xbu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We use Npµ, Σq to denote a Gaussian distribution  with mean µ and covariance matrix Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Measurement model  To formulate our measurement model we assume that the acquired image at time index  k, for any imaging modality, is a spatially degraded and spectrally transformed version of  the high resolution latent reflectance image Sk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Following this assumption our measurement  model for the m-th modality becomes:  ym  k,ℓ “ Hm  ℓ pSkqcm  ℓ ` rm  k,ℓ ,  ℓ “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , Lm ,  (1)  where cm  ℓ P RLH denotes a spectral transformation vector, mapping all bands in Sk to the  ℓ-th measured band at modality m;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Hm  ℓ  is a linear operator representing the band-wise  spatial degradation, modeling blurring and downsampling effects of each high resolution  band, and rm  k,ℓ represents the measurement noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that, while we consider the spatial  5  resolution of the high resolution bands in Sk to be the same, different bands from the  same modality can have different resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We also assume the measurement noise to  be Gaussian and uncorrelated among bands, that is, rm  k,ℓ „ Np0, Rm  ℓ q with time-invariant  covariance matrix given by Rm  ℓ P RNm,ℓˆNm,ℓ, and covprm  k,j, rm  k,ℓq “ 0 for all j ‰ ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Note that satellite images may be corrupted by several effects, including dead pixels  in the sensor, incorrect atmospheric compensation, and the presence of heavy cloud cover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Such pixels cannot be reliably used in the image fusion process as they may degrade the  performance of the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Directly addressing these effects using a statistical model  would require the choice of a non-Gaussian distribution for the noise vector rm  k,ℓ, which  could make the computational complexity of the fusion procedure prohibitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, we  consider a matrix Dm  k P R r  NmˆNm, which eliminates outlier pixels from the image, leading  to the following transformed measurement model:  rym  k,ℓ “ Dm  k Hm  ℓ pSkqcm  ℓ ` rrm  k,ℓ ,  (2)  where rym  k,ℓ “ Dm  k ym  k,ℓ and rrm  k,ℓ “ Dm  k rm  k,ℓ denotes the measured image band and the mea-  surement noise in which the outlier values have been removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Using (2) and the properties of the vectorization operator, we can write this model  equivalently as  rym  k,ℓ “  “  pcm  ℓ qJ b Dm  k  ‰  vec  `  Hm  ℓ pSkq  ˘  ` rrm  k,ℓ  “  “  pcm  ℓ qJ b Dm  k  ‰  Hm  ℓ sk ` rrm  k,ℓ  (3)  where b denotes the Kronecker product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The variable sk P RLHNH denotes a vector-  ordering of the high-resolution image Sk which is obtained by grouping all pixels such that  the bands of a single HR pixel are adjacent to each other, and the pixels that are contained  within a single “lowest-resolution” pixel are also adjacent to each other, that is:  sk “  »  —————————–  »  ————————–  sk,1,ιp1,1q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  sk,LH,ιp1,1q  sk,1,ιp2,1q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  sk,LH,ιpd,1q  fi  ffiffiffiffiffiffiffiffifl  J  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' ,  »  —————————–  sk,1,ιp1,Nm1,ℓ1q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  sk,LH,ιp1,Nm1,ℓ1q  sk,1,ιp2,Nm1,ℓ1q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  sk,LH,ιpd,Nm1,ℓ1q  fi  ffiffiffiffiffiffiffiffiffifl  Jfi  ffiffiffiffiffiffiffiffiffifl  J  ,  (4)  where sk,i,j is the pi, jq-th position of Sk, m1 and ℓ1 are the modality and spectral band with  the lowest spatial resolution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', for which Nm,ℓ is smallest), d “ NH{Nm1,ℓ1 is the number of  HR pixels inside each low resolution pixel of band ℓ1 and modality m1, and ι : N˚ ˆN˚ Ñ N˚  is a function such that ιpi, jq returns the index (in Sk) of the of the i-th HR pixel contained  inside the j-th low resolution pixel (where i P t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , du) for modality m1 and band ℓ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Hm  ℓ  is a matrix form representation of the operator Hm  ℓ , such that vecpHm  ℓ pSkqq “ Hm  ℓ sk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  6  We can now represent all bands from each modality in the form of a single vector  rym  k P R r  NmLm as  rym  k “  ¨  ˚  ˝  “  pcm  1 qJ b Dm  k  ‰  Hm  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  “  pcm  LmqJ b Dm  k  ‰  Hm  Lm  ˛  ‹‚  looooooooooooooomooooooooooooooon  Ă  H  m  k  sk ` rrm  k ,  (5)  where rrm  k „ Np0, rR  m  k q, and  rym  k “ col  ␣  rym  k,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , rym  k,Lm  (  ,  (6)  rrm  k “ col  ␣  rrm  k,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , rrm  k,Lm  (  ,  (7)  rR  m  k “ blkdiag  ␣  Dm  k Rm  1 pDm  k qJ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , Dm  k Rm  LmpDm  k qJ(  (8)  Note that at most time instants k, one or more of the modalities m P Ω is not observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In  this case, we set the matrix Dm  k as an empty (zero-dimensional) matrix, which simplifies  the problem and avoids introducing additional notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Dynamical evolution model  Defining reasonable dynamical models for image fusion requires detailed knowledge re-  garding the scene evolution over time, which is often unattainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In this contribution, we  aim at a complete data driven strategy assuming very little knowledge regarding the scene  evolution except for past data coming from the imaging modalities being used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To match  such lack of prior knowledge we consider a simple random-walk process to model the latent  state dynamics as:  sk`1 “ F ksk ` qk ,  (9)  where F k P RLHNHˆLHNH is the state transition matrix, which is assumed to satisfy  }F k}2 ď 1, and qk „ Np0, Qkq with Qk P RLHNHˆLHNH being the state process noise  covariance matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that the above model plays a crucial role in the estimation results,  as it describes both the distribution of the changes occurring in the image at time k, as well  as the marginal distribution of the states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This means that more sophisticated dynamics  can be introduced in the problem through the appropriate design of the process noise co-  variance matrix Qk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Although expectation maximization (EM) can be used to estimate Qk  in time invariant models [49], the problem becomes extremely ill-posed in the time-varying  setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Another issue relates to the computational complexity of EM-based strategies re-  quiring the solution of the Kalman filter and smoother systems multiple times, becoming  unfeasible when dealing with large images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' For these reasons, we propose an alternative  route to estimate Qk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' A weakly supervised approach for estimating Qk  We consider QkpDkq as a function of the set Dk “ t˜ymPΩH  ℓ  uℓăk of past high resolution  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The set Dk represents historical data and images currently being fused up the the  time step k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Although many strategies could be leveraged to find suitable past time windows  to account for more relevant covariance estimation and consider full covariance matrices,  in this preliminary work we choose a simple route to validate this type of approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' For  this, let ymPΩH  k´τ  be the the most recently observed high resolution image1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We compute Qk  by finding in our historical data the most similar image to ymPΩH  k´τ  and then computing the  pixelwise variance across the following n P N˚ images in our historical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' That is, we  compute Qk executing the following three steps for every time step k:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Identify the most similar state over Dk, that is, the image that is most similar, ac-  cording to a metric L  ℓ˚ “ arg min  ℓPIDk  L  `  ymPΩH  k´τ  , rDksℓ  ˘  ,  (10)  with rDksℓ being the ℓ-th image in the historical set Dk, and IDk Ď Z is the set  containing the time index of each image in Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' select a time window rDksℓ˚:ℓ˚`n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' compute the diagonal process noise covariance matrix, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', Qk “ diagtq2  k,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , q2  k,LHNHu,  as  q2  k,j “ max  ˆvar  `  rDkspjq  ℓ˚:ℓ˚`n  ˘  ∆ℓ˚  Dk  , ε2  ˙  ˆ ∆k ,  (11)  where rDkspjq  ℓ˚:ℓ˚`n “ r˜ymPΩH  ℓ˚,j  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , ˜ymPΩH  ℓ˚`n,js, ε ą 0 is a small scalar allowing for changes on the  scene that were unseen on the historical data window rDksℓ˚:ℓ˚`n, ∆k is the time interval  (in days) between ymPΩH  k  and ymPΩH  k`1  , and ∆ℓ˚  Dk is the time interval (in days) between rDksℓ˚  and rDksℓ˚`n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' As similarity metric we used the cosine similarity Lpy, zq “ cospy, zq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Multimodal image fusion using a weakly supervised constrained Kalman fil-  ter  Considering models (5) and (9), the online multimodal image fusion problem can be  formulated as the problem of computing the posterior distribution of the high resolution  image given all previous measurements available, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=',  p  `  sk  ˇˇtrym  1:kumPΩ  ˘  “ N  `  sk|k, P k|k  ˘  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (12)  Due to the choice of a linear Gaussian model, this distribution is also Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover,  its mean vector sk|k and covariance matrix P k|k can be computed recursively using the  standard Kalman filter with a prediction and update steps [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  1That is, τ P Z` is the smallest integer such that a high resolution image was observed at time instant  k ´ τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  8  More precisely, the prediction step of the Kalman filter computes the first and second  order moments of p  `  sk  ˇˇtrym  1:k´1umPΩ  ˘  as:  sk|k´1 “ F k´1sk´1|k´1  (13)  P k|k´1 “ F k´1P k´1|k´1F J  k´1 ` Qk´1  (14)  The update step computes then computes of (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Note that the update step can be  simplified and implemented separately for each data modality by using the Markov property  of the model and the independence between noise vectors of different modelities:  p  `  sk  ˇˇtrym  1:kumPΩ  ˘  9p  `  trym  k umPΩ  ˇˇsk  ˘  p  `  sk  ˇˇtrym  1:k´1umPΩ  ˘  “ p  `  sk  ˇˇtryu  1:k´1uuPΩ  ˘ ź  mPΩ  p  `  rym  k  ˇˇsk  ˘  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (15)  By computing the first product in the right hand side as:  p  `  sk  ˇˇtryu  1:k´1uuPΩ  ˘  p  `  rym  k  ˇˇsk  ˘  9p  `  sk  ˇˇtryu  1:k´1uuPΩ, rym  k  ˘  ,  (16)  which is an update step of the Kalman filter with image modality m to yield a new posterior  in the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' of (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This can be computed as:  vm  k “ rym  k ´ Ă  H  m  k sk|k´1  (17)  T m  k “ Ă  H  m  k P k|k´1  `Ă  H  m  k  ˘J ` rR  m  k  (18)  Km  k “ P k|k´1  `Ă  H  m  k  ˘J`  T m  k  ˘´1  (19)  sk|k “ sk|k´1 ` Km  k vm  k  (20)  P k|k “ P k|k´1 ´ Km  k T m  k  `  Km  k  ˘J  (21)  for m P Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  By proceeding with the computation of the product in the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  of (15)  recursively, the Kalman update can then be performed separately for each of the modalities  observed at time instant k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that after the first modality is processed, the update  equations above are used again for the subsequent modalities by setting sk`1|k and P k`1|k  as equal to the posterior estimates from the previously processed modality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The Linear Smoother  Given a window of K image samples, the Bayesian smoothing problem consists of com-  puting the posterior distribution of the high resolution image given all available measure-  ments available, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=',  p  `  sk  ˇˇtrym  1:KumPΩ  ˘  “ N  `  sk|K, P k|K  ˘  ,  (22)  9  which is also a Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Just like in the filtering problem, the linear and Gaussian model  allows this solution to be computed efficiently using the Rauch-Tung-Striebel (RTS) smooth-  ing equations [50], which consist of a forward pass of the Kalman filter (as described before),  followed by a backwards recursion that updates the previously computed mean and covari-  ances matrices of the state with information from future time instants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  We note that the smoothing can also be performed efficiently for the case when multiple  image modalities are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Let us consider the Bayesian smoothing equations as defined  in [51, 50], which is performed in two steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Starting from the Kalman state estimate at  time K, given by p  `  sK  ˇˇtrym  1:KumPΩ  ˘  , the smoothing distribution is computed recursively for  k “ k ´ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' according to the following relation:  p  `  sk  ˇˇtrym  1:KumPΩ  ˘  “ p  `  sk  ˇˇtrym  1:kumPΩ  ˘  ˆ  ż ppsk`1|skqp  `  sk`1  ˇˇtrym  1:KumPΩ  ˘  p  `  sk`1  ˇˇtrym  1:kumPΩ  ˘  dsk`1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (23)  where p  `  sk  ˇˇtrym  1:kumPΩ  ˘  “ Npsk|k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' P k|kq is the Kalman estimate of the state PDF at time k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  ppsk`1|skqq is the state transition PDF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' computed according to (9),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' p  `  sk`1  ˇˇtrym  1:KumPΩ  ˘  “  Npsk`1|K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' P k`1|Kq is the smoothing distribution obtained at the previous iteration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' and  p  `  sk`1  ˇˇtrym  1:kumPΩ  ˘  is the predictive state distribution,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' which is computed exactly as in the  prediction step of the Kalman filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  In the linear and Gaussian case this translates into the following closed form solution [50],  with  sk`1|k “ F ksk|k  (24)  P k`1|k “ F kP k|kF J  k ` Qk  (25)  being used to compute the predictive state distribution, and  Gk “ P k|kF J  k P ´1  k`1|k  (26)  sk|K “ sk|k ` Gkpsk`1|K ´ sk`1|kq  (27)  P k|K “ P k ` GkpP k`1|K ´ P k`1|kqGJ  k  (28)  to update the covariances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' It should be noted that the mean and covariance sk|k and P k|k  used in the Smoothing equations are the final result obtained from the Kalman update after  processing all image modalities that were available at instant k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Thus, while in the Kalman filtering the update equations must be computed sequentially  at each time step w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' the different image modalities, smoothing only needs only the final  state estimates at each instant, no matter how many modalities are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Constraining the estimates  Although the Kalman filter provides closed-form solutions to the estimation of the high-  resolution image sequence, it relies on a Gaussian assumption on the states and observations  10  which does not correspond to the physics of the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In fact, represented in reflectance  values, each pixel and band of a high-resolution images sk is actually constrained to an  interval sk,i,j P r0, smaxs, where smax is the maximum reflectance values of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Since  this information can potentially improve the accuracy of the estimated states, we propose  to incorporate this information by considering the linearly constrained Kalman filter [52],  in which the final constrained state s`  k|k is obtained as the solution to a constrained opti-  mization problem:  s`  k|k “ arg min  s  `  s ´ sk|k  ˘JP ´1  k|k  `  s ´ sk|k  ˘  subject to s P r0, smaxsNHLH  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (29)  Problem (29) consists in a constrained quadratic program, which can be costly to solve due  to the high dimensionality of the variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, we propose a simple solution consisting  of truncating the result of the traditional Kalman update:  s`  k|k “ max  `  min  `  sk|k, smax  ˘  , 0  ˘  ,  (30)  where functions maxp¨, ¨q and minp¨, ¨q compute the elementwise maximum and minimum  value between a vector and a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that this truncation provides the exact solution  when P k|k is diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The same truncation strategy was also applied to the results of the  linear smoother sk|K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We generally observed that this gave good results in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' smax  can be estimated as the maximum value of the observed images in a time window, or from  the historical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' A distributed implementation  A problem with the Kalman filter is the need to compute and store the state covariance  matrix, P k|k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This incurs in storage and operations asymptotic complexity in the order of  OpN2  HL2  Hq and OpN3  HL3  Hq, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This can make the method intractable for images  with a large number of pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Thus, to reduce the complexity of the filter and of the  smoother, we consider splitting the pixels in the estimated state sk into multiple groups  which are assumed to be statistically independent [53, 54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To this end, we divide the  state space into G groups as:  sk “ vec  `  rsp1q  k , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , spGq  k  s  ˘  ,  (31)  where the variables within each block spgq  k  are correlated, but different blocks spg1q  k  and spg2q  k  are assumed to be independent for g1 ‰ g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This leads to the following approximation for  the predictive and posterior covariance matrices P k|k´1 and P k|k as block diagonal matrices:  P k|k´1 “ blkdiag  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  P p1q  k|k´1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , P pGq  k|k´1  )  (32)  P k|k “ blkdiag  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  P p1q  k|k, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , P pGq  k|k  )  (33)  We consider different splitting possibilities, with different trade-offs between approxi-  mation accuracy with respect to the full-state-covariance Kalman filter and complexity:  11  iq A fully diagonal model (with G “ NHLH blocks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  iiq A block diagonal model where each block consists of all bands of one single high-  resolution pixel (with G “ NH blocks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  iiiq A block diagonal model, with blocks corresponding to the high-resolution pixels which  reside inside a single MODIS pixel (with G “ NHLH{NMODIS blocks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Following [54], the Kalman equations for the prediction step (13)–(14) can be written  for each block as:  spgq  k`1|k “  “  F k  ‰  pgq,:sk  (34)  P pgq  k`1|k “  “  F k  ‰  pgq,:P k  `“  F k  ‰  pgq,:  ˘J ` Qpgq  k  (35)  where  “  F k  ‰  pgq,: means the matrix formed by taking from F k the rows which correspond to  the indices in the group of states g, and all columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Matrices Qpgq  k  are defined as:  Qk “ blkdiag  ␣  Qp1q  k , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , QpGq  k  (  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (36)  Similarly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' the Kalman update equations (17)–(21) are performed separately for each block  of variables,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' and are given by:  spgq  k  “ spgq  k|k´1 ` Kpgq  k vm  k  (37)  P pgq  k  “ P pgq  k|k´1 ´ Kpgq  k T m  k  `  Kpgq  k  ˘J  (38)  with:  Kpgq  k  “ Σpgq  xy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='k|k´1  `  T m  k  ˘´1  (39)  vm  k “ rym  k ´ Ă  H  m  k sk|k´1  (40)  T m  k “ Ă  H  m  k P k|k´1  `Ă  H  m  k  ˘J ` rR  m  k  (41)  Σpgq  xy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='k|k´1 “  “  P k|k´1  `Ă  H  m  k  ˘J‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=':  “  “  P k|k´1  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=':  `Ă  H  m  k  ˘J  (42)  where  “  P k|k´1  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=': means the matrix formed by taking from P k|k´1 the rows which corre-  spond to the indices in the group of states g,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' and all columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that the block diagonal  structure of P k|k´1 and P k|k can be explored to perform the above operations efficiently,  since these matrices are very sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Following the same approach,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' the linear smoother can also be approximated in blockwise  fashion as in [55],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' for the predictive equations (24)–(25):  spgq  k`1|k “  “  F k  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=':sk  (43)  P pgq  k`1|k “  “  F k  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=':P k  `“  F k  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=':  ˘J ` Qpgq  k  (44)  12  and for the smoothing equations (26)–(28):  Gpgq  k  “  “  P kF J  k  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='pgq  `  P pgq  k`1|k  ˘´1  “ rP kspgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='pgq  `“  F k  ‰  pgq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='pgq  ˘J`  P pgq  k`1|k  ˘´1  (45)  spgq  k|K “ spgq  k  ` Gpgq  k  `  spgq  k`1|K ´ spgq  k`1|k  ˘  (46)  P pgq  k|K “ P pgq  k  ` Gpgq  k pP pgq  k`1|K ´ P pgq  k`1|kqpGpgq  k qJ  (47)  where  Gk “ blkdiag  ␣  Gp1q  k ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , GpGq  k  (  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (48)  One last issue is that the innovation covariance matrix T m  k can also be large for big  images (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', Landsat measurements), as it has pLm  śLm  ℓ“1 Nm,ℓq2 elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Fortunately, the  model implicitly imposes a simple structure for this matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To show this, let us consider a  permutation of the pixels Πm, such that Πmrym  k reorders rym  k by making different bands of  each LR pixel contiguous:  Πmrym  k “  »  —–  »  —–  rym  k,1,1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  rym  k,Lm,1  fi  ffifl  J  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' ,  »  —–  rym  k,1,Nm  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  rym  k,Lm,Nm  fi  ffifl  Jfi  ffifl  J  ,  (49)  where rym  k,ℓ,n is the n-th pixel of the ℓ-th band of ryk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  If we assume that Hm  ℓ  is a local filter, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', each pixel in the low-resolution image is  generated according to a fixed linear combination of a distinct subset of HR pixels, this  allows us to express the row-permuted version of Ă  H  m  k equivalently as:  ΠmĂ  H  m  k “ blkdiag  ␣  H, H, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , H  looooooomooooooon  Nm times  (  ,  (50)  where matrix H P RLmˆd2LH is given by:  H “ hm b Cm ,  (51)  where Cm “  “  pcm  1 qJ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , pcm  LmqJ‰J is the spectral response function for all bands, hm P  R1ˆd is the local spatial response filter, which defined how the HI pixels inside each LR  pixels are combined, and d is the number of HR pixel in each LR pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Using this permutation, the innovation covariance matrix can be written as:  ΠmT m  k ΠJ  m “ ΠmĂ  H  m  k P k|k´1  `Ă  H  m  k  ˘JΠJ  m ` Πm rR  m  k ΠJ  m  “ blkdiagtH, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , HuP k|k´1 blkdiagtHJ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , HJu  ` Πm rR  m  k ΠJ  m  “ blkdiagtHP p1q  k|k´1HJ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , HP pGq  k|k´1HJu  ` Πm rR  m  k ΠJ  m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  (52)  13  Algorithm 1: Weakly supervised online image fusion  Input  : Measured multimodal images ym  k , for all time instants k “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , K and  modalities m, historical datasets of high-resolution images Dk, parameters smax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Output: Estimated image sequence sk|K  1 Initialize P 0|0 and s0|0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2 // Filter ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  3 for k “ 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , K do  4  Compute innovation covariance matrix Qk using sk´1 and Dk according to Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5  Compute sk|k´1 and P k|k´1 using equations (31), (32), (34) and (35) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' // Prediction  6  Compute sk|k and P k|k using equation (33) and equations (37)–(42) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  // Update  7  Constrain sk|k using (30) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  8 end  9 // Smoother ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  10 for k “ K, K ´ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' , 1 do  11  Compute sk`1|k and P k`1|k using equations (31), (32), (43) and (44) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' // Prediction  12  Compute sk|K and P k|K using equations (45)–(47) and equation (48) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  // Backwards  update  13 end  14 return Estimated images sk|K  Thus, as long as the noise is independent among different pixels (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', rR  m  k is block diago-  nal), it is possible to express the innovation covariance matrix in block diagonal form by  adequately permuting the LR image pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This shows that each pixel from the lowest  resolution image modality can be processed independently when Qk and P 0|0 also have a  block diagonal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The proposed image fusion method is summarized in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Experiments  In this section, we use the proposed methodology to fuse Landsat and MODIS image  over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The Kalman filter and smoother are built under the three different assumptions  for the state covariance matrices regarding the distributed implementation discussed in  Section 4: iq diagonal state covariance (denoted by KF-D and SM-D);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' iiq block-diagonal  state covariance with one block per Landsat multispectral pixel (denoted by KF-B and SM-  B);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' and iiiq block-diagonal with blocks for all Landsat multispectral pixels corresponding to  the same coarse pixel in a MODIS image being correlated (denoted by KF-F and SM-F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' A  filter in which Landsat multispectral pixels corresponding to more than one coarse pixel in  a MODIS image being all correlated could not be implemented due to computational and  memory limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Although in our experiments we consider only two modalities the proposed methodology  admits multiple different modalities provided that enough computational power is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  As benchmark, we compare the performance of Kalman filter and smoother under all three  assumptions to that of the Enhanced Spatial and Temporal Adaptive ReFlectancefusion  Model (ESTARFM) algorithm [25], and the Prediction Smooth Reflectance Fusion Model  14  (PSRFM) algorithm [56, 57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The ESTARFM algorithm requires two high-resolution (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=',  Landsat) images at the beginning of the image sequence, and can generate high-resolution  reconstructions at later time instants based on MODIS measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, it is a good  candidate for comparison with the Kalman filtering based strategies, which also do not  require future data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The PSRFM method, on the other hand, uses two high-resolution (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=',  Landsat) images (one at the beginning and one at the end of the sequence), and provides  high-resolution reconstruction for the intermediate MODIS images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, it consists in an  adequate comparison to the smoother algorithms, which also require future high-resolution  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In the following, we describe the data and simulation setup, followed by the results  and the discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Study region  For the experiments, we consider two sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The first is the Oroville dam (Figure 2, left  panel), located on the Feather River, in the Sierra Nevada Foothills (38° 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3’ North and  122° 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8’ W) is the tallest dam in USA and is major water storage facility in California  State Water Project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The reservoir has a maximum storage capacity of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='54 ˆ 1011 ft3  or 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='36 ˆ 109 m3, which fills during heavy rains or large spring snow melts and water is  carefully released to prevent flooding in downstream areas, mainly to prevent large flooding  in Butte County and area along the Feather River.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The reservoir water storage change in  between 07/03 and 09/21 of 2018 is as shown as the hydrograph curve in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Another  unique characteristic is that it has three power plants at this reservoir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The water released  downstream is used to maintain the Feather and Sacramento Rivers and the San Francisco-  San Joaquin delta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Lake Oroville is at an elevation of 935 feet (285 meters) above sea level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  We focus at a particular area of the Oroville dam delimited by the red box in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The second site is the Elephant Butte reservoir (Figure 2, right panel), located in the  southern part of the Rio Grande river, in New Maxico, USA (33° 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4’ N and 107° 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2’ W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  It is the largest reservoir in New Mexico, providing power and irrigation to southern New  Mexico and Texas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Elephant Butte reservoir is at an elevation of 4,414 ft (1,345 meters),  and has a surface area of 36,500 acres (14,800 ha).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Table 1: Spectral angle mapper between the estimated high-resolution image and the Landsat measurement  for the Oroville Dam example (note that the Landsat images at dates 07/19, 08/20, and 09/05 were not  supplied to the algorithms and only used for evaluation purposes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, the Landsat image at 09/21  was available to all algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that the spectral angle is not reported for PSRFM at 09/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This is so  since PSRFM uses the last pair (MODIS-Landsat) of images and directly sets its estimations at this dates  to the ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Method  KF-F  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  PSRFM  Image (07/19)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1240  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8537  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2356  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1515  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9304  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9064  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0810  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8837  Image (08/20)  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6343  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2786  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1229  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1520  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1928  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1758  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0892  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='7802  Image (09/05)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5741  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0366  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6246  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6838  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4482  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4135  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4553  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0354  Image (09/21)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0588  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6385  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4042  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5471  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9754  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6960  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9584  –  Average  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8478  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='7019  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8468  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8836  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6367  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2979  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6460  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1748  15  National Geographic, Esri, Garmin, HERE, UNEP-WCMC, USGS, NASA,  ESA, METI, NRCAN, GEBCO, NOAA, increment P Corp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='55  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='28  mi  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='45  km  1:44,418  National Geographic, Esri, Garmin, HERE, UNEP-WCMC, USGS, NASA,  ESA, METI, NRCAN, GEBCO, NOAA, increment P Corp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  0  5  10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  mi  0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  17  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='25  km  1:368,824  Figure 2: (Left) Oroville dam site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' (Right) Elephant Butte site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The red boxes delimit the specific study  areas used in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Table 2: Percentage of misclassified pixels for the Oroville Dam example (the Landsat image at 09/21 was  available to all algorithms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that the misclassification percentage is not reported for PSRFM at 09/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  This is so since PSRFM uses the last pair (MODIS-Landsat) of images and directly sets its estimations at  this dates to the ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Method  KF-F  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  PSRFM  Image (07/19)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5412  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6360  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4472  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2914  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1119  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0171  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='2431  Image (08/20)  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9215  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='9851  Image (09/05)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4888  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2152  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='4345  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5877  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='7404  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8962  Image (09/21)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='7360  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='2591  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3374  –  Average  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4219  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5332  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3333  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3553  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0171  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1610  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2137  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0311  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Remote Sensed data  For our simulations with the Oroville Dam site, we collected MODIS and Landsat data  acquired from the region marked with a red square on Figure 2, and on a interval ranging  from 2018{07{03 to 2018{09{21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This interval was selected since the hydrograph analysis  indicates high variation in the water level of the reservoir, see, the hydrograph curve in  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Such variation in the water levels result in large changes in the acquired images,  exposing flooded areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In this experiment we will focus on the red and near-infrared (NIR)  bands since they are often used to distinguish water from other landcover elements in the  image [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We also collected 5 Landsat data from 2017{08{01 to 2017{12{07 to serve as a  past historical dataset Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The study region marked in the left panel of Figure 2 corresponds to Landsat and  MODIS images with 81 ˆ 81 and 9 ˆ 9 pixels, respectively2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' After filtering for heavy cloud  cover during the designated time periods, a set of 6 Landsat and 16 MODIS images were  obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We used the first MODIS and Landsat images for initialization of all methods  leading to 5 and 15 images used in the remaining fusion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  2The Landsat images were also upsampled to a spatial resolution of 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='77 meters to make its resolution  exactly 9 times that of MODIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  16  Lake Oroville  Lake Oroville  State  Recreation AreaNOSA  SPRINGDRAW  Elephant  Butte  Reservoi  R  52  M  Conseqgences  Truhort  MuniAirport  V  A  1991m  GARCIA  PEAKS  TruthOr  Z  Consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  R  o-Grande  JOHNSON  IEMESA  MCCLENFrom the set of 5 Landsat images of the Oroville Dam site that were available for  testing, three of them were set aside and not processed by any of the the algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  These images were acquired at dates 07/19, 08/20 and 09/05, when MODIS observations  were also available, and will be used in the form of a reference for the evaluation of the  algorithms’ capability of estimating the high resolution images at these dates solely from  the low resolution MODIS measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  For the simulations with the Elephant Butte site, shown in the right panel of Figure 2, we  aim to evaluate the performance of the algorithms when processing a larger geographical  area, with an area of approximately 9km ˆ 9km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The setup is similar to the Oroville  Dam example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We focus on the red and near-infrared bands of the Landsat and MODIS  instruments, and collect 47 Landsat images from 2014/01/16 to 2017/11/24 to serve as the  past historical dataset Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The study region corresponds to Landsat and MODIS images with 324ˆ324 and 36ˆ36  pixels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' After removing images with significant cloud cover, we obtained a set  of 5 Landsat and 7 MODIS images to process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We used the first MODIS and Landsat  image pair to initialize the algorithms, leading to 4 Landsat and 6 MODIS images to be  used in the remaining fusion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' From the set of 4 Landsat images that were available  for testing, 2 of them were set aside as ground truth to evaluate the algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Theses  images are acquired at dates 06/07 and 06/23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, the MODIS measurements at those  dates contained significant cloud cover, and had to be discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Therefore, we evaluate  the performance of the algorithms through the estimation results obtained dates 06/14 and  06/27 (in which the MODIS observations were available).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Algorithm setup  We initialized the proposed Kalman filter and smoother using a high resolution Landsat  observation as the state, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', s0|0 “ ryL  0, and set P 0|0 “ 10´10P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The structure of P 0  varies with different assumptions: iq P 0 “ I if the state covariance is diagonal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' iiq P 0 “  blkdiagtP 0,1, P 0,2, ¨ ¨ ¨ , P 0,NHu, where P 0,i “ 1  21 ` 1  2I, with 1 being an all ones matrix,  if the state covariance matrix has a block-diagonal structure with one block per Landsat  multispectral pixel;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' iiiq P 0 “ blkdiagtP 0,1, P 0,2, ¨ ¨ ¨ , P 0, ˜  NmˆLmu, where P 0,i “ 1  21 ` 1  2I if  the state covariance matrix has a block-diagonal structure with each block containing all  Landsat multispectral pixels corresponding to the same coarse pixel in a MODIS image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Figure 7 shows an example of the final P k|k, k “ 13, obtained with the KF under all the  assumptions discussed in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The noise covariance matrices were set as RL  ℓ “ 10´10I  and RM  ℓ “ 10´4I, for all ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The blurring and downsampling matrices were set as HL  ℓ “ I  for Landsat, while for MODIS HM  ℓ consisted of a convolution by an uniform 9 ˆ 9 filter,  defined by h “  1  8119ˆ9 (where 19ˆ9 is a 9 ˆ 9 matrix of ones), followed by decimation by  a factor of 9, which represents the degradation occurring at the sensor (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', [44]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We  also set F k “ I for all k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The vectors cm  ℓ  contained a positive gain in the ℓ-th position  which compensated for scaling differences between Landsat and MODIS sensors, and zeros  elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The matrices DM  k were constructed based on the quality codes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', the QA bits) released  17  by MODIS for each image pixel [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' QA bits provides information regarding pixel quality  and cloud cover for all pixels and all bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In our experiments we dropped any pixel not  classified as corrected product produced at ideal quality in the QA bits [59] by adding zeros  at corresponding positions in DM  k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Matrices Qk were computed following our data-driven  strategy described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4 where ε2 “ 10´5 and n “ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The ESTARFM algorithm was parametrized as follows [25], w “ 14 as half of the window  size, the number of classes was set to 4, and the pixels range was set to r0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The PSRFM  algorithm was parametrized as follows, CLUSTER METHOD “ KMEAN, and CLUSTER DATA “  fine`coarse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We highlight that all methods have access only to the first (07/03) and last  (09/21) Landsat images, which allows the algorithms to produce estimates for the MODIS  images observed from the second (07/09, k “ 2) up to the last date (09/21, k “ 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  However, PSRFM uses the the last pair (MODIS-Landsat) during its inference process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' For  this reason, error metrics computed for PSRFM on (09/21) should be disregarded as the  estimate is directly the ground-truth (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', the Landsat image) and, thus, are not reported  in the experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  All algorithms are evaluated using three metrics, which are computed taking as reference  the Landsat images, three of which are not observed by the algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The first metric  is the Spectral Angle Mapper (SAM), which attempts to measure the estimation accuracy  directly:  SAMpS, pSq “  1  NH  NH  ÿ  r“1  arccos  ´  sJ  r psr  }sr}}psr}  ¯  ,  (53)  where S and pS denote the true and the estimated images, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' sr and psr denote  the r-th pixels of different bands in S and pS, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The two remaining metrics are  related to downstream tasks of water classification and water level monitoring, which are  performed on the reconstructed image sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  We evaluate the direct benefit of the different fusion strategies in classifying water pixels  from the estimated images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To classify water pixels we resorted to a KNN classifier whose  centroids of water and non-water 2-band pixels were computed using K-Means algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Finally, we evaluate the performance of the algorithms for hydrograph estimation by plot-  ting the proportion of pixels in the image classified as water over time against the true  hydrograph for the period, for all algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Results for the Oroville Dam site  As discussed, we fused the red and NIR reflectance bands of MODIS and Landsat for  the selected study region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In Figure 3, we show the fused red (Figure 3a) and NIR (Fig-  ure 3b) reflectances as well as the acquired red and NIR reflectance values from MODIS and  Landsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Acquisition dates are displayed in the top labels at each column with a character,  M for MODIS and L for Landsat, indicating the image used in the fusion algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We  recall that only the first and last Landsat images were used in the fusion process, keep-  ing the remaining three images as ground-truth for evaluation purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Analyzing the  18  results we can see that the images estimated by the proposed Kalman filter and smoother  methods, under different assumptions, produce better visual similarity with the Landsat  (ground-truth) images for both bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' For instance, the increase in the island and the  expansion of other land parts are clearly visible for the proposed methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In contrast,  analyzing ESTARFM results we note that land parts remain mainly constant through time  until a new Landsat image is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Although lighter areas on the water portions can  be noticed, specially for k ą 8, its distribution does not resemble the ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This  is expected since ESTARFM is not designed to acknowledge prior information or historical  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' PSRFM results show an improvement compared with ESTARFM results, since it  uses both the first and the last Landsat images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' However, the PSRFM results does not  resemble the ground-truth very closely, and significant blurring occurs around the edge of  the island when k ă 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The blurring results in PSRFM are caused by the fact that the  reconstructions provided by this algorithm are based on a form of interpolation which does  not consider any information about the transition of the pixel reflectance values, whereas  in our proposed methods we use the historical data to calibrate the time-varying dynamical  model by means of matrix Qk, which can increase the accuracy of the estimations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Note that the images estimated by KF-F and SM-F (which used a full state covariance  matrix) contained more artifacts when compared to the ones obtained by KF-B, SM-B,  KF-D and SM-D (which constrained the state covariance matrix to be diagonal or block  diagonal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This occurs due to the high-dimensionality of the state vector (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', equivalent  to a vectorized Landsat image) when compared to the MODIS measurements, as this leads  to the amount of measurements not being sufficient to provide an accurate estimate of the  full state vector and its covariance matrix, as shown in [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Thus, the extra degrees of  freedom of KF-F and SM-F end up impacting their performance negatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' By setting the  covariance matrix of the Kalman filter and smoother to be block diagonal or fully diagonal,  the amount of parameters to be estimated is greatly reduced in KF-B, SM-B, KF-D and  SM-D, leading to better results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The results discussed above are corroborated by the absolute error maps displayed in  Figure 4, and SAM results shown in Table 1 for dates in which ground-truth is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Analyzing Figure 4 we highlight that SM-B and SM-D clearly present the smallest errors  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', overall darker pixels) for both bands and all dates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' KF-B also presents low absolute  error except for contour regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' PSRFM is the third overall darker image, followed by  KF-B, KF-D, SM-F, KF-F and ESTARFM with exception of the results on 07/19 (first col-  umn), where ESTARFM is close to the ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Similar conclusions can be achieved  by analyzing Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The difference between the images estimated by the Kalman filter  and smoother under the different approximations for the state covariance matrices (which  are discussed in Section 4 and illustrated for this example in Figure 7) is shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  It can be seen that the approximations had a more pronounced effect on the Kalman filter  compared to the smoother.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, the differences between the filter with a diagonal  (assumption i) and block diagonal state covariance with one block per Landsat pixel (as-  sumption ii) was relatively small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Taking in to consideration the quantitative metrics in  Table 1, this indicates that using a diagonal or block diagonal assumption on the state  19  covariance matrix with small blocks has a positive effect on the estimation performance,  which likely occurs since it drastically reduces the amount of unknowns in the model that  have to be estimated by the methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The left panel in Figure 6 presents the water maps for the ground-truth (first row) and  all studied algorithms obtained using K-means clustering, while the right panel in Figure 6  shows the misclassification maps (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', the absolute error between the water maps obtained  by each algorithm and the ground-truth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' When comparing the resulting classification maps  and the misclassification error with the ground-truth, the proposed methods present classi-  fication maps that are semantically better than the competing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This conclusion is  also reached by considering the quantitative misclassification results presented in Table 2,  in which the Kalman filter- and smoother-based methods led to smaller misclassification  rates for all images except the ones on 07/19 and 09/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' A closer analysis reveals that the  SM-D and SM-B methods hold the first and second best performance on average, followed  by SM-F, KF-D, KF-B, PSRFM, KF-F and ESTARFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Note that the PSRFM method  requires access to the ground-truth (Landsat image) on 09/21 in order to produce an esti-  mation for the MODIS image observed in this same date (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', measurement k “ 16), which  is why the corresponding misclassification percentage is not reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We also remark that  KF-D and KF-B also obtained competitive misclassification performance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', better than  PSRFM), despite using no knowledge of the Landsat image at 09/21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, comparing  the results in Table 1 and 2, it can be seen that the higher SAM results observed for all  methods at date 08/20 does not translates into a worse classification performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This  indicates that the SAM results at this date were influenced by the acquisition conditions of  the Landsat image which was used for ground truth, making the classification performance  more straightforward to interpret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Finally, we plotted the percentage of pixels classified as water over the time index k in  Figure 8, as well as a hydrograph which serves as an indicative of the dynamical evolution  of the true level of the reservoir over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' It can be seen that ESTARFM was not able to  properly identify the dynamical evolution of the reservoir level, leading to an estimation that  was almost constant for all k ă 17 and very different from the hydrograph curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' PSRFM  led to results that, although showing relatively high day-to-day variations, were closer to  the hydrograph curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The Kalman filter and smoother-based algorithms, particularly those  with the diagonal and block diagonal state covariance assumption (KF-D, KF-B, SM-B and  SM-D) led to curves that were very close to the hydrograph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Thus, the Kalman filter  methods captured the general trends of the hydrograph curves, even without having access  to information from the Landsat image at the end of the sequence (like the smoothers and  PSRFM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We note, however, that the connection between the hydrograph and the water  surface area is indirect;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' thus, small differences between the algorithms have to be interpreted  with proper care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Contribution of the temporal dynamics calibration strategy  This subsection aims to show the impact of the proposed calibration strategy, which  learns the temporal dynamical model parameters Qk using historical data, on the perfor-  mance of the proposed KF and SM algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To this end, we compared the proposed  20  KF-D and SM-D (which estimate Qk and use a diagonal assumption on the state covari-  ance matrix), to a Kalman filter and smoother with a fixed Qk “ 10´2I, which we denote  by KF-I and SM-I, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In Figure 9, we show the fused red (Figure 9a) and NIR  (Figure 9b) reflectance images, as well as the acquired red and NIR reflectance values from  MODIS and Landsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Acquisition dates are displayed in the top labels at each column with  a character, M for MODIS and L for Landsat indicating the image used in the fusion algo-  rithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' We recall that only the first and last Landsat images were used in the fusion process,  keeping the remaining three images as ground-truth for evaluation purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Analyzing the  results, we can see that the images estimated by the proposed KF-D and SM-D methods  produce significantly better visual similarity with the Landsat (ground-truth) images for  both bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' For instance, the increase in the island and the expansion of other land parts  at date 08/20 are clearly visible for the proposed methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' On the other hand, analyzing  the results of the KF-I and SM-I methods, where the temporal dynamics matrix Qk was  kept constant and independent of past data, we observe that the results appear very blurry,  with a resolution that is comparable to that of the MODIS images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This shows that the  proposed weakly supervised calibration strategy is key in order for the KF- and SM-based  strategies to obtain high quality reconstructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Results for larger scale Elephant Butte site  In this subsection, we compare the proposed strategies to ESTARFM and PSRFM in  the Elephant Butte example, which comprises a larger geographical area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' For simplicity  and to reduce the use of space, we compare only proposed Kalman filter and smoother  methods with the block diagonal assumption on the state covariance matrices (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', KF-B  and SM-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The fusion results for both bands and all algorithms are shown in Figure 10, while  Figure 11 shows the corresponding water mapping results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To measure the performances  of different methods in this large area, the Landsat images at dates 06/07 and 06/23 were  chosen as a ground truth to evaluate the quality of the reconstructed images at dates 06/14  and 06/27 (we remark that the MODIS images at dates 06/07 and 06/23 were not available  due to the presence of cloud cover).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' It can be seen that the proposed KF-B, SM-B and the  PSRFM methods provide estimates that are close to the ground truth images, whereas the  ESTARFM method shows an inferior performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This can be seen more clearly for the  image at date 06/14 (k “ 5), in which the smoother method better captured the increase in  the area of the reservoir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' To evaluate the performances of different methods more clearly,  Figure 12 shows the absolute error of water maps of images compared with the ground  truth, and Figures 13 and 14 show a zoomed-in area of the image of the fused image and  water mapping result, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' It can be seen from Figure 12 that the misclassification  errors are concentrated at the borders of the reservoir, which is the area that undergoes the  largest amounts of changes over time, and consequently the hardest to classify correctly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The SM-B algorithm shows the best results, followed by KF-B, PSRFM and ESTARFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Nevertheless, PSRFM provides results that contain less artifacts compared to KF-B, despite  the lower classification accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The superior visual quality of the results of SM-B and  21  PSRFM is explained by their use of Landsat images both at the beginning and at the end of  the image sequence, whereas KF-B and ESTARFM do not have access to the last Landsat  image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Table 3 presents the SAM results, and Table 4 shows the corresponding percentage of  misclassified pixels for the different methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' It can be seen that in terms of SAM, the SM-B  method obtained the best results for both dates, followed by PSRFM and ESTARFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' How-  ever, the KF-B strategy was able to obtain a better water mapping performance compared  to PSRFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This indicates that the artifacts seen in the (comparatively noisier) reconstruc-  tions of KF-B impact the the classification performance in a less substantial way compared  to the SAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This shows that the proposed Kalman-filter based strategy can provide mean-  ingful water mapping results in a real-time setting, in which we do not have access to future  Landsat images, precluding smoothing-based algorithms (such as SM-B and PSRFM) to be  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Table 3: Spectral angle mapper between the estimated high-resolution image and the Land- sat measurement  for the Elephant Butte example (note that the Landsat images at dates 06/07 and 06/23 were not supplied  to the algorithms and only used for evaluation purposes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Method  KF-B  SM-B  ESTARFM  PSRFM  Image (06/07)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5416  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='9993  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2678  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2698  Image (06/23)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='7514  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='8719  Average  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6465  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4958  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='5709  Table 4: Percentage of misclassified pixels for the Elephant Butte example (note that the Landsat images  at dates 06/07 and 06/23 were not supplied to the algorithms and only used for evaluation purposes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Method  KF-B  SM-B  ESTARFM  PSRFM  Image (06/07)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='2678  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6606  Image (06/23)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='8250  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='8675  Average  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6413  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1269  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0504  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2640  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Discussion  The results presented above clearly indicate that the proposed weakly supervised smoother-  based image fusion strategy outperforms the ESTARFM and PSRFM algorithms in terms of  image reconstruction when an appropriate covariance structure is selected (SM-D and SM-  B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This highlights that having less model parameters to estimate (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=', a more constrained  state covariance model) can lead to better results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, even the Kalman filter strate-  gies (particularly KF-B and KF-D), which estimate high-resolution images from MODIS  without having access to any future data, have shown very competitive performance, with  great potential for tasks in which high-resolution estimates are required online and one can-  not wait for another Landsat image to be available before computing the high-resolution  reconstructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  The advantage of the proposed filter and smoother strategies is more clear when eval-  uated semantically by means of the water classification performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  For instance, the  22  growth of the island portion over time in regions that are semantically meaningful leads  to more meaningful results that cannot be entirely captured by one standard metric such  as the SAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' This can be observed more clearly through the spatial distribution of the  misclassification error maps in Figure 6, which for ESTARFM and PSRFM are signifi-  cantly more concentrated on the borders between land and water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' In general, the proposed  filtering-based strategies clearly outperformed both the ESTARFM and PSRFM algorithms,  a standard and a state of the art remote sensing image fusion algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, the  proposed distributed implementation, described in Section 4, is able to reduce the com-  putational power and memory demand of the standard Kalman filter and smoother when  applied for large images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Conclusions  In this paper, an online Bayesian approach for fusing multi-resolution space-borne mul-  tispectral images was proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' By formulating the image acquisition process as a linear  and Gaussian measurement model, the proposed method leveraged the Kalman filter and  smoother to perform image fusion by estimating the latent high resolution image from the  different observed modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Moreover, a weakly supervised strategy is also proposed to  define an informative time-varying dynamical image model by leveraging historical data,  which leads to a better localization of changes occurring in the high-resolution image even  in intervals where only coarse resolution observations are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Experimental results  indicate that the proposed strategy can lead to considerable improvements compared to  both classical and state-of-the-art image fusion algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Acknowledgments  The authors would like to thank the support of the National Geographic Society under  Grant NGS-86713T-21, the National Science Foundation under Award ECCS-1845833, and  NASA – GRACE–FO Science Team (80NSSC20K0742).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  23  Landsat  07/03L  07/09M  07/14M  07/19M  07/26M  08/01M  08/03M  08/08M  08/13M  08/20M  08/24M  08/29M  09/05M  09/11M  09/16M  09/21M  09/21L  MODIS  KF-F  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  k = 1  PSRFM  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  k = 9  k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='20  (a) Fused images in band 1 (MODIS) and band 4 (LandSat)  Landsat  07/03L  07/09M  07/14M  07/19M  07/26M  08/01M  08/03M  08/08M  08/13M  08/20M  08/24M  08/29M  09/05M  09/11M  09/16M  09/21M  09/21L  MODIS  KF-F  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  k = 1  PSRFM  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  k = 9  k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='35  (b) Fused images in band 2 (MODIS) and band 5 (LandSat)  Figure 3: Fused bands from MODIS and Landsat for the Oroville Dam example using different strategies over  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The first two rows of each subfigure depict MODIS and Landsat bands acquired at dates displayed on  top labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' At each time index estimation with KF and SM under different model assumptions, ESTARFM  and PSRFM are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Some Landsat images were omitted from the estimation process and used solely  as ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Images used at each update step are indicated on top labels where “M” stands for MODIS  and “L” for Landsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  24  KF-F  07/19  08/20  09/05  09/21  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  k = 4  PSRFM  k = 10  k = 13  k = 16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='20  KF-F  07/19  08/20  09/05  09/21  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  k = 4  PSRFM  k = 10  k = 13  k = 16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='35  Figure 4: Absolute difference between the estimated and ground truth (Landsat) images for the Oroville  Dam example in the red (upper panel) and NIR (lower panel) bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  25  --Landsat  07/03L  07/09M  07/14M  07/19M  07/26M  08/01M  08/03M  08/08M  08/13M  08/20M  08/24M  08/29M  09/05M  09/11M  09/16M  09/21M  09/21L  MODIS  KF-BF  KF-DF  KF-DB  SM-BF  SM-DF  k = 1  SM-DB  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  k = 9  k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  Landsat  07/03L  07/09M  07/14M  07/19M  07/26M  08/01M  08/03M  08/08M  08/13M  08/20M  08/24M  08/29M  09/05M  09/11M  09/16M  09/21M  09/21L  MODIS  KF-BF  KF-DF  KF-DB  SM-BF  SM-DF  k = 1  SM-DB  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  k = 9  k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  Figure 5: Absolute differences between the images estimated by the KF and Smoother under different model  assumptions for red (upper panel) and NIR (lower panel) bands, for the Oroville Dam example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' KF-BF:  difference between the estimates of KF-B and KF-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' KF-DF: difference between the estimates of KF-D and  KF-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' KF-DB: difference between the estimates of KF-D and KF-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' An analogous notation holds for the  smoother (SM) estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  26  Landsat  07/19  08/20  09/05  09/21  KF-F  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  k = 4  PSRFM  k = 10  k = 13  k = 16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  Landsat  08/07  08/23  09/08  09/24  KF-F  SM-F  KF-B  SM-B  KF-D  SM_D  ESTARFM  k = 4  PSRFM  k = 7  k = 11  k = 14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  Figure 6: (Upper Panel) Water map of the reconstructed images of the Oroville Dam example based  on K-means clustering strategy, where 1 indicates land and 0 indicates water pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Classification maps  obtained from Landsat images not observed by the image fusion algorithms establish the ground-truth (first  row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' (Lower Panel) Absolute error of Water map of images based on K-means clustering strategy, where  0 indicates correctly classified pixels and 1 indicates misclassifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The ground-truth is shown in the  first row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  27  :-  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  1二  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='--12  10  8  6  4  14  12  10  8  6  4  20  15  10  5  7  6  5  4  3  7  6  5  4  3  15  10  5  Modis Observation in Band 1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='5  Modis Observation in Band 2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='5  Landsat Observation in Band 4  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  Landsat Observation in Band 5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  Figure 7: (Top Colored Panel) Estimated state covariance structure of the Kalman filter under model  assumptions i, ii and iii for a small image area in the Oroville Dam example and k “ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Top row depicts  the whole covariance matrix with a red square indicating the zoomed part displayed on the bottom row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The  plots indicate that correlations are present when assuming block diagonal covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' (Bottom  Panel) Zoom of the MODIS image for bands 1 and 2 (left), and the corresponding Landsat observations for  bands 4 and 5 (right) corresponding to the covariance matrices plotted in the right panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  28  0  2  4  6  8  10  12  14  16  18  20  Image Indices (k)  45  50  55  60  65  70  75  80  Water pixel percentage  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  Volume [m3]  109  KF-F  SM-F  KF-B  SM-B  KF-D  SM-D  ESTARFM  PSRFM  Hydrograph  Figure 8: Percentage of water pixels in the estimated images over image index (time) and the reservoir  volume in m3 (hydrograph) for the Oroville Dam example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Classification of water was done by performing  clustering on the estimated bands for each method and time index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' High resolution Landsat images were  observed at indices k P t1, 17u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  29  Landsat  07/03L  07/09M  07/14M  07/19M  07/26M  08/01M  08/03M  08/08M  08/13M  08/20M  08/24M  08/29M  09/05M  09/11M  09/16M  09/21M  09/21L  MODIS  KF-D  SM-D  KF-I  k = 1  SM-I  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  k = 9  k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='20  (a) Fused images in band 1 (MODIS) and band 4 (LandSat)  Landsat  07/03L  07/09M  07/14M  07/19M  07/26M  08/01M  08/03M  08/08M  08/13M  08/20M  08/24M  08/29M  09/05M  09/11M  09/16M  09/21M  09/21L  MODIS  KF-D  SM-D  KF-I  k = 1  SM-I  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  k = 9  k = 10 k = 11 k = 12 k = 13 k = 14 k = 15 k = 16 k = 17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='35  (b) Fused images in band 2 (MODIS) and band 5 (LandSat)  Figure 9: Fused bands from MODIS and Landsat for the Oroville Dam example using different strategies  over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The first two rows of each subfigure depict MODIS and Landsat bands acquired at dates displayed  on top labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' At each time index estimation results of the diagonal Kalman filter and smoother with the  proposed weakly supervised calibration strategy (KF-D and SM-D) are compared to the result of a Kalman  filter and smoother with Qk being proportional to the identity (denoted by KF-I and SM-I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Landsat images  at dates 07/19, 08/20 and 08/29 were omitted from the estimation process and used solely as ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  Images used at each update step are indicated on top labels where “M” stands for MODIS and “L” for  Landsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  30  Landsat  03/19M  03/19L  04/18M  05/18M  06/07  06/14M  06/23  06/27M  07/09M  07/09L  MODIS  KF-B  SM-B  ESTARFM  k = 1  PSRFM  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='30  (a) Fused images in band 1 (MODIS) and band 4 (LandSat)  Landsat  03/19M  03/19L  04/18M  05/18M  06/07  06/14M  06/23  06/27M  07/09M  07/09L  MODIS  KF-B  SM-B  ESTARFM  k = 1  PSRFM  k = 2  k = 3  k = 4  k = 5  k = 6  k = 7  k = 8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='5  (b) Fused images in band 2 (MODIS) and band 5 (LandSat)  Figure 10: Fused bands from MODIS and Landsat for the Elephant Butte example using different strategies  over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' The first two rows of each subfigure depict MODIS and Landsat bands acquired at dates displayed  on top labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' At each time index estimation with KF and SM under block diagonal model assumptions,  ESTARFM and PSRFM are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Some Landsat images were omitted from the estimation process and  used solely as ground-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Images used at each update step are indicated on top labels where “M” stands  for MODIS and “L” for Landsat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  31  06/14  Landsat  KF-B  SM-B  ESTARFM  k = 5  PSRFM  06/27  k = 6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  Figure 11: Water map of images for the Elephant Butte example based on K-means clustering strategy where  1 indicates land and 0 indicates water pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Unused Landsat classification maps establish the ground-truth  (first column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  06/14  Landsat  KF-B  SM-B  ESTARFM  k = 5  PSRFM  06/27  k = 6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  Figure 12: Absolute error of Water map of images for the Elephant Butte example based on K-means  clustering strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Unused Landsat classification maps establish the ground-truth (first column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  06/27  Landsat  KF-B  SM-B  ESTARFM  k = 6  PSRFM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='0  Figure 13: Zoomed-in water map of images for the Elephant Butte example based on K-means clustering  strategy where 1 indicates land and 0 indicates water pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content=' Unused Landsat classification map at date  06/23 establish the ground-truth (first column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='  32  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='4B4  Landsat  KF-B  SM-B  ESTARFM  k = 6  PSRFM  B5  k = 6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
+page_content='30  Figure 14: Zoomed-in version of the fused bands from MODIS and Landsat for the Elephant Butte example  using different strategies at date 06/27 (ground-truth at 06/23 is shown in the first column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0NE0T4oBgHgl3EQfuAEL/content/2301.02598v1.pdf'}
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+Modified Query Expansion Through Generative Adversarial Networks
+for Information Extraction in E-Commerce
+Altan Cakir∗,1, Mert Gurkan2
+A R T I C L E I N F O
+Keywords:
+Generative Adversarial Networks
+Query Expansion
+Conditional Neural Networks
+Information Retrieval
+E-Commerce
+A B S T R A C T
+This work addresses an alternative approach for query expansion (QE) using a generative adversarial
+network (GAN) to enhance the effectiveness of information search in e-commerce. We propose a
+modified QE conditional GAN (mQE-CGAN) framework, which resolves keywords by expanding the
+query with a synthetically generated query that proposes semantic information from text input. We
+train a sequence-to-sequence transformer model as the generator to produce keywords and use a re-
+current neural network model as the discriminator to classify an adversarial output with the generator.
+With the modified CGAN framework, various forms of semantic insights gathered from the query-
+document corpus are introduced to the generation process. We leverage these insights as conditions
+for the generator model and discuss their effectiveness for the query expansion task. Our experi-
+ments demonstrate that the utilization of condition structures within the mQE-CGAN framework can
+increase the semantic similarity between generated sequences and reference documents up to nearly
+10% compared to baseline models.
+1. Introduction
+In search based business models, such as e-commerce,
+given a search query, the system needs to match it to some
+relevant keywords/categories/frequencies by business part-
+ners and then pull out the related category/product for query
+searching and ranking. The query keyword matching can
+be done by some simple matching rules like exact match,
+similarity match, and phrase match, which are all based on
+matching the similar tokens shared by query and keywords.
+On the other hand, using AI-based recent techniques for smart
+match is an important yet difficult match type that can asso-
+ciate a query to some relevant keywords even they do not
+generate many similar tokens.
+In general, it is well defined that search queries math-
+ematically follow the power law distribution (Spink, Wol-
+fram, Jansen and Saracevic, 2001). The curve formed by the
+most frequent queries constitutes the main center, while the
+rare queries with low frequency form the tail of the curve.
+Although they are few in such cases, low-frequency queries
+are excluded from the query volume traffic as a whole and
+therefore cause problems in systems as a data deficiency that
+needs to be generated synthetically.
+Because of the incoming query distribution to the search
+engine, the performance of matching rare queries with docu-
+ments existing in the database is a challenging task. It is of-
+ten the case that an additional process is required to assist the
+match between rare queries and documents. To address the
+problem, various methodologies such as relevance feedback
+methods, similarity-based methods for query-document match-
+ing, machine translation models for query transformation,
+∗Corresponding author
+ORCID(s): 0000-0002-8627-7689 (A. Cakir)
+1Physics Engineering, Faculty of Science and Letters, Istanbul Tech-
+nical University, Istanbul, Turkey and Istanbul Technical University Artifi-
+cial Intelligence, Data Science Research and Application Center, Istanbul
+Turkey
+2Insider (useinsider.com), Istanbul, Turkey
+and query expansion methods are discussed in the literature.
+Query expansion is one of the significant problems stud-
+ied in the Information Retrieval (IR) domain with various
+applications such as question answering, information filter-
+ing, or multimedia document matching tasks (Carpineto and
+Romano, 2012). The problem can be described as the at-
+tempt of the increasing performance of matching input se-
+quences and document the corpus of an IR system by refor-
+mulating given input sequences (Azad and Deepak, 2019b).
+Query expansion methodologies are often applied where the
+input queries are words or sequences originating from real
+human users, while documents to match or rank them con-
+sist of predefined items. Natural language queries that match
+to same documents can differ verbally and semantically (Fur-
+nas, Landauer, Gomez and Dumais, 1987). Because of this
+ambiguity, the complexity of query-document matching is
+often increased by the innate characteristics of the data.
+Earlier studies in the query expansion domain seem to
+focus on rule-based applications. These applications evalu-
+ate candidate expansion terms by the frequency of appear-
+ing together with the words in the original query (Carpineto,
+de Mori, Romano and Bigi, 2001). In addition to word fre-
+quency based studies, systems built upon pseudo-relevance
+feedback structures are also widely utilized in the literature.
+(Metzler and Croft, 2007) uses the Markov random fields for
+modelling dependencies to assist the query expansion pro-
+cess. (Symonds, Bruza, Sitbon and Turner, 2011) provides
+a different approach to the query expansion methods with
+pseudo-relevance feedback, where they build tensor repre-
+sentations of queries that enables obtaining relevance feed-
+back based on word meanings.
+Adoption of the deep learning applications in the nat-
+ural language domains generated word embeddings as ef-
+ficient ways to represent semantic information of text data
+(Mikolov, Chen, Corrado and Dean, 2013). The utilization
+of word embeddings made it possible to evaluate the seman-
+tic relationship between words. This capability is employed
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 1 of 10
+arXiv:2301.00036v1  [cs.LG]  30 Dec 2022
+
+Modified Query Expansion Through Generative Adversarial Networks
+for query expansion problems by using various ways to eval-
+uate the similarity of words that make up the queries and
+candidate terms to expand these queries.
+The popularity of the word embedding methods for vari-
+ous problems for IR and NLP, led research efforts to increase
+the accuracy of word representations in specific cases. To
+this end, alternative ways to produce different embeddings
+of tokens for query expansions are proposed (Sordoni, Ben-
+gio and Nie, 2014). Additionally, research conducted uti-
+lization of task-specific trained word embeddings for query
+expansion (Diaz, Mitra and Craswell, 2016). This way, word
+representations are more likely to capture the context and
+semantic properties of the trained corpus. Following these
+works, (Qi, Gong, Yan, Jiao, Shao, Zhang, Li, Duan and
+Zhou, 2020; Lian, Chen, Jia, You, Tian, Hu, Zhang, Yan,
+Tong, Han et al., 2021) proposed a query expansion approach
+for search engine optimization by utilizing a prefix tree to
+serve as look ahead strategy for generating expansion terms
+for given queries.
+Recent applications of GAN methods provide alternative
+methods to approach the problem. GAN models can directly
+generate expansion terms or expanded user queries by train-
+ing over user search queries and their matching documents.
+In GANs the discriminative network can learn to distinguish
+between the synthetic data created by the generator and the
+real data examples. This way, the generation process is chal-
+lenged by the network itself to create high-quality samples.
+This approach of training has proven to be very successful
+in the computer vision domain and increasing its popular-
+ity in natural language processing problems. Additionally,
+the research focusing on establishing back-propagation be-
+tween discriminator and generator models with discrete to-
+kens in text data (Yu, Zhang, Wang and Yu, 2017; Kusner
+and Hernández-Lobato, 2016) provided highly performing
+generative models.
+With initial GAN models, the model is trained with noise
+for the generation process. With conditional structures, the
+query generation of the GAN models can be assisted with
+the chosen condition mechanism. Similar to earlier works
+in the query expansion domain, enhancing user queries with
+existing relevant information is adopted by GAN-based ar-
+chitectures too. GAN models can utilize part of text data,
+class labels present during the training, or extracted proper-
+ties of the query and documents as conditions to increase the
+likelihood of matching queries with desired documents. The
+study of (Lee, Gao and Zhang, 2018) proposes a conditional
+GAN structure with a query expansion approach for enrich-
+ing rare queries in search engines. The study of (Huang,
+Wang, Liu and Ding, 2021) employs a well-known method
+of pseudo-relevance feedback in the query expansion do-
+main as the condition for their expansion term generation.
+Studies discussed intend to create a conditional GAN-
+based framework to leverage query expansion to match key-
+words for an effective search selection. In general, a sequence-
+to-sequence model, in which the input sequence is a random
+word vector followed by a query vector, is commonly used
+for the generator. The output sequence composes of the vec-
+tors of the generated keywords. As the discriminator, the
+parallelized Recurrent Neural Network (RNN) model is used
+as a binary classifier. However, most of these studies are not
+conducted from the perspective of improving search engines
+by enhancing query-document matching performance. Our
+study aims to combine GAN architecture and existing query-
+enhancing methods by utilizing them as condition structures
+for the generator model. Proposed conditional GAN models
+aim to alleviate the performance drop of search engines, by
+increasing the query-document matching performance with
+condition-assisted query expansion mechanisms.
+To alleviate the effects of the problem described, we in-
+troduce the mQE-CGAN (Modified Query Expansion Con-
+ditional Generative Adversarial Network) framework to study
+the query expansion to enhance the performance of a search
+engine by increasing the query-document matching perfor-
+mance. The generator of the model is a sequence-to-sequence
+encoder-decoder model that takes user search queries and the
+vectors from the applied condition mechanism. The output
+of the generator, expanded queries, is evaluated by the dis-
+criminator model. We use an LSTM model for the binary
+classification task between the synthetic and real samples.
+During adversarial learning, the evaluation of the discrimi-
+nator guides the performance of the generator model. With
+the mQE-CGAN framework, our contributions can be listed
+below;
+• Model: We propose a novel conditional generative
+adversarial network model that takes the semantic re-
+lationship between the query and document pairs as
+conditions. The generator of the model is a sequence-
+to-sequence encoder decoder model, while the discrim-
+inator is an LSTM-based binary classifier. We provide
+details of the model framework and the evaluation of
+the training process with a conditional approach.
+• Conditional Query Expansion: We provide alterna-
+tive methods for condition structures with generative
+adversarial networks. Condition structures discussed
+in this paper aim to capture semantic relationships be-
+tween query-document pairs.
+• Datasets: We test our generative model with the user
+query and document pairs from the customers of In-
+sider1. By testing the proposed models with differ-
+ent customer datasets, we evaluate our models against
+data with different characteristics.
+The primary aspect that mQE-CGAN framework differs
+from the existing conditional GAN frameworks is that the
+models of the framework are conditioned on the semantic
+and statistical relationships between the query-document data.
+Employed conditions are not limited to the individual re-
+lationships between the query and the matching document
+pairs. They are rather constructed with the consideration of
+the entire corpus. Hence, the generation process of the GAN
+framework utilizes conditions produced after the semantic
+analysis of the entire corpus.
+1https://useinsider.com
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 2 of 10
+
+Modified Query Expansion Through Generative Adversarial Networks
+Figure 1: Diagram of the mQE-CGAN framework.
+2. System Architecture
+2.1. mQE-CGAN Framework
+The proposed framework for adversarial training with
+the mQE-CGAN framework can be observed in the Figure
+2 below. The generator model of the framework takes input
+queries and the selected condition vectors assigned for input
+queries. With a sequence-to-sequence structure, it generates
+expansion terms from the given queries. The discriminator
+model of the adversarial schema performs binary classifica-
+tion on the expanded synthetic queries and documents that
+match to original queries of users.
+Condition generation mechanisms discussed in the study
+aim to take advantage of the data used. As the query-document
+pairs in datasets denote user searches and matching docu-
+ments, condition approaches focus on the semantic and simi-
+larity metrics of given queries and their matching documents
+by the search engine.
+2.1.1. Generator Model
+The generator model of the architecture is an encoder-
+decoder sequence-to-sequence model that takes FastText (Bo-
+janowski, Grave, Joulin and Mikolov, 2016) word embed-
+ding representations of the user search queries and their cor-
+responding condition vectors as input. To be able to achieve
+back-propagation with the discrete input sequences, similar
+to the existing studies (Yu et al., 2017; Lee et al., 2018)
+Monte Carlo rollouts are used in the decoder of the gener-
+ator. With this method, rewards produced by the discrimi-
+nator can be transferred to the generator for each generation
+step.
+2.1.2. Condition Structures
+GAN models can be extended into conditional models
+if the adversarial learning process is performed with addi-
+tional information (Mirza and Osindero, 2014). With the
+introduction of conditions, the models can be inclined to
+generate samples with the desired qualities (Sohn, Lee and
+Yan, 2015). Conditions are introduced to guide the generator
+model during the sequence generation process. Condition
+structures utilized in this study are generated before training
+the model. Condition vectors of queries are concatenated
+with the word embedding representation of the user queries
+during training. To retrieve them, Ball Tree-based look-up
+tables are used.
+To this end, four different condition structures are ap-
+plied with the following expected priorities; (1) It should
+enrich the user query with other similar queries, and (2) it
+should provide information that will assist in distinction be-
+tween similar documents that can be mapped with the given
+query. To address these requirements, various condition vec-
+tor generation strategies displayed are implemented. Uti-
+lized methods are considered to be addressing the shortcom-
+ings of the encoder-decoder generator model. These condi-
+tion generation strategies are described in the list below.
+1. Query Weighting with TF-IDF Scores: Condition vec-
+tors are generated with CBOW representations of the
+TF-IDF weighed input word embeddings
+2. Search Tree Based Document Similarity: Condition
+vectors are generated with CBOW representations of
+the most similar documents to the given input query.
+3. Search Tree Based Word Similarity: Condition vec-
+tors are generated with CBOW representations of the
+most similar words in the corpus of documents to the
+given input query.
+Although these methods are commonly utilized in query
+expansion approaches (Azad and Deepak, 2019a), their in-
+tegration as condition mechanisms is not adequately experi-
+mented with generative models.
+2.1.3. Discriminator Model
+The discriminator model of the mQE-CGAN framework
+is built with the same pre-trained Fasttext word embeddings
+and LSTM layers processing embedded representations of
+generated and real document sequences. Unlike the gener-
+ator model of the framework, the discriminator model does
+not utilize the condition structures for its pre-training and ad-
+versarial learning processes. The model is designed for the
+binary classification task between real documents in corpus
+and sequences formed by the generator as the synthetic data.
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 3 of 10
+
+P1: Classification as
+p2
+Real Data
+p2: Classification as
+Generated Sequences
+Generated Data
+Linear Layer
+Query 1
+ Condition 1
+Query 2
+Condition 2
+Expanded
+User Query
+ Matched Document
+queries
+Condition
+Generation
+W1
+W1
+Query n
+Condition n
+Generator model input
+Search Engine
+Discriminator Model InputModified Query Expansion Through Generative Adversarial Networks
+Figure 2: Diagram of the Monte Carlo rollouts. At each step, a batch of sequences are generated by the decoder of the
+network. These batches are evaluated by the discriminator to guide the generation process of the generator model.
+Figure 3: LSTM based discriminator model of the mQE-
+CGAN framework.
+2.2. Implementation Details
+We conducted the implementation with the PyTorch li-
+brary (Paszke, Gross, Massa, Lerer, Bradbury, Chanan, Killeen,
+Lin, Gimelshein, Antiga, Desmaison, Kopf, Yang, DeVito,
+Raison, Tejani, Chilamkurthy, Steiner, Fang, Bai and Chin-
+tala, 2019) in this study. The encoder-decoder generator model
+is implemented by using the TransformerEncoder and Trans-
+formerDecoder classes in PyTorch. The generator model
+uses 2 layers for both the encoder and the decoder parts.
+Initially, the input user queries are transformed to FastText
+word embedding representations with each word being rep-
+resented with a tensor of size 100. Originally, FastText word
+embeddings are available for Turkish with a size of 300. To
+reduce the amount of GPU RAM required, we transformed
+these embedding representations to vectors with size 100
+with the reduce_model implementation of the FastText li-
+brary. It is followed by applying positional embedding to
+assign the order context to tokens in sequences with the help
+of the attention heads (Vaswani, Shazeer, Parmar, Uszko-
+reit, Jones, Gomez, Kaiser and Polosukhin, 2017). For the
+forward pass, the given query and its paired condition vector
+are concatenated. The encoder and decoder of the generator
+take an input size of 200 from the concatenated tensors, and
+they have a hidden size of 512.
+Pre-training of the generator is performed by training the
+generator model with the learning rate 10−3 and the Adam
+(Kingma and Ba, 2014) optimizer. During pre-training, the
+generator uses a softmax layer of size 푁, where 푁 is the
+total vocabulary size of the query and document corpus. Se-
+quence generation is performed iteratively by predicting an
+expansion term at each step until the generator predicts the
+next token as < 퐸푂푆 > (end of the sequence) token. For
+many cases, it was observed that after training the genera-
+tor 16 epochs the Cross-Entropy Loss of the model does not
+improve.
+The discriminator model of the framework is intention-
+ally kept simpler than the generator. For the discriminator,
+we used a 1 layer LSTM model. To decide on the hyper-
+parameters of the discriminator, a grid search is applied to
+hyper-parameters by training discriminator models with com-
+bined datasets of synthetic data from the generator and the
+samples from the document corpus. The discriminator model
+where the loss is optimized was obtained with the number of
+epochs as 24, the learning rate as 10−2, dropout as 0.1, and
+the batch size as 256.
+3. Experiments
+3.1. Datasets
+The datasets utilized in the study are generated by the
+analysis of user behavior in a search engine product of In-
+sider. More specifically, these datasets consist of user search
+queries and the first-ranked resulting products in the plat-
+forms of Insider customers. It should be noted that the datasets
+utilized in this study do not include any specific user infor-
+mation. During the data collection step, any information that
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 4 of 10
+
+Backpropagation of the
+average reward collected
+from the discriminator
+Rewards from the
+Discriminator Model
+Generated
+sequences
+current
+with Monte
+Discriminator
+t2
+Batch of
+word
+Carlo
+expanded
+Rollouts
+sequences
+t1
+t2
+Encoded
+Queryp1: Classification as Real Data
+p1
+p2
+P2: Classification as Generated Data
+Linear Layer
+h21
+h22
+h23
+h24
+h25
+LSTM
+Layers
+h11
+h12
+h13
+h14
+h15
+Word
+Embeddings
+W1
+W2
+W3
+W4
+W5
+Synthetic data
+Real data source
+source
+The
+Generator
+Model
+User queries and
+matching productsModified Query Expansion Through Generative Adversarial Networks
+can be exploited to identify the user information is discarded.
+As the general user behavior in search engines is to en-
+ter fewer words to match the desired documents (Pal, Mitra
+and Bhattacharya, 2015), queries in search engines tend to
+compose fewer words compared to the documents. This gen-
+eral observation is also present in the datasets utilized in our
+study. The average number of words in queries and docu-
+ments in datasets used in the study can be observed in Figure
+4 below.
+Figure 4: Statistics of the query and the document datasets
+utilized in the study. For each dataset, bars at the top display
+the maximum, average, and minimum number of words in
+queries. Similarly, bottom bars display statistics of the doc-
+ument corpus. For all datasets, the average number of words
+in user searches are almost four times less than their match-
+ing product equivalents, suggesting further ways to employ
+semantic information to be extracted from document data.
+The difference between the number of words in queries
+and documents introduces various challenges for search en-
+gines. In the case of rare query inputs of users, similar to
+recommendation systems search engines are more prone to
+the cold start problem (Camacho and Alves-Souza, 2018).
+Datasets generated in the study aim to challenge the mQE-
+CGAN framework in this regard.
+3.2. Experimented Evaluation Metrics
+Both the generator and the discriminator of the mQE-
+CGAN framework are trained with cross-entropy loss during
+pre-training processes. For model comparisons, changes in
+the perplexity metric were analyzed for the generator. For
+the discriminator, the accuracy of the trained models was
+tracked.
+In addition to these metrics, we track the language diver-
+sity of the expanded queries. To this end, a new evaluation
+metric, the Word Coverage (WC), is defined. Word Cover-
+age metric checks the ratio of the number of unique words
+selected as expansion terms by the generator to the number
+of unique words in the document corpus. For a successful
+model, we expect this metric to be close to 1. Obtaining a
+Word Coverage metric lower than one suggests that the gen-
+erator model was not able to cover words in the tested set in
+the query expansion process. On the other hand, obtaining
+a Word Coverage metric higher than one indicates that the
+word selection process during query expansion utilized more
+unique words from the training corpus than it should have.
+The formula of the metric can be observed below. In the
+formula, 푠푄퐸 denotes words that are selected as expansion
+terms by the generator, 푠퐶 denotes the words in the tested
+corpus.
+푊 퐶 =
+∑ 푢푛푖푞(푠푄퐸)
+∑ 푢푛푖푞(푠퐶)
+In addition to analyzing the expansion term diversity in
+generated sequences, models are also evaluated by the se-
+mantic similarity between generated sequences and refer-
+ence sequences. To this end, we utilized average cosine simi-
+larity between the generated sequences obtained with expan-
+sion terms and their corresponding references in the docu-
+ment corpus. To assess the similarity, the average CBOW
+representations of both sets are compared. CBOW represen-
+tations are obtained by averaging the embedding represen-
+tations of the words that make generated and reference se-
+quences. The formula below summarizes the Semantic Sim-
+ilarity (SS) analysis between generated and reference docu-
+ments.
+푆푆 =
+푁
+∑
+푖
+̂푤푖 ⋅ 푤푖
+‖‖ ̂푤푖‖‖2 ‖‖푤푖‖‖2
+These metrics allow us to assess the success of gener-
+ated sequences without penalizing the n-gram matching per-
+formance of the generator. As the significance of n-gram
+matching and the word order are less crucial for matching
+user queries and products, the metric provides significant in-
+sights into the generation performance with different datasets.
+3.3. Generator Evaluation Metrics
+Resulting evaluation metrics after integrating the con-
+dition generation strategies to the generator model can be
+found from the table below.
+Dataset
+Condition
+CE Loss
+Perplexity
+WC
+SS (휇, 휖)
+C1
+Baseline Generator
+1.266
+3.650
+1.07
+(0.602, 0.173)
+Word Sim.
+1.328
+3.792
+1.02
+(0.696, 0.169)
+Document Sim.
+1.258
+3.536
+0.99
+(0.659, 0.178)
+TF-IDF
+1.288
+3.644
+1.15
+(0.606, 0.176)
+C2
+Baseline Generator
+0.267
+1.307
+0.46
+(0.898, 0.144)
+Word Sim.
+0.27
+1.311
+0.45
+(0.911, 0.14)
+Document Sim.
+0.272
+1.313
+0.46
+(0.902, 0.1412)
+TF-IDF
+0.267
+1.307
+0.46
+(0.894, 0.146)
+C3
+Baseline Generator
+0.34
+1.405
+1.07
+(0.662, 0.173)
+Word Sim.
+0.337
+1.401
+0.84
+(0.81, 0.169)
+Document Sim.
+0.344
+1.411
+0.98
+(0.809, 0.171)
+TF-IDF
+0.33
+1.391
+0.74
+(0.819, 0.162)
+C4
+Baseline Generator
+1.292
+3.650
+1.26
+(0.709, 0.217)
+Word Sim.
+1.285
+3.626
+1.02
+(0.736, 0.209)
+Document Sim.
+1.28
+3.605
+1.15
+(0.721, 0.203)
+TF-IDF
+1.218
+3.39
+1.20
+(0.686, 0.272)
+Table 1: Generator evaluation metrics of the selected dataset of companies. Company
+names are replaced with placeholders as C. To provide further context; Company 1
+(C1) is a Turkey-based cosmetics company, Company 2 (C2) and 4 (C4) are fashion
+retailers originated in Turkey, and Company 3 (C3) is a worldwide technology com-
+pany.
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 5 of 10
+
+Query and Document Length Statistics
+Avg.
+Query Length
+Avg. Document Length
+Company 1
+Company 2
+Average Length
+Company 3 -
+Company 4 -
+2
+10
+11
+12
+0
+3
+5
+8
+9
+13
+14
+15
+16
+4
+6
+7
+17
+18Modified Query Expansion Through Generative Adversarial Networks
+In Table 1 above, the Baseline Generator is trained by
+self-conditioning the input user queries. This way, the ef-
+fectiveness of the condition structures is evaluated against a
+condition mechanism that will not provide further positive
+cues for the generation process. WC denotes the Word Cov-
+erage metric discussed earlier, and SS denotes the Semantic
+Similarity metrics of trained generators. The mean and stan-
+dard deviation of cosine similarities between generated se-
+quences and reference documents can be observed in the ta-
+ble. Although generators with different models yield similar
+Cross Entropy Loss values, the Semantic Similarity obtained
+from generators with word similarity as conditions result in
+more successful generation processes. The Word Coverage
+metric is higher than it should have been for baseline gen-
+erator models, compared to models trained with additional
+conditions.
+These metrics were obtained after training each genera-
+tor model 16 epochs with the Cross-Entropy Loss function.
+As our initial observations demonstrated that generator pre-
+training tends to not improve after 16 epochs, Table 1 dis-
+plays the effectiveness of condition methods before adver-
+sarial learning.
+3.4. Adversarial Learning
+For adversarial learning, we pre-trained the generator and
+the discriminator models with half the number of epochs
+mentioned in the Implementation Details section. Thus, these
+models were not optimized for the underlying dataset. The
+pre-training of the generator is performed with the train and
+validation splits, where the discriminator is trained with the
+test splits. Below, the adversarial learning algorithm we use
+with these configurations can be observed.
+Algorithm 1 Adversarial Learning with Policy Gradients
+Require: Generator pre-training policy 퐺; rollout policy
+퐺푟; Discriminator pre-training policy 퐷; query-document
+dataset 푆 = {푋1∶푁, 푌1∶푁}
+Pre-train G using Cross-Entropy Loss on 푆
+Generate synthetic examples using G for training D as 푆휃
+Pre-train D using Cross-Entropy Loss on {푆, 푆휃}
+repeat
+for e in epochs do
+for b in batches do
+Generate 푁 rollout sequences with 퐺푟 for 푆푏
+Obtain average reward from 퐷 as 푅푏
+end for
+Update 퐺푟 with 푎푣푔(푅푏)
+end for
+until G loss of mQE-CGAN does not improve
+During adversarial learning, at each expansion term gen-
+eration step the generator model samples 푁 finished sequences
+from unfinished sequences with Monte Carlo rollouts. These
+sampled sequences are evaluated by the discriminator 퐷 to
+inform the generator model 퐺푟 about the current generation
+step. The average discriminator loss 푎푣푔(푅푏) obtained for
+this operation is used for rewarding the generator model and
+updating its parameters. These operations are repeated for
+each batch in the query-document dataset. By employing
+Policy Gradients (Sutton, McAllester, Singh and Mansour,
+1999), we convert the discriminator loss to the format that
+the generator can utilize.
+4. Results & Discussion
+Table 1 demonstrates that the generator models condi-
+tioned with the Word Similarity method result in the best
+semantic evaluation metrics. Word Similarity provides pre-
+cise embedding vectors of words that are the most similar in
+meaning to the words in the query. In this manner, models
+conditioned with it receive more insights about the context of
+the given query. The approach can also be considered similar
+to the pseudo-relevance feedback methods where the query
+is enhanced with the documents that initially matched with
+them. Compared to Word Similarity conditions, Document
+Similarity and TF-IDF Weighting conditions yield slightly
+worse semantic evaluation metrics. In some cases, condition
+methods do not increase the generator model performance
+compared to the baseline model. Our analysis displayed that
+Document Similarity conditions tend to guide the generation
+process in inaccurate ways, as the most similar documents to
+given input queries were possible to be differentiating from
+the reference documents. For many cases, TF-IDF Weight-
+ing seems to omit words in a given query to incline the gener-
+ator model to narrow the space for expansion term selection.
+When model performances are compared among datasets,
+it can be seen that the models were most successful in the Se-
+mantic Similarity metric for the dataset of Company 2 (C2
+in Table 1) and least successful for the dataset of Company
+1 (C1). This result was expected after we analyzed the prop-
+erties of different datasets in the study. The C1 dataset is the
+most challenging dataset having the largest vocabulary size
+among utilized datasets. On the other hand, the C2 dataset
+can be considered more trivial among others as having the
+smallest vocabulary size and documents are composed of
+more keywords. The evaluation metrics of conditioned mod-
+els tested with the C3 dataset should also be noted. As it is a
+dataset of a technology company, product name documents
+are often composed of words that do not have much meaning
+and context when separate. Here, prioritizing the words with
+higher TF-IDF scores for the generator model can increase
+the generator performance to select more precise expansion
+terms within the same query context.
+When the extended queries produced by the models are
+examined, it is seen that the expansion terms in the generated
+sequences have a high success in being in the same context
+as the reference document, but the prediction of the terms
+in the documents is not at the same level. It should also be
+noted that the datasets used for training the models are lim-
+ited. When the system we proposed in our study works inte-
+grated with a search engine, it will be better optimized with
+real-time data flow with higher traffic. We expect the suc-
+cess of word prediction in sequences to increase even more.
+Furthermore, due to the nature of the problem we aim to ad-
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 6 of 10
+
+Modified Query Expansion Through Generative Adversarial Networks
+dress, it is more important that the added words bring the
+semantic values of the extended queries closer to the docu-
+ments instead of directly matching the words added in the ex-
+panded queries with the documents tested. Therefore, eval-
+uation metrics such as BLEU (Papineni, Roukos, Ward and
+Zhu, 2002) and ROUGE (Lin, 2004) that prioritize correct
+word prediction was not prioritized in our study. It is consid-
+ered that previously discussed Word Coverage and Semantic
+Similarity metrics were better suited for evaluating the pro-
+posed framework.
+The approach taken for condition structures is similar
+to pseudo-relevance feedback approaches. The differenti-
+ating aspect here is that obtaining a document or a list of
+documents that are likely to match the user query requires
+multiple operations within the search engine. As this re-
+quirement would hinder the time performance of the query-
+document matching, we avoided utilizing pseudo-relevance
+feedback approaches directly in our studies. Applied condi-
+tion mechanisms are designed to be stored outside the search
+engine environment and memory. Hence, operations needed
+for reaching condition vectors are not reflected in the perfor-
+mance of the search engine. However, the time and space re-
+quirements of these conditions are the primary drawbacks of
+these approaches. As for all condition structures discussed
+construction of a lookup table is necessary, these lookup ta-
+bles should be generated or updated before model training
+and tuning. Thus, these structures form an additional step
+for complete model training.
+Applying the word and document similarity for condi-
+tions intends to enrich the initial user query that often con-
+sists of one to two words. However, we observed that with
+the word and document similarity condition mechanisms as-
+sistance for rare user queries may not be adequate to decrease
+the effects of the cold start problem. The reason for this is
+that the condition vectors obtained by word similarity and
+document similarity may affect the sentence production of
+the model in undesirable ways. The sequences that can be
+produced with the word and document information added
+with the conditions can be differentiated from the document
+information corresponding to the search made by the user.
+When a user query consisting of very few words is combined
+with conditions that are almost the same size and contain the
+same amount of semantic meaning, the indexes produced by
+the model can diverge from the sequences desired to be ob-
+tained.
+There are differences between the conditioned GAN ar-
+chitectures in the literature and the conditioned GAN archi-
+tectures presented in this study. It has been seen that the
+conditional GAN architectures in the literature utilize condi-
+tions for both the generator and the discriminator models. In
+these studies, it is a correct approach to feed both the genera-
+tor and the discriminator with this information, as the condi-
+tions are usually made up of class labels. In our study, since
+the condition structures consist of semantic information that
+increases the sentence generation performance of the model,
+the condition structures were used only in the generators.
+The discriminator model only performs binary classification
+between synthetic data and product information correspond-
+ing to user queries. Another differentiating issue is the train-
+ing phase of the generative model. In the mQE-CGAN archi-
+tecture, Monte Carlo simulations were not used in the pre-
+training phase of the generative models. Softmax operations
+were used in an iterative manner for the models to predict the
+next words in the sequences. Monte Carlo simulations were
+used only during adversarial learning.
+It is observed that similar semantic evaluation metric val-
+ues can be obtained with adversarial learning. For the dataset
+of Company 2, the adversarial learning phase improves the
+Semantic Similarity metric between generated and reference
+sequences from 0.911 to 0.914. Likewise, the Semantic Sim-
+ilarity metric increases from 0.736 to 0.808 for the dataset of
+Company 4. Hence, the average cosine similarity between
+generated sequences and reference documents increase by
+nearly 10% after the adversarial learning phase compared to
+the generator evaluation metrics with the baseline model.
+For other datasets, adversarial training until the generator
+loss function does not improve did not yield better semantic
+evaluation metrics. It suggests that there are further tuning
+and optimization steps for the adversarial learning process of
+the framework. Due to this, we take the 10% performance
+increase as the best improvement of the adversarial learning
+phase.
+The table below displays the sequences obtained after the
+adversarial learning phase of the mQE-CGAN framework.
+When examples in Table 2 are analyzed, it can be seen
+that the model tends to generate the company name as an
+expansion term. It is because company names are the most
+common words in the case of C2 and C4 datasets. Thus, the
+models have the bias of outputting the most occurred word
+in the dataset. For these datasets, the expansion terms seem
+to be meaningful in general. For user queries such as "mont"
+(coat) or "gömlek" (shirt), the model generates terms such as
+"regular fit" or "slim fit". On the other hand, when the initial
+user query does not have a matching document in the dataset,
+the generated expansion terms seem to be less successful.
+The most obvious example of this observation is the first ex-
+ample given for C2. The query "bandana" is expanded with
+"siyah parka" (black parka) where the query initially matches
+with the document "sarı bucket çanta" (yellow bucket bag).
+It seems that trained models are more successful for the
+expansion generation task where the relationship between
+words is more precise. If the candidate words to expand the
+given query are more limited, models seem to capture the
+semantic relationship between different words in a smaller
+space. Generation results of the C3 dataset exemplify this
+phenomenon. In the first example, the query "şarj" (charge)
+is expanded with words such as "c-type", "hızlı" (fast), and
+"seyehat" (travel). The second example adds the memory
+information that is very common to be included in product
+names to the search query of a specific device. The third
+example adds "kablolu" (wired) and "mikrofonlu" (with mi-
+crophone) to the user query of "kulaklık" (headphones).
+The presence of this phenomenon can also be seen in
+the results of the C1 dataset. The query "saçlar" (hair) is
+Cakir A., Gurkan M.: Preprint submitted to Elsevier
+Page 7 of 10
+
+Modified Query Expansion Through Generative Adversarial Networks
+Dataset
+Query
+Generated Sequence
+Reference Document
+C1
+saçlar
+saçlar nemlendirici krem 50
+water nemlendirici şampuan
+köpük
+karma köpük 150
+vitaminli 150 ml yüz köpüğü
+yıpranma krem
+yıpranmış nemlendirici krem 50
+brand name yıpranma karşıtı nemlendirici krem 50 ml
+C2
+bandana
+siyah parka
+sarı bucket çanta
+krem ceket
+kapüşonlu siyah ceket
+kapüşonlu beyaz ceket
+{company name} black jake
+jake {company name} black jean pantolon
+jake {company name} black gölgeli jean pantolon
+C3
+şarj
+{company name} {model name} c-type hızlı seyahat
+{company name} {model name} siyah
+{company name} {model name}
+{company name} {model name} 128 gb
+{company name} {model name} 128 gb
+kulaklık
+{company name} {model name} kablolu mikrofonlu
+{company name} {model name} kulaklık
+C4
+mont
+{company name} klasik regular fit
+standart fit mont
+kareli gömlek
+slim fit gömlek
+slim fit kareli gömlek
+polo yaka tisort
+{company name} polo yaka cepsiz
+regular fit polo yaka tisort
+Table 2: Randomly selected generated samples and their corresponding query and reference document pairs. Generated sequences are obtained after the adversarial learning The
+generator of the framework was selected as Word Similarity model. For each different company dataset, three examples are displayed in the table. Whenever the company name
+is included in the generated sequence, they are marked as {company name}. {brand name} is added to not reveal specific brand names in the C3 dataset. {model name} is added
+to hide specific product models in the C3 to not reveal the further information about the company.
+paired with "nemlendirici" (moisturizer) and "krem" (con-
+ditioner). In the third example, the query "yıpranma krem"
+is expanded with "nemlendirici" (moisturizer) and the cor-
+rect volume of the product. As the C1 dataset is mostly
+composed of cosmetics products, the dataset usually con-
+sists of documents that have volume information. Results
+display that the trained model is not successful at generat-
+ing sequences with correct volume information consisting of
+the volume value and its unit. We observed that our model
+tended to include a numerical value to generated sequences
+often but did not include its unit such as "ml" or "cc". It
+suggests that models can be further optimized to capture the
+relationships between individual word pairs in a better way.
+5. Conclusion
+Our work focused on bringing concepts of generative
+adversarial networks, query expansion, and condition struc-
+tures originated from query-document relationships together.
+Results from the mQE-CGAN framework demonstrate that
+given user queries with limited information can be enriched
+with query expansion to obtain sequences that are semanti-
+cally more similar to the documents in the datasets. As the
+trained models yield successful evaluation metrics for cap-
+turing the context of given query-document pairs, utilization
+of the framework can be beneficial for optimizing search en-
+gines in the e-commerce domain.
+Various aspects of the proposed GAN framework can
+be improved. Firstly, we believe that the sequence gener-
+ation process could benefit from utilizing context-specific
+word embeddings. To this end, word embeddings obtained
+from language models fine-tuned for datasets will be tested
+in the future. Secondly, alternative condition mechanisms
+can be introduced during the training process. The proposed
+framework allows the replacement of condition mechanisms
+to adapt specific cases by capturing different semantic re-
+lationships in query-document data. One of the condition
+structures to be applied is the combination of the conditions
+experimented with in this study. Lastly, we aim to experi-
+ment with the integration of the proposed GAN framework
+with the existing search engine. This way, the advantages
+and shortcomings of a search engine with an integrated GAN
+model for query expansion can be observed in high-traffic
+environments. In future works, we aim to assess the practi-
+cal evaluation metrics of the query expansion approach for
+its performance against the cold start problem.
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf,len=891
+page_content='Modified Query Expansion Through Generative Adversarial Networks  for Information Extraction in E-Commerce  Altan Cakir∗,1, Mert Gurkan2  A R T I C L E I N F O  Keywords:  Generative Adversarial Networks  Query Expansion  Conditional Neural Networks  Information Retrieval  E-Commerce  A B S T R A C T  This work addresses an alternative approach for query expansion (QE) using a generative adversarial  network (GAN) to enhance the effectiveness of information search in e-commerce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We propose a  modified QE conditional GAN (mQE-CGAN) framework, which resolves keywords by expanding the  query with a synthetically generated query that proposes semantic information from text input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We  train a sequence-to-sequence transformer model as the generator to produce keywords and use a re-  current neural network model as the discriminator to classify an adversarial output with the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  With the modified CGAN framework, various forms of semantic insights gathered from the query-  document corpus are introduced to the generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We leverage these insights as conditions  for the generator model and discuss their effectiveness for the query expansion task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Our experi-  ments demonstrate that the utilization of condition structures within the mQE-CGAN framework can  increase the semantic similarity between generated sequences and reference documents up to nearly  10% compared to baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Introduction  In search based business models, such as e-commerce,  given a search query, the system needs to match it to some  relevant keywords/categories/frequencies by business part-  ners and then pull out the related category/product for query  searching and ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The query keyword matching can  be done by some simple matching rules like exact match,  similarity match, and phrase match, which are all based on  matching the similar tokens shared by query and keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  On the other hand, using AI-based recent techniques for smart  match is an important yet difficult match type that can asso-  ciate a query to some relevant keywords even they do not  generate many similar tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  In general, it is well defined that search queries math-  ematically follow the power law distribution (Spink, Wol-  fram, Jansen and Saracevic, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The curve formed by the  most frequent queries constitutes the main center, while the  rare queries with low frequency form the tail of the curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Although they are few in such cases, low-frequency queries  are excluded from the query volume traffic as a whole and  therefore cause problems in systems as a data deficiency that  needs to be generated synthetically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Because of the incoming query distribution to the search  engine, the performance of matching rare queries with docu-  ments existing in the database is a challenging task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It is of-  ten the case that an additional process is required to assist the  match between rare queries and documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To address the  problem, various methodologies such as relevance feedback  methods, similarity-based methods for query-document match-  ing, machine translation models for query transformation,  ∗Corresponding author  ORCID(s): 0000-0002-8627-7689 (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Cakir)  1Physics Engineering, Faculty of Science and Letters, Istanbul Tech-  nical University, Istanbul, Turkey and Istanbul Technical University Artifi-  cial Intelligence, Data Science Research and Application Center, Istanbul  Turkey  2Insider (useinsider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='com), Istanbul, Turkey  and query expansion methods are discussed in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Query expansion is one of the significant problems stud-  ied in the Information Retrieval (IR) domain with various  applications such as question answering, information filter-  ing, or multimedia document matching tasks (Carpineto and  Romano, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The problem can be described as the at-  tempt of the increasing performance of matching input se-  quences and document the corpus of an IR system by refor-  mulating given input sequences (Azad and Deepak, 2019b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Query expansion methodologies are often applied where the  input queries are words or sequences originating from real  human users, while documents to match or rank them con-  sist of predefined items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Natural language queries that match  to same documents can differ verbally and semantically (Fur-  nas, Landauer, Gomez and Dumais, 1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Because of this  ambiguity, the complexity of query-document matching is  often increased by the innate characteristics of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Earlier studies in the query expansion domain seem to  focus on rule-based applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' These applications evalu-  ate candidate expansion terms by the frequency of appear-  ing together with the words in the original query (Carpineto,  de Mori, Romano and Bigi, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In addition to word fre-  quency based studies, systems built upon pseudo-relevance  feedback structures are also widely utilized in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  (Metzler and Croft, 2007) uses the Markov random fields for  modelling dependencies to assist the query expansion pro-  cess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' (Symonds, Bruza, Sitbon and Turner, 2011) provides  a different approach to the query expansion methods with  pseudo-relevance feedback, where they build tensor repre-  sentations of queries that enables obtaining relevance feed-  back based on word meanings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Adoption of the deep learning applications in the nat-  ural language domains generated word embeddings as ef-  ficient ways to represent semantic information of text data  (Mikolov, Chen, Corrado and Dean, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The utilization  of word embeddings made it possible to evaluate the seman-  tic relationship between words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This capability is employed  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  Page 1 of 10  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='00036v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='LG]  30 Dec 2022  Modified Query Expansion Through Generative Adversarial Networks  for query expansion problems by using various ways to eval-  uate the similarity of words that make up the queries and  candidate terms to expand these queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The popularity of the word embedding methods for vari-  ous problems for IR and NLP, led research efforts to increase  the accuracy of word representations in specific cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To  this end, alternative ways to produce different embeddings  of tokens for query expansions are proposed (Sordoni, Ben-  gio and Nie, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Additionally, research conducted uti-  lization of task-specific trained word embeddings for query  expansion (Diaz, Mitra and Craswell, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This way, word  representations are more likely to capture the context and  semantic properties of the trained corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Following these  works, (Qi, Gong, Yan, Jiao, Shao, Zhang, Li, Duan and  Zhou, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Lian, Chen, Jia, You, Tian, Hu, Zhang, Yan,  Tong, Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', 2021) proposed a query expansion approach  for search engine optimization by utilizing a prefix tree to  serve as look ahead strategy for generating expansion terms  for given queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Recent applications of GAN methods provide alternative  methods to approach the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' GAN models can directly  generate expansion terms or expanded user queries by train-  ing over user search queries and their matching documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  In GANs the discriminative network can learn to distinguish  between the synthetic data created by the generator and the  real data examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This way, the generation process is chal-  lenged by the network itself to create high-quality samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  This approach of training has proven to be very successful  in the computer vision domain and increasing its popular-  ity in natural language processing problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Additionally,  the research focusing on establishing back-propagation be-  tween discriminator and generator models with discrete to-  kens in text data (Yu, Zhang, Wang and Yu, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Kusner  and Hernández-Lobato, 2016) provided highly performing  generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  With initial GAN models, the model is trained with noise  for the generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' With conditional structures, the  query generation of the GAN models can be assisted with  the chosen condition mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Similar to earlier works  in the query expansion domain, enhancing user queries with  existing relevant information is adopted by GAN-based ar-  chitectures too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' GAN models can utilize part of text data,  class labels present during the training, or extracted proper-  ties of the query and documents as conditions to increase the  likelihood of matching queries with desired documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The  study of (Lee, Gao and Zhang, 2018) proposes a conditional  GAN structure with a query expansion approach for enrich-  ing rare queries in search engines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The study of (Huang,  Wang, Liu and Ding, 2021) employs a well-known method  of pseudo-relevance feedback in the query expansion do-  main as the condition for their expansion term generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Studies discussed intend to create a conditional GAN-  based framework to leverage query expansion to match key-  words for an effective search selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In general, a sequence-  to-sequence model, in which the input sequence is a random  word vector followed by a query vector, is commonly used  for the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The output sequence composes of the vec-  tors of the generated keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As the discriminator, the  parallelized Recurrent Neural Network (RNN) model is used  as a binary classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' However, most of these studies are not  conducted from the perspective of improving search engines  by enhancing query-document matching performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Our  study aims to combine GAN architecture and existing query-  enhancing methods by utilizing them as condition structures  for the generator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Proposed conditional GAN models  aim to alleviate the performance drop of search engines, by  increasing the query-document matching performance with  condition-assisted query expansion mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  To alleviate the effects of the problem described, we in-  troduce the mQE-CGAN (Modified Query Expansion Con-  ditional Generative Adversarial Network) framework to study  the query expansion to enhance the performance of a search  engine by increasing the query-document matching perfor-  mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The generator of the model is a sequence-to-sequence  encoder-decoder model that takes user search queries and the  vectors from the applied condition mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The output  of the generator, expanded queries, is evaluated by the dis-  criminator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We use an LSTM model for the binary  classification task between the synthetic and real samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  During adversarial learning, the evaluation of the discrimi-  nator guides the performance of the generator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' With  the mQE-CGAN framework, our contributions can be listed  below;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Model: We propose a novel conditional generative  adversarial network model that takes the semantic re-  lationship between the query and document pairs as  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The generator of the model is a sequence-  to-sequence encoder decoder model, while the discrim-  inator is an LSTM-based binary classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We provide  details of the model framework and the evaluation of  the training process with a conditional approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Conditional Query Expansion: We provide alterna-  tive methods for condition structures with generative  adversarial networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Condition structures discussed  in this paper aim to capture semantic relationships be-  tween query-document pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Datasets: We test our generative model with the user  query and document pairs from the customers of In-  sider1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' By testing the proposed models with differ-  ent customer datasets, we evaluate our models against  data with different characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The primary aspect that mQE-CGAN framework differs  from the existing conditional GAN frameworks is that the  models of the framework are conditioned on the semantic  and statistical relationships between the query-document data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Employed conditions are not limited to the individual re-  lationships between the query and the matching document  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' They are rather constructed with the consideration of  the entire corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Hence, the generation process of the GAN  framework utilizes conditions produced after the semantic  analysis of the entire corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1https://useinsider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='com  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  Page 2 of 10  Modified Query Expansion Through Generative Adversarial Networks  Figure 1: Diagram of the mQE-CGAN framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' System Architecture  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' mQE-CGAN Framework  The proposed framework for adversarial training with  the mQE-CGAN framework can be observed in the Figure  2 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The generator model of the framework takes input  queries and the selected condition vectors assigned for input  queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' With a sequence-to-sequence structure, it generates  expansion terms from the given queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The discriminator  model of the adversarial schema performs binary classifica-  tion on the expanded synthetic queries and documents that  match to original queries of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Condition generation mechanisms discussed in the study  aim to take advantage of the data used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As the query-document  pairs in datasets denote user searches and matching docu-  ments, condition approaches focus on the semantic and simi-  larity metrics of given queries and their matching documents  by the search engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Generator Model  The generator model of the architecture is an encoder-  decoder sequence-to-sequence model that takes FastText (Bo-  janowski, Grave, Joulin and Mikolov, 2016) word embed-  ding representations of the user search queries and their cor-  responding condition vectors as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To be able to achieve  back-propagation with the discrete input sequences, similar  to the existing studies (Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', 2018)  Monte Carlo rollouts are used in the decoder of the gener-  ator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' With this method, rewards produced by the discrimi-  nator can be transferred to the generator for each generation  step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Condition Structures  GAN models can be extended into conditional models  if the adversarial learning process is performed with addi-  tional information (Mirza and Osindero, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' With the  introduction of conditions, the models can be inclined to  generate samples with the desired qualities (Sohn, Lee and  Yan, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Conditions are introduced to guide the generator  model during the sequence generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Condition  structures utilized in this study are generated before training  the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Condition vectors of queries are concatenated  with the word embedding representation of the user queries  during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To retrieve them, Ball Tree-based look-up  tables are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  To this end, four different condition structures are ap-  plied with the following expected priorities;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' (1) It should  enrich the user query with other similar queries, and (2) it  should provide information that will assist in distinction be-  tween similar documents that can be mapped with the given  query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To address these requirements, various condition vec-  tor generation strategies displayed are implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Uti-  lized methods are considered to be addressing the shortcom-  ings of the encoder-decoder generator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' These condi-  tion generation strategies are described in the list below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Query Weighting with TF-IDF Scores: Condition vec-  tors are generated with CBOW representations of the  TF-IDF weighed input word embeddings  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Search Tree Based Document Similarity: Condition  vectors are generated with CBOW representations of  the most similar documents to the given input query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Search Tree Based Word Similarity: Condition vec-  tors are generated with CBOW representations of the  most similar words in the corpus of documents to the  given input query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Although these methods are commonly utilized in query  expansion approaches (Azad and Deepak, 2019a), their in-  tegration as condition mechanisms is not adequately experi-  mented with generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Discriminator Model  The discriminator model of the mQE-CGAN framework  is built with the same pre-trained Fasttext word embeddings  and LSTM layers processing embedded representations of  generated and real document sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Unlike the gener-  ator model of the framework, the discriminator model does  not utilize the condition structures for its pre-training and ad-  versarial learning processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The model is designed for the  binary classification task between real documents in corpus  and sequences formed by the generator as the synthetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  Page 3 of 10  P1: Classification as  p2  Real Data  p2: Classification as  Generated Sequences  Generated Data  Linear Layer  Query 1  Condition 1  Query 2  Condition 2  Expanded  User Query  Matched Document  queries  Condition  Generation  W1  W1  Query n  Condition n  Generator model input  Search Engine  Discriminator Model InputModified Query Expansion Through Generative Adversarial Networks  Figure 2: Diagram of the Monte Carlo rollouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' At each step, a batch of sequences are generated by the decoder of the  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' These batches are evaluated by the discriminator to guide the generation process of the generator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Figure 3: LSTM based discriminator model of the mQE-  CGAN framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Implementation Details  We conducted the implementation with the PyTorch li-  brary (Paszke, Gross, Massa, Lerer, Bradbury, Chanan, Killeen,  Lin, Gimelshein, Antiga, Desmaison, Kopf, Yang, DeVito,  Raison, Tejani, Chilamkurthy, Steiner, Fang, Bai and Chin-  tala, 2019) in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The encoder-decoder generator model  is implemented by using the TransformerEncoder and Trans-  formerDecoder classes in PyTorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The generator model  uses 2 layers for both the encoder and the decoder parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Initially, the input user queries are transformed to FastText  word embedding representations with each word being rep-  resented with a tensor of size 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Originally, FastText word  embeddings are available for Turkish with a size of 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To  reduce the amount of GPU RAM required, we transformed  these embedding representations to vectors with size 100  with the reduce_model implementation of the FastText li-  brary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It is followed by applying positional embedding to  assign the order context to tokens in sequences with the help  of the attention heads (Vaswani, Shazeer, Parmar, Uszko-  reit, Jones, Gomez, Kaiser and Polosukhin, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For the  forward pass, the given query and its paired condition vector  are concatenated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The encoder and decoder of the generator  take an input size of 200 from the concatenated tensors, and  they have a hidden size of 512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Pre-training of the generator is performed by training the  generator model with the learning rate 10−3 and the Adam  (Kingma and Ba, 2014) optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' During pre-training, the  generator uses a softmax layer of size 푁, where 푁 is the  total vocabulary size of the query and document corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Se-  quence generation is performed iteratively by predicting an  expansion term at each step until the generator predicts the  next token as < 퐸푂푆 > (end of the sequence) token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For  many cases, it was observed that after training the genera-  tor 16 epochs the Cross-Entropy Loss of the model does not  improve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The discriminator model of the framework is intention-  ally kept simpler than the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For the discriminator,  we used a 1 layer LSTM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To decide on the hyper-  parameters of the discriminator, a grid search is applied to  hyper-parameters by training discriminator models with com-  bined datasets of synthetic data from the generator and the  samples from the document corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The discriminator model  where the loss is optimized was obtained with the number of  epochs as 24, the learning rate as 10−2, dropout as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1, and  the batch size as 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Experiments  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Datasets  The datasets utilized in the study are generated by the  analysis of user behavior in a search engine product of In-  sider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' More specifically, these datasets consist of user search  queries and the first-ranked resulting products in the plat-  forms of Insider customers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It should be noted that the datasets  utilized in this study do not include any specific user infor-  mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' During the data collection step, any information that  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Page 4 of 10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Backpropagation of the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='average reward collected  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='from the discriminator  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Rewards from the  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Discriminator Model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Generated  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='sequences  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='current  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='with Monte  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Discriminator  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='t2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Batch of  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='word  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Carlo  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='expanded  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Rollouts  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='sequences  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='t1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='t2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Encoded  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Queryp1: Classification as Real Data  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='p1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='p2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='P2: Classification as Generated Data  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Linear Layer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h24  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='LSTM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Layers  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='h15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Word  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='W1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='W2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='W3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='W4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='W5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Synthetic data  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Real data source  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='source  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='The  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Generator  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='User queries and  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='matching productsModified Query Expansion Through Generative Adversarial Networks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='can be exploited to identify the user information is discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  As the general user behavior in search engines is to en-  ter fewer words to match the desired documents (Pal, Mitra  and Bhattacharya, 2015), queries in search engines tend to  compose fewer words compared to the documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This gen-  eral observation is also present in the datasets utilized in our  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The average number of words in queries and docu-  ments in datasets used in the study can be observed in Figure  4 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Figure 4: Statistics of the query and the document datasets  utilized in the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For each dataset, bars at the top display  the maximum, average, and minimum number of words in  queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Similarly, bottom bars display statistics of the doc-  ument corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For all datasets, the average number of words  in user searches are almost four times less than their match-  ing product equivalents, suggesting further ways to employ  semantic information to be extracted from document data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The difference between the number of words in queries  and documents introduces various challenges for search en-  gines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In the case of rare query inputs of users, similar to  recommendation systems search engines are more prone to  the cold start problem (Camacho and Alves-Souza, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Datasets generated in the study aim to challenge the mQE-  CGAN framework in this regard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Experimented Evaluation Metrics  Both the generator and the discriminator of the mQE-  CGAN framework are trained with cross-entropy loss during  pre-training processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For model comparisons, changes in  the perplexity metric were analyzed for the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For  the discriminator, the accuracy of the trained models was  tracked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  In addition to these metrics, we track the language diver-  sity of the expanded queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To this end, a new evaluation  metric, the Word Coverage (WC), is defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Word Cover-  age metric checks the ratio of the number of unique words  selected as expansion terms by the generator to the number  of unique words in the document corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For a successful  model, we expect this metric to be close to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Obtaining a  Word Coverage metric lower than one suggests that the gen-  erator model was not able to cover words in the tested set in  the query expansion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' On the other hand, obtaining  a Word Coverage metric higher than one indicates that the  word selection process during query expansion utilized more  unique words from the training corpus than it should have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The formula of the metric can be observed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In the  formula, 푠푄퐸 denotes words that are selected as expansion  terms by the generator, 푠퐶 denotes the words in the tested  corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  푊 퐶 =  ∑ 푢푛푖푞(푠푄퐸)  ∑ 푢푛푖푞(푠퐶)  In addition to analyzing the expansion term diversity in  generated sequences, models are also evaluated by the se-  mantic similarity between generated sequences and refer-  ence sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To this end, we utilized average cosine simi-  larity between the generated sequences obtained with expan-  sion terms and their corresponding references in the docu-  ment corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To assess the similarity, the average CBOW  representations of both sets are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' CBOW represen-  tations are obtained by averaging the embedding represen-  tations of the words that make generated and reference se-  quences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The formula below summarizes the Semantic Sim-  ilarity (SS) analysis between generated and reference docu-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  푆푆 =  푁  ∑  푖  ̂푤푖 ⋅ 푤푖  ‖‖ ̂푤푖‖‖2 ‖‖푤푖‖‖2  These metrics allow us to assess the success of gener-  ated sequences without penalizing the n-gram matching per-  formance of the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As the significance of n-gram  matching and the word order are less crucial for matching  user queries and products, the metric provides significant in-  sights into the generation performance with different datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Generator Evaluation Metrics  Resulting evaluation metrics after integrating the con-  dition generation strategies to the generator model can be  found from the table below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Dataset  Condition  CE Loss  Perplexity  WC  SS (휇, 휖)  C1  Baseline Generator  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='266  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='650  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='07  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='602, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='173)  Word Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='328  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='792  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='02  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='696, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='169)  Document Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='99  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='659, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='178)  TF-IDF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='288  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='644  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='15  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='606, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='176)  C2  Baseline Generator  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='267  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='307  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='46  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='898, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='144)  Word Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='27  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='311  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='911, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='14)  Document Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='902, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='1412)  TF-IDF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='267  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='307  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='146)  C3  Baseline Generator  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='34  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='405  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='173)  Word Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='169)  Document Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='171)  TF-IDF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='33  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='391  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='162)  C4  Baseline Generator  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='292  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='217)  Word Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='209)  Document Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='203)  TF-IDF  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='218  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='39  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='20  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='272)  Table 1: Generator evaluation metrics of the selected dataset of companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Company  names are replaced with placeholders as C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To provide further context;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Company 1  (C1) is a Turkey-based cosmetics company, Company 2 (C2) and 4 (C4) are fashion  retailers originated in Turkey, and Company 3 (C3) is a worldwide technology com-  pany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  Page 5 of 10  Query and Document Length Statistics  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Query Length  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Document Length  Company 1  Company 2  Average Length  Company 3 -  Company 4 -  2  10  11  12  0  3  5  8  9  13  14  15  16  4  6  7  17  18Modified Query Expansion Through Generative Adversarial Networks  In Table 1 above, the Baseline Generator is trained by  self-conditioning the input user queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This way, the ef-  fectiveness of the condition structures is evaluated against a  condition mechanism that will not provide further positive  cues for the generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' WC denotes the Word Cov-  erage metric discussed earlier, and SS denotes the Semantic  Similarity metrics of trained generators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The mean and stan-  dard deviation of cosine similarities between generated se-  quences and reference documents can be observed in the ta-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Although generators with different models yield similar  Cross Entropy Loss values, the Semantic Similarity obtained  from generators with word similarity as conditions result in  more successful generation processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The Word Coverage  metric is higher than it should have been for baseline gen-  erator models, compared to models trained with additional  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  These metrics were obtained after training each genera-  tor model 16 epochs with the Cross-Entropy Loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  As our initial observations demonstrated that generator pre-  training tends to not improve after 16 epochs, Table 1 dis-  plays the effectiveness of condition methods before adver-  sarial learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Adversarial Learning  For adversarial learning, we pre-trained the generator and  the discriminator models with half the number of epochs  mentioned in the Implementation Details section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Thus, these  models were not optimized for the underlying dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The  pre-training of the generator is performed with the train and  validation splits, where the discriminator is trained with the  test splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Below, the adversarial learning algorithm we use  with these configurations can be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Algorithm 1 Adversarial Learning with Policy Gradients  Require: Generator pre-training policy 퐺;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' rollout policy  퐺푟;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Discriminator pre-training policy 퐷;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' query-document  dataset 푆 = {푋1∶푁,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' 푌1∶푁}  Pre-train G using Cross-Entropy Loss on 푆  Generate synthetic examples using G for training D as 푆휃  Pre-train D using Cross-Entropy Loss on {푆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' 푆휃}  repeat  for e in epochs do  for b in batches do  Generate 푁 rollout sequences with 퐺푟 for 푆푏  Obtain average reward from 퐷 as 푅푏  end for  Update 퐺푟 with 푎푣푔(푅푏)  end for  until G loss of mQE-CGAN does not improve  During adversarial learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' at each expansion term gen-  eration step the generator model samples 푁 finished sequences  from unfinished sequences with Monte Carlo rollouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' These  sampled sequences are evaluated by the discriminator 퐷 to  inform the generator model 퐺푟 about the current generation  step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The average discriminator loss 푎푣푔(푅푏) obtained for  this operation is used for rewarding the generator model and  updating its parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' These operations are repeated for  each batch in the query-document dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' By employing  Policy Gradients (Sutton, McAllester, Singh and Mansour,  1999), we convert the discriminator loss to the format that  the generator can utilize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Results & Discussion  Table 1 demonstrates that the generator models condi-  tioned with the Word Similarity method result in the best  semantic evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Word Similarity provides pre-  cise embedding vectors of words that are the most similar in  meaning to the words in the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In this manner, models  conditioned with it receive more insights about the context of  the given query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The approach can also be considered similar  to the pseudo-relevance feedback methods where the query  is enhanced with the documents that initially matched with  them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Compared to Word Similarity conditions, Document  Similarity and TF-IDF Weighting conditions yield slightly  worse semantic evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In some cases, condition  methods do not increase the generator model performance  compared to the baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Our analysis displayed that  Document Similarity conditions tend to guide the generation  process in inaccurate ways, as the most similar documents to  given input queries were possible to be differentiating from  the reference documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For many cases, TF-IDF Weight-  ing seems to omit words in a given query to incline the gener-  ator model to narrow the space for expansion term selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  When model performances are compared among datasets,  it can be seen that the models were most successful in the Se-  mantic Similarity metric for the dataset of Company 2 (C2  in Table 1) and least successful for the dataset of Company  1 (C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This result was expected after we analyzed the prop-  erties of different datasets in the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The C1 dataset is the  most challenging dataset having the largest vocabulary size  among utilized datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' On the other hand, the C2 dataset  can be considered more trivial among others as having the  smallest vocabulary size and documents are composed of  more keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The evaluation metrics of conditioned mod-  els tested with the C3 dataset should also be noted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As it is a  dataset of a technology company, product name documents  are often composed of words that do not have much meaning  and context when separate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Here, prioritizing the words with  higher TF-IDF scores for the generator model can increase  the generator performance to select more precise expansion  terms within the same query context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  When the extended queries produced by the models are  examined, it is seen that the expansion terms in the generated  sequences have a high success in being in the same context  as the reference document, but the prediction of the terms  in the documents is not at the same level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It should also be  noted that the datasets used for training the models are lim-  ited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' When the system we proposed in our study works inte-  grated with a search engine, it will be better optimized with  real-time data flow with higher traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We expect the suc-  cess of word prediction in sequences to increase even more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Furthermore, due to the nature of the problem we aim to ad-  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  Page 6 of 10  Modified Query Expansion Through Generative Adversarial Networks  dress, it is more important that the added words bring the  semantic values of the extended queries closer to the docu-  ments instead of directly matching the words added in the ex-  panded queries with the documents tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Therefore, eval-  uation metrics such as BLEU (Papineni, Roukos, Ward and  Zhu, 2002) and ROUGE (Lin, 2004) that prioritize correct  word prediction was not prioritized in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It is consid-  ered that previously discussed Word Coverage and Semantic  Similarity metrics were better suited for evaluating the pro-  posed framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The approach taken for condition structures is similar  to pseudo-relevance feedback approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The differenti-  ating aspect here is that obtaining a document or a list of  documents that are likely to match the user query requires  multiple operations within the search engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As this re-  quirement would hinder the time performance of the query-  document matching, we avoided utilizing pseudo-relevance  feedback approaches directly in our studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Applied condi-  tion mechanisms are designed to be stored outside the search  engine environment and memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Hence, operations needed  for reaching condition vectors are not reflected in the perfor-  mance of the search engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' However, the time and space re-  quirements of these conditions are the primary drawbacks of  these approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As for all condition structures discussed  construction of a lookup table is necessary, these lookup ta-  bles should be generated or updated before model training  and tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Thus, these structures form an additional step  for complete model training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Applying the word and document similarity for condi-  tions intends to enrich the initial user query that often con-  sists of one to two words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' However, we observed that with  the word and document similarity condition mechanisms as-  sistance for rare user queries may not be adequate to decrease  the effects of the cold start problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The reason for this is  that the condition vectors obtained by word similarity and  document similarity may affect the sentence production of  the model in undesirable ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The sequences that can be  produced with the word and document information added  with the conditions can be differentiated from the document  information corresponding to the search made by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  When a user query consisting of very few words is combined  with conditions that are almost the same size and contain the  same amount of semantic meaning, the indexes produced by  the model can diverge from the sequences desired to be ob-  tained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  There are differences between the conditioned GAN ar-  chitectures in the literature and the conditioned GAN archi-  tectures presented in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It has been seen that the  conditional GAN architectures in the literature utilize condi-  tions for both the generator and the discriminator models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In  these studies, it is a correct approach to feed both the genera-  tor and the discriminator with this information, as the condi-  tions are usually made up of class labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In our study, since  the condition structures consist of semantic information that  increases the sentence generation performance of the model,  the condition structures were used only in the generators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The discriminator model only performs binary classification  between synthetic data and product information correspond-  ing to user queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Another differentiating issue is the train-  ing phase of the generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In the mQE-CGAN archi-  tecture, Monte Carlo simulations were not used in the pre-  training phase of the generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Softmax operations  were used in an iterative manner for the models to predict the  next words in the sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Monte Carlo simulations were  used only during adversarial learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  It is observed that similar semantic evaluation metric val-  ues can be obtained with adversarial learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For the dataset  of Company 2, the adversarial learning phase improves the  Semantic Similarity metric between generated and reference  sequences from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='911 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='914.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Likewise, the Semantic Sim-  ilarity metric increases from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='736 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='808 for the dataset of  Company 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Hence, the average cosine similarity between  generated sequences and reference documents increase by  nearly 10% after the adversarial learning phase compared to  the generator evaluation metrics with the baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  For other datasets, adversarial training until the generator  loss function does not improve did not yield better semantic  evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It suggests that there are further tuning  and optimization steps for the adversarial learning process of  the framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Due to this, we take the 10% performance  increase as the best improvement of the adversarial learning  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The table below displays the sequences obtained after the  adversarial learning phase of the mQE-CGAN framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  When examples in Table 2 are analyzed, it can be seen  that the model tends to generate the company name as an  expansion term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It is because company names are the most  common words in the case of C2 and C4 datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Thus, the  models have the bias of outputting the most occurred word  in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For these datasets, the expansion terms seem  to be meaningful in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For user queries such as "mont"  (coat) or "gömlek" (shirt), the model generates terms such as  "regular fit" or "slim fit".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' On the other hand, when the initial  user query does not have a matching document in the dataset,  the generated expansion terms seem to be less successful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The most obvious example of this observation is the first ex-  ample given for C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The query "bandana" is expanded with  "siyah parka" (black parka) where the query initially matches  with the document "sarı bucket çanta" (yellow bucket bag).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  It seems that trained models are more successful for the  expansion generation task where the relationship between  words is more precise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' If the candidate words to expand the  given query are more limited, models seem to capture the  semantic relationship between different words in a smaller  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Generation results of the C3 dataset exemplify this  phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In the first example, the query "şarj" (charge)  is expanded with words such as "c-type", "hızlı" (fast), and  "seyehat" (travel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The second example adds the memory  information that is very common to be included in product  names to the search query of a specific device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The third  example adds "kablolu" (wired) and "mikrofonlu" (with mi-  crophone) to the user query of "kulaklık" (headphones).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  The presence of this phenomenon can also be seen in  the results of the C1 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The query "saçlar" (hair) is  Cakir A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=', Gurkan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=': Preprint submitted to Elsevier  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Page 7 of 10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Modified Query Expansion Through Generative Adversarial Networks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Dataset  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Query  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Generated Sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Reference Document  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='C1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='saçlar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='saçlar nemlendirici krem 50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='water nemlendirici şampuan  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='köpük  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='karma köpük 150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='vitaminli 150 ml yüz köpüğü  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='yıpranma krem  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='yıpranmış nemlendirici krem 50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='brand name yıpranma karşıtı nemlendirici krem 50 ml  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='C2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='bandana  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='siyah parka  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='sarı bucket çanta  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='krem ceket  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='kapüşonlu siyah ceket  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='kapüşonlu beyaz ceket  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} black jake  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='jake {company name} black jean pantolon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='jake {company name} black gölgeli jean pantolon  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='C3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='şarj  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name} c-type hızlı seyahat  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name} siyah  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name}  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name} 128 gb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name} 128 gb  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='kulaklık  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name} kablolu mikrofonlu  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} {model name} kulaklık  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='C4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='mont  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} klasik regular fit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='standart fit mont  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='kareli gömlek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='slim fit gömlek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='slim fit kareli gömlek  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='polo yaka tisort  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='{company name} polo yaka cepsiz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='regular fit polo yaka tisort  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='Table 2: Randomly selected generated samples and their corresponding query and reference document pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Generated sequences are obtained after the adversarial learning The  generator of the framework was selected as Word Similarity model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' For each different company dataset, three examples are displayed in the table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Whenever the company name  is included in the generated sequence, they are marked as {company name}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' {brand name} is added to not reveal specific brand names in the C3 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' {model name} is added  to hide specific product models in the C3 to not reveal the further information about the company.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  paired with "nemlendirici" (moisturizer) and "krem" (con-  ditioner).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In the third example, the query "yıpranma krem"  is expanded with "nemlendirici" (moisturizer) and the cor-  rect volume of the product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As the C1 dataset is mostly  composed of cosmetics products, the dataset usually con-  sists of documents that have volume information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Results  display that the trained model is not successful at generat-  ing sequences with correct volume information consisting of  the volume value and its unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' We observed that our model  tended to include a numerical value to generated sequences  often but did not include its unit such as "ml" or "cc".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' It  suggests that models can be further optimized to capture the  relationships between individual word pairs in a better way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Conclusion  Our work focused on bringing concepts of generative  adversarial networks, query expansion, and condition struc-  tures originated from query-document relationships together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Results from the mQE-CGAN framework demonstrate that  given user queries with limited information can be enriched  with query expansion to obtain sequences that are semanti-  cally more similar to the documents in the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' As the  trained models yield successful evaluation metrics for cap-  turing the context of given query-document pairs, utilization  of the framework can be beneficial for optimizing search en-  gines in the e-commerce domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Various aspects of the proposed GAN framework can  be improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Firstly, we believe that the sequence gener-  ation process could benefit from utilizing context-specific  word embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' To this end, word embeddings obtained  from language models fine-tuned for datasets will be tested  in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Secondly, alternative condition mechanisms  can be introduced during the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' The proposed  framework allows the replacement of condition mechanisms  to adapt specific cases by capturing different semantic re-  lationships in query-document data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' One of the condition  structures to be applied is the combination of the conditions  experimented with in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' Lastly, we aim to experi-  ment with the integration of the proposed GAN framework  with the existing search engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' This way, the advantages  and shortcomings of a search engine with an integrated GAN  model for query expansion can be observed in high-traffic  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=' In future works, we aim to assess the practi-  cal evaluation metrics of the query expansion approach for  its performance against the cold start problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  References  Azad,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='com/  science/article/pii/S0020025519303263,  doi:https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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+page_content='ins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Azad,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=',  Deepak,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content=',  2019b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Query expan-  sion techniques for information retrieval:  A sur-  vey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  Information Processing and Management  56,  1698–1735.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='  URL:  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AyT4oBgHgl3EQfP_aH/content/2301.00036v1.pdf'}
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diff --git a/39AzT4oBgHgl3EQf9f54/content/tmp_files/2301.01920v1.pdf.txt b/39AzT4oBgHgl3EQf9f54/content/tmp_files/2301.01920v1.pdf.txt
new file mode 100644
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@@ -0,0 +1,610 @@
+arXiv:2301.01920v1  [math.NA]  5 Jan 2023
+Double-Exponential transformation:
+A quick review of a Japanese tradition*
+Kazuo Murota†and Takayasu Matsuo‡
+January 5, 2023
+Abstract
+This article is a short introduction to numerical methods using the double exponential
+(DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The
+DE-based methods for numerical computation have been developed intensively in Japan
+and the objective of this article is to describe the history in addition to the underlying
+mathematical ideas.
+Keywords: Double exponential transformation, DE integration formula, tanh-sinh quadra-
+ture, DE-Sinc method.
+1
+Introduction
+The double exponential (DE) transformation is a generic name of variable transformations
+(changes of variables) used effectively in numerical computation on analytic functions, such
+as numerical quadrature and function approximation. A typical DE transformation is a change
+of variable x to another variable t by x = φ(t) with the function
+φ(t) = tanh
+�π
+2 sinh t
+�
+.
+The term “double exponential” refers to the property that the derivative
+φ′(t) =
+π
+2 cosh t
+cosh2(π
+2 sinh t)
+decays double exponentially
+φ′(t) ≈ exp
+�
+−π
+2 exp |t|
+�
+(1)
+as |t| → ∞.
+*This is a preliminary version of an article to be included in ICIAM 2023, Tokyo Intelligencer.
+†The Institute of Statistical Mathematics, Tokyo 190-8562, Japan; and Faculty of Economics and Business
+Administration, Tokyo Metropolitan University, Tokyo 192-0397, Japan, murota@tmu.ac.jp
+‡Department of Mathematical Informatics, Graduate School of Information Science and Technology, Uni-
+versity of Tokyo, Tokyo 113-8656, Japan matsuo@mist.i.u-tokyo.ac.jp
+1
+
+This article is a short introduction to numerical methods using DE transformations such as
+the double exponential formula (tanh-sinh quadrature) for numerical integration and the DE-
+Sinc method for function approximation. The DE-based methods for numerical computation
+have been developed intensively in Japan [5, 7, 34, 38] and a workshop titled “Thirty Years of
+the Double Exponential Transforms” was held at RIMS (Research Institute for Mathematical
+Sciences, Kyoto University) on September 1–3, 2004 [14]. The objective of this article is to
+describe the history of the development of the DE-based methods in addition to the underlying
+mathematical ideas.
+This article is written to the memory of Professors Masao Iri (President of Japan SIAM,
+1996), Masatake Mori (President of Japan SIAM, 1998), and Masaaki Sugihara (Vice Presi-
+dent of Japan SIAM, 2008).
+2
+DE formula for numerical integration
+The DE formula for numerical integration invented by Hidetosi Takahasi and Masatake Mori
+[37] was first presented at the RIMS workshop “Studies on Numerical Algorithms,” held on
+October 31–November 2, 1972. The celebrated term of “double exponential formula” was
+proposed there, as we can see in the proceedings paper [36].
+2.1
+Quadrature formula
+The DE formula was motivated by the fact that the trapezoidal rule is highly effective for
+integrals over the infinite interval (−∞, +∞). For an integral
+I =
+� 1
+−1
+f (x)dx,
+for example, we employ a change of variable x = φ(t) using some function φ(t) satisfying
+φ(−∞) = −1 and φ(+∞) = 1, and apply the trapezoidal rule to the transformed integral
+I =
+� +∞
+−∞
+f (φ(t))φ′(t)dt,
+to obtain an infinite sum of discretization
+Ih = h
+∞
+�
+k=−∞
+f (φ(kh))φ′(kh).
+(2)
+A finite-term approximation to this infinite sum results in an integration formula
+I(N)
+h
+= h
+N
+�
+k=−N
+f (φ(kh))φ′(kh).
+(3)
+Such combination of the trapezoidal rule with a change of variables was conceived by several
+authors [2, 24, 25, 35] around 1970.
+The error I − I(N)
+h
+of the formula (3) consists of two parts, the error ED ≡ I − Ih incurred
+by discretization (2) and the error ET ≡ Ih − I(N)
+h
+caused by truncation of an infinite sum Ih to
+a finite sum I(N)
+h .
+2
+
+The major findings of Takahasi and Mori consisted of two ingredients. The first was that
+the double exponential decay of the transformed integrand f (φ(t))φ′(t) achieves the optimal
+balance (or trade-off) between the discretization error ED and the truncation error ET. The
+second finding was that a concrete choice of
+φ(t) = tanh
+�π
+2 sinh t
+�
+(4)
+is suitable for this purpose thanks to the double exponential decay shown in (1). With this
+particular function φ(t) the formula (3) reads
+I(N)
+h
+= h
+N
+�
+k=−N
+f
+�
+tanh
+�π
+2 sinh(kh)
+��
+(π/2) cosh(kh)
+cosh2((π/2) sinh(kh))
+,
+which is sometimes called “tanh-sinh quadrature.” The error of this formula is estimated
+roughly as
+���I − I(N)
+h
+��� ≈ exp(−CN/ log N)
+(5)
+with some C > 0. The DE formula has an additional feature that it is robust against end-point
+singularities of integrands.
+The idea of the DE formula can be applied to integrals over other types of intervals of
+integration. For example,
+I =
+� +∞
+0
+f (x)dx, x = exp
+�π
+2 sinh t
+�
+,
+(6)
+I =
+� +∞
+−∞
+f (x)dx, x = sinh
+�π
+2 sinh t
+�
+.
+(7)
+Such formulas are also referred to as the double exponential formula. The DE formula is
+available in Mathematica (NIntegrate), Python library SymPy, Python library mpmath, C++
+library Boost, Haskell package integration, etc.
+2.2
+Optimality
+Optimality of the DE transformation (4) was discussed already by Takahasi and Mori [37].
+Numerical examples also support its optimality. Figure 1 (taken from [5]) shows the compar-
+ison of the DE transformation (4) against other transformations
+φ(t) = tanh t,
+φ(t) = tanh
+�π
+2 sinh t3�
+,
+φ(t) = erf(t) =
+2√π
+� t
+0
+exp(−s2)ds
+for
+� 1
+−1
+1
+(x − 2)(1 − x)1/4(1 + x)3/4 dx
+that has integrable singularities at both ends of the interval of integration. The DE formula
+converges much faster than others. It is known that the tanh-rule (using φ(t) = tanh t) has
+3
+
+Discovery of the DE Transformation
+915
+Figure 4. Comparison of the efficiency of several variable transformations for
+the integral
+dx/
+2)(1
+(1 +
+uations and the ordinate is the absolute error
+in logarithmic scale
+actually computed. The number attached to each curve in the figure is the
+mesh size
+used for actual computation. Transformation c gives the DE for-
+mula. From this figure we see that the efficiency becomes higher as the decay
+of
+is faster, and it attains the highest when the DE transformation is ap-
+plied. Then, as the decay becomes faster than double exponential the efficiency
+turns to be lower.
+Thus, Takahasi and Mori were convinced of the optimality of the DE trans-
+formation and presented the result orally at a RIMS symposium in 1973 [79]
+and published as a paper in Publ. RIMS in 1974 [80].
+4.3.
+Application of the DE transformation to
+other types of integrals
+The idea of the DE transformation can be applied to various kinds of
+integrals.
+Takahasi and Mori gave some examples other than (4.8) in their
+paper in 1974 [80]. We list here typical types of integrals and corresponding
+Figure 1: Comparison of the efficiency of several variable transformations for the integral
+� 1
+−1 dx/{(x − 2)(1 − x)1/4(1 + x)3/4}; taken from Mori [5, Fig. 4] with permission from the
+European Mathematical Society; u and N in the figure correspond, respectively, to t and
+2N + 1 in the present notation.
+the (rough) convergence rate exp(−C
+√
+N), in contrast to exp(−CN/ log N) in (5) of the DE
+formula.
+The optimality argument of [37], based on complex function theory, was convincing
+enough for the majority of scientists and engineers, but not perfectly satisfactory for theo-
+reticians. Rigorous mathematical argument for optimality of the DE formula was addressed
+by Masaaki Sugihara [28, 29, 30] in the 1980–1990s in a manner comparable to Stenger’s
+framework [26] for optimality of the tanh rule. It is shown in [30] (also [42]) that the DE
+formula is optimal with respect to a certain class (Hardy space) of integrand functions.
+In principle, for each class of integrand functions we may be able to find an optimal
+quadrature formula, and the optimal formula naturally depends on our choice of the admissi-
+ble class of integrands. Thus the optimality of a quadrature formula is only relative. However,
+it was shown by Sugihara that no nontrivial class of integrand functions exists that admits a
+quadrature formula with smaller errors than the DE formula. We can interpret this fact as the
+absolute optimality of the DE formula.
+2.3
+Fourier-type integrals
+For Fourier-type integrals like
+I =
+� +∞
+0
+f1(x) sin x dx,
+the DE formula like (6) is not very successful. To cope with Fourier-type integrals, a novel
+technique, in the spirit of DE transformation, was proposed by Ooura and Mori [22, 23]. In
+[22] they proposed to use
+φ(t) =
+t
+1 − exp(−K sinh t)
+4
+
+h
+口
+Q8
+0.8
+10--5
+W0.1
+0.6=h
+tanh u
+04
+0.075
+K
+0.5
+045
+aok
+0.3
+0425
+10-10
+0.05
+0.25
+0.3
+?0.04
+0.2
+0.25
+erf
+10-15
+u
+0.03
+T
+TT
+tanh
+tanh
+sinh u
+0.1$
+2
+2
+0.2
+10-20
+150
+250
+100
+200
+N
+0
+50(K > 0), which maps (−∞, +∞) to (0, +∞) in such a way that (i) φ′(t) → 0 double exponen-
+tially as t → −∞ and (ii) φ(t) → t double exponentially as t → +∞. The proposed formula
+changes the variable by x = Mφ(t) to obtain
+I = M
+� +∞
+−∞
+f1(Mφ(t)) sin(Mφ(t))φ′(t)dt,
+to which the trapezoidal rule with equal mesh h is applied, where M and h are chosen to
+satisfy Mh = π. The transformed integrand decays double-exponentially toward t → −∞
+because of the factor φ′(t) and also toward t → +∞ because Mφ(t) for t = kh (sample point
+of the trapezoidal rule) tends double-exponentially to Mt = Mkh = kπ, at which sine function
+vanishes. Another (improved) transformation function
+φ(t) =
+t
+1 − exp(−2t − α(1 − e−t) − β(et − 1)),
+is given in [23], where β = 1/4 and α = β/
+�
+1 + M log(1 + M)/(4π).
+2.4
+IMT rule
+In 1969, prior to the DE formula, a remarkable quadrature formula was proposed by Masao
+Iri, Sigeiti Moriguti, and Yoshimitsu Takasawa [2]. The formula is known today as the “IMT
+rule,” which name was introduced in [35] and used in [1].
+For an integral
+I =
+� 1
+0
+f (x)dx
+over [0, 1], the IMT rule applies the trapezoidal rule to the integral
+I =
+� 1
+0
+f (φ(t))φ′(t)dt
+resulting from the transformation by
+φ(t) = 1
+Q
+� t
+0
+exp
+�
+−
+�1
+τ +
+1
+1 − τ
+��
+dτ,
+where
+Q =
+� 1
+0
+exp
+�
+−
+�1
+τ +
+1
+1 − τ
+��
+dτ
+is a normalizing constant to render φ(1) = 1.
+The transformed integrand g(t) = f (φ(t))φ′(t) has the property that all the derivatives
+g(j)(t) (j = 1, 2, . . .) vanish at t = 0, 1. By the Euler–Maclaurin formula, this indicates that
+the IMT rule should be highly accurate. Indeed, it was shown in [2] via a complex analytic
+method that the error of the IMT rule can be estimated roughly as exp(−C
+√
+N), which is
+much better than N−4 of the Simpson rule, say, but not as good as exp(−CN/ log N) of the DE
+formula. Variants of the IMT rule have been proposed for possible improvement [4, 10, 21,
+29], but it turned out that an IMT-type rule, transforming
+� 1
+0 dx to
+� 1
+0 dt rather than to
+� +∞
+−∞ dt,
+cannot outperform the DE formula.
+5
+
+3
+DE-Sinc methods
+Changing variables is also useful in the Sinc numerical methods. The book [27] of Stenger
+in 1993 describes this methodology to the full extent, focusing on single exponential (SE)
+transformations like φ(t) = tanh(t/2). Use of the double exponential transformation in the
+Sinc numerical methods was initiated by Sugihara [31, 33] around 2000, with subsequent
+development mainly in Japan. Such numerical methods are often called the DE-Sinc methods.
+The subsequent results obtained in the first half of 2000s are described in [5, 7, 34].
+3.1
+Sinc approximation
+The Sinc approximation of a function f (x) over (−∞, ∞) is given by
+f (x) ≈
+N
+�
+k=−N
+f (kh)S (k, h)(x),
+(8)
+where S (k, h)(x) is the so-called Sinc function defined by
+S (k, h)(x) = sin[(π/h)(x − kh)]
+(π/h)(x − kh)
+and the step size h is chosen appropriately, depending on N. The technique of variable trans-
+formation x = φ(t) is also effective in this context. By applying the formula (8) to f (φ(t)) we
+obtain
+f (φ(t)) ≈
+N
+�
+k=−N
+f (φ(kh))S (k, h)(t),
+or equivalently,
+f (x) ≈
+N
+�
+k=−N
+f (φ(kh))S (k, h)(φ−1(x)).
+To approximate f (x) over [0, 1], for example, we choose
+φ(t) = 1
+2 tanh t
+2 + 1
+2,
+(9)
+φ(t) = 1
+2 tanh
+�π
+2 sinh t
+�
++ 1
+2,
+(10)
+etc. The methods using (9) and (10) are often called the SE- and DE-Sinc approximations,
+respectively. The error of the SE-Sinc approximation is roughly exp(−C
+√
+N) and that of the
+DE-Sinc approximation is exp(−CN/ log N).
+These approximation schemes are compared in Fig. 2 (taken from [34]) for function
+f (x) = x1/2(1 − x)3/4
+over [0, 1]. In Fig. 2, “Ordinary-Sinc” means the SE-Sinc approximation using (9), and the
+polynomial interpolation with the Chebyshev nodes is included for comparison.
+Detailed theoretical analyses on the DE-Sinc method can be found in Sugihara [33] as
+well as Tanaka et al. [41] and Okayama et al. [16, 20]. An optimization technique is used to
+improve the DE-Sinc method in Tanaka and Sugihara [39].
+6
+
+M. Sugihara, T. Matsuo / Journal of Computational and Applied Mathematics 164–165 (2004) 673–689
+10−14
+10−12
+10−10
+10−8
+10−6
+10−4
+10−2
+100
+0
+10 20 30 40 50 60 70 80 90 100 110 120
+|ERROR|
+n
+Chebyshev
+Ordinary-Sinc
+DE-Sinc
+3. Errors in the Sinc approximation for the function
+(1
+) and (13
+in the polynomial interpolation with the Chebyshev nodes is also displayed).
+An
+n=
+))
+of the Sinc-collocation method
+We here consider the Sinc-collocation method for the problem whose solution decays double ex-
+on the real line. We can prove the following theorem, which shows that the convergence
+of the Sinc-collocation method is given by O(exp(
+n=
+18
+a unique solution
+),
+is analytic on the real line. Furthermore assume
+A; B; ; ; 
+; 
+in the strip region
+on the real line are
+as follows
+y
+to
+);
+on the real line
+Re
+to
+on the real line
+is
+))
+to
+on the real line
+is
+))
+we have
+−∞¡x¡
++3
+Figure 2:
+Errors in the Sinc approximations for x1/2(1 − x)3/4 using (9) and (10) and the
+Chebyshev interpolation; taken from Sugihara and Matsuo [34, Fig. 3] with permission from
+Elsevier; n in the figure corresponds to N in (8).
+3.2
+Application to other problems
+Once a function approximation scheme is at hand, we can apply it to a variety of numerical
+problems. Indeed this is also the case with the DE-Sinc approximation as follows.
+• Indefinite integration by Muhammad and Mori [8], Tanaka et al. [40], and Okayama
+and Tanaka [19].
+• Initial value problem of differential equations by Nurmuhammad et al. [11] and Okayama
+[15].
+• Boundary value problem of differential equations by Sugihara [32], followed by Nur-
+muhammad et al. [12, 13] and Mori et al. [6].
+• Volterra integral equation by Muhammad et al. [9] and Okayama et al. [18].
+• Fredholm integral equation by Kobayashi et al. [3], Muhammad et al. [9], and Okayama
+et al. [17].
+Acknowledgement. The authors are thankful to Ken’ichiro Tanaka and Tomoaki Okayama
+for their support in writing this article.
+References
+[1] P. J. Davis and P. Rabinowitz: Methods of Numerical Integration, Academic Press, 1st
+ed., 1975; 2nd ed., 1984.
+[2] M. Iri, S. Moriguti and Y. Takasawa: On a certain quadrature formula (in Japanese),
+RIMS Kokyuroku, 91 (1970), 82–118. English translation in J. Comput. Appl. Math.,
+17 (1987), 3–20.
+7
+
+[3] K. Kobayashi, H. Okamoto, and J. Zhu: Numerical computation of water and solitary
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+Comput. Appl. Math., 164/165 (2004), 673–689.
+9
+
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+10
+
diff --git a/39AzT4oBgHgl3EQf9f54/content/tmp_files/load_file.txt b/39AzT4oBgHgl3EQf9f54/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf,len=387
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='01920v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='NA]  5 Jan 2023  Double-Exponential transformation:  A quick review of a Japanese tradition*  Kazuo Murota†and Takayasu Matsuo‡  January 5, 2023  Abstract  This article is a short introduction to numerical methods using the double exponential  (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The  DE-based methods for numerical computation have been developed intensively in Japan  and the objective of this article is to describe the history in addition to the underlying  mathematical ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Keywords: Double exponential transformation, DE integration formula, tanh-sinh quadra-  ture, DE-Sinc method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  1  Introduction  The double exponential (DE) transformation is a generic name of variable transformations  (changes of variables) used effectively in numerical computation on analytic functions, such  as numerical quadrature and function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' A typical DE transformation is a change  of variable x to another variable t by x = φ(t) with the function  φ(t) = tanh  �π  2 sinh t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  The term “double exponential” refers to the property that the derivative  φ′(t) =  π  2 cosh t  cosh2(π  2 sinh t)  decays double exponentially  φ′(t) ≈ exp  �  −π  2 exp |t|  �  (1)  as |t| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  This is a preliminary version of an article to be included in ICIAM 2023, Tokyo Intelligencer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  †The Institute of Statistical Mathematics, Tokyo 190-8562, Japan;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' and Faculty of Economics and Business  Administration, Tokyo Metropolitan University, Tokyo 192-0397, Japan, murota@tmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='jp  ‡Department of Mathematical Informatics, Graduate School of Information Science and Technology, Uni-  versity of Tokyo, Tokyo 113-8656, Japan matsuo@mist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='u-tokyo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='jp  1  This article is a short introduction to numerical methods using DE transformations such as  the double exponential formula (tanh-sinh quadrature) for numerical integration and the DE-  Sinc method for function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The DE-based methods for numerical computation  have been developed intensively in Japan [5, 7, 34, 38] and a workshop titled “Thirty Years of  the Double Exponential Transforms” was held at RIMS (Research Institute for Mathematical  Sciences, Kyoto University) on September 1–3, 2004 [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The objective of this article is to  describe the history of the development of the DE-based methods in addition to the underlying  mathematical ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  This article is written to the memory of Professors Masao Iri (President of Japan SIAM,  1996), Masatake Mori (President of Japan SIAM, 1998), and Masaaki Sugihara (Vice Presi-  dent of Japan SIAM, 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  2  DE formula for numerical integration  The DE formula for numerical integration invented by Hidetosi Takahasi and Masatake Mori  [37] was first presented at the RIMS workshop “Studies on Numerical Algorithms,” held on  October 31–November 2, 1972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The celebrated term of “double exponential formula” was  proposed there, as we can see in the proceedings paper [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='1  Quadrature formula  The DE formula was motivated by the fact that the trapezoidal rule is highly effective for  integrals over the infinite interval (−∞, +∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' For an integral  I =  � 1  −1  f (x)dx,  for example, we employ a change of variable x = φ(t) using some function φ(t) satisfying  φ(−∞) = −1 and φ(+∞) = 1, and apply the trapezoidal rule to the transformed integral  I =  � +∞  −∞  f (φ(t))φ′(t)dt,  to obtain an infinite sum of discretization  Ih = h  ∞  �  k=−∞  f (φ(kh))φ′(kh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  (2)  A finite-term approximation to this infinite sum results in an integration formula  I(N)  h  = h  N  �  k=−N  f (φ(kh))φ′(kh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  (3)  Such combination of the trapezoidal rule with a change of variables was conceived by several  authors [2, 24, 25, 35] around 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  The error I − I(N)  h  of the formula (3) consists of two parts, the error ED ≡ I − Ih incurred  by discretization (2) and the error ET ≡ Ih − I(N)  h  caused by truncation of an infinite sum Ih to  a finite sum I(N)  h .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  2  The major findings of Takahasi and Mori consisted of two ingredients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The first was that  the double exponential decay of the transformed integrand f (φ(t))φ′(t) achieves the optimal  balance (or trade-off) between the discretization error ED and the truncation error ET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The  second finding was that a concrete choice of  φ(t) = tanh  �π  2 sinh t  �  (4)  is suitable for this purpose thanks to the double exponential decay shown in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' With this  particular function φ(t) the formula (3) reads  I(N)  h  = h  N  �  k=−N  f  �  tanh  �π  2 sinh(kh)  ��  (π/2) cosh(kh)  cosh2((π/2) sinh(kh))  ,  which is sometimes called “tanh-sinh quadrature.” The error of this formula is estimated  roughly as  ���I − I(N)  h  ��� ≈ exp(−CN/ log N)  (5)  with some C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The DE formula has an additional feature that it is robust against end-point  singularities of integrands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  The idea of the DE formula can be applied to integrals over other types of intervals of  integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' For example,  I =  � +∞  0  f (x)dx, x = exp  �π  2 sinh t  �  ,  (6)  I =  � +∞  −∞  f (x)dx, x = sinh  �π  2 sinh t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  (7)  Such formulas are also referred to as the double exponential formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The DE formula is  available in Mathematica (NIntegrate), Python library SymPy, Python library mpmath, C++  library Boost, Haskell package integration, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='2  Optimality  Optimality of the DE transformation (4) was discussed already by Takahasi and Mori [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Numerical examples also support its optimality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Figure 1 (taken from [5]) shows the compar-  ison of the DE transformation (4) against other transformations  φ(t) = tanh t,  φ(t) = tanh  �π  2 sinh t3�  ,  φ(t) = erf(t) =  2√π  � t  0  exp(−s2)ds  for  � 1  −1  1  (x − 2)(1 − x)1/4(1 + x)3/4 dx  that has integrable singularities at both ends of the interval of integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The DE formula  converges much faster than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' It is known that the tanh-rule (using φ(t) = tanh t) has  3  Discovery of the DE Transformation  915  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Comparison of the efficiency of several variable transformations for  the integral  dx/  2)(1  (1 +  uations and the ordinate is the absolute error  in logarithmic scale  actually computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The number attached to each curve in the figure is the  mesh size  used for actual computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Transformation c gives the DE for-  mula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' From this figure we see that the efficiency becomes higher as the decay  of  is faster, and it attains the highest when the DE transformation is ap-  plied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Then, as the decay becomes faster than double exponential the efficiency  turns to be lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Thus, Takahasi and Mori were convinced of the optimality of the DE trans-  formation and presented the result orally at a RIMS symposium in 1973 [79]  and published as a paper in Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' RIMS in 1974 [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Application of the DE transformation to  other types of integrals  The idea of the DE transformation can be applied to various kinds of  integrals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Takahasi and Mori gave some examples other than (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='8) in their  paper in 1974 [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' We list here typical types of integrals and corresponding  Figure 1: Comparison of the efficiency of several variable transformations for the integral  � 1  −1 dx/{(x − 2)(1 − x)1/4(1 + x)3/4};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' taken from Mori [5, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' 4] with permission from the  European Mathematical Society;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' u and N in the figure correspond, respectively, to t and  2N + 1 in the present notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  the (rough) convergence rate exp(−C  √  N), in contrast to exp(−CN/ log N) in (5) of the DE  formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  The optimality argument of [37], based on complex function theory, was convincing  enough for the majority of scientists and engineers, but not perfectly satisfactory for theo-  reticians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Rigorous mathematical argument for optimality of the DE formula was addressed  by Masaaki Sugihara [28, 29, 30] in the 1980–1990s in a manner comparable to Stenger’s  framework [26] for optimality of the tanh rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' It is shown in [30] (also [42]) that the DE  formula is optimal with respect to a certain class (Hardy space) of integrand functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  In principle, for each class of integrand functions we may be able to find an optimal  quadrature formula, and the optimal formula naturally depends on our choice of the admissi-  ble class of integrands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Thus the optimality of a quadrature formula is only relative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' However,  it was shown by Sugihara that no nontrivial class of integrand functions exists that admits a  quadrature formula with smaller errors than the DE formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' We can interpret this fact as the  absolute optimality of the DE formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='3  Fourier-type integrals  For Fourier-type integrals like  I =  � +∞  0  f1(x) sin x dx,  the DE formula like (6) is not very successful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' To cope with Fourier-type integrals, a novel  technique, in the spirit of DE transformation, was proposed by Ooura and Mori [22, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' In  [22] they proposed to use  φ(t) =  t  1 − exp(−K sinh t)  4  h  口  Q8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='8  10--5  W0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='6=h  tanh u  04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='075  K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='5  045  aok  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='3  0425  10-10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='3  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='25  erf  10-15  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='03  T  TT  tanh  tanh  sinh u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='1$  2  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='2  10-20  150  250  100  200  N  0  50(K > 0), which maps (−∞, +∞) to (0, +∞) in such a way that (i) φ′(t) → 0 double exponen-  tially as t → −∞ and (ii) φ(t) → t double exponentially as t → +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The proposed formula  changes the variable by x = Mφ(t) to obtain  I = M  � +∞  −∞  f1(Mφ(t)) sin(Mφ(t))φ′(t)dt,  to which the trapezoidal rule with equal mesh h is applied, where M and h are chosen to  satisfy Mh = π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The transformed integrand decays double-exponentially toward t → −∞  because of the factor φ′(t) and also toward t → +∞ because Mφ(t) for t = kh (sample point  of the trapezoidal rule) tends double-exponentially to Mt = Mkh = kπ, at which sine function  vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Another (improved) transformation function  φ(t) =  t  1 − exp(−2t − α(1 − e−t) − β(et − 1)),  is given in [23], where β = 1/4 and α = β/  �  1 + M log(1 + M)/(4π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='4  IMT rule  In 1969, prior to the DE formula, a remarkable quadrature formula was proposed by Masao  Iri, Sigeiti Moriguti, and Yoshimitsu Takasawa [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The formula is known today as the “IMT  rule,” which name was introduced in [35] and used in [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  For an integral  I =  � 1  0  f (x)dx  over [0, 1], the IMT rule applies the trapezoidal rule to the integral  I =  � 1  0  f (φ(t))φ′(t)dt  resulting from the transformation by  φ(t) = 1  Q  � t  0  exp  �  −  �1  τ +  1  1 − τ  ��  dτ,  where  Q =  � 1  0  exp  �  −  �1  τ +  1  1 − τ  ��  dτ  is a normalizing constant to render φ(1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  The transformed integrand g(t) = f (φ(t))φ′(t) has the property that all the derivatives  g(j)(t) (j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=') vanish at t = 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' By the Euler–Maclaurin formula, this indicates that  the IMT rule should be highly accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Indeed, it was shown in [2] via a complex analytic  method that the error of the IMT rule can be estimated roughly as exp(−C  √  N), which is  much better than N−4 of the Simpson rule, say, but not as good as exp(−CN/ log N) of the DE  formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Variants of the IMT rule have been proposed for possible improvement [4, 10, 21,  29], but it turned out that an IMT-type rule, transforming  � 1  0 dx to  � 1  0 dt rather than to  � +∞  −∞ dt,  cannot outperform the DE formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  5  3  DE-Sinc methods  Changing variables is also useful in the Sinc numerical methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The book [27] of Stenger  in 1993 describes this methodology to the full extent, focusing on single exponential (SE)  transformations like φ(t) = tanh(t/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Use of the double exponential transformation in the  Sinc numerical methods was initiated by Sugihara [31, 33] around 2000, with subsequent  development mainly in Japan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Such numerical methods are often called the DE-Sinc methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  The subsequent results obtained in the first half of 2000s are described in [5, 7, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='1  Sinc approximation  The Sinc approximation of a function f (x) over (−∞, ∞) is given by  f (x) ≈  N  �  k=−N  f (kh)S (k, h)(x),  (8)  where S (k, h)(x) is the so-called Sinc function defined by  S (k, h)(x) = sin[(π/h)(x − kh)]  (π/h)(x − kh)  and the step size h is chosen appropriately, depending on N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The technique of variable trans-  formation x = φ(t) is also effective in this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' By applying the formula (8) to f (φ(t)) we  obtain  f (φ(t)) ≈  N  �  k=−N  f (φ(kh))S (k, h)(t),  or equivalently,  f (x) ≈  N  �  k=−N  f (φ(kh))S (k, h)(φ−1(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  To approximate f (x) over [0, 1], for example, we choose  φ(t) = 1  2 tanh t  2 + 1  2,  (9)  φ(t) = 1  2 tanh  �π  2 sinh t  �  + 1  2,  (10)  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The methods using (9) and (10) are often called the SE- and DE-Sinc approximations,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The error of the SE-Sinc approximation is roughly exp(−C  √  N) and that of the  DE-Sinc approximation is exp(−CN/ log N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  These approximation schemes are compared in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' 2 (taken from [34]) for function  f (x) = x1/2(1 − x)3/4  over [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' 2, “Ordinary-Sinc” means the SE-Sinc approximation using (9), and the  polynomial interpolation with the Chebyshev nodes is included for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Detailed theoretical analyses on the DE-Sinc method can be found in Sugihara [33] as  well as Tanaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [41] and Okayama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [16, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' An optimization technique is used to  improve the DE-Sinc method in Tanaka and Sugihara [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  6  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Sugihara, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Matsuo / Journal of Computational and Applied Mathematics 164–165 (2004) 673–689  10−14  10−12  10−10  10−8  10−6  10−4  10−2  100  0  10 20 30 40 50 60 70 80 90 100 110 120  |ERROR|  n  Chebyshev  Ordinary-Sinc  DE-Sinc  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Errors in the Sinc approximation for the function  (1  ) and (13  in the polynomial interpolation with the Chebyshev nodes is also displayed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  An  n=  ))  of the Sinc-collocation method  We here consider the Sinc-collocation method for the problem whose solution decays double ex-  on the real line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' We can prove the following theorem, which shows that the convergence  of the Sinc-collocation method is given by O(exp(  n=  18  a unique solution  ),  is analytic on the real line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Furthermore assume  A;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  \x16;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' \x16  in the strip region  on the real line are  as follows  \x17y  to  );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  on the real line  Re  to  on the real line  is  ))  to  on the real line  is  ))  we have  −∞¡x¡  +3  Figure 2:  Errors in the Sinc approximations for x1/2(1 − x)3/4 using (9) and (10) and the  Chebyshev interpolation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' taken from Sugihara and Matsuo [34, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' 3] with permission from  Elsevier;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' n in the figure corresponds to N in (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='2  Application to other problems  Once a function approximation scheme is at hand, we can apply it to a variety of numerical  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Indeed this is also the case with the DE-Sinc approximation as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Indefinite integration by Muhammad and Mori [8], Tanaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [40], and Okayama  and Tanaka [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Initial value problem of differential equations by Nurmuhammad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [11] and Okayama  [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Boundary value problem of differential equations by Sugihara [32], followed by Nur-  muhammad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [12, 13] and Mori et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Volterra integral equation by Muhammad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [9] and Okayama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Fredholm integral equation by Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [3], Muhammad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [9], and Okayama  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content='  Acknowledgement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' The authors are thankful to Ken’ichiro Tanaka and Tomoaki Okayama  for their support in writing this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
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+page_content=' Nurmuhammad, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
+page_content=' Muhammad: DE-sinc method for second order  singularly perturbed boundary value problems, Japan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/39AzT4oBgHgl3EQf9f54/content/2301.01920v1.pdf'}
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+Pseudopotential Bethe-Salpeter calculations for shallow-core x-ray absorption
+near-edge structures: excitonic effects in α-Al2O3
+M. Laura Urquiza,1, 2 Matteo Gatti,1, 2, 3 and Francesco Sottile1, 2
+1LSI, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, F-91120 Palaiseau, France
+2European Theoretical Spectroscopy Facility (ETSF)
+3Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette, France
+(Dated: January 12, 2023)
+We present an ab initio description of optical and X-ray absorption spectroscopies, in a unified
+formalism based on the pseudopotential plane-wave method at the level of the Bethe-Salpeter Equa-
+tion (BSE) within Green’s functions theory. We show that norm-conserving pseudopotentials are
+very reliable and accurate not only for valence, but also for semi-core electron absorption spectra.
+In order to validate our approach, we compare BSE results with two codes: EXC, based on pseu-
+dopotentials, and Exciting, an all-electron full-potential code. We take corundum α-Al2O3 as an
+example, a prototypical system that presents strong electron-hole interaction in both valence and
+core electron excitations. We analyze the optical, as well as the L1 and L2,3 edges, in detail in terms
+of anisotropy, crystal local fields, interference and excitonic effects. We conclude with a thorough
+inspection of the origin and localization of bright and dark excitons.
+I.
+INTRODUCTION
+X-ray absorption spectroscopy (XAS) and optical ab-
+sorption are complementary techniques to determine ma-
+terials properties. In optical absorption, valence electrons
+are excited into unoccupied conduction states across the
+band gap (or the Fermi energy in metals). Their excita-
+tions determine the color (or the transparency) of materi-
+als and are crucial to many materials properties and func-
+tionalities, spanning from optoelectronics to solar energy
+conversion and storage. In XAS, promoted to unoccu-
+pied conduction bands are instead core electrons, tightly
+bound to the nuclei. X-ray absorption near-edge struc-
+tures (XANES), also known as near-edge X-ray absorp-
+tion fine structure (NEXAFS), being element specific,
+is a probe of the atomic environment, giving structural
+and chemical information1. In the simplest independent-
+particle picture, XANES spectra are proportional to the
+unoccupied density of states, projected on the absorbing
+atom and the angular momentum component that is se-
+lected by dipole selection rules, whereas optical spectra
+can be interpreted on the basis of the joint density of
+states of valence and conduction bands. In both spectro-
+scopies, the interaction between the excited electron and
+the hole left behind can strongly alter this independent-
+particle picture. Indeed, the electron-hole attraction can
+give rise to excitons, i.e bound electron-hole pairs, lead-
+ing to a transfer of spectral weight to lower energies in
+the spectra, including the formation of sharp peaks at
+their onset.
+Given the importance of XANES spectroscopy, sev-
+eral theoretical methods have been developed to interpret
+the measured spectra in solids, taking care of core-hole
+effects at different levels of approximation2. The most
+efficient approaches are, on one side, multiple scattering
+methods3–8, and, on the other side, multiplet models9–11.
+While the former usually neglect the electronic interac-
+tions, the latter are often semi-empirical (i.e., not entirely
+parameter-free) and generally neglect solid-state effects,
+being a many-body solution of finite-cluster models.
+Since the excitations of the core electrons are localised at
+the absorbing atoms, delta-self-consistent-field (∆SCF)
+methods can be also employed, nowadays usually within
+first-principles density-functional theory12–20. The core-
+excited atom is treated as an impurity in a supercell ap-
+proach, and the presence of the core hole is taken into ac-
+count in different ways, from the Z+1 approximation21,22
+(the absorbing atom is assumed to have one additional
+nuclear charge), to the half core-hole approximation23,24
+(also known as Slater’s transition-state method) or the
+full core-hole approximation (the electron removed from
+the core is put at lowest conduction band, or ionized).
+Alternatively, XANES excitation spectra can be directly
+obtained within linear-response theory25,26, which is the
+standard approach for valence excitations and optical
+spectra as well27. In this case, two possible options are
+time-dependent density-functional theory28–30 (TDDFT)
+and the Bethe-Salpeter equation31–35 (BSE) of Green’s
+function theory36,37. Since TDDFT lacks of efficient ap-
+proximations for describing accurately excitonic effects in
+solids38, the BSE, even though computationally more ex-
+pensive, is usually more reliable27. In the present work,
+the solution of the BSE will therefore be also our pre-
+ferred choice to simulate valence and shallow-core exci-
+tation spectra within the same formalism.
+In the simulation of core excitation spectra, the in-
+tuitive technique to represent the single-particle wave
+functions are all-electron methods. They explicitly deal
+with core electrons in extended materials by partitioning
+the space into interstitial and muffin-tin (MT) regions,
+where wave functions are described differently according
+to their localisation degree39–42. Instead, methods that
+are based on plane-wave expansions cannot deal explic-
+itly with the quickly oscillatory behavior of core elec-
+trons, tightly localised near the nuclei, which are instead
+generally taken into account effectively through the de-
+sign of suitable pseudopotentials43. Plane-wave methods
+arXiv:2301.04199v1  [cond-mat.mtrl-sci]  10 Jan 2023
+
+2
+are computationally cheaper and new theoretical devel-
+opments are easier to implement in plane-waves computer
+codes. Moreover, the separation between core electrons,
+kept frozen, and valence electrons, treated explicitly, is
+often not rigid. Between valence and deep core electrons,
+there are often also shallow core (or semicore) electrons,
+which in the pseudopotential framework can be in princi-
+ple also treated as valence electrons, although at a price of
+higher computational cost. However, in all the cases, the
+pseudopotential formalism also introduces an important
+approximation, requiring a pseudization of the valence
+wave functions near the nuclei that make them smoother
+and node free. In the recent past, much work has been de-
+voted to assess pseudopotential calculations for excited-
+state properties with respect to all-electron methods, no-
+tably for self-energy calculations of quasiparticle band
+structure energies44–51. In the present work, we directly
+address the question of the validity of the pseudopotential
+approximation for XANES spectra of shallow-core edges
+(i.e., for electron binding energies smaller than ∼180 eV),
+investigating the limits of use of pseudo wave functions
+for shallow core states in many-body BSE calculations.
+It is clear that the description of deep core levels will
+be always out of reach for plane-wave basis methods.
+However, the high plane-wave cutoff required by semi-
+core states can be now alleviated by the new generation
+of ultrasoft norm-conserving pseudopotentials52. Besides
+the promised lower computational cost for shallower core
+levels, an advantage of pseudopotential plane-wave calcu-
+lations with respect to all-electron methods is that they
+do not make any hypothesis concerning the localisation
+of the core hole inside the muffin tin53.
+In particular, here we investigate the effects of the
+electron-hole interactions on the optical absorption and
+shallow-core XANES spectra of alumina. α-Al2O3 is a
+wide-gap insulator, with many possible applications as a
+structural ceramic (e.g. as a replacement to SiO2 gate ox-
+ide technology) and optical material (also thanks to the
+high-damage threshold for UV laser applications), and
+a prototypical system to investigate core-hole effects in
+XANES spectroscopy12,54–59.
+The article is organised as follows. After a short de-
+scription of the employed methodology in Sec. II, com-
+prising a review of the theoretical background (Sec. II A)
+and a summary of the computational details (Sec. II B),
+Sec. III presents the results of the calculations together
+with their analysis. In Sec. III B pseudopotential cal-
+culations are assessed with respect to all-electron bench-
+marks for both optical and Al L2,3 XANES spectra, while
+Sec. III C contains a discussion on the issue of the core-
+hole localisation in the muffin tin for the Al L1 XANES
+spectrum.
+Sec.
+III D compares the calculated spectra
+with available experiments and analyses the effects of the
+electron-hole interactions on the spectra.
+Finally, Sec.
+IV draws the conclusions summarizing the results of the
+work.
+II.
+METHODOLOGY
+A.
+Theoretical background
+In the framework of Green’s function theory36, the
+Bethe-Salpeter equation (BSE) yields the density re-
+sponse function from the solution of a Dyson-like equa-
+tion for the two-particle correlation function60. In the
+GW approximation (GWA) to the self-energy61, with
+a statically screened Coulomb interaction W, the BSE
+takes the form of an excitonic Hamiltonian27 in the basis
+|vck⟩ of transitions between occupied vk and unoccupied
+bands ck (i.e., uncorrelated electron-hole pairs):
+⟨vck|Hexc|v′c′k′⟩ = Evckδvv′δcc′δkk′+⟨vck|¯vc−W|v′c′k′⟩.
+(1)
+Here Evck = Eck − Evk are the interband transition en-
+ergies calculated in the GWA, while ¯vc is the Coulomb
+interaction without its macroscopic component (i.e., the
+component G = 0 in reciprocal space).
+The stati-
+cally screened Coulomb interaction W = ϵ−1vc is usu-
+ally calculated adopting the random-phase approxima-
+tion (RPA) for the inverse dielectric function ϵ−1.
+The GWA-BSE is nowadays the state-of-the-art ap-
+proach for the simulation, interpretation and prediction
+of optical spectra in solids36,37,62–64, and is more and
+more used also for the simulation of core-level excita-
+tion spectra2,65–81. A great advantage of theory with re-
+spect to experiments is the possibility to separately sup-
+press (or activate) the various interactions at play in the
+materials, which allows one to single out their specific
+effect on the spectra and the materials properties. By
+setting to zero the two electron-hole interactions, ¯vc and
+−W, the excitonic Hamiltonian (1) reduces to a diago-
+nal matrix and corresponds to the independent-particle
+approximation (IPA). By switching on the electron-hole
+exchange interaction ¯vc in Eq.
+(1), one retrieves the
+RPA. With respect to the IPA, the RPA includes the
+so-called crystal local field effects. They are related to
+the inhomogeneous charge response of materials through
+the induced microscopic Hartree potentials counteract-
+ing the external perturbations. Finally, by also switch-
+ing on the electron-hole direct interaction −W, the full
+BSE (1) describes excitonic effects, which are due to the
+electron-hole attraction.82 The electron-hole interactions
+contributing to the off-diagonal matrix elements of the
+BSE (1) give rise to a mixing of the independent-particle
+transitions, which is formally obtained from the solution
+of the eigenvalue equation for the excitonic hamiltonian:
+HexcAλ = EλAλ.
+The absorption spectra, expressed both in the opti-
+cal and XANES regimes by the imaginary part of the
+macroscopic dielectric function, ImϵM(ω), in the long
+wavelength limit q → 0,in the so-called Tamm-Dancoff
+approximation can be directly written in terms of eigen-
+vectors Aλ and eigenvalues Eλ of the BSE Hamiltonian
+
+3
+(1) as:
+ImϵM(ω) = lim
+q→0
+8π2
+Ωq2
+�
+λ
+�����
+�
+vck
+Avck
+λ
+˜ρvck(q)
+�����
+2
+δ(ω − Eλ),
+(2)
+where
+Ω
+is
+the
+crystal
+volume,
+and
+˜ρvck(q)
+=
+�
+ϕ∗
+vk−q(r)e−iq·rϕck(r)dr are the independent-particle
+oscillator strengths. Here the single-particle orbitals ϕi
+are usually Kohn-Sham orbitals. If the exciton energy Eλ
+is smaller than the smallest independent-particle transi-
+tion energy Evck, the exciton λ is said to be bound: the
+difference between Evck and Eλ is its binding energy.
+The contribution of each exciton λ to the spectrum can
+be analysed by introducing the cumulative function:
+Sλ(ω) = lim
+q→0
+8π
+Ωq2
+�����
+Evck<ω
+�
+vck
+Avck
+λ
+˜ρvck(q)
+�����
+2
+.
+(3)
+Since the eigenvectors Aλ and the oscillator strengths
+˜ρ(q) are both complex quantities, the cumulative func-
+tion (3) is not a monotonic function of ω.
+The limit
+Sλ(ω → ∞) is the oscillator strength of the exciton λ
+in the absorption spectrum. If it is negligibly small, the
+exciton is said to be dark, otherwise it is called a bright
+exciton, for it contributes to the spectrum. Even in the
+q → 0, the oscillator strengths ˜ρ(q) depends on the di-
+rection of q, so each exciton λ can at the same time be a
+bright exciton in one polarization direction and dark in
+another.
+Finally, the investigation of the electron-hole correla-
+tion function for each exciton λ,
+Ψλ(rh, re) =
+�
+vck
+Avck
+λ
+φ∗
+vk(rh)φck(re),
+(4)
+gives information about the localisation in real space of
+the electron-hole pair, which results from the electron-
+hole attraction. Assuming that the hole is in a specific
+position rh = r0
+h, one can visualize the corresponding
+density distribution of the electron |Ψλ(r0
+h, re)|2.
+B.
+Computational details
+We have performed calculations using both a pseu-
+dopotential
+(PP)
+plane-wave
+method
+and
+a
+full-
+potential all-electron (AE) linearized augmented plane-
+wave method. AE calculations have been done in partic-
+ular to assess the validity of PP calculations for the core-
+level excitations (see Sec.
+III B). The converged BSE
+absorption spectra and their analysis (see Sec.
+III D)
+have been then obtained in the PP framework. In the
+pseudopotential case, we have used the Abinit code83
+for the ground-state and screening calculations, and the
+EXC code84 for the BSE calculations. In the all-electron
+case, we have used the Exciting code85 for obtaining all
+the benchmark results.
+The Kohn-Sham ground-state calculations have been
+performed within the local density approximation86
+(LDA).
+We
+have
+employed
+norm-conserving
+Troullier-
+Martins87
+(TM)
+and
+optimized
+norm-conserving
+Vanderbilt52,88
+(ONCVPSP)
+pseudopotentials.
+In
+particular, for the absorption spectra a special TM
+pseudopotential89 treating also Al 2s and 2p states as
+valence electrons has been used.
+Calculation with the
+ONCVPSP pseudopotential converged with 42 Hartree
+cutoff of the plane-wave expansion, while the hard TM
+pseudopotential required 320 Hartree.
+The statically screened Coulomb interaction W has
+been obtained (within the RPA) with the ONCVPSP
+pseudopotential (without Al 2s and 2p core levels), in-
+cluding 100 bands, and with a cutoff of 8 and 14.7 Hartree
+for the Kohn-Sham wave functions for the optical and
+shallow-core excitations, respectively.
+The size of the
+screening matrix in the plane-wave basis was 6 Hartree
+for the optical and 8 Hartree for the core spectrum. We
+have verified that, contrary to calculations of the screened
+interaction for other materials like silicon50 or simple
+metals90–92, the effect of core polarization is negligible
+in α-Al2O3.
+In the all-electron results, the ground-state calcula-
+tions were performed using a plane wave cutoff, RMT|G+
+k|max, of 18 Hartree and muffin-tin (MT) spheres RMT
+of 2a0 and 1.45a0 for aluminum and oxygen, respectively.
+The RPA screening was obtained with 100 conduction
+bands and a cutoff in the matrix size of 5 Hartree (main-
+taining the same cutoff of the ground state for the plane
+waves).
+The GW band structure has been approximated within
+a scissor correction model. The LDA conduction bands
+have been rigidly shifted upwards by 2.64 eV, which cor-
+responds to the band gap correction obtained within
+the perturbative G0W0 scheme by Marinopoulos and
+Grüning93.
+The BSE calculations for the absorption spectra have
+been performed with shifted k-point grids (i.e., not con-
+taining high-symmetry k points), which allowed for a
+quicker convergence of the spectra63.
+The optical ab-
+sorption spectrum converged with a 10×10×10 k-point
+grid, while the XANES spectra at the Al L2,3 and L1
+edges converged with a 8×8×8 k-point grid. The exciton
+analysis and plot have been instead done with a smaller
+Γ-centered 4×4×4 k-point grid.
+The BSE spectra for the optical spectrum or the
+XANES spectra at the Al L2,3 and L1 edges had a dif-
+ferent convergence rate with respect to the number of
+empty bands considered in the BSE hamiltonian. Fig. 1
+shows their convergence study (carried out here with a re-
+duced number of k points in a Γ-centered 2×2×2 k-point
+grid).
+While the optical spectrum (left panel) quickly
+converges with the number of empty bands, the XANES
+spectra (middle and right panels) require many more
+empty bands, also to converge the lowest energy peak.
+In the converged spectra, obtained with many more k
+
+4
+FIG. 1: Convergence of BSE absorption spectra with the number of unoccupied conduction bands (cb). (Left)
+Optical spectrum. (Middle) XANES at L2,3 edge. (Right) XANES at L1 edge.
+points, this slow convergence is partially attenuated by
+the fact that the spectra become smoother. The opti-
+cal absorption spectra have been thus obtained with 12
+valence bands and 12 unoccupied bands. The XANES
+spectra at the L2,3 and L1 edges included all the corre-
+sponding core levels together with 30 unoccupied bands.
+A 0.1 eV Lorentzian broadening has been applied to the
+spectra.
+In the all-electron BSE calculations, we considered the
+same parameters used in the calculation of the screen-
+ing: 9 Hartree for the wavefunction cutoff and 5 Hartree
+to describe the electron-hole terms. In the pseudopoten-
+tial BSE calculations, we have used a 30 Hartree cut-
+off for the Kohn-Sham wavefunctions expansion and 7.3
+Hartree for the plane-wave representation of the electron-
+hole interactions.
+We note that, as usual (see e.g.94),
+the plane-wave cutoffs for the BSE matrixelements can
+be significantly reduced with respect to the high cutoff
+needed for the ground-state calculation. Therefore, even
+for pseudopotential BSE calculations of shallow-core ex-
+citations, the limiting factor remains the large size of the
+BSE hamiltonian (1) in extended systems, which is given
+by the number of electron-hole transitions (i.e., the num-
+ber of occupied bands × the number of unoccupied bands
+× the number of k points in the full Brillouin zone).
+III.
+RESULTS
+A.
+Crystal and electronic structure of α-Al2O3
+The crystal structure of corundum α-Al2O3 is trigo-
+nal (see Fig. 2). In the primitive rhombohedral unit cell
+(space group R¯3c, number 167) there are two formula
+units.
+The corundum structure can also be viewed as
+a hexagonal cell containing six formula units with alter-
+nate layers of Al and O atoms in planes perpendicular
+to the hexagonal cH axis. In the α-Al2O3 structure all
+Al atoms occupy octahedral sites coordinated with 6 O
+atoms, which form two equilateral triangles located re-
+spectively slightly above and below each Al atom along
+the cH direction.
+FIG. 2: Primitive rhombohedral unit cell of the crystal
+structure of α-Al2O3. Red and grey balls represent O
+and Al atoms, respectively. The Al atoms are aligned
+along the cartesian z axis, which is the vertical direction
+in the figure, while the O atoms belong to the xy planes
+perpendicular to it.
+We adopted the experimental lattice parameters from
+Ref.95: aH = bH = 4.7589 Å and cH = 12.991 Å in the
+hexagonal unit cell, which corresponds to aR = 5.128 Å
+and α = 55.287◦ in the rhombohedral primitive cell. In
+the reference frame used in the simulations, the hexago-
+nal cH axis is aligned along the cartesian z axis, which is
+the vertical direction in Fig. 2.
+The left panel of Fig. 3 shows the Kohn-Sham LDA
+band structure along a high symmetry path in the first
+Brillouin zone, together with the projected density of
+states on the O (middle panel) and Al (right panel)
+atoms. α-Al2O3 has a direct bandgap at the Γ point,
+
+a
+C5
+FIG. 3: (Left) LDA Kohn-Sham band structure of
+α-Al2O3. The top of the valence band has been set to
+zero. Density of states projected on (middle) O and
+(right) Al atoms, resolved in the angular components: s
+(red), p (blue) and d (green).
+which amounts to 6.21 eV in the LDA. This value is
+in very good agreement with the result of Ref. 96 ob-
+tained with the same experimental lattice parameters.
+Calculations93,96–98 that adopt a crystal structure opti-
+mised within the LDA, rather than the experimental one,
+instead obtain larger band gaps. In particular, the dif-
+ference with respect to Ref. 93 is 0.51 eV. We refer to
+Ref. 98 for a detailed analysis of the dependence on the
+band gap on the lattice parameters. As usual, the Kohn-
+Sham band gap underestimates the experimental funda-
+mental gap, estimated to be 9.57 eV from temperature-
+dependent vacuum ultraviolet (VUV) spectroscopy55 and
+9.6 eV from conductivity measurements99.
+The 6 bands located between -19 eV and -15.9 eV are
+the O 2s states, while the upper 18 valence bands, start-
+ing at ∼ -7 eV, are mostly due to O 2p states, partially
+hybridised with Al states. The valence bands are quite
+flat along the entire path. The bottom conduction band
+consists of Al 3s hybridised with O 3s at the Γ point and
+also with O 2p elsewhere, showing a strong dispersion
+around the Γ point. The higher conduction bands have
+mainly Al 3p and 3d character, also hybridised with O
+states.
+This overview of the electronic properties con-
+firms the intermediate covalent-ionic nature of the chem-
+ical bond in α-Al2O3.
+Finally, the Al 2p and 2s core levels (not shown in
+Fig. 3) in LDA are located 61.7 eV and 99.4 eV below
+the top valence, which, as usual, largely underestimates
+the experimental values100 of 70.7 eV and 115.6 eV, re-
+spectively. The calculations do not include the spin-orbit
+coupling, so the 2p1/2 and 2p3/2 levels are not split. In
+all cases, we have verified that pseudopotential and all-
+electron calculations give the same band structures and
+core-level energies.
+B.
+All-electron benchmark
+One of the main goals of this work is to demonstrate
+that shallow core spectra can be calculated with high
+accuracy using the pseudopotential (PP) approximation.
+The importance of this objective is underlined by the
+many works in the same spirit101–104. However, at vari-
+ance with previous works that concern tests on ground-
+state properties, mostly related to total-energy calcula-
+tions, here we aim at a much more stringent test, which
+involves occupied (both valence and semi-core) and unoc-
+cupied states. The latter could be in particular affected
+by the presence of ghost states105, which could jeopardize
+completely the excitation spectrum, while leaving unaf-
+fected a total energy calculation. Therefore, in order to
+validate the optical and core spectra calculated with PPs,
+we benchmark the results with full-potential all-electron
+(AE) calculations, considered as a gold-standard method
+for solving DFT in extended systems85,106. In order to
+perform this comparison properly, for both optical and
+L2,3 edge absorption spectra the same choice of valence
+electrons is made in the two calculations, and the num-
+ber of plane wave was converged consistently in the two
+cases.
+The valence and L2,3 spectra obtained at different lev-
+els of approximations, IPA, RPA and BSE, are shown in
+the top and bottom panels of Fig. 4, respectively. We
+can make several observations: i) The results of the left
+panels of Fig.4 show that the pseudopotential approxi-
+mation reproduces the all-electron spectra with excellent
+accuracy within the IPA. ii) For the RPA spectrum (cen-
+tral panels) we find a similar result. This is in part related
+to the fact that local fields effects are not important in
+the energy ranges considered. iii) Finally, also the BSE
+calculations with the two approaches are in very good
+agreement.
+Recent comparisons81 between all-electron
+and projected augmented wave method approaches, for
+instance, present much bigger discrepancies than our re-
+sults appearing in the right panels of Fig.4. The origin of
+this residual difference lies in the different treatment be-
+tween the two codes of the integrable singularity of the di-
+agonal matrix elements of W in (1), calculated in recipro-
+cal space, when k − k′ = q = 0 and the reciprocal-lattice
+vectors are G = G′ = 0.
+We note that the different
+treatment of this singularity was already mentioned also
+recently in a comparison among different GW codes107.
+This singularity is, in fact, eliminated, by evaluating the
+integral
+−4π
+Ω ϵ−1
+G=0,G′=0(q → 0)
+1
+(2π)3
+�
+Ωq=0
+dq 1
+q2 ,
+where Ωq=0 = ΩBZ/Nk. In order to carry out, numer-
+ically or analytically, the integral, one has to define the
+shape for the little volume Ωq=0 around the origin of the
+Brillouin zone and, in anisotropic materials, choose the
+q → 0 direction in order to evaluate the inverse dielectric
+function ϵ−1(q → 0). The details about how this inte-
+gral is performed are in Ref.108 and Refs.109,110, for EXC
+
+6
+6
+8
+10
+12
+14
+16
+18
+20
+Energy [eV]
+0
+2
+4
+6
+8
+Im εM
+IPA - pseudopotential
+IPA - all-electron
+6
+8
+10
+12
+14
+16
+18
+20
+Energy [eV]
+0
+2
+4
+6
+8
+Im εM
+RPA - pseudopotential
+RPA - all-electron 
+6
+8
+10
+12
+14
+16
+18
+20
+Energy [eV]
+0
+2
+4
+6
+8
+Im εM
+BSE - pseudopotential
+BSE - all-electron
+68
+70
+72
+74
+76
+78
+80
+Energy [eV]
+0
+0.02
+0.04
+0.06
+0.08
+Im εM
+IPA - pseudopotential
+IPA - all-electron
+RPA - pseudopotential
+RPA - all-electron
+66
+68
+70
+72
+74
+76
+78
+80
+Energy [eV]
+0
+0.1
+0.2
+0.3
+0.4
+Im εM
+BSE - pseudopotential
+BSE - all-electron
+FIG. 4: Comparison of absorption spectra calculated with pseudopotential (red lines) and all-electron (blue lines)
+methods, using an unshifted 8 × 8 × 8 k-point grid, (left panels) in the independent particle approximation (IPA),
+(middle panels) in the random-phase approximation (RPA), (right panels) from the full Bethe-Salpeter equation
+(BSE). (Upper panels) Optical spectra (with 12 valence bands and 20 conduction bands). (Bottom panels) XANES
+spectra at Al L23 edge (with 12 core levels and 12 conduction bands).
+and Exciting, respectively. If we exclude this singular
+contribution, the two BSE results become superposed, as
+in the IPA case. In addition, this contribution vanishes
+(more or less rapidly according to the kind of exciton111)
+in the convergency with k points. Fig. 5 indeed shows
+that the differences in the spectra obtained with the two
+codes tend to vanish with increasing number of k points.
+Most importantly for the scope of the present work, we
+find that the differences between the PP and AE codes
+remain always of the same order of magnitude for both
+valence and shallow-core spectra. Therefore, in summary,
+we can safely conclude that the benchmarks with the all-
+electron approach show that pseudopotential calculations
+for optical and XANES spectroscopies (with semi-core
+states) are reliable and accurate.
+C.
+Interference effects at the L1 edge
+The comparison between all-electron and pseudopoten-
+tial approximation is more delicate for the L1 edge, since
+the electrons are treated differently in the two codes.
+While Exciting includes the 2s states of Al inside the
+muffin-tin, in EXC they are considered as valence and
+treated with plane-waves.
+One of the limitations of the linearized augmented-
+plane-wave (LAPW) method is that it could give a wrong
+description of semicore states when they are considered
+inside the muffin-tin (MT) sphere, but they overlap sig-
+nificantly with valence electrons or are too extended to be
+8
+9
+Energy [eV]
+0
+0.5
+1
+1.5
+2
+  8 kp - PP
+  8 kp - AE
+0
+0.5
+1
+1.5
+2
+Im εM
+10 kp - PP
+10 kp - AE
+0
+0.5
+1
+1.5
+2
+12 kp - PP
+12 kp - AE
+FIG. 5: Convergence of BSE absorption spectra
+calculated with pseudopotential (solid lines) and
+all-electron (dot-dashed lines) methods (with 2
+conduction and 2 valence bands), for increasing number
+of k points (Γ-centered grids with 8, 10 and 12 divisions
+for bottom, central and top panel, respectively).
+entirely contained inside the MT85,112. In order to over-
+come this problem, local orbitals are included to com-
+plement the basis.
+However, the quality of this basis
+set depends on the choice of energy parameters85,113. In
+addition, there could be some interference effects that
+
+7
+106
+108
+110
+112
+114
+116
+118
+120
+Energy [eV]
+0
+0.005
+0.01
+0.015
+0.02
+Im εM
+IPA - pseudopotential
+IPA - all-electron x 4
+106
+108
+110
+112
+114
+116
+118
+120
+Energy [eV]
+0
+0.005
+0.01
+0.015
+0.02
+Im εM
+RPA - pseudopotential
+RPA - all-electron x 4
+106
+108
+110
+112
+114
+116
+118
+120
+Energy [eV]
+0
+0.01
+0.02
+0.03
+0.04
+0.05
+Im εM
+BSE - pseudopotential
+BSE - all-electron x 4
+FIG. 6: Absorption spectra at the L1 calculated with EXC (pseudopotential code) and Exciting (all-electron code).
+All the calculations are performed using a Γ-centered 8 × 8 × 8 grid of k points and 30 unoccupied bands. In EXC we
+include the 4 2s levels corresponding to the 4 Al atoms, while in Exciting we include only one 2s level (i.e., the 2s
+state on the Al atom where the core hole is created). For this reason, the spectra of Exciting are multiplied × 4.
+play an important role, and are not obviously included
+when considering the states inside the muffin-tin80. For
+all these reasons, since we validated the pseudopotential
+approach for the valence electrons (optical and L23 edge),
+we will use it to benchmark the L1 edge.
+The absorption spectra calculated for the L1 edge using
+different levels of approximations are shown in Fig. 6.
+Notice that in EXC, the 4 bands corresponding to the 2s
+state of the 4 Al atoms need to be considered in order
+to properly represent the electronic transitions, while in
+Exciting, only one occupied level is considered, the 2s
+state of the Al atom where the core-hole is sitting. Since
+there are 4 equivalent Al atoms in the cell, the overall
+spectrum coming out of Exciting needs to be multiplied
+by 4, for a correct comparison.
+In all level of approximations, the pseudopotential and
+all-electron results differ slightly (and more than in the
+optical or L2,3 edge cases), showing that small interfer-
+ence effects among the Al atoms come to play. These
+interferences are small in the system under study, for the
+Al atoms lie in equivalent positions in the cell, but they
+are detectable. We have verified that in other systems80
+these effects can be quantitative and qualitatively more
+important. While including these effects is still feasible
+with Exciting (and all approaches that create a core-
+hole in a specific position), by doing multiple calcula-
+tions and generalizing Eq.
+(2), interferences come up
+naturally in pseudopotential approaches, for all electrons
+are treated on the same footing and belong to the whole
+system, not just to one atom.
+D.
+Optical and XANES spectra: valence and
+shallow core excitations
+1.
+Comparison with experiments
+Fig.
+7 compares the calculated absorption spectra,
+ImϵM(ω), with experiment, for both the optical absorp-
+tion corresponding to valence excitations and the XANES
+spectrum of the shallow-core excitations at the Al L2,3
+edge.
+The same figure also displays the results of the
+calculations at the Al L1 edge, where, to best of our
+knowledge, no experimental XANES spectra are avail-
+able for α-Al2O3, since this core level excitation is less
+commonly studied than the Al K edge57,58,117,118. In all
+cases, the presence of sharp and pronounced peaks at the
+onset of the BSE spectra (red lines), which are absent in
+the RPA and IPA spectra (orange and green lines), is an
+evidence of strong excitonic effects. Taking into account
+the electron-hole attraction in the BSE is the key to bring
+the calculations in agreement with experiment.
+As already discussed in Ref. 93, for the optical absorp-
+tion in the polarization direction perpendicular to the z
+axis (i.e. in the xy plane), where two VUV spectroscopy
+experiments114,115 are available, there are large discrep-
+ancies between the experimental spectra themselves [see
+Fig. 7(a)]. They agree on the position of the absorption
+onset and the presence of a sharp peak at ∼ 9.2 eV, while
+they largely differ in the intensities of the various spectral
+features. Those differences can be attributed to the fact
+that both absorption spectra have been obtained from
+measured reflectivity data using the Kramers-Kroning re-
+lations, which introduces uncertainties in the ImϵM(ω)
+spectra. The calculated optical spectra in Fig. 7(a)-(b)
+have been blueshifted by 0.7 eV. This underestimation of
+the onset of the absorption spectrum is a manifestation
+of the underestimation of the band gap by the pertur-
+bative G0W0 approach, which is a systematic error for
+large gap materials119. As a matter of fact, the 2.64 eV
+scissor correction that we have employed here, which is
+taken from the G0W0 calculation in Ref. 93, underes-
+timates the band gap correction to the LDA. The BSE
+calculation in Ref.
+93 is also in very good agreement
+with the present result: the difference in the peak posi-
+tions is actually due to the LDA band gap difference (see
+Sec. III A). The BSE spectrum in the xy polarization re-
+produces well the spectral shape measured by French et
+al.115, while there are larger differences with the experi-
+mental spectra in both polarizations measured by Tomiki
+et al.114.
+At the Al L2,3 edge, see Fig. 7(c), the calculated spec-
+
+8
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+Energy [eV]
+0
+2
+4
+6
+8
+Im εM
+IPA xy
+RPA xy
+BSE xy
+Exp Tomiki et al
+Exp French et al.
+(a)
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+Energy [eV]
+0
+1
+2
+3
+4
+5
+6
+7
+8
+Im εM
+IPA z
+RPA z
+BSE z
+Exp Tomiki et al.
+(b)
+75 76 77 78 79 80
+81 82
+83 84 85 86 87 88
+89 90
+Energy [eV]
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+Im εM
+Exp Weigel et al.
+BSE xy
+BSE z
+RPA xy
+RPA z
+IPA xy
+IPA z
+(c)
+124
+126
+128
+130
+132
+134
+Energy [eV]
+0
+0.01
+0.02
+0.03
+0.04
+0.05
+Im εM
+IPA xy
+IPA z
+RPA xy
+RPA z
+BSE xy
+BSE z
+(d)
+FIG. 7: Comparison of theoretical results with experimental data from Tomiki et al.114 and French et al.115 for the
+optical absorption, and Weigel et al.116 for the XANES at the L2,3 edge. The calculated spectra are obtained in the
+independent particle approximation (IPA), green lines, in the random-phase approximation (RPA), orange lines, and
+from the solution of the Bethe-Salpeter equation (BSE), red lines. Optical absorption spectra for polarization in the
+(a) xy plane and (b) in the z direction: the calculated spectra have been blueshifted by 0.7 eV. (c) Absorption
+spectra at the L2,3 edge in the xy (solid lines) and z (dot-dashed lines) polarizations compared to the isotropic
+XANES experimental spectrum116, to which a vertical offset has been added for improved clarity. (d) Absorption
+spectra at the L1 edge in the xy (solid lines) and z (dot-dashed lines) polarizations.
+tra have been blueshifted by 9.75 eV, which matches well
+the needed correction to the LDA Al 2p core level energy
+(see Sec. III A). The calculations neglect the spin-orbit
+coupling and therefore miss the splitting of the main peak
+into a doublet separated by 0.47 eV in the high-resolution
+experimental XANES spectrum from Ref.
+116 (which
+also agrees well with previous experiments114,120,121). In
+the spectra, the first, most prominent, excitonic peak
+is followed by a series of lower intensity peaks. While
+the absolute intensity of the experimental spectrum116
+is arbitrary, the relative intensity of the first and second
+peaks gives information about the coordination number
+of Al and the nature of the chemical bond: a lower sym-
+metry enhances the intensity of the second peak. More-
+over, a lower coordination shifts the edge to lower ener-
+gies, while higher bond ionicity shifts the edge to higher
+energies59,116.
+At the Al L1 edge there is no available experiment.
+Therefore, the curves in Fig. 7(d) have been shifted by
+19.5 eV, in order for the smallest independent-particle
+transition energy, from the 2s band to the bottom-
+conduction band, to match the experimental value of
+125.2 eV, which corresponds to the sum of the fundamen-
+tal band gap plus the binding energy of the 2s states55,100
+(see Sec. III A). We find that the main prominent exci-
+tonic peak in the BSE spectra is preceded by a pre-edge
+structure, more evident in the xy direction (solid lines).
+At the Al K edge, which mainly probes the analogous
+1s → 3p transition, there has been much work to ex-
+plain the origin of a similar prepeak structure12,57,122–127,
+which has been finally interpreted in terms of atomic vi-
+brations enabling monopole transitions to unoccupied Al
+
+9
+3s states. In the present case, the calculations do not
+take into account the coupling with atomic vibrations
+and nevertheless the BSE spectra show a prepeak struc-
+ture. This finding therefore calls for a detailed compar-
+ison with other calculations including atomic vibrations
+and, possibly, experiments at the Al L1 edge.
+2.
+Anisotropy and local field effects
+The α-Al2O3 crystal is optically uniaxial. As shown
+by Fig. 7(a)-(b), at the onset of the optical spectrum
+the anisotropy is rather small, while it becomes larger
+for higher energy features. The lowest energy exciton is
+visible along the z polarization, while it is dark in the
+perpendicular xy polarization. It is separated by ∼ 25
+meV from a pair of degenerate excitons that are visible
+in the perpendicular xy direction and, conversely, dark
+in the z direction. Tomiki et al.114 experimentally deter-
+mined a similar splitting of the exciton peaks in the two
+polarization directions (35 meV at room temperature and
+86 meV at 10 K). We find that the binding energy of these
+excitons is of order of 0.3 eV, which is more than twice
+the 0.13 eV value estimated from temperature-dependent
+VUV spectroscopy55. A similar splitting of the lowest
+energy exciton occurs also at the L2,3 edge114, where its
+binding energy largely increases up to 1.6 eV. For the op-
+tical and the L2,3 cases, both the lowest energy exciton
+in the BSE spectrum and the excitation at the smallest
+independent-particle transition energy in the IPA spec-
+trum have a significant oscillator strength. Instead, at
+the L1 edge the lowest energy transitions have a 2s → 3s
+character and are dipole forbidden.
+We find that the
+binding energy of the lowest dark exciton at the L1 edge
+is 1.2 eV. The lowest bright excitons in the z and xy po-
+larization directions are located 1.6 eV and 1.8 eV above
+it, respectively. They belong to the prepeak in the spec-
+trum. In this case, we define their binding energy as the
+difference with respect to the corresponding first allowed
+transition in the IPA spectrum: it amounts to 0.6 eV.
+The splitting of the main exciton peak in the two polar-
+izations is also the largest one at the L1 edge, being more
+than 0.2 eV.
+By comparing the RPA and IPA optical spectra, or-
+ange and green lines in Fig. 7(a)-(b), respectively, we
+note that the effect of crystal local fields is quite small
+for both polarizations, in contrast to typical layered van
+der Waals materials like graphite, where local field ef-
+fects are strong for the polarization along the hexagonal
+axis128. Marinopoulos and Grüning93 also found that lo-
+cal field effects are not essential to describe satisfactorily
+the low energy part of the experimental spectra, whereas
+they become crucial for higher energies (above 16 eV, not
+shown in Fig. 7), in correspondence to the excitation of
+the more localised O 2s electrons. Indeed, the degree of
+electron localisation directly correlates with the degree
+of charge inhomogeneity, which is a key factor for the
+induced microscopic local fields. One may therefore ex-
+pect that the excitation spectra of shallow core levels,
+which are even more localised, should be more affected
+by local field effects. This phenomenon has been in fact
+observed for many shallow core levels129–133. However,
+in α-Al2O3 for both the L2,3 and L1 edges the compari-
+son of the absorption spectra calculated within the RPA
+and in the IPA shows that local field effects are actually
+negligible134 (even weaker than in the optical regime).
+We can understand this result by noticing that the in-
+tensity of the L2,3 and L1 absorption spectra is one or
+two orders of magnitude smaller than for the optical ab-
+sorption. This large intensity difference reflects the fact
+that Al 2p and 2s states are much less polarizable than
+valence states. Therefore, even though their electronic
+charge is much more localized and inhomogeneous, local
+fields associated to the excitations of Al 2p and 2s are
+small because they are weakly polarizable, which also
+leads to weak induced potentials.
+3.
+Analysis of excitonic effects
+Excitonic effects in solids can be understood as the re-
+sult of the mixing of the independent-particle, vertical
+interband transitions at various k points in the Brillouin
+zone, which are weighted by the excitonic coefficients
+Aλ
+vck, i.e., the eigenvectors of the excitonic Hamiltonian
+(1). The analysis of the excitonic coefficients therefore
+directly informs on the character of the exciton.
+Fig. 8 represents, projected on the LDA band struc-
+ture, the partial contributions
+��Aλ
+vck˜ρvck
+�� to the oscilla-
+tor strength of the lowest energy bright excitons in the
+absorption spectra of Fig. 7. Each independent-particle
+transition vk → ck is represented by a pair of circles, one
+in the occupied band v and one in the unoccupied band
+c, whose size is proportional to the value of the contri-
+bution. For the optical spectrum (left panel of Fig. 8),
+we consider the exciton giving rise to the first peak in
+the absorption spectrum in the z polarization. Our anal-
+ysis shows that the largest contribution stems from the
+top-valence bottom-conduction transition at the Γ point,
+in correspondence to the direct band gap. The next k
+points along the LΓX line in the conduction band give a
+contribution that is already 10 times smaller. The others
+are even smaller. This is due to the fact that for this exci-
+ton the top-valence bottom-conduction transition at the
+Γ point has the predominant coefficient Avck
+λ
+, together
+with a large single-particle oscillator strength ˜ρvck in the
+z direction. Instead, the same ˜ρvck is negligibly small in
+the x or y direction, explaining why the same exciton is
+dark in the xy plane.
+For the L2,3 and L1 excitation spectra, all the k points
+for the corresponding core levels are involved in the spec-
+tra, as one may expect from the fact that the core levels
+are not dispersive. Also for first exciton peak in the L2,3
+XANES spectrum (middle panel of Fig. 8), the lowest
+conduction band at the Γ point gives the largest con-
+tribution, having a large Al 3s character (see Sec. 3).
+
+10
+T
+L
+X
+10
+5
+0
+5
+10
+15
+20
+Energy [eV]
+100
+101
+102
+103
+0
+10
+20
+30
+40
+T
+L
+X
+62.0
+61.5
+10
+4
+10
+3
+10
+2
+10
+1
+FIG. 8: Contributions of independent transitions to the lowest energy bright exciton intensity in the absorption
+spectra: (left) for the optical spectrum; (middle) for the XANES at L2,3; (right) for the XANES at the L1 edge. The
+size of the circles is proportional to |˜ρvckAvck
+λ
+|.
+However, in this case the other k points of the bottom
+conduction band and the higher conduction bands signif-
+icantly contribute to the spectrum as well. This illustrate
+the deviation from a simple independent-particle picture
+of a Al 2p → 3s atomic transition, since many transitions
+are mixed together to produce the excitonic peak at the
+onset of the L2,3 XANES spectrum.
+For the L1 XANES spectrum (right panel of Fig. 8),
+we consider the first bright exciton in the z polariza-
+tion direction, which belongs to the prepeak in the spec-
+trum in Fig. 7(d). Contrary to the other two cases, the
+bottom-conduction band at the Γ point gives no contri-
+bution, consistently with the 2s → 3s character of the
+transition, which is dipole forbidden. The largest contri-
+butions are instead given by the k points along the ΓT
+line of the bottom conduction band, which have 3p char-
+acter as well. Even in this case higher conduction bands
+contribute significantly to the intensity of the excitonic
+prepeak.
+The plot in Fig.
+9 of the cumulative sums Sλ(ω),
+see Eq. (3), as a function of the number of conduction
+bands explains the different convergence behavior be-
+tween the optical and L2,3 XANES spectra shown in Fig.
+1. By increasing the number of conduction bands in the
+BSE Hamiltonian (1), the largest possible independent-
+particle transition energy progressively increases. There-
+fore, the curves for larger numbers of conduction bands
+extend to higher energies. However, in the case of the
+optical spectrum (top panel), the cumulative sum Sλ(ω)
+rapidly converges to the final result. Already considering
+transition energies within 12 eV from the smallest one
+and including 15 conduction bands in the BSE hamil-
+tonian give a result of the oscillator strength very close
+to 100%. Instead, in the case of the L2,3 edge (bottom
+panel), the range of transition energies needed to get close
+to 100% has to be much larger, of the order of 50 eV
+above the smallest transition energy. Moreover, the var-
+ious curves in the bottom panel of Fig. 9 do not overlap,
+as it is the case for the optical spectrum in the upper
+panel.
+This behavior indicates that, at the L2,3 edge,
+interband transitions to higher conduction bands in the
+BSE hamiltonian mix together with transitions to lower
+conductions bands, which affects the behavior of the cu-
+mulative sum Sλ(ω) also at lower energies. The reason
+of this strong mixing is the fact that at the L2,3 edge
+there are many interband transitions with similar weak
+intensity. This, in turns, explains why the convergence
+of the XANES spectrum with the number of conduction
+bands is slow (see Fig. 1), and requires extra care.
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+22
+Energy [eV]
+0
+0.2
+0.4
+0.6
+0.8
+1
+Sλ(ω)
+30 cb
+20 cb
+15 cb
+10 cb
+0
+10
+20
+30
+40
+50
+60
+70
+80
+Energy [eV]
+0
+0.2
+0.4
+0.6
+0.8
+1
+Sλ(ω)
+160 cb
+100 cb
+60 cb
+10 cb
+FIG. 9: Cumulative sums Sλ(ω) as a function of
+number of conduction bands (cb) in the BSE
+hamiltonian for the lowest energy bright exciton in the
+z direction for (top panel) the optical spectrum (bottom
+panel) and the XANES spectrum at the L2,3 edge. In
+each case, the zero of the energy axis has been set to
+the smallest independent-particle transition energy and
+Sλ(ω) has been normalised to its largest value.
+
+10-
+10-3
+10-4
+10-511
+The lowest-energy dark excitons, both in the opti-
+cal spectrum and the L2,3 edge, have a cumulative sum
+Sλ(ω) that is always close to zero. It means that all the
+independent-particle oscillator strengths ˜ρvck are always
+small, indicating dipole forbidden transitions. The situ-
+ation is instead different for the lowest dark exciton at
+the L1 edge. In this case, some transitions to the lowest
+conduction bands have a weak but not zero contribu-
+tion |˜ρvckAλ| to the spectrum, as shown by their repre-
+sentation on the LDA band structure in the top panel
+of Fig. 10. The corresponding cumulative sum Sλ(ω),
+bottom panel of Fig. 10, is indeed not always zero: it
+has even two distinct peaks, before progressively decreas-
+ing to zero, giving rise to a dark exciton. This suggests
+the occurrence of destructive interference of contributions
+˜ρvckAλ of different sign, involving transitions over a large
+range of energy. Moreover, it also shows that including
+not enough conduction bands in the BSE hamiltonian (1)
+would produce a weak excitonic peak in the spectrum. It
+is another indication that an independent-particle pic-
+ture is here inadequate, whereas the strong electron-hole
+interaction manifest itself as the (positive or negative)
+interference of many electron-hole pairs.
+0
+10
+20
+30
+40
+T
+L
+X
+100.0
+99.5
+10
+5
+10
+4
+10
+3
+10
+2
+0
+5
+10
+15
+20
+25
+30
+35
+Energy [eV]
+0
+0.2
+0.4
+0.6
+0.8
+1
+Sλ(ω)
+FIG. 10: Contributions of independent transitions to
+the dipole strength of the lowest energy dark exciton in
+the XANES spectrum at the L1 edge. (Top panel) The
+size of the circle is proportional to |˜ρvckAλ|. (Bottom
+panel) Corresponding cumulative sum Sλ(ω). The zero
+of the energy axis has been set to the smallest
+independent-particle transition energy and the intensity
+normalised to the largest value.
+Fig.
+11 displays the electron density distribution
+|Ψλ(r0
+h, re)|2 for a fixed position of the hole r0
+h for the
+wavefunction of the lowest bright excitons in the spec-
+tra. In the color plots, we consider a cut of the three-
+dimensional distribution in the xy plane, perpendicular
+to the z axis, containing the hole. In all cases, the hole
+position (represented by the black ball in Fig. 11) has
+been chosen slightly away from the atoms, in order to
+avoid the nodes of the orbitals. This is the reason why
+the electron distribution is not symmetrical around the
+hole.
+For an uncorrelated electron-hole pair, the elec-
+tron density would be delocalised all over the crystal,
+corresponding to a Bloch wavefunction. The effect of the
+electron-hole correlation is instead to localise the electron
+density around the hole.
+For the optical spectrum (left panel), the hole has been
+placed near an O atom, consistently with the main char-
+acter of the valence band (see Sec. III A). Here we dis-
+cover that the electron charge is also surprisingly located
+at the O atoms, and quite delocalised in the xy plane.
+This picture is indeed in contrast with the naive expec-
+tation of a charge transfer O → Al nature of the exciton,
+which is based on the largely ionic character of the elec-
+tronic properties of α-Al2O3. However, the strong Al-
+O hybridisation of the bottom conduction bands makes
+it possible for the exciton to localise entirely on the O
+atoms. The nature of the exciton in α-Al2O3 therefore
+turns out to be similar to what found135,136 in other ionic
+materials like LiF, where, analogously, for a hole fixed at
+a F atom, the electron charge is located mainly on F
+atoms as well.
+Finally, the right panel of Fig.
+11 shows the wave-
+function of the first bright exciton in the prepeak of
+the L1 edge. The hole is localised close to an Al atom.
+The resulting electron charge has partially the shape of
+a deformed 2p orbital pointing to the next neighbor O
+atom.
+In this case, the electron charge is entirely lo-
+calised around the same Al site, displaying the atomic
+character of the core exciton.
+IV.
+CONCLUSIONS
+In summary, we have presented a norm-conserving
+pseudopotential approach that permits one to evaluate
+optical and XANES spectra on the same footing, using
+the same basis set for valence and shallow-core electrons.
+We have validated the approach by comparison with full
+potential all-electron calculations, at three different lev-
+els of theory, independent-particle approximation, RPA
+and full excitonic calculation, within the BSE formalism.
+We have applied this approach to study the optical and
+semi-core excitations of corundum α-Al2O3, a promising
+material for its optical and structural properties. Both
+regimes, optical and XANES, present strong many-body
+effects that require the highest level of theory for an accu-
+rate and quantitative description. The BSE calculations
+show good agreement with experiments, when available,
+
+12
+FIG. 11: Exciton correlation function Ψλ(rh, re) for the lowest bright exciton in the optical spectrum and at the
+prepeak at the L1 edge. The position of the hole rh is fixed at r0
+h (see black ball). The color plots show the
+corresponding electron density distribution |Ψλ(r0
+h, re)|2 in the xy plane perpendicular to the z axis contaning the
+hole. In order to avoid nodes of the orbitals, the hole position has been slightly displaced from an oxygen atom for
+the optical exciton, and from an aluminum atom for the L1 edge. (This explains why the density distributions are
+not symmetric around r0
+h). The intensity follows a blue-cyan-green-yellow-orange-red gradient, and goes from 0
+(blue) to the maximum value of the square of the excitonic wavefunctions (red).
+but more importantly permit one to explain the physical
+origin of the various excitations, thanks to a thorough
+analysis of the excitons. The small anisotropy in the op-
+tical regime, for instance, reveals a different order of ex-
+citons in the z and perpendicular xy directions: the first
+exciton in bright along z, followed by dark excitons, while
+it is the contrary in the perpendicular xy direction. This
+splitting appears also for the L2,3 edge. The dark/bright
+character of the excitons in the optical, L1 and L2,3 edges
+is analysed both by projecting the excitonic eigenvectors
+on the LDA band structure, as well as by looking at the
+cumulative function, Eq. (3). The first analysis tool is
+particularly useful to understand the origin of each ex-
+citon, in terms of the single-particle transitions and of
+the atomic characters of the single bands; the cumula-
+tive function can reveal purely many-body effects, like
+the distructive interference that takes place at the L1
+edge, making the first exciton dark. In addition, the ex-
+citonic wavefunction, by showing the localization of the
+different excitons, can reveal counter-intuitive behaviour,
+like the electron localization on the oxygen atom, for the
+bright exciton in the optical spectrum, in contrast to a
+naive charge-transfer O→Al character.
+This work opens the way to the treatment of other
+shallow-core spectroscopies, like electron energy loss
+near-edge structures (ELNES). Moreover, the unified
+footing to tackle shallow core, valence, and conduction
+states, will be particularly useful to describe Resonant In-
+elastic X-ray Scattering (RIXS) and X-ray Raman Scat-
+tering (XRS).
+ACKNOWLEDGMENTS
+We thank the French Agence Nationale de la Recherche
+(ANR) for financial support (Grant Agreements No.
+ANR-19-CE30-0011). Computational time was granted
+by GENCI (Project No. 544).
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+page_content=' F-91120 Palaiseau,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' France  2European Theoretical Spectroscopy Facility (ETSF)  3Synchrotron SOLEIL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' L’Orme des Merisiers,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Saint-Aubin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' BP 48,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' F-91192 Gif-sur-Yvette,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' France  (Dated: January 12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 2023)  We present an ab initio description of optical and X-ray absorption spectroscopies,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' in a unified  formalism based on the pseudopotential plane-wave method at the level of the Bethe-Salpeter Equa-  tion (BSE) within Green’s functions theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We show that norm-conserving pseudopotentials are  very reliable and accurate not only for valence, but also for semi-core electron absorption spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In order to validate our approach, we compare BSE results with two codes: EXC, based on pseu-  dopotentials, and Exciting, an all-electron full-potential code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We take corundum α-Al2O3 as an  example, a prototypical system that presents strong electron-hole interaction in both valence and  core electron excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We analyze the optical, as well as the L1 and L2,3 edges, in detail in terms  of anisotropy, crystal local fields, interference and excitonic effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We conclude with a thorough  inspection of the origin and localization of bright and dark excitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  INTRODUCTION  X-ray absorption spectroscopy (XAS) and optical ab-  sorption are complementary techniques to determine ma-  terials properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In optical absorption, valence electrons  are excited into unoccupied conduction states across the  band gap (or the Fermi energy in metals).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Their excita-  tions determine the color (or the transparency) of materi-  als and are crucial to many materials properties and func-  tionalities, spanning from optoelectronics to solar energy  conversion and storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In XAS, promoted to unoccu-  pied conduction bands are instead core electrons, tightly  bound to the nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' X-ray absorption near-edge struc-  tures (XANES), also known as near-edge X-ray absorp-  tion fine structure (NEXAFS), being element specific,  is a probe of the atomic environment, giving structural  and chemical information1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the simplest independent-  particle picture, XANES spectra are proportional to the  unoccupied density of states, projected on the absorbing  atom and the angular momentum component that is se-  lected by dipole selection rules, whereas optical spectra  can be interpreted on the basis of the joint density of  states of valence and conduction bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In both spectro-  scopies, the interaction between the excited electron and  the hole left behind can strongly alter this independent-  particle picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Indeed, the electron-hole attraction can  give rise to excitons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e bound electron-hole pairs, lead-  ing to a transfer of spectral weight to lower energies in  the spectra, including the formation of sharp peaks at  their onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Given the importance of XANES spectroscopy, sev-  eral theoretical methods have been developed to interpret  the measured spectra in solids, taking care of core-hole  effects at different levels of approximation2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The most  efficient approaches are, on one side, multiple scattering  methods3–8, and, on the other side, multiplet models9–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  While the former usually neglect the electronic interac-  tions, the latter are often semi-empirical (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', not entirely  parameter-free) and generally neglect solid-state effects,  being a many-body solution of finite-cluster models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Since the excitations of the core electrons are localised at  the absorbing atoms, delta-self-consistent-field (∆SCF)  methods can be also employed, nowadays usually within  first-principles density-functional theory12–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The core-  excited atom is treated as an impurity in a supercell ap-  proach, and the presence of the core hole is taken into ac-  count in different ways, from the Z+1 approximation21,22  (the absorbing atom is assumed to have one additional  nuclear charge), to the half core-hole approximation23,24  (also known as Slater’s transition-state method) or the  full core-hole approximation (the electron removed from  the core is put at lowest conduction band, or ionized).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Alternatively, XANES excitation spectra can be directly  obtained within linear-response theory25,26, which is the  standard approach for valence excitations and optical  spectra as well27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In this case, two possible options are  time-dependent density-functional theory28–30 (TDDFT)  and the Bethe-Salpeter equation31–35 (BSE) of Green’s  function theory36,37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Since TDDFT lacks of efficient ap-  proximations for describing accurately excitonic effects in  solids38, the BSE, even though computationally more ex-  pensive, is usually more reliable27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the present work,  the solution of the BSE will therefore be also our pre-  ferred choice to simulate valence and shallow-core exci-  tation spectra within the same formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In the simulation of core excitation spectra, the in-  tuitive technique to represent the single-particle wave  functions are all-electron methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' They explicitly deal  with core electrons in extended materials by partitioning  the space into interstitial and muffin-tin (MT) regions,  where wave functions are described differently according  to their localisation degree39–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Instead, methods that  are based on plane-wave expansions cannot deal explic-  itly with the quickly oscillatory behavior of core elec-  trons, tightly localised near the nuclei, which are instead  generally taken into account effectively through the de-  sign of suitable pseudopotentials43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Plane-wave methods  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='04199v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='mtrl-sci]  10 Jan 2023  2  are computationally cheaper and new theoretical devel-  opments are easier to implement in plane-waves computer  codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Moreover, the separation between core electrons,  kept frozen, and valence electrons, treated explicitly, is  often not rigid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Between valence and deep core electrons,  there are often also shallow core (or semicore) electrons,  which in the pseudopotential framework can be in princi-  ple also treated as valence electrons, although at a price of  higher computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' However, in all the cases, the  pseudopotential formalism also introduces an important  approximation, requiring a pseudization of the valence  wave functions near the nuclei that make them smoother  and node free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the recent past, much work has been de-  voted to assess pseudopotential calculations for excited-  state properties with respect to all-electron methods, no-  tably for self-energy calculations of quasiparticle band  structure energies44–51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the present work, we directly  address the question of the validity of the pseudopotential  approximation for XANES spectra of shallow-core edges  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', for electron binding energies smaller than ∼180 eV),  investigating the limits of use of pseudo wave functions  for shallow core states in many-body BSE calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  It is clear that the description of deep core levels will  be always out of reach for plane-wave basis methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  However, the high plane-wave cutoff required by semi-  core states can be now alleviated by the new generation  of ultrasoft norm-conserving pseudopotentials52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Besides  the promised lower computational cost for shallower core  levels, an advantage of pseudopotential plane-wave calcu-  lations with respect to all-electron methods is that they  do not make any hypothesis concerning the localisation  of the core hole inside the muffin tin53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In particular, here we investigate the effects of the  electron-hole interactions on the optical absorption and  shallow-core XANES spectra of alumina.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' α-Al2O3 is a  wide-gap insulator, with many possible applications as a  structural ceramic (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' as a replacement to SiO2 gate ox-  ide technology) and optical material (also thanks to the  high-damage threshold for UV laser applications), and  a prototypical system to investigate core-hole effects in  XANES spectroscopy12,54–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The article is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' After a short de-  scription of the employed methodology in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' II, com-  prising a review of the theoretical background (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' II A)  and a summary of the computational details (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' II B),  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III presents the results of the calculations together  with their analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III B pseudopotential cal-  culations are assessed with respect to all-electron bench-  marks for both optical and Al L2,3 XANES spectra, while  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III C contains a discussion on the issue of the core-  hole localisation in the muffin tin for the Al L1 XANES  spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  III D compares the calculated spectra  with available experiments and analyses the effects of the  electron-hole interactions on the spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Finally, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  IV draws the conclusions summarizing the results of the  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  METHODOLOGY  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Theoretical background  In the framework of Green’s function theory36, the  Bethe-Salpeter equation (BSE) yields the density re-  sponse function from the solution of a Dyson-like equa-  tion for the two-particle correlation function60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the  GW approximation (GWA) to the self-energy61, with  a statically screened Coulomb interaction W, the BSE  takes the form of an excitonic Hamiltonian27 in the basis  |vck⟩ of transitions between occupied vk and unoccupied  bands ck (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', uncorrelated electron-hole pairs):  ⟨vck|Hexc|v′c′k′⟩ = Evckδvv′δcc′δkk′+⟨vck|¯vc−W|v′c′k′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (1)  Here Evck = Eck − Evk are the interband transition en-  ergies calculated in the GWA, while ¯vc is the Coulomb  interaction without its macroscopic component (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', the  component G = 0 in reciprocal space).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The stati-  cally screened Coulomb interaction W = ϵ−1vc is usu-  ally calculated adopting the random-phase approxima-  tion (RPA) for the inverse dielectric function ϵ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The GWA-BSE is nowadays the state-of-the-art ap-  proach for the simulation, interpretation and prediction  of optical spectra in solids36,37,62–64, and is more and  more used also for the simulation of core-level excita-  tion spectra2,65–81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' A great advantage of theory with re-  spect to experiments is the possibility to separately sup-  press (or activate) the various interactions at play in the  materials, which allows one to single out their specific  effect on the spectra and the materials properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' By  setting to zero the two electron-hole interactions, ¯vc and  −W, the excitonic Hamiltonian (1) reduces to a diago-  nal matrix and corresponds to the independent-particle  approximation (IPA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' By switching on the electron-hole  exchange interaction ¯vc in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (1), one retrieves the  RPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' With respect to the IPA, the RPA includes the  so-called crystal local field effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' They are related to  the inhomogeneous charge response of materials through  the induced microscopic Hartree potentials counteract-  ing the external perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Finally, by also switch-  ing on the electron-hole direct interaction −W, the full  BSE (1) describes excitonic effects, which are due to the  electron-hole attraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='82 The electron-hole interactions  contributing to the off-diagonal matrix elements of the  BSE (1) give rise to a mixing of the independent-particle  transitions, which is formally obtained from the solution  of the eigenvalue equation for the excitonic hamiltonian:  HexcAλ = EλAλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The absorption spectra,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' expressed both in the opti-  cal and XANES regimes by the imaginary part of the  macroscopic dielectric function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' ImϵM(ω),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' in the long  wavelength limit q → 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='in the so-called Tamm-Dancoff  approximation can be directly written in terms of eigen-  vectors Aλ and eigenvalues Eλ of the BSE Hamiltonian  3  (1) as:  ImϵM(ω) = lim  q→0  8π2  Ωq2  �  λ  �����  �  vck  Avck  λ  ˜ρvck(q)  �����  2  δ(ω − Eλ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (2)  where  Ω  is  the  crystal  volume,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  and  ˜ρvck(q)  =  �  ϕ∗  vk−q(r)e−iq·rϕck(r)dr are the independent-particle  oscillator strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Here the single-particle orbitals ϕi  are usually Kohn-Sham orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' If the exciton energy Eλ  is smaller than the smallest independent-particle transi-  tion energy Evck, the exciton λ is said to be bound: the  difference between Evck and Eλ is its binding energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The contribution of each exciton λ to the spectrum can  be analysed by introducing the cumulative function:  Sλ(ω) = lim  q→0  8π  Ωq2  �����  Evck<ω  �  vck  Avck  λ  ˜ρvck(q)  �����  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (3)  Since the eigenvectors Aλ and the oscillator strengths  ˜ρ(q) are both complex quantities, the cumulative func-  tion (3) is not a monotonic function of ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The limit  Sλ(ω → ∞) is the oscillator strength of the exciton λ  in the absorption spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' If it is negligibly small, the  exciton is said to be dark, otherwise it is called a bright  exciton, for it contributes to the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Even in the  q → 0, the oscillator strengths ˜ρ(q) depends on the di-  rection of q, so each exciton λ can at the same time be a  bright exciton in one polarization direction and dark in  another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Finally, the investigation of the electron-hole correla-  tion function for each exciton λ,  Ψλ(rh, re) =  �  vck  Avck  λ  φ∗  vk(rh)φck(re),  (4)  gives information about the localisation in real space of  the electron-hole pair, which results from the electron-  hole attraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Assuming that the hole is in a specific  position rh = r0  h, one can visualize the corresponding  density distribution of the electron |Ψλ(r0  h, re)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Computational details  We have performed calculations using both a pseu-  dopotential  (PP)  plane-wave  method  and  a  full-  potential all-electron (AE) linearized augmented plane-  wave method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' AE calculations have been done in partic-  ular to assess the validity of PP calculations for the core-  level excitations (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  III B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The converged BSE  absorption spectra and their analysis (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  III D)  have been then obtained in the PP framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the  pseudopotential case, we have used the Abinit code83  for the ground-state and screening calculations, and the  EXC code84 for the BSE calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the all-electron  case, we have used the Exciting code85 for obtaining all  the benchmark results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The Kohn-Sham ground-state calculations have been  performed within the local density approximation86  (LDA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We  have  employed  norm-conserving  Troullier-  Martins87  (TM)  and  optimized  norm-conserving  Vanderbilt52,88  (ONCVPSP)  pseudopotentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In  particular, for the absorption spectra a special TM  pseudopotential89 treating also Al 2s and 2p states as  valence electrons has been used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Calculation with the  ONCVPSP pseudopotential converged with 42 Hartree  cutoff of the plane-wave expansion, while the hard TM  pseudopotential required 320 Hartree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The statically screened Coulomb interaction W has  been obtained (within the RPA) with the ONCVPSP  pseudopotential (without Al 2s and 2p core levels), in-  cluding 100 bands, and with a cutoff of 8 and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='7 Hartree  for the Kohn-Sham wave functions for the optical and  shallow-core excitations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The size of the  screening matrix in the plane-wave basis was 6 Hartree  for the optical and 8 Hartree for the core spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We  have verified that, contrary to calculations of the screened  interaction for other materials like silicon50 or simple  metals90–92, the effect of core polarization is negligible  in α-Al2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In the all-electron results, the ground-state calcula-  tions were performed using a plane wave cutoff, RMT|G+  k|max, of 18 Hartree and muffin-tin (MT) spheres RMT  of 2a0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='45a0 for aluminum and oxygen, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The RPA screening was obtained with 100 conduction  bands and a cutoff in the matrix size of 5 Hartree (main-  taining the same cutoff of the ground state for the plane  waves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The GW band structure has been approximated within  a scissor correction model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The LDA conduction bands  have been rigidly shifted upwards by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='64 eV, which cor-  responds to the band gap correction obtained within  the perturbative G0W0 scheme by Marinopoulos and  Grüning93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The BSE calculations for the absorption spectra have  been performed with shifted k-point grids (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', not con-  taining high-symmetry k points), which allowed for a  quicker convergence of the spectra63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The optical ab-  sorption spectrum converged with a 10×10×10 k-point  grid, while the XANES spectra at the Al L2,3 and L1  edges converged with a 8×8×8 k-point grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The exciton  analysis and plot have been instead done with a smaller  Γ-centered 4×4×4 k-point grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The BSE spectra for the optical spectrum or the  XANES spectra at the Al L2,3 and L1 edges had a dif-  ferent convergence rate with respect to the number of  empty bands considered in the BSE hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 1  shows their convergence study (carried out here with a re-  duced number of k points in a Γ-centered 2×2×2 k-point  grid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  While the optical spectrum (left panel) quickly  converges with the number of empty bands, the XANES  spectra (middle and right panels) require many more  empty bands, also to converge the lowest energy peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In the converged spectra, obtained with many more k  4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 1: Convergence of BSE absorption spectra with the number of unoccupied conduction bands (cb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Left)  Optical spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Middle) XANES at L2,3 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Right) XANES at L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  points, this slow convergence is partially attenuated by  the fact that the spectra become smoother.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The opti-  cal absorption spectra have been thus obtained with 12  valence bands and 12 unoccupied bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The XANES  spectra at the L2,3 and L1 edges included all the corre-  sponding core levels together with 30 unoccupied bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  A 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='1 eV Lorentzian broadening has been applied to the  spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In the all-electron BSE calculations, we considered the  same parameters used in the calculation of the screen-  ing: 9 Hartree for the wavefunction cutoff and 5 Hartree  to describe the electron-hole terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the pseudopoten-  tial BSE calculations, we have used a 30 Hartree cut-  off for the Kohn-Sham wavefunctions expansion and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='3  Hartree for the plane-wave representation of the electron-  hole interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We note that, as usual (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='94),  the plane-wave cutoffs for the BSE matrixelements can  be significantly reduced with respect to the high cutoff  needed for the ground-state calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Therefore, even  for pseudopotential BSE calculations of shallow-core ex-  citations, the limiting factor remains the large size of the  BSE hamiltonian (1) in extended systems, which is given  by the number of electron-hole transitions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', the num-  ber of occupied bands × the number of unoccupied bands  × the number of k points in the full Brillouin zone).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  RESULTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Crystal and electronic structure of α-Al2O3  The crystal structure of corundum α-Al2O3 is trigo-  nal (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the primitive rhombohedral unit cell  (space group R¯3c, number 167) there are two formula  units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The corundum structure can also be viewed as  a hexagonal cell containing six formula units with alter-  nate layers of Al and O atoms in planes perpendicular  to the hexagonal cH axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the α-Al2O3 structure all  Al atoms occupy octahedral sites coordinated with 6 O  atoms, which form two equilateral triangles located re-  spectively slightly above and below each Al atom along  the cH direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 2: Primitive rhombohedral unit cell of the crystal  structure of α-Al2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Red and grey balls represent O  and Al atoms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The Al atoms are aligned  along the cartesian z axis, which is the vertical direction  in the figure, while the O atoms belong to the xy planes  perpendicular to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We adopted the experimental lattice parameters from  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='95: aH = bH = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='7589 Å and cH = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='991 Å in the  hexagonal unit cell, which corresponds to aR = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='128 Å  and α = 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='287◦ in the rhombohedral primitive cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In  the reference frame used in the simulations, the hexago-  nal cH axis is aligned along the cartesian z axis, which is  the vertical direction in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 3 shows the Kohn-Sham LDA  band structure along a high symmetry path in the first  Brillouin zone, together with the projected density of  states on the O (middle panel) and Al (right panel)  atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' α-Al2O3 has a direct bandgap at the Γ point,  a  C5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 3: (Left) LDA Kohn-Sham band structure of  α-Al2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The top of the valence band has been set to  zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Density of states projected on (middle) O and  (right) Al atoms, resolved in the angular components: s  (red), p (blue) and d (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  which amounts to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='21 eV in the LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This value is  in very good agreement with the result of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 96 ob-  tained with the same experimental lattice parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Calculations93,96–98 that adopt a crystal structure opti-  mised within the LDA, rather than the experimental one,  instead obtain larger band gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In particular, the dif-  ference with respect to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 93 is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='51 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We refer to  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 98 for a detailed analysis of the dependence on the  band gap on the lattice parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' As usual, the Kohn-  Sham band gap underestimates the experimental funda-  mental gap, estimated to be 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='57 eV from temperature-  dependent vacuum ultraviolet (VUV) spectroscopy55 and  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6 eV from conductivity measurements99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The 6 bands located between -19 eV and -15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='9 eV are  the O 2s states, while the upper 18 valence bands, start-  ing at ∼ -7 eV, are mostly due to O 2p states, partially  hybridised with Al states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The valence bands are quite  flat along the entire path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The bottom conduction band  consists of Al 3s hybridised with O 3s at the Γ point and  also with O 2p elsewhere, showing a strong dispersion  around the Γ point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The higher conduction bands have  mainly Al 3p and 3d character, also hybridised with O  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  This overview of the electronic properties con-  firms the intermediate covalent-ionic nature of the chem-  ical bond in α-Al2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Finally, the Al 2p and 2s core levels (not shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 3) in LDA are located 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='7 eV and 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4 eV below  the top valence, which, as usual, largely underestimates  the experimental values100 of 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='7 eV and 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6 eV, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The calculations do not include the spin-orbit  coupling, so the 2p1/2 and 2p3/2 levels are not split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In  all cases, we have verified that pseudopotential and all-  electron calculations give the same band structures and  core-level energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  All-electron benchmark  One of the main goals of this work is to demonstrate  that shallow core spectra can be calculated with high  accuracy using the pseudopotential (PP) approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The importance of this objective is underlined by the  many works in the same spirit101–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' However, at vari-  ance with previous works that concern tests on ground-  state properties, mostly related to total-energy calcula-  tions, here we aim at a much more stringent test, which  involves occupied (both valence and semi-core) and unoc-  cupied states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The latter could be in particular affected  by the presence of ghost states105, which could jeopardize  completely the excitation spectrum, while leaving unaf-  fected a total energy calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Therefore, in order to  validate the optical and core spectra calculated with PPs,  we benchmark the results with full-potential all-electron  (AE) calculations, considered as a gold-standard method  for solving DFT in extended systems85,106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In order to  perform this comparison properly, for both optical and  L2,3 edge absorption spectra the same choice of valence  electrons is made in the two calculations, and the num-  ber of plane wave was converged consistently in the two  cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The valence and L2,3 spectra obtained at different lev-  els of approximations, IPA, RPA and BSE, are shown in  the top and bottom panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We  can make several observations: i) The results of the left  panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4 show that the pseudopotential approxi-  mation reproduces the all-electron spectra with excellent  accuracy within the IPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' ii) For the RPA spectrum (cen-  tral panels) we find a similar result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This is in part related  to the fact that local fields effects are not important in  the energy ranges considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' iii) Finally, also the BSE  calculations with the two approaches are in very good  agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Recent comparisons81 between all-electron  and projected augmented wave method approaches, for  instance, present much bigger discrepancies than our re-  sults appearing in the right panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The origin of  this residual difference lies in the different treatment be-  tween the two codes of the integrable singularity of the di-  agonal matrix elements of W in (1), calculated in recipro-  cal space, when k − k′ = q = 0 and the reciprocal-lattice  vectors are G = G′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We note that the different  treatment of this singularity was already mentioned also  recently in a comparison among different GW codes107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  This singularity is, in fact, eliminated, by evaluating the  integral  −4π  Ω ϵ−1  G=0,G′=0(q → 0)  1  (2π)3  �  Ωq=0  dq 1  q2 ,  where Ωq=0 = ΩBZ/Nk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In order to carry out, numer-  ically or analytically, the integral, one has to define the  shape for the little volume Ωq=0 around the origin of the  Brillouin zone and, in anisotropic materials, choose the  q → 0 direction in order to evaluate the inverse dielectric  function ϵ−1(q → 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The details about how this inte-  gral is performed are in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='108 and Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='109,110, for EXC  6  6  8  10  12  14  16  18  20  Energy [eV]  0  2  4  6  8  Im εM  IPA - pseudopotential  IPA - all-electron  6  8  10  12  14  16  18  20  Energy [eV]  0  2  4  6  8  Im εM  RPA - pseudopotential  RPA - all-electron  6  8  10  12  14  16  18  20  Energy [eV]  0  2  4  6  8  Im εM  BSE - pseudopotential  BSE - all-electron  68  70  72  74  76  78  80  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='08  Im εM  IPA - pseudopotential  IPA - all-electron  RPA - pseudopotential  RPA - all-electron  66  68  70  72  74  76  78  80  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4  Im εM  BSE - pseudopotential  BSE - all-electron  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 4: Comparison of absorption spectra calculated with pseudopotential (red lines) and all-electron (blue lines)  methods, using an unshifted 8 × 8 × 8 k-point grid, (left panels) in the independent particle approximation (IPA),  (middle panels) in the random-phase approximation (RPA), (right panels) from the full Bethe-Salpeter equation  (BSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Upper panels) Optical spectra (with 12 valence bands and 20 conduction bands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Bottom panels) XANES  spectra at Al L23 edge (with 12 core levels and 12 conduction bands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  and Exciting, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' If we exclude this singular  contribution, the two BSE results become superposed, as  in the IPA case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In addition, this contribution vanishes  (more or less rapidly according to the kind of exciton111)  in the convergency with k points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 5 indeed shows  that the differences in the spectra obtained with the two  codes tend to vanish with increasing number of k points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Most importantly for the scope of the present work, we  find that the differences between the PP and AE codes  remain always of the same order of magnitude for both  valence and shallow-core spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Therefore, in summary,  we can safely conclude that the benchmarks with the all-  electron approach show that pseudopotential calculations  for optical and XANES spectroscopies (with semi-core  states) are reliable and accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Interference effects at the L1 edge  The comparison between all-electron and pseudopoten-  tial approximation is more delicate for the L1 edge, since  the electrons are treated differently in the two codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  While Exciting includes the 2s states of Al inside the  muffin-tin, in EXC they are considered as valence and  treated with plane-waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  One of the limitations of the linearized augmented-  plane-wave (LAPW) method is that it could give a wrong  description of semicore states when they are considered  inside the muffin-tin (MT) sphere, but they overlap sig-  nificantly with valence electrons or are too extended to be  8  9  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  2  8 kp - PP  8 kp - AE  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  2  Im εM  10 kp - PP  10 kp - AE  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  2  12 kp - PP  12 kp - AE  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 5: Convergence of BSE absorption spectra  calculated with pseudopotential (solid lines) and  all-electron (dot-dashed lines) methods (with 2  conduction and 2 valence bands), for increasing number  of k points (Γ-centered grids with 8, 10 and 12 divisions  for bottom, central and top panel, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  entirely contained inside the MT85,112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In order to over-  come this problem, local orbitals are included to com-  plement the basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  However, the quality of this basis  set depends on the choice of energy parameters85,113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In  addition, there could be some interference effects that  7  106  108  110  112  114  116  118  120  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='02  Im εM  IPA - pseudopotential  IPA - all-electron x 4  106  108  110  112  114  116  118  120  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='02  Im εM  RPA - pseudopotential  RPA - all-electron x 4  106  108  110  112  114  116  118  120  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='05  Im εM  BSE - pseudopotential  BSE - all-electron x 4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 6: Absorption spectra at the L1 calculated with EXC (pseudopotential code) and Exciting (all-electron code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  All the calculations are performed using a Γ-centered 8 × 8 × 8 grid of k points and 30 unoccupied bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In EXC we  include the 4 2s levels corresponding to the 4 Al atoms, while in Exciting we include only one 2s level (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', the 2s  state on the Al atom where the core hole is created).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' For this reason, the spectra of Exciting are multiplied × 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  play an important role, and are not obviously included  when considering the states inside the muffin-tin80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' For  all these reasons, since we validated the pseudopotential  approach for the valence electrons (optical and L23 edge),  we will use it to benchmark the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The absorption spectra calculated for the L1 edge using  different levels of approximations are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Notice that in EXC, the 4 bands corresponding to the 2s  state of the 4 Al atoms need to be considered in order  to properly represent the electronic transitions, while in  Exciting, only one occupied level is considered, the 2s  state of the Al atom where the core-hole is sitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Since  there are 4 equivalent Al atoms in the cell, the overall  spectrum coming out of Exciting needs to be multiplied  by 4, for a correct comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In all level of approximations, the pseudopotential and  all-electron results differ slightly (and more than in the  optical or L2,3 edge cases), showing that small interfer-  ence effects among the Al atoms come to play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' These  interferences are small in the system under study, for the  Al atoms lie in equivalent positions in the cell, but they  are detectable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We have verified that in other systems80  these effects can be quantitative and qualitatively more  important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' While including these effects is still feasible  with Exciting (and all approaches that create a core-  hole in a specific position), by doing multiple calcula-  tions and generalizing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (2), interferences come up  naturally in pseudopotential approaches, for all electrons  are treated on the same footing and belong to the whole  system, not just to one atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Optical and XANES spectra: valence and  shallow core excitations  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Comparison with experiments  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  7 compares the calculated absorption spectra,  ImϵM(ω), with experiment, for both the optical absorp-  tion corresponding to valence excitations and the XANES  spectrum of the shallow-core excitations at the Al L2,3  edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The same figure also displays the results of the  calculations at the Al L1 edge, where, to best of our  knowledge, no experimental XANES spectra are avail-  able for α-Al2O3, since this core level excitation is less  commonly studied than the Al K edge57,58,117,118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In all  cases, the presence of sharp and pronounced peaks at the  onset of the BSE spectra (red lines), which are absent in  the RPA and IPA spectra (orange and green lines), is an  evidence of strong excitonic effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Taking into account  the electron-hole attraction in the BSE is the key to bring  the calculations in agreement with experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  As already discussed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 93, for the optical absorp-  tion in the polarization direction perpendicular to the z  axis (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' in the xy plane), where two VUV spectroscopy  experiments114,115 are available, there are large discrep-  ancies between the experimental spectra themselves [see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' They agree on the position of the absorption  onset and the presence of a sharp peak at ∼ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2 eV, while  they largely differ in the intensities of the various spectral  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Those differences can be attributed to the fact  that both absorption spectra have been obtained from  measured reflectivity data using the Kramers-Kroning re-  lations, which introduces uncertainties in the ImϵM(ω)  spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The calculated optical spectra in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(a)-(b)  have been blueshifted by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='7 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This underestimation of  the onset of the absorption spectrum is a manifestation  of the underestimation of the band gap by the pertur-  bative G0W0 approach, which is a systematic error for  large gap materials119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' As a matter of fact, the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='64 eV  scissor correction that we have employed here, which is  taken from the G0W0 calculation in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 93, underes-  timates the band gap correction to the LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The BSE  calculation in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  93 is also in very good agreement  with the present result: the difference in the peak posi-  tions is actually due to the LDA band gap difference (see  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The BSE spectrum in the xy polarization re-  produces well the spectral shape measured by French et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='115, while there are larger differences with the experi-  mental spectra in both polarizations measured by Tomiki  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  At the Al L2,3 edge, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(c), the calculated spec-  8  6  7  8  9  10  11  12  13  14  15  16  Energy [eV]  0  2  4  6  8  Im εM  IPA xy  RPA xy  BSE xy  Exp Tomiki et al  Exp French et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (a)  6  7  8  9  10  11  12  13  14  15  16  Energy [eV]  0  1  2  3  4  5  6  7  8  Im εM  IPA z  RPA z  BSE z  Exp Tomiki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  (b)  75 76 77 78 79 80  81 82  83 84 85 86 87 88  89 90  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  Im εM  Exp Weigel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  BSE xy  BSE z  RPA xy  RPA z  IPA xy  IPA z  (c)  124  126  128  130  132  134  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='05  Im εM  IPA xy  IPA z  RPA xy  RPA z  BSE xy  BSE z  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7: Comparison of theoretical results with experimental data from Tomiki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='114 and French et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='115 for the  optical absorption, and Weigel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='116 for the XANES at the L2,3 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The calculated spectra are obtained in the  independent particle approximation (IPA), green lines, in the random-phase approximation (RPA), orange lines, and  from the solution of the Bethe-Salpeter equation (BSE), red lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Optical absorption spectra for polarization in the  (a) xy plane and (b) in the z direction: the calculated spectra have been blueshifted by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='7 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (c) Absorption  spectra at the L2,3 edge in the xy (solid lines) and z (dot-dashed lines) polarizations compared to the isotropic  XANES experimental spectrum116, to which a vertical offset has been added for improved clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (d) Absorption  spectra at the L1 edge in the xy (solid lines) and z (dot-dashed lines) polarizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  tra have been blueshifted by 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='75 eV, which matches well  the needed correction to the LDA Al 2p core level energy  (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The calculations neglect the spin-orbit  coupling and therefore miss the splitting of the main peak  into a doublet separated by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='47 eV in the high-resolution  experimental XANES spectrum from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  116 (which  also agrees well with previous experiments114,120,121).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In  the spectra, the first, most prominent, excitonic peak  is followed by a series of lower intensity peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' While  the absolute intensity of the experimental spectrum116  is arbitrary, the relative intensity of the first and second  peaks gives information about the coordination number  of Al and the nature of the chemical bond: a lower sym-  metry enhances the intensity of the second peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' More-  over, a lower coordination shifts the edge to lower ener-  gies, while higher bond ionicity shifts the edge to higher  energies59,116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  At the Al L1 edge there is no available experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Therefore, the curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(d) have been shifted by  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5 eV, in order for the smallest independent-particle  transition energy, from the 2s band to the bottom-  conduction band, to match the experimental value of  125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2 eV, which corresponds to the sum of the fundamen-  tal band gap plus the binding energy of the 2s states55,100  (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We find that the main prominent exci-  tonic peak in the BSE spectra is preceded by a pre-edge  structure, more evident in the xy direction (solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  At the Al K edge, which mainly probes the analogous  1s → 3p transition, there has been much work to ex-  plain the origin of a similar prepeak structure12,57,122–127,  which has been finally interpreted in terms of atomic vi-  brations enabling monopole transitions to unoccupied Al  9  3s states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the present case, the calculations do not  take into account the coupling with atomic vibrations  and nevertheless the BSE spectra show a prepeak struc-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This finding therefore calls for a detailed compar-  ison with other calculations including atomic vibrations  and, possibly, experiments at the Al L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Anisotropy and local field effects  The α-Al2O3 crystal is optically uniaxial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' As shown  by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(a)-(b), at the onset of the optical spectrum  the anisotropy is rather small, while it becomes larger  for higher energy features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The lowest energy exciton is  visible along the z polarization, while it is dark in the  perpendicular xy polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' It is separated by ∼ 25  meV from a pair of degenerate excitons that are visible  in the perpendicular xy direction and, conversely, dark  in the z direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Tomiki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='114 experimentally deter-  mined a similar splitting of the exciton peaks in the two  polarization directions (35 meV at room temperature and  86 meV at 10 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' We find that the binding energy of these  excitons is of order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='3 eV, which is more than twice  the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='13 eV value estimated from temperature-dependent  VUV spectroscopy55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' A similar splitting of the lowest  energy exciton occurs also at the L2,3 edge114, where its  binding energy largely increases up to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' For the op-  tical and the L2,3 cases, both the lowest energy exciton  in the BSE spectrum and the excitation at the smallest  independent-particle transition energy in the IPA spec-  trum have a significant oscillator strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Instead, at  the L1 edge the lowest energy transitions have a 2s → 3s  character and are dipole forbidden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We find that the  binding energy of the lowest dark exciton at the L1 edge  is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The lowest bright excitons in the z and xy po-  larization directions are located 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6 eV and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='8 eV above  it, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' They belong to the prepeak in the spec-  trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In this case, we define their binding energy as the  difference with respect to the corresponding first allowed  transition in the IPA spectrum: it amounts to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The splitting of the main exciton peak in the two polar-  izations is also the largest one at the L1 edge, being more  than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  By comparing the RPA and IPA optical spectra, or-  ange and green lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(a)-(b), respectively, we  note that the effect of crystal local fields is quite small  for both polarizations, in contrast to typical layered van  der Waals materials like graphite, where local field ef-  fects are strong for the polarization along the hexagonal  axis128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Marinopoulos and Grüning93 also found that lo-  cal field effects are not essential to describe satisfactorily  the low energy part of the experimental spectra, whereas  they become crucial for higher energies (above 16 eV, not  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7), in correspondence to the excitation of  the more localised O 2s electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Indeed, the degree of  electron localisation directly correlates with the degree  of charge inhomogeneity, which is a key factor for the  induced microscopic local fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' One may therefore ex-  pect that the excitation spectra of shallow core levels,  which are even more localised, should be more affected  by local field effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This phenomenon has been in fact  observed for many shallow core levels129–133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' However,  in α-Al2O3 for both the L2,3 and L1 edges the compari-  son of the absorption spectra calculated within the RPA  and in the IPA shows that local field effects are actually  negligible134 (even weaker than in the optical regime).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We can understand this result by noticing that the in-  tensity of the L2,3 and L1 absorption spectra is one or  two orders of magnitude smaller than for the optical ab-  sorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This large intensity difference reflects the fact  that Al 2p and 2s states are much less polarizable than  valence states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Therefore, even though their electronic  charge is much more localized and inhomogeneous, local  fields associated to the excitations of Al 2p and 2s are  small because they are weakly polarizable, which also  leads to weak induced potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Analysis of excitonic effects  Excitonic effects in solids can be understood as the re-  sult of the mixing of the independent-particle, vertical  interband transitions at various k points in the Brillouin  zone, which are weighted by the excitonic coefficients  Aλ  vck, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', the eigenvectors of the excitonic Hamiltonian  (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The analysis of the excitonic coefficients therefore  directly informs on the character of the exciton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 8 represents, projected on the LDA band struc-  ture, the partial contributions  ��Aλ  vck˜ρvck  �� to the oscilla-  tor strength of the lowest energy bright excitons in the  absorption spectra of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Each independent-particle  transition vk → ck is represented by a pair of circles, one  in the occupied band v and one in the unoccupied band  c, whose size is proportional to the value of the contri-  bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' For the optical spectrum (left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 8),  we consider the exciton giving rise to the first peak in  the absorption spectrum in the z polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Our anal-  ysis shows that the largest contribution stems from the  top-valence bottom-conduction transition at the Γ point,  in correspondence to the direct band gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The next k  points along the LΓX line in the conduction band give a  contribution that is already 10 times smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The others  are even smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This is due to the fact that for this exci-  ton the top-valence bottom-conduction transition at the  Γ point has the predominant coefficient Avck  λ  , together  with a large single-particle oscillator strength ˜ρvck in the  z direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Instead, the same ˜ρvck is negligibly small in  the x or y direction, explaining why the same exciton is  dark in the xy plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  For the L2,3 and L1 excitation spectra, all the k points  for the corresponding core levels are involved in the spec-  tra, as one may expect from the fact that the core levels  are not dispersive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Also for first exciton peak in the L2,3  XANES spectrum (middle panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 8), the lowest  conduction band at the Γ point gives the largest con-  tribution, having a large Al 3s character (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  10  T  L  X  10  5  0  5  10  15  20  Energy [eV]  100  101  102  103  0  10  20  30  40  T  L  X  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='0  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  10  4  10  3  10  2  10  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 8: Contributions of independent transitions to the lowest energy bright exciton intensity in the absorption  spectra: (left) for the optical spectrum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (middle) for the XANES at L2,3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (right) for the XANES at the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The  size of the circles is proportional to |˜ρvckAvck  λ  |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  However, in this case the other k points of the bottom  conduction band and the higher conduction bands signif-  icantly contribute to the spectrum as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This illustrate  the deviation from a simple independent-particle picture  of a Al 2p → 3s atomic transition, since many transitions  are mixed together to produce the excitonic peak at the  onset of the L2,3 XANES spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  For the L1 XANES spectrum (right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 8),  we consider the first bright exciton in the z polariza-  tion direction, which belongs to the prepeak in the spec-  trum in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 7(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Contrary to the other two cases, the  bottom-conduction band at the Γ point gives no contri-  bution, consistently with the 2s → 3s character of the  transition, which is dipole forbidden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The largest contri-  butions are instead given by the k points along the ΓT  line of the bottom conduction band, which have 3p char-  acter as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Even in this case higher conduction bands  contribute significantly to the intensity of the excitonic  prepeak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  9 of the cumulative sums Sλ(ω),  see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (3), as a function of the number of conduction  bands explains the different convergence behavior be-  tween the optical and L2,3 XANES spectra shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' By increasing the number of conduction bands in the  BSE Hamiltonian (1), the largest possible independent-  particle transition energy progressively increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' There-  fore, the curves for larger numbers of conduction bands  extend to higher energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' However, in the case of the  optical spectrum (top panel), the cumulative sum Sλ(ω)  rapidly converges to the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Already considering  transition energies within 12 eV from the smallest one  and including 15 conduction bands in the BSE hamil-  tonian give a result of the oscillator strength very close  to 100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Instead, in the case of the L2,3 edge (bottom  panel), the range of transition energies needed to get close  to 100% has to be much larger, of the order of 50 eV  above the smallest transition energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Moreover, the var-  ious curves in the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 9 do not overlap,  as it is the case for the optical spectrum in the upper  panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  This behavior indicates that, at the L2,3 edge,  interband transitions to higher conduction bands in the  BSE hamiltonian mix together with transitions to lower  conductions bands, which affects the behavior of the cu-  mulative sum Sλ(ω) also at lower energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The reason  of this strong mixing is the fact that at the L2,3 edge  there are many interband transitions with similar weak  intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This, in turns, explains why the convergence  of the XANES spectrum with the number of conduction  bands is slow (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 1), and requires extra care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  0  2  4  6  8  10  12  14  16  18  20  22  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='8  1  Sλ(ω)  30 cb  20 cb  15 cb  10 cb  0  10  20  30  40  50  60  70  80  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='8  1  Sλ(ω)  160 cb  100 cb  60 cb  10 cb  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 9: Cumulative sums Sλ(ω) as a function of  number of conduction bands (cb) in the BSE  hamiltonian for the lowest energy bright exciton in the  z direction for (top panel) the optical spectrum (bottom  panel) and the XANES spectrum at the L2,3 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In  each case, the zero of the energy axis has been set to  the smallest independent-particle transition energy and  Sλ(ω) has been normalised to its largest value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  10-  10-3  10-4  10-511  The lowest-energy dark excitons, both in the opti-  cal spectrum and the L2,3 edge, have a cumulative sum  Sλ(ω) that is always close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' It means that all the  independent-particle oscillator strengths ˜ρvck are always  small, indicating dipole forbidden transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The situ-  ation is instead different for the lowest dark exciton at  the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In this case, some transitions to the lowest  conduction bands have a weak but not zero contribu-  tion |˜ρvckAλ| to the spectrum, as shown by their repre-  sentation on the LDA band structure in the top panel  of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The corresponding cumulative sum Sλ(ω),  bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 10, is indeed not always zero: it  has even two distinct peaks, before progressively decreas-  ing to zero, giving rise to a dark exciton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This suggests  the occurrence of destructive interference of contributions  ˜ρvckAλ of different sign, involving transitions over a large  range of energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Moreover, it also shows that including  not enough conduction bands in the BSE hamiltonian (1)  would produce a weak excitonic peak in the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' It  is another indication that an independent-particle pic-  ture is here inadequate, whereas the strong electron-hole  interaction manifest itself as the (positive or negative)  interference of many electron-hole pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  0  10  20  30  40  T  L  X  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='0  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='5  10  5  10  4  10  3  10  2  0  5  10  15  20  25  30  35  Energy [eV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='8  1  Sλ(ω)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 10: Contributions of independent transitions to  the dipole strength of the lowest energy dark exciton in  the XANES spectrum at the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Top panel) The  size of the circle is proportional to |˜ρvckAλ|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (Bottom  panel) Corresponding cumulative sum Sλ(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The zero  of the energy axis has been set to the smallest  independent-particle transition energy and the intensity  normalised to the largest value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  11 displays the electron density distribution  |Ψλ(r0  h, re)|2 for a fixed position of the hole r0  h for the  wavefunction of the lowest bright excitons in the spec-  tra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In the color plots, we consider a cut of the three-  dimensional distribution in the xy plane, perpendicular  to the z axis, containing the hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In all cases, the hole  position (represented by the black ball in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 11) has  been chosen slightly away from the atoms, in order to  avoid the nodes of the orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This is the reason why  the electron distribution is not symmetrical around the  hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  For an uncorrelated electron-hole pair, the elec-  tron density would be delocalised all over the crystal,  corresponding to a Bloch wavefunction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The effect of the  electron-hole correlation is instead to localise the electron  density around the hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  For the optical spectrum (left panel), the hole has been  placed near an O atom, consistently with the main char-  acter of the valence band (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' III A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Here we dis-  cover that the electron charge is also surprisingly located  at the O atoms, and quite delocalised in the xy plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  This picture is indeed in contrast with the naive expec-  tation of a charge transfer O → Al nature of the exciton,  which is based on the largely ionic character of the elec-  tronic properties of α-Al2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' However, the strong Al-  O hybridisation of the bottom conduction bands makes  it possible for the exciton to localise entirely on the O  atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The nature of the exciton in α-Al2O3 therefore  turns out to be similar to what found135,136 in other ionic  materials like LiF, where, analogously, for a hole fixed at  a F atom, the electron charge is located mainly on F  atoms as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Finally, the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  11 shows the wave-  function of the first bright exciton in the prepeak of  the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The hole is localised close to an Al atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  The resulting electron charge has partially the shape of  a deformed 2p orbital pointing to the next neighbor O  atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  In this case, the electron charge is entirely lo-  calised around the same Al site, displaying the atomic  character of the core exciton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  CONCLUSIONS  In summary, we have presented a norm-conserving  pseudopotential approach that permits one to evaluate  optical and XANES spectra on the same footing, using  the same basis set for valence and shallow-core electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We have validated the approach by comparison with full  potential all-electron calculations, at three different lev-  els of theory, independent-particle approximation, RPA  and full excitonic calculation, within the BSE formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  We have applied this approach to study the optical and  semi-core excitations of corundum α-Al2O3, a promising  material for its optical and structural properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Both  regimes, optical and XANES, present strong many-body  effects that require the highest level of theory for an accu-  rate and quantitative description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The BSE calculations  show good agreement with experiments, when available,  12  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 11: Exciton correlation function Ψλ(rh, re) for the lowest bright exciton in the optical spectrum and at the  prepeak at the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The position of the hole rh is fixed at r0  h (see black ball).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The color plots show the  corresponding electron density distribution |Ψλ(r0  h, re)|2 in the xy plane perpendicular to the z axis contaning the  hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In order to avoid nodes of the orbitals, the hole position has been slightly displaced from an oxygen atom for  the optical exciton, and from an aluminum atom for the L1 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (This explains why the density distributions are  not symmetric around r0  h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The intensity follows a blue-cyan-green-yellow-orange-red gradient, and goes from 0  (blue) to the maximum value of the square of the excitonic wavefunctions (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  but more importantly permit one to explain the physical  origin of the various excitations, thanks to a thorough  analysis of the excitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The small anisotropy in the op-  tical regime, for instance, reveals a different order of ex-  citons in the z and perpendicular xy directions: the first  exciton in bright along z, followed by dark excitons, while  it is the contrary in the perpendicular xy direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' This  splitting appears also for the L2,3 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The dark/bright  character of the excitons in the optical, L1 and L2,3 edges  is analysed both by projecting the excitonic eigenvectors  on the LDA band structure, as well as by looking at the  cumulative function, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' The first analysis tool is  particularly useful to understand the origin of each ex-  citon, in terms of the single-particle transitions and of  the atomic characters of the single bands;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' the cumula-  tive function can reveal purely many-body effects, like  the distructive interference that takes place at the L1  edge, making the first exciton dark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' In addition, the ex-  citonic wavefunction, by showing the localization of the  different excitons, can reveal counter-intuitive behaviour,  like the electron localization on the oxygen atom, for the  bright exciton in the optical spectrum, in contrast to a  naive charge-transfer O→Al character.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  This work opens the way to the treatment of other  shallow-core spectroscopies, like electron energy loss  near-edge structures (ELNES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Moreover, the unified  footing to tackle shallow core, valence, and conduction  states, will be particularly useful to describe Resonant In-  elastic X-ray Scattering (RIXS) and X-ray Raman Scat-  tering (XRS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  We thank the French Agence Nationale de la Recherche  (ANR) for financial support (Grant Agreements No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  ANR-19-CE30-0011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Computational time was granted  by GENCI (Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' 544).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  1 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' van Bokhoven and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Lamberti, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=', X-Ray Absorption  and X-Ray Emission Spectroscopy: Theory and Applica-  tions (Wiley, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  2 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' de Groot, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Elnaggar, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Frati, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' pan Wang,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Delgado-Jaime, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' van Veenendaal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Fernandez-  Rodriguez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Haverkort, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Green, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' van der  Laan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Kvashnin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Hariki, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Ikeno, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Ramanan-  toanina, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Daul, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Delley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Odelius, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Lundberg,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Kuhn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Bokarev, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Shirley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vinson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Gilmore,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Stener, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Fronzoni, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Decleva, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Kruger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rete-  gan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Joly, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vorwerk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Draxl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rehr,  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Tanaka, Journal of Electron Spectroscopy and Related  Phenomena 249, 147061 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Albers, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Kas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Taki-  moto,  and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vila, Comptes Rendus Physique 10, 548  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Jorissen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Zwierzycki,  and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Mauri, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Taillefumier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Flank, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Mauri,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Torrent, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Recoules, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Hetényi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' De Angelis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Giannozzi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Car, The  Journal of Chemical Physics 120, 8632 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  18 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Prendergast and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Galli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Perlov,  and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Milman,  Journal of Physics: Condensed Matter 21, 104203 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Prentice, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Aarons, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Womack, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Anton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Bell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Charlton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Clements, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Cole, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Corsetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Dubois,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Duff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Greco, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Hill, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Lee,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Linscott, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' O’Regan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rat-  cliff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Teobaldi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vitale,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Yeung, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Haynes,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Joannopoulos, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' García-González, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rubio, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Scheffler,  and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Ambrosch-  Draxl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Kaltak, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Reining, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Del Sole, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Onida, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Vinson,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Shirley,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Prendergast,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Vila, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rehr, Computer  Physics Communications 197, 109 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  68 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Gilmore, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Pelliciari, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Huang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Dantz,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Strocov,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Puschnig, and  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Ambrosch-Draxl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' B 79, 041102 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  74 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Olovsson,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Tanaka,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Mizoguchi,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Radtke,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Puschnig, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Ambrosch-Draxl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' B 83,  195206 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  75 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vorwerk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Cocchi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Draxl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' B 95,  155121 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  76 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vorwerk, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Aurich, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Cocchi,  and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Draxl, Elec-  tronic Structure 1, 037001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  77 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vorwerk, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Sottile, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Draxl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Research  2, 042003 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  78 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Laskowski and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Blaha, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' B 82, 205104  (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  79 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Yao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Golze, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rinke, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Blum,  and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Kanai,  Journal of Chemical Theory and Computation 18, 1569  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  80 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Vorwerk, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Sottile, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Draxl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Unzog, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Tal,  and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' B 106,  155133 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  82 There is also the possibility to include −W and exclude  ¯vc, which corresponds to the description of spin-triplet  excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Abreu Araujo,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rangel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rignanese, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Rousseau, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rubel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Shukri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Stankovski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Tor-  rent, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Van Setten, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Van Troeye, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Xu,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Zhou,  and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Zwanziger, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='  Reining,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Efimenko,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content=' Gatti,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+page_content='  134 It is well known that local field effects, expressed as  electron-hole exchange interaction in the BSE framework,  are essential to get the correct branching ratios between  L2 and L3 components, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='66,67,139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' However, in the  present case the neglect of spin-orbit coupling does not  allow us to resolve the two components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content=' For α-Al2O3  an electron–hole exchange energy of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='3 eV has been  estimated116,120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
+page_content='  135 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE2T4oBgHgl3EQf6Qjc/content/2301.04199v1.pdf'}
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+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a
+transonic nacelle-aircraft configuration
+Marius Herr1*, Axel Probst2 and Rolf Radespiel1
+1*Institute of Fluid Mechanics, TU Braunschweig,
+Hermann-Blenk-Str. 37, Braunschweig, 38108, Lower Saxony,
+Germany.
+2Institute for Aerodynamics and Flow Technology, DLR,
+Bunsenstr. 10, G¨ottingen, 37073, Lower Saxony, Germany.
+*Corresponding author(s). E-mail(s): m.herr@tu-bs.de;
+Contributing authors: axel.probst@dlr.de; r.radespiel@tu-bs.de;
+Abstract
+A scale resolving hybrid RANS-LES technique is applied to an air-
+craft - nacelle configuration under transonic flow conditions using the
+unstructured, compressible TAU solver. Therefore a wall modelled LES
+methodology is locally applied to the nacelle lower surface in order to
+examine shock induced separation. In this context a synthetic turbu-
+lence generator (STG) is used to shorten the adaption region at the
+RANS – LES interface. Prior to the actual examinations, fundamen-
+tal features of the simulation technique are validated by simulations of
+decaying isotropic turbulence as well as a flat plate flow. For the aircraft
+- nacelle configuration at a Reynolds number of 3.3 million a sophisti-
+cated mesh with 420 million points was designed which refines 32 % of
+the outer casing surface of the nacelle. The results show a development
+of a well resolved turbulent boundary layer with a broad spectrum of
+turbulent scales which demonstrates the applicability of the mesh and
+method for aircraft configurations. Furthermore, the necessity of a low
+dissipation low dispersion scheme is demonstrated. However, the dis-
+tinct adaption region downstream of the STG limits the employment
+of the method in case of shock buffet for the given flow conditions.
+Keywords: hybrid RANS-LES, wall-modelled LES, synthetic turbulence,
+aircraft configuration, transonic flow, shock induced separation
+1
+arXiv:2301.05299v1  [physics.flu-dyn]  12 Jan 2023
+
+Springer Nature 2021 LATEX template
+2
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+1 Introduction
+Transonic flows about aircraft configurations exhibit complex, instationary
+flow phenomena such as oscillating shock fronts with boundary layer sepa-
+ration. This so-called buffet phenomenon causes unsteady aerodynamic loads
+which might endanger the flight safety. Therefore a fundamental understand-
+ing of the related flow physics is of particular interest to be able to find
+specific technical solutions which control this phenomenon. The present study
+examines a XRF-1 aircraft model which represents a wide-body long-range con-
+figuration and was designed by Airbus. An Ultra High Bypass Ratio (UHBR)
+nacelle is coupled to the model which represents a modern and efficient jet
+engine that is modelled as flow-through nacelle for wind tunnel testing. Due
+to the large circumference of the nacelle, a close coupling by means of a pylon
+to the wing lower side is necessary. This channel-like arrangement of nacelle,
+pylon, wing and fuselage causes the development of an accelerated flow which
+triggers the formation of transonic shocks within this area. Depending on the
+exact flow conditions these shocks evolve into buffet with significant loads.
+Initial investigations in the framework of the DFG (Deutsche Forschungsge-
+meinschaft) funded research group have shown a complex system of shock
+fronts [1]. As a first step toward representing this complex system with a sophis-
+ticated numerical method this study focuses on a single shock front located at
+the lower side of the nacelle.
+Numerous numerical investigations have investigated the problem of buf-
+fet onset with well established unsteady Reynolds-averaged Navier-Stokes
+(URANS) methods. However, it is well known that even highly developed
+Reynolds stress based URANS models show deficiencies in describing the
+dynamics of separated boundary layer as well as the aerodynamic effects of
+large flow separations [2]. Also, due to high, flight relevant Reynolds numbers
+a broad scale of turbulent structures arise for the given flow phenomenon.
+Therefore a simulation technique that provide both high spatial and temporal
+resolution is required. Direct Numerical Simulation (DNS) resolves all turbu-
+lent scales but is so far restricted to simple geometries at low Reynolds numbers
+due to its unfeasible computational effort for flight relevant flows. Therefore a
+Large Eddy Simulation (LES) technique is required which only resolves large
+turbulent scales whereas small, isotropic scales are modelled. Since an appli-
+cation of LES to the entire aircraft configuration is still computationally too
+expensive a hybrid RANS - LES technique is employed. In the present study the
+wall modelled LES (WMLES) method within the Improved Delayed Detached
+Eddy Simulation (IDDES) methodology is used [3]. Depending on the spatial
+discretisation, up to 5 % of the wall adjacent boundary layer is modelled by
+the RANS equations. Additionally, the area of WMLES is embedded around
+the transonic shock such that all relevant flow areas are enclosed. This cor-
+responds to 32 % of the outer casing surface of the nacelle. The remaining
+flow field of wing, body, pylon and nacelle is modelled with a URANS model.
+The embedded WMLES (EWMLES) requires an injection of synthetic turbu-
+lence at the RANS-LES interface which is located at the leading edge of the
+
+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+3
+nacelle for the present configuration. Otherwise, a so-called grey area would
+arise which describes a region of underresolved turbulence directly downstream
+of the RANS-LES boundary. To this end the synthetic turbulence generator
+(STG) devised by [4] is employed. Nevertheless, using this method, a transi-
+tional region from modelled to fully resolved turbulence is still present and is
+referred to as adaption region in this study. The analysis of this adaption region
+with regard to its length and behaviour of relevant flow quantities in this area
+are of major interest. Thus, especially the transient establishment of resolved
+turbulence within the WMLES area and the fundamental applicability of the
+method to the aircraft configuration are the focus of this study.
+The study is structured as follows. The employed WMLES model in
+conjunction with the STG is described in detail in subsection 2.1 and 2.2,
+respectively. Subsequently a thorough description of the employed low dissi-
+pation low dispersion (LD2) numerical scheme is given in 2.3. The following
+section 3 provides a basic validation of the Embedded WMLES based on the
+SST-RANS model by means of flows of decaying isotropic turbulence and a
+flow about a flat plate. The results of the application to the XRF-1 configu-
+ration are presented in section 4. An extensive description of the mesh design
+with regard to the extension of the WMLES area, the used refinement criteria
+and its application to the actual mesh environment are presented (Sec. 4.2).
+Results of the transient WMLES establishment are then shown and assessed
+in section 4.3. The analysis of temporally and spatially averaged flow quanti-
+ties in the area related to the STG is carried out (Sec. 4.4). Finally, sensitivity
+studies with regard to the position of the RANS-LES boundary (Sec. 4.5.1)
+and the effect of using a standard numerical scheme instead of the low dissipa-
+tion scheme (Sec. 4.5.2) is presented. This paper is closed by a final summary
+of all research findings (Sec. 5).
+2 Numerical Methods
+The flow simulations in this paper use the unstructured compressible DLR-
+TAU code [5] which numerically solves the flow and model equations on
+mixed-element grids (e.g. hexahedra, tetrahedra, prims) via the finite-volume
+approach. It applies 2nd-order discretization schemes for both space and time,
+together with low-Mach-number preconditioning for flows that are close to
+the incompressible limit. Implicit dual-time stepping allows adapting the time
+step in unsteady simulation to the physical requirements (i.e. related to the
+convective CFL-criterion), avoiding numerical stability restrictions.
+The relevant methods for embedded wall-modelled LES, i.e. the overall
+(hybrid) turbulence model, the method to generate and inject synthetic turbu-
+lence and the required local adaptation of the numerical scheme, are outlined
+in the following.
+
+Springer Nature 2021 LATEX template
+4
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+2.1 Hybrid RANS-LES Model
+The present embedded wall-modelled LES approach relies on the Improved
+Delayed Detached-Eddy Simulation (IDDES) [3] which combines local RANS,
+DES (i.e. RANS-LES) and wall-modelled LES (WMLES) functionalities in a
+seamless, automatic manner. This is achieved by a single hybrid length scale
+replacing the integral turbulent scale lRANS in the underlying RANS model,
+which is the two-equation SST model [6] in the present work. The hybrid length
+scale reads:
+lhyb = ˜fd (1 + fe) lRANS +
+�
+1 − ˜fd
+�
+lLES
+.
+(1)
+Here, the function ˜fd = max {(1 − fdt) , fB} is the main blending switch
+between the different modelling modes, where fdt and fB depend on local grid
+and flow properties (cf. [3]).
+In WMLES mode (fdt ≡ 1 and, thus, ˜fd ≡ fB), if resolved turbulent
+content enters an attached boundary layer, a RANS layer is kept near the
+wall and sized according to the local grid resolution, thus circumventing the
+extreme grid requirements of wall-resolved LES at high Reynolds numbers.
+However, since no wall-functions are applied in the present work, the equations
+need to be solved down to the wall with a (normalized) near-wall grid spacing
+of y+(1) ≤ 1. The additional elevating function fe is designed to reduce the
+well-known log-layer mismatch in WMLES.
+In the largest (outer) parts of the boundary layer, lhyb ≡ lLES = CDES∆,
+which approximates the behaviour of a Smagorinsky-type sub-grid model for
+LES. The model constant CDES is usually calibrated for canonical turbulent
+flow, such as decaying isotropic turbulence (DIT), see Sec. 3.1. However, since
+wall-bounded flows typically require a different calibration than free turbu-
+lence, another modification compared to standard DES/LES is introduced in
+the filter width ∆:
+∆ = ∆IDDES = min {max [Cw · dw, Cw · hmax, hwn] , ∆DES}
+,
+(2)
+where Cw = 0.15. In essence, this near-wall limitation of the filter width
+compensates for this flow-type dependency and allows using a unique CDES
+value for both wall-bounded and off-wall turbulent flow. More details on this
+modification are found in [3].
+For embedded WMLES, the IDDES in TAU can be locally forced to
+WMLES mode according to external user input, e.g. inside boxes or other suit-
+able geometric sub-areas of the flow domain. This is achieved by setting the
+function fdt to 1 downstream of the desired RANS-WMLES interface, thus
+safely reducing the eddy viscosity from RANS to WMLES level [7].
+2.2 Synthetic Turbulence Generation
+In this work, synthetic turbulent fluctuations at the streamwise RANS-LES
+interface are provided by the Synthetic Turbulence Generator (STG) of
+
+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+5
+Adamian and Travin [8] with extensions for volumetric forcing by Francois [9].
+This STG generates local velocity fluctuations from a superimposed set of N
+Fourier modes as:
+⃗u′
+ST = ⃗A ·
+√
+6
+N
+�
+n=1
+√qn
+�
+⃗σn cos
+�
+kn ⃗dn · ⃗r′ + φn + sn t′
+τ
+��
+,
+(3)
+where the direction vectors ⃗dn and ⃗σn ⊥ ⃗dn, the mode phase φn, and the mode
+frequency sn are randomly distributed. A realistic spectral energy distribution
+of the mode amplitudes qn is achieved by constructing a von K´arm´an model
+spectrum from RANS input data and a local grid cut-off. The RANS data,
+which is automatically extracted from just upstream the RANS/LES inter-
+face, is also used to scale the fluctuations via the Cholesky-decomposed RANS
+Reynolds-stress tensor ⃗A.
+For realistic temporal correlations in a volumetric forcing domain, the posi-
+tion vector ⃗r′ and the time t′ are modified in accordance with Taylor’s frozen
+velocity hypothesis, see [9] for details.
+Synthetic-Turbulence Injection
+To inject the synthetic fluctuations from Eq. (3), a forcing volume with a
+streamwise extent of about half the local boundary-layer thickness is marked
+just downstream of the RANS/LES interface. Inside this volume, a momentum
+source term is added [10] which approximates the partial time derivative of
+the synthetic fluctuations as:
+⃗Q = ∂ (ρ⃗u′
+ST )
+∂t
+≈ 3 (ρ⃗u′
+ST − ρ⃗u′n) −
+�
+ρ⃗u′n − ρ⃗u′n−1�
+2∆t
+.
+(4)
+This discretization corresponds to the 2nd-order backward difference scheme
+used for unsteady simulations with TAU. By computing the fluctuation values
+of the previous time steps from the actual flow field, i.e. as ⃗u′n = ⃗un − ⟨⃗u⟩ and
+⃗u′n−1 = ⃗un−1 −⟨⃗u⟩, the synthetic target field (Eq. 3) can be reproduced rather
+accurately in the simulation, even though running time averages are required.
+An additional Gauss-like blending function with a maximum value of 1 around
+the streamwise center of the forcing volume is multiplied to the source term
+in order to prevent abrupt variation of the forcing.
+2.3 Hybrid Low-Dissipation Low-Dispersion Scheme
+Since scale-resolving simulation methods like IDDES involve explicit modelling
+of the sub-grid stresses, the overall accuracy relies on low spatial discretization
+errors in the LES regions of a given grid. Concerning resolved turbulence, there
+are two types of error that mainly stem from the discretized convection of
+momentum: while numerical dissipation damps the turbulent fluctuations and
+
+Springer Nature 2021 LATEX template
+6
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+would lead to under-predicted Reynolds stress, numerical dispersion distorts
+the shape of resolved turbulent structures.
+For that reason, the present simulations apply a hybrid low-dissipation
+low-dispersion scheme (HLD2) [11], which combines different techniques to
+optimize the convection scheme for local scale-resolving simulations using
+unstructured finite-volume solvers.
+To provide low numerical dissipation, the spatial fluxes are calculated
+from Kok’s [12] skew-symmetric central convection operator, which allows for
+kinetic-energy conservation (i.e., it is non-dissipative) on curvilinear grids in
+the incompressible limit. For compressible flow on general unstructured grids,
+a classic blend of 2nd- / 4th-order artificial matrix-dissipation is added to
+ensure stability around shocks and in smooth flow regions. Compared to RANS
+computations, however, the 4th-order dissipation has been strongly reduced
+by manually optimizing its parameters in LES computations of the channel
+flow, yielding e.g. a global scaling factor of κ(4) = 1/1024 and a reduced
+Mach-number cut-off in the low-Mach-number preconditioning matrix.
+Moreover, to minimize the dispersion error of the second-order scheme, the
+skew-symmetric central fluxes are based on linearly-reconstructed face values
+φL,ij, φR,ij using the local Green-Gauss gradients ∇0φ. Exemplarily, a generic
+central flux term reads:
+φij,α = 1
+2 (φL,ij + φR,ij) = 1
+2 (φi + φj) + 1
+2α (∇0φi − ∇0φj) · dij
+,
+(5)
+where dij is the distance between the points i and j. With an extrapolation
+parameter of α = 0.36 the scheme was found to minimize the required points
+per wavelength for achieving a given error level in a 1-D wave problem, see
+[13] for details.
+Blended Scheme for Hybrid RANS-LES
+While the low-error properties of the LD2 scheme are essential for accurate
+LES and WMLES predictions with TAU [11], the pure RANS and outer flow
+regions in hybrid RANS-LES are less dependent on such numerical accuracy.
+Moreoever, although the LD2 scheme has been globally applied in hybrid
+RANS-LES, complex geometries like the present XRF-1 configuration and cor-
+responding unstructured grids may induce local numerical instabilities that
+are not damped by low-dissipative schemes. For this reason, we apply the LD2
+scheme in a hybrid form [11] where all parameters of the spatial scheme, Ψi,
+are locally computed from a blending formula:
+Ψi = (1 − σ) · Ψi,LD2 + σ · Ψi,Ref
+.
+(6)
+Here, Ψi,LD2 are the parameter values of the LD2 scheme (e.g. κ(4) = 1/1024,
+α = 0.36), whereas Ψi,Ref corresponds to standard central-scheme parameters
+typically used in RANS computations (e.g. κ(4) = 1/64, α = 0). The blending
+
+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+7
+function σ is adopted from [4] and discerns between the well-resolved vortex-
+dominated flow regions (LD2) and coarse-grid irrotational regions (Ref ).
+By now, the hybrid LD2 scheme (HLD2) has been successfully applied
+in a number of hybrid RANS-LES computations ranging from canonical
+flows on structured grids [11] to complex high-lift aircraft on mixed-element
+unstructured meshes [14].
+3 Basic Validation of Embedded WMLES
+Before analyzing the embedded WMLES approach from Sec. 2 for a complex
+transonic aircraft configuration with UHBR nacelle in Sec. 4, we investigate
+and demonstrate its basic scale-resolving functionalities in fundamental test
+cases, i.e. decaying isotropic turbulence for pure LES and a developing flat-
+plate boundary layer for WMLES.
+3.1 Decaying Isotropic Turbulence
+Although SST-based IDDES is a well-known hybrid model present in many
+CFD codes, a proper verification for a given flow solver and the applied
+numerical scheme requires fundamental tests of the different modelling modes.
+This includes the pure LES functionality, where the hybrid model acts
+as Smagorinsky-type sub-grid model and mostly relies on the ”outer-flow”
+calibration constant of SST-based IDDES, i.e. CDES = 0.61.1
+For this reason, we present for the first time TAU simulations of decaying
+isotropic turbulence (DIT) using SST-IDDES with the LD2 scheme and com-
+pare the results with classic experimental data from [15]. In particular, the
+turbulent-kinetic-energy (TKE) spectra at two different time levels after the
+start of decay, i.e. t = 0.87 s and t = 2.0 s, are considered. Additionally, to
+emphasize the effect of the LD2 scheme, further SST-IDDES simulations are
+performed using a reference central-scheme with higher artificial dissipation
+(cf. Eq. 6 in Sec. 2.3).
+As for the computational setup, a cubic domain with normalized edge
+length of 2π is discretized by Cartesian meshes with 323, 643 and 1283 cells,
+respectively. Periodic boundary conditions are applied in all three directions.
+The initial velocity field has been generated by a Kraichnan-type synthetic
+turbulence approach [16] and retains the TKE spectrum of the experiment at
+t = 0 s. Due to the compressible formulation of the DLR-TAU code, appropri-
+ate initial density and pressure fields are derived from the isentropic relations of
+compressible fluids, describing the change of state from stagnation (Ma∞ = 0)
+to the local Mach number, i.e. ρ/ρ∞ = f (Ma) and p/p∞ = f (Ma). Moreover,
+the initial fields of modeled TKE and specific dissipation rate ω are computed
+in a preliminary steady-state SST-IDDES computation, where all equations
+except for the hybrid turbulence model are frozen. The temporal resolutions
+1Note that the calibration constant in SST-based DES-variants takes a different value close to
+walls, but this region is usually treated in RANS mode anyway..
+
+Springer Nature 2021 LATEX template
+8
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+Fig. 1 TKE spectra of decaying isotropic turbulence (DIT) for two different times along
+with experimental data [15]. Results for the LD2 scheme (left) and a reference central-scheme
+(right) are shown.
+of ∆t/s ∈ { 5·10−3, 5·10−3, 2·10−3} for the coarse, middle and fine grid were
+determined in time-step convergence studies.
+Fig. 1 (left) shows the results for the SST-IDDES with LD2 scheme which
+demonstrate a good agreement with the experimental results for all spatial
+resolutions and both time levels. For the reference central-scheme however,
+the picture is different. Although there are agreements with the experimental
+results for small wave numbers scales k+ ≤ 8 for all resolutions and time levels,
+deviations arise for larger wave numbers. These deviations are growing with
+increasing wave number and finally result in a significant underestimation of
+the TKE for all setups.
+As a result we successfully demonstrated the LES functionality of SST-
+IDDES in conjunction with the LD2 scheme. The low dissipation feature of
+the numerical scheme was confirmed and additionally emphasized by reference
+simulations with higher artificial dissipation.
+3.2 Developing Flat Plate Boundary Layer
+For a basic assessment of the full embedded WMLES functionality, we consider
+the test case of a developing flat-plate boundary layer, which transitions from
+RANS to WMLES at a fixed streamwise position. It starts with zero thickness
+at the inflow and is computed in SST-RANS mode up to the position, where
+the momentum-thickness Reynolds number reaches Reθ = 3040. Here, a zonal
+switch to WMLES within IDDES is placed, along with a synthetic-turbulence
+forcing region of about half a boundary layer thickness in streamwise direction,
+see Sec. 2.2.
+A hybrid grid with 5.8 million points and hexahedral cells in the WMLES
+area is used, which ensures ∆x+ ≈ 100 − 200, ∆y+ ≈ 1, ∆z+ ≈ 50 like the
+structured grid used in [17]. More relevant for WMLES, the streamwise spacing
+fulfills ∆x ≤ δ/10 throughout the flow domain, where δ is the approximate
+local boundary layer thickness. The normalized timestep (in wall units) is
+
+E+
+10-2
+10
+Experiment t = 0.84
+Experiment t = 2
+SST -- IDDES, 323, LD2
+SST -- IDDES, 643, LD2
+SST -- IDDES, 1283, LD2
+k*
+20
+40
+60E+
+10
+10
+Experiment t = 0.84
+Experiment t = 2
+SST -- IDDES, 323, ref. Scheme
+SST -- IDDES, 643, ref. scheme
+SST -- IDDES. 128, ref. scheme
+k*
+20
+40 
+60Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+9
+Fig. 2 Evolution of averaged skin friction along streamwise position x of the flat plate test
+case.
+∆t+ ≈ 0.4 and safely fulfills the convective CFL criterion (CFLconv < 1) in
+the whole LES region.
+The statistical input data for the STG methods is given by external input
+from a precursor RANS profile at Reθ = 3040 which has been augmented with
+an anisotropic normal-stress approximation according to [18].
+The spanwise and temporal averaged results of the skin friction distribu-
+tion mean-cf are depicted in Fig. 2 along with the Coles-Fernholz correlation
+[19]. After an initial overshoot of mean-cf at the position of the STG, mean-cf
+shows good agreement with the Coles-Fernholz correlation and remains within
+an acceptable error margin of 5 %. Note that the adaption region downstream
+of the STG is hardly visible but still present. This region is defined as underpre-
+diction of mean-cf compared to the previous mean-cf level directly upstream
+of the STG. The adaption-length which respresents the distance between the
+position of the STG and the first peak in mean-cf downstream of the overshoot
+amounts 7 δST G where δST G is the boundary layer thickness at the position of
+the STG. Within this adaption region the sum of modelled and resolved tur-
+bulent stresses are lower than the previous level of modelled turbulence of the
+RANS region which results in an underprediction of mean-cf [20].
+Finally, this examination confirms the embedded WMLES functionality of
+SST-IDDES with STG for a flat plate flow. Thus this methodic is basically
+verified for comparable geometry sections at the XRF-1-UHBR configuration.
+4 Grey-Area Investigation on Nacelle-Aircraft
+Configuration
+4.1 Geometry, Flow Conditions and RANS Mesh
+The actual target configuration consists of a half model of a modern trans-
+port aircraft configuration in conjunction with a through flow nacelle (cf. Fig.
+3). The employed XRF-1 aircraft model represents a wide-body long-range
+
+0.004
+0.003
+mean-cf
+0.002
+0.001
+Coles-Fernholz
+SST - IDDES + STG (LD2)
+0
+20
+40
+60
+X/Springer Nature 2021 LATEX template
+10
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+research configuration and is designed by Airbus. A Ultra High Bypass Ratio
+(UHBR) nacelle is integrated with the aid of a pylon and positioned close to
+the wing lower side. The UHBR design consists of an outer casing and a core
+body with plug. The casing is shaped circularly with a cross section similar to
+an airfoil. Both, nacelle and a specifically designed pylon were developed by
+DLR [1].
+In order to find a suitable flow condition with shock induced separation in
+the surrounding of the nacelle surface a comprehensive numerical study was
+performed where various high speed off-design conditions were assessed. As
+key parameter for the occurrence of transonic shocks at a Reynolds number
+of Re = 3.3 million a low angle of attack (α) was identified. For a farfield
+Mach number of 0.84 and α = −4◦ shock induced separation is present at
+the wing lower side, the pylon and the nacelle. A single, locally separated
+transonic shock could be found at the outer surface of the nacelle lower side
+(cf. Fig. 4). Thus, a flow condition which allows to examine an isolated shock
+with subsequent boundary layer separation in the context of a nacelle-aircraft
+configuration was found.
+In a prelinimary work a high quality RANS mesh for the XRF-1 - UHBR
+half model was designed and constructed by projects partners of the research
+unit at the University of Stuttgart and DLR. The surface RANS mesh mainly
+consists of structured areas which are extruded to hexahedral blocks. These
+are designed to contain the entire RANS boundary layer with a safety factor
+of 2. The wall adjacent cell spacing fulfills y+(1) ≤ 0.4 and a growth rate of
+1.12 is applied in wall normal direction. A h-type mesh topology is employed
+at the intersections of the aircraft components to be able to accurately resolve
+flow features in these areas. The farfield region is discreticed by tetrahedra
+and extends to 50 wingspans in all coordinate directions. The total grid size
+before refinement amounts 112 million points.
+4.2 Grid Design for Embedded WMLES
+In the following the mesh design for the WMLES refinement region is intro-
+duced. A sophisticated meshing strategy, that aims to reduce the grid size
+as far as possible but follows basic refinement and extension constraints for
+WMLES, is developed. This is necessary in order to limit mesh size and result-
+ing computing time to a reasonable level. Special care was taken to the mesh
+resolution of all coordinate directions (∆x, ∆y and ∆z) which depend on the
+local boundary layer thickness δ. Additionally, a potential shock movement is
+considered with regard to the refinement extension as well as mesh resolution.
+The refinement region is embedded within the previously described RANS
+mesh with the aid of unstructured bands in the surface mesh (cf. Fig. 4 and
+Fig. 5). This strategy allows to drastically increase the resolution within the
+structured boundary layer such that the surrounding RANS region remains
+unchanged. An unstructured nearfield block, which is also present in the pure
+RANS mesh, serves as an interface between the hexahedral blocks and the
+
+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+11
+Fig. 3 Bottom view of XRF-1 - aircraft configuration with UHBR nacelle. The nacelle
+lower side includes the mesh refinement region for embedded WMLES.
+farfield, exhibits a mesh decay rate of 0.85. The total mesh size of the combina-
+tion of RANS mesh and refinement region for WMLES comprises 420 million
+points.
+4.2.1 Extension of the refinement region
+To describe locations on the nacelle surface more precisely a cylindrical coor-
+dinate system r, ϕ and x/c is introduced, where c represents the nacelle chord
+length. Its reference point r = 0, x/c = 0 is located in the nacelle center within
+a cross section that includes the entire nacelle leading edge. ϕ is set to 0◦ at
+the intersection between nacelle and pylon and increases in clockwise direction
+that 90◦ points towards the fuselage.
+According to [21] the first step in designing hybrid RANS LES mesh for
+DES based algorithms is the definition of the RANS and LES regions for the
+given configuration. Since the aim of this research topic is the application of a
+WMLES methodology to a flow region with shock induced separation, all flow
+regions directly related to this phenomenon are of interest and should be highly
+resolved. The primary region is the area of recirculation (AOR) downstream
+of the shock position (cf. Fig. 4 left). Flow regions related to this are the
+attached boundary layer upstream of the AOR and separated boundary layer
+downstream of the AOR until the trailing edge of the nacelle. To this end the
+average shock front position and extension of the AOR are calculated by a
+preceding SST-RANS calculation. Fig. 4 (left) shows a surface plot of the skin
+friction coefficient (cf) where the cf is only plotted for cf < 0 which serves as
+an indicator of the AOR. The refinement region in spanwise direction (ϕ) is
+chosen such that the entire area of recirculation is included with some margins
+in ϕ-direction and extends 105◦ starting from 120◦ until 225◦ (cf. Fig. 4).
+
+X
+ZSpringer Nature 2021 LATEX template
+12
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+Fig. 4
+Bottom view of the UHBR-nacelle. Left: Area of recirculation of SST-RANS solu-
+tion for Ma∞ = 0.84 and α = −4◦. The shown RANS surface mesh already includes the
+boundaries for the refinement region in form of unstructured streaks. Right: Extension of
+refinement area with stepwise increase in streamwise direction. The colorbar visualizes the
+cell surface area where yellow and purple represent large and low areas, respectively.
+Since the boundary layers thickness is not only a function of x but also
+of ϕ we introduce the new variables δϕ,max(x) and δϕ,min(x) which refer to
+the maximum and minimum boundary layer thickness for a given streamwise
+position x. In x/c direction the refinement is applied between xa/c = 0.06
+and xb/c = 1. The choice of xa/c = 0.06 as the most upstream position
+is the result of the dependence of mesh resolution on the boundary layer
+thickness δϕ,min(x). The smaller the boundary layer thickness δϕ,min(x) at
+location xa the smaller the required cell lengths ∆ζ(xa) for ζ ∈ {r, ϕ, x}
+since ∆ζ(x) ≤ δϕ,min(x)/10. The refinement in wall normal direction r is
+applied for wall distances that hold dw(x) ≤ 1.2 · δϕ,max(x) in the interval
+0.06 ≤ x/c ≤ 0.16 and dw ≤ 1.5 · δϕ,max(x) within 0.16 ≤ x/c ≤ 1. Thus dw/c
+ranges from 0.2% at x/c = 0.06 to 15% at the trailing edge (cf. Fig. 4 right).
+Although these distances are smaller than dw ≤ 2 · δ(x) suggested by [22] we
+show in Sec. 4.3 that the whole resolved boundary layer remains within the
+refined area with distance drefined(x) over the entire simulated time period.
+Additionally, the extension of the refinement area in r-direction also consid-
+ers a potential oscillation of the boundary layer separation point around its
+average position at xs/c = 0.13 (SST-RANS solution). We assumed an oscil-
+lation amplitude of ±0.03 c which also allows to employ this mesh in case of
+shock buffet. As a consequence, at position x/c = 0.16 a refinement distance
+of drefined(0.16c) = 1.2 · δϕ,max(0.19c) is used.
+4.2.2 Resolution of the refinement region
+The resolution in x-direction depends on the local boundary layer thick-
+ness and is set to a limit of ∆x(x) ≤ δϕ,min(x)/10 which leads to a total
+number of 1350 points in x-direction from the leading edge to the trail-
+ing edge. Again an oscillation of separation due to shock buffet point is
+considered. Thus it is assumed to have a attached boundary layer until
+
+C,<0
+XZSpringer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+13
+Fig. 5 Surface mesh of refinement region on lower side of UHBR nacelle. Left:
+Discrete
+coarsening of ∆ϕ is apparent which subdivides the refinement area into five subregions.
+Right:
+Vertical unstructured (triangular based) streak enables to refine locally and keep
+surrounding RANS resolution untouched. Horizontal unstructured stripe allows to coarsen
+the refinement region in ϕ-direction.
+xs/c = 0.13 + 0.03 leading to reduced boundary layer thickness compared to
+the preliminary SST-RANS solution. Therefore the boundary layer thickness
+at x/c = 0.16 is estimated to δϕ,min(x/c = 0.08) · 24/5 according to turbu-
+lent boundary layer theory. As before the resolution in ϕ-direction is limited
+to r∆ϕ(x) ≤ δϕ,min(x)/10. In contrast to the resolution in x-direction the
+adaption of ∆ϕ(x) to δϕ,min(x) is realised in a discrete manner. Therefore the
+refinement region is separated into five subregions with its boundaries located
+at x/c ∈ {0.06; 0.16; 0.25; 0.4; 0.82; 1} (cf. Fig. 5). ∆ϕ(x) remains con-
+stant within each subregion Ωi and is set to r∆ϕ(x ∈ Ωi) = δϕ,min(xi)/10 with
+xi defined as the most upstream position of Ωi. With this protocol the res-
+olution in ϕ-direction is always smaller than δϕ,min(x)/10 which results into
+{4350; 1660; 870; 603; 250} points in ϕ-direction within the correspond-
+ing subregion. Without this stepwise increase of ∆ϕ the total grid number
+would increase by a factor of 3 to 1.2 · 109 points. Again a potential move-
+ment of the boundary layer separation point is considered and therefore
+r∆ϕ(x = 0.16c) =
+1
+10δϕ,min(x = 0.08c) · 24/5. In r-direction the wall normal
+spacing of the wall adjacent cells is limited to r+(1) = 0.4. The cells of the
+entire refinement area are extruded geometrically with a growth factor of 1.12
+until ∆r = ∆x(x = 0.06c) is reached and ∆r is initially kept constant to obtain
+locally isotropic cells. Since the distance of the refinement region drefined(x)
+increases in x-direction in a cascading manner (cf. Fig. 4 (right) and 6) the
+geometric growth is continued for refinement areas with larger wall distances.
+Exemplarily, ∆r is further increased to ∆r = ∆x(x = 0.16c) for wall distances
+in the interval drefined(x = 0.16c) ≤ r ≤ drefined(x = 0.25c) and applied
+where 0.16 ≤ x/c ≤ 1. Subsequently ∆r is again increased until ∆r = ∆x(x =
+
+X
+Y
+ZSpringer Nature 2021 LATEX template
+14
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+Fig. 6 Cross section of nacelle lower side at ϕ = 180◦. Subregion Ω1 (0.06 ≤ x/c ≤ 0.16)
+of the refinement region includes 200 Mio. cells which corresponds to 48% of the entire grid
+size.
+0.25c) for wall distances in the intervall drefined(x = 0.25c) ≤ r ≤ drefined(x =
+0.4c) and applied where 0.25 ≤ x/c ≤ 1. This protocol is repeated until ∆r
+amounts ∆r = ∆x(x = 0.82c) for drefined(x = 0.82c) ≤ r ≤ drefined(x = 1c)
+and 0.82 ≤ x/c ≤ 1. Finally, the total number of grid points in wall normal
+direction comprises {113; 168; 183; 230; 258} points within the corresponding
+subregion.
+4.3 Results of Transient WMLES Establishment
+As initial solution for the SST-IDDES a converged SST-RANS solution
+was employed. The physical time step size amounts ∆t = 5.5 · 10−8 s =
+1/16750 CTU where 1 CTU = u∞ · c represents a single convective time unit
+(CTU). ∆t is chosen that CFL < 1 is fulfilled for all grid cells.
+Fig. 7 represents the temporal evolution of the Mach number in a cross
+section at ϕ = 180◦ and four different times. With regard to the turbulent
+boundary layer thickness δ it should be noted that δ is entirely located within
+the refinement volume with sufficient distance to its boundary (indicated by
+black lines). After the depicted maximal extension at 0.5 CTU the boundary
+layer thickness significantly decreases at later times. This decrease appears
+to be related with the shock movement in downstream direction since this
+correlation is also observed for various transonic flows of wing profiles [23].
+As mentioned before the root of the shock front xs is moving from its initial
+SST-RANS position xs(t0) = 0.13c downstream to xs(t1 CTU) = 0.17c and
+remains at the same position until xs(t1.5 CTU). Although xs is located further
+downstream as we assumed for the mesh design (0.1 ≤ xs/c ≤ 0.16) one has
+to note that such shock displacements are common in transient simulations
+(e.g. t ≤ 7.5 CTU). The shock position will most likely move upstream again
+for more advanced simulation times.
+Another perspective on the temporal evolution is given in Fig. 8. Here the
+cf-distribution is shown at four different times. This figure confirms that the
+resolved turbulence develops over the entire refinement area. The transonic
+shock front is visible in form of a sudden decrease in cf. As in Fig. 7 it can
+be seen that the whole front is moving downstream until it remains in an area
+of 0.16 ≤ xs/c ≤ 0.2. A minor numerical effect appears at the lateral edge
+
+-0.7
+-0.75
+-0.8
+-0.85
+-0.9
+0.4
+0.8
+0
+0.2
+0.6
+X/cSpringer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+15
+Fig. 7
+Ma-number fields within a cross section of the refinement volume at ϕ = 180◦ for
+four different times.
+of the refined mesh in ϕ-direction where underresolved turbulence is present.
+This is due to the fact that the STG does not directly connect to the lateral
+RANS zones at the edges of the refinement region. Therefore two small gaps
+appear where little resolved and significantly reduced modelled turbulence
+exists which result in low values of cf. This artefact can easily be circumvented
+in future simulations by narrowing the LES zone in spanwise direction and
+thus generate modelled turbulence in the respective regions. Nevertheless, the
+
+Ma 0.1
+0.5
+0.9
+1.3
+1.7
+-0.76
+-0.78
+-0.8
+N
+-0.82
+-0.84
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.3
+0.35
+0.02 CTU
+x/c-0.76
+-0.78
+C
+-0.8
+N
+-0.82
+-0.84
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.3
+0.35
+0.5 CTU
+x/c-0.76
+-0.78
+-0.8
+N
+-0.82
+-0.84
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.3
+0.35
+1 CTU
+x/c-0.76
+-0.78
+-0.8
+N
+-0.82
+-0.84
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.3
+0.35
+1.5 CTU
+x/cSpringer Nature 2021 LATEX template
+16
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+described phenomenon is limited to the boundaries and does not affect the
+actual focus region.
+To give an impression of the vortex structure of the resolved turbulence an
+isosurface of the Q-criterion (Q = 1010) at t = 1.5 CTU is depicted in Fig.
+9. As already observed in Fig. 8 an extensive formation of turbulent struc-
+tures within the refinement region is present. These structures are growing
+with increasing streamwise position and partially evolve into horseshoe vortices
+which corresponds to expected flow behaviour.
+4.4 Investigation of grey area
+In the following a quantitave analysis of the grey area / adaption region is
+performed. Therefore the flow field was averaged with regard to time and
+spanwise direction ϕ. The temporal average was applied for 0.42 ≤ t/CTU ≤
+1.5. The start time t = 0.42 is chosen such that the resolved turbulence is
+completely established within the focus region (0.06 ≤ x/c ≤ 0.25) and no
+remains of the initial RANS-solution are present in this area (cf. Fig. 8 at
+t = 0.5 CTU). The spanwise average was applied over the refinement section
+such that the areas of underresolved turbulence at its margins were omitted
+(ϕ ∈ [125◦; 220◦]).
+Fig. 10 (top) shows the result of the EWMLES mean pressure distribution
+(mean-cp) along with the initial RANS solution. Good agreement between
+these curves are present for x/c ≤ 0.13 where x/c = 0.13 is the average location
+of the shock front of the SST-RANS solution which results into a sudden rise in
+mean-cp. It is apparent that this agreement also persists for positions upstream
+of the STG (x/c ≤ 0.06) which indicates that no upstream effect of the STG
+exists. With regard to the EWMLES shock position the already described
+shift in downstream direction is also present in this depiction and located at
+x/c = 0.15. Due to the comparatively early start in the averaging of mean-cp
+it is not reasonable to compare the curves for x/c ≥ 0.3 since transient effects
+from the switch from RANS to EWMLES still exist in this area.
+A further quantitive flow comparison between SST-RANS and EWMLES is
+given in Fig. 10 (bottom) which shows mean skin friction distributions (mean-
+cf). In the flow region upstream of the STG (x/c ≤ 0.06) good agreement
+are visible again which confirms the previously mentioned absence of potential
+STG upstream effects. However, for 0.06 ≤ x/c ≤ 0.16 remarkable deviations
+appear. One observes a significant drop in mean-cf directly downstream of
+the STG and its increase with a peak value at x/c = 0.13 and a mean-cf-
+level which is comparable to the mean-cf value at the STG position. Although
+a similar behaviour is present for the flat plate flow as described in Sec. 3.2
+the flat plate variations in mean-cf are of significantly smaller. The adaption
+length which measures the distance between STG position and subsequent
+peak in mean-cf amounts 46 δST G where δST G represents the boundary layer
+thickness at the STG position. In case of the flat plate flow this adaption
+length only amounts 6 δST G (cf. Fig. 2). A further analysis of these deviations
+with reference to the flat plate flow are given in Sec. 4.6. Considering now the
+
+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+17
+Fig. 8 Temporal evolution of cf-distribution within the refinement area on projected nacelle
+surface.
+
+0.000
+0.002
+0.003
+0.005
+0.007
+0.008
+0.010
+0.65
+y/c
+0.6
+0.55
+0.5
+0.45
+0.4
+0.35
+0.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+0.02 CTU
+X/C0.65
+C
+0.6
+0.55
+0.5
+0.45
+0.4
+0.35
+0.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+0.5 CTU
+X/C0.65
+0.6
+0.55
+0.5
+0.45
+0.4
+0.35
+0.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1 CTU
+X/C0.65
+y/c
+0.6
+0.55
+0.5
+0.45
+0.4
+0.35
+0.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+1.5 CTU
+X/CSpringer Nature 2021 LATEX template
+18
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+Fig. 9 Isosurface of Q-Criterion (Q = 1010) at nacelle lower surface for LD2 scheme at
+t = 1.5 CTU.
+region where 0.16 ≤ x/c ≤ 0.25 we observe that the region of recirculation has
+disappeared, at least for this transient period of time averaging since mean-cf
+is always positive. Furthermore additional distortions in the EWMLES mean-
+cf distribution appear at x/c = 0.25 and x/c = 0.40 which corresponds to
+locations of the ∆ϕ coarsening steps of the mesh (cf. Sec. 4.2.2). This indicates
+that the local mesh resolutions of r∆ϕ = δϕ,min/10 might be locally at the
+lower limit at these positions.
+4.5 Sensitivity studies
+4.5.1 Positioning of the RANS-LES interface
+Preliminary grid number estimations for different locations of the RANS-LES
+interface in x-direction (xST G) demonstrated a strong dependence of xST G
+and the total grid number. A shift of this boundary in downstream direction
+allows to reduce the total grid number significantly. Exemplarily, moving xST G
+by 0.02c enables to reduce the total grid size about 100 Mio points without
+violating the applied extension and resolution constraints for the refinement
+area. This dependence is a consequence of the shortening of the refinement area
+in x-direction by which the subregion with the highest cell density is narrowed.
+Also, due to the dependence of ∆ϕΩ1 on δϕ,min(xST G) in subregion Ω1 it is
+possible to increase ∆ϕΩ1 in the entire interval x/c ∈ [xST G; 0.16] (cf. 4.2.2).
+This dependency on the STG position suggests to place the RANS-LES
+boundary as close as possible to the shock front and examine its effect on the
+flow solution. Based on the original assumption that the adaption length of the
+STG amounts less than 10 δST G we estimated xST G/c = 0.08 as latest possible
+position in order to avoid direct interactions with the shock front. Additionally,
+for this estimation a potential shock movement in upstream direction until
+xs,min = 0.1 was taken into account. For the following examinations we used
+
+Ma 0.2
+0.6
+1.4
+1.8Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+19
+Fig. 10 Quantitave comparison of time and spanwise averaged pressure - (top) and skin
+friction distributions (bottom) between the initial RANS and EWMLES solutions.
+the same mesh as before to verify a basic applicability of a late RANS-LES
+interface.
+Fig. 11 shows mean-cp and mean-cf distributions of the EWMLES results
+for xST G/c = 0.08 (green curves) where the same averaging procedure as in
+Sec. 4.4 is employed. It is striking that the mean-cp distribution is almost
+identical to the previous xST G/c = 0.06 result (red) with maximum deviations
+of two line thicknesses for x/c ≥ 0.16. However, with respect to mean-cf and
+its adaption area downstream of the STG distinct differences compared to the
+xST G/c = 0.06 result exist. Firstly, the initial decay is significantly weaker than
+before. Furthermore, its adaption length is reduced and only amounts 19 δST G
+so that its peak is located at almost the same position as for the xST G/c = 0.06
+result. The peak value though, is significantly reduced and corresponding to
+the initial RANS solution directly upstream of the shock position. A further
+discussion of these features of the adaption regions is given in Sec. 4.6. It is
+remarkable that for x/c ≥ 0.16 the subsequent mean-cf evolution is almost
+identical to the xST G/c = 0.06 result which demonstrates an independence of
+the flow solution with regard to the location of the RANS-LES interface.
+4.5.2 Impact of Numerical Scheme
+A further objective of our research was to compare the effect of different numer-
+ical schemes for the central discretisation of viscous fluxes which is applied in
+the refinement region (LES). In addition to the already employed LD2 scheme
+(Sec. 2.3) a reference central-scheme (Eq. 6 in Sec. 2.3) is applied on the same
+
+RANS
+EWMLES, STG 0.06, LD2
+-1.2
+-1
+mean-cp
+-0.8
+-0.6
+-0.4
+-0.2
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c
+-0.75
+N
+-0.8
+-0.85
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c0.006
+RANS
+EWMLES. STG 0.06, LD2
+0.005
+0.004
+mean-cf
+0.003
+0.002
+0.001
+0
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c
+-0.75
+N
+-0.8
+-0.85
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/cSpringer Nature 2021 LATEX template
+20
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+Fig. 11 Effect of positioning of the RANS-LES interface on averaged surface pressure and
+skin friction distributions.
+numerical setup as in Sec. 4.4. Although the necessity of the high quality LD2
+scheme against the reference scheme has been demonstrated with the aid of
+the DIT-testcase in 3.1 it is not obvious how the reference scheme performs for
+transonic flows on a 3D configuration. To give a qualitative impression of the
+flowfield the Q-Criterion at Q = 1010 for a snapshot at t = 1.5 CTU is shown
+in Fig. 12 which can directly compared to Fig. 9. The comparison shows that
+the previous formation of turbulent structures is now partially interrupted.
+Especially the region directly downstream of the STG lacks turbulent struc-
+tures. It is striking that coarser structures such as the clearly visible horseshoe
+vortexes are preserved whereas tiny structures are vanished. This is in direct
+agreement with the results from the DIT testcase which demonstrates that
+small turbulent scales are strongly damped by the reference scheme (cf. Fig.1).
+These observations are also present in the analysis of the average skin fric-
+tion distribution (blue curve in Fig. 13). Whereas the mean surface pressure
+is hardly affected by the numerical scheme, mean-cf shows large deviations.
+Especially the decay downstream of the STG indicates a lack of resolved
+turbulence. Additionally, compared to the LD2 results the mean-cf level is
+underestimated in the area downstream of the shock - boundary layer interac-
+tion (0.35 ≤ x/c ≤ 0.6). This confirms the previous observation of Fig. 12 of
+underresolved turbulence throughout the entire refinement region.
+
+RANS
+EWMLES, STG 0.06, LD2
+-1.2
+EWMLES, STG 0.08, LD2
+-1
+mean-cp
+-0.8
+-0.6
+-0.4
+-0.2
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c
+-0.75
+N
+-0.8
+-0.85
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c0.006
+RANS
+EWMLES, STG 0.06. LD2
+0.005
+EWMLES, STG 0.08, LD2
+0.004
+mean-cf
+0.003
+0.002
+0.001
+0
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c
+-0.75
+N
+-0.8
+-0.85
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/cSpringer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+21
+Fig. 12 Isosurface of Q-Criterion (Q = 1010) for reference central-scheme at nacelle lower
+at t = 1.5 CTU.
+Fig. 13 Effect of different numerical schemes on averaged surface pressure and skin friction
+distributions.
+4.6 Reynolds number and mesh resolution effect on STG
+adaption region
+In the following we address the so far unsound behaviour of the adaption
+region downstream of the STG arising for all shown configurations. As already
+described before the adaption region displays the largest deviations with regard
+to adaption length as well as maximal and minimal mean-cf-deviations for the
+
+Ma 0.2
+0.6
+1.4
+1.8RANS
+-1.2
+EWMLES. STG 0.06. LD2
+EWMLES. STG 0.08. LD2
+EWMLES, STG 0.06, Reference
+-1
+mean-cp
+-0.8
+-0.6
+-0.4
+-0.2
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c
+-0.75
+Ni
+-0.8
+-0.85
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c0.006
+RANS
+EWMLES. STG 0.06. LD2
+0.005
+EWMLES. STG 0.08. LD2
+EWMLES, STG 0.06, Reference
+0.004
+mean-cf
+0.003
+0.002
+0.001
+0
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/c
+-0.75
+Ni
+-0.8
+-0.85
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+x/cSpringer Nature 2021 LATEX template
+22
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+nacelle at xST G = 0.06c. These features reduce for xST G = 0.08c and almost
+vanish but are still present for the flat plate test case (cf. Fig. 2 and 11). A
+closer look into the flow properties and mesh resolution at the location of the
+STG suggests a dependency on Reδ,ST G (Tab. 1). Here, Reδ,ST G is defined as a
+Reynolds number referring to the local boundary layer thickness δST G as well
+as velocity and kinematic viscosity at the outer edge of δST G. This Reynolds
+number, which directly impacts the input statistics of the STG, has its lowest
+number for the nacelle case at xST G = 0.06c (4989) and increases for xST G =
+0.06c (6975) and the flat plate flow (24200). The ratio of turbulent- and laminar
+viscosity (max (µt/µl)) which serves as measure of modelled turbulence shows
+a comparable trend. Since low Reynolds numbers enhance the stability of the
+boundary layer and hence suppress turbulent fluctuations, this might lead to a
+damping of the injected turbulent structures. As a consequence the boundary
+layer evolves into a flow with significantly reduced turbulence which is visible
+in a strongly reduced level of mean-cf. Thus, it appears that the distinct
+adaption region can be traced back to a low-Reynolds number effect.
+Another reason might be due to the mesh resolution ∆y which amounts
+δ/20 for the flat plate flow and coarsens to δ/16 and δ/12 for xST G = 0.08c
+and xST G = 0.06c, respectively (cf. Tab. 1). Since a resolution of ∆y = δ/20 is
+actually defined as coarsest resolution in this flow direction the here observed
+somewhat coarser resolutions might perturb a proper development of the
+turbulent boundary layer [3].
+Therefore further examinations of the transonic nacelle flow for higher Re∞
+(resulting in larger Reδ) as well as finer resolutions ∆y will be performed in
+future work in order to provide a verification of the here detected limits of
+synthetic turbulence generation at locally low Reynolds numbers.
+Re∞
+δST G/m
+Reδ,ST G
+∆x
+∆y
+max (µt/µl)
+Flat Plate
+4.7 Mio
+0.006
+24200
+δ/10
+δ/20
+87
+Nacelle
+3.3 Mio
+0.00024
+4989
+δ/11.2
+δ/11.76
+9
+xST G = 0.06c
+Nacelle
+3.3 Mio
+0.00033
+6975
+δ/13.75
+δ/16.17
+10
+xST G = 0.08c
+Table 1 Comparison of several local flow quantities at the location of the synthetic
+turbulence generator for all presented configurations.
+5 Conclusions
+A scale-resolving WMLES methodology in conjunction with the SST tur-
+bulence model was applied to the XRF-1 aircraft configuration with UHBR
+nacelle at transonic flow conditions. The method was applied locally at the
+
+Springer Nature 2021 LATEX template
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+23
+nacelle surface in order to examine shock induced separation. A Synthetic
+Turbulence Generator (STG) was employed to enhance the transition from
+modelled to resolved turbulence at the RANS-LES interface.
+Prior to the actual examination on the aircraft configurations basic func-
+tionalities of the methodology were successfully verified for flows of decaying
+isotropic turbulence and a flow over a flat plate for Reθ = 3030.
+With regard to the target configuration a sophisticated mesh which refines
+32 % of the nacelle outer surfaces and comprises 420 million grid points was
+constructed. The main features of the mesh design are the dependence of mesh
+resolution (∆x, ∆y and ∆z) on the local boundary layer thickness and the
+consideration of a potential shock movement due to buffet.
+Analysis of the transient process of the simulation showed a well resolved
+formation of turbulent structures over almost the entire refinement region with
+a broad spectrum of turbulent scales. It has been demonstrated that these
+features are also the result of the employed LD2 scheme. For a reference central-
+scheme with higher artificial dissipation, small turbulent scales are damped
+leading to globally underresolved turbulence.
+Another outcome of this study is the observation that the STG - adaption
+region correlates to the local Reynolds number as well as mesh resolution in
+spanwise direction. For decreasing Reynolds numbers and coarser mesh resolu-
+tions an increasing adaption length and more distinct decay in the skin friction
+distribution were observed. We note that the methodology is only applicable
+if the STG adaption region does not interfere with the transonic shock front
+and therefore sufficient distance to the shock is required. This distance might
+not be given in case of an upstream moving shock which would arise for strong
+shock buffet at the given Reynolds number. Therefore further research on the
+transonic nacelle flow for higher Reynolds numbers as well as finer resolutions
+will be performed in future work to verify a potential reduction of the adaption
+length.
+Acknowledgments.
+The authors gratefully acknowledge the Deutsche
+Forschungsgemeinschaft DFG (German Research Foundation) for funding this
+work in the framework of the research unit FOR 2895. The authors thank the
+Helmholtz Gemeinschaft HGF (Helmholtz Association), Deutsches Zentrum
+f¨ur Luft- und Raumfahrt DLR (German AerospaceCenter) and Airbus for pro-
+viding the wind tunnel model and financing the wind tunnel measurements
+Additionally, the authors gratefully acknowledge the computing time granted
+by the Resource Allocation Board and provided on the supercomputer Lise and
+Emmy at NHR@ZIB and NHR@G¨ottingen as part of the NHR infrastructure.
+The calculations for this research were conducted with computing resources
+under the project nii00164.
+Declarations
+• Funding: This study was funded by DFG (German Research Foundation).
+
+Springer Nature 2021 LATEX template
+24
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+• Competing interests: The authors have no competing interests to declare
+that are relevant to the content of this article.
+• Ethics approval: Not applicable
+• Consent to participate: Not applicable
+• Consent for publication: Not applicable
+• Availability of data and materials: Not applicable
+• Code availability: Not applicable
+• Authors’ contributions: Not applicable
+References
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+[2] R.D. C´ecora, R. Radespiel, B. Eisfeld, A. Probst, Differential reynolds-
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+[3] M.L. Shur, P.R. Spalart, M.K. Strelets, A.K. Travin, A hybrid rans-les
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+[9] D.G. Francois, R. Radespiel, A. Probst, Forced synthetic turbulence
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+81–92 (2015). https://doi.org/10.1007/978-3-319-15141-0 6
+
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+https://doi.org/10.1007/978-3-030-27607-2 15
+[11] A. Probst, J. L¨owe, S. Reuß, T. Knopp, R. Kessler, Scale-Resolving Simu-
+lations with a Low-Dissipation Low-Dispersion Second-Order Scheme for
+Unstructured Flow Solvers. AIAA Journal 54(10), 2972–2987 (2016)
+[12] J. Kok, A high-order low-dispersion symmetry-preserving finite-volume
+method for compressible flow on curvilinear grids. Journal of Computa-
+tional Physics 228(18), 6811–6832 (2009)
+[13] J. L¨owe, A. Probst, T. Knopp, R. Kessler, Low-Dissipation Low-
+Dispersion Second-Order Scheme for Unstructured Finite-Volume Flow
+Solvers. AIAA Journal 54(10), 2961–2971 (2016)
+[14] A. Probst, S. Melber-Wilkending, Hybrid RANS/LES of a generic high-
+lift aircraft configuration near maximum lift.
+International Journal of
+Numerical Methods for Heat & Fluid Flow 32(4), 1204–1221 (2022).
+https://doi.org/10.1108/hff-08-2021-0525
+[15] G. Comte-Bellot, S. Corrsin, Simple eulerian time correlation of full-
+and narrow-band velocity signals in grid-generated,‘isotropic’turbulence.
+Journal of fluid mechanics 48(2), 273–337 (1971)
+[16] R.H. Kraichnan, Diffusion by a Random Velocity Field. The Physics of
+Fluids 13(1), 22–31 (1970)
+[17] A. Probst, Implementation and assessment of the synthetic-eddy method
+in an unstructured compressible flow solver. Notes on Numerical Fluid
+Mechanics and Multidisciplinary Design 137, 91–101 (2018). https://doi.
+org/10.1007/978-3-319-70031-1 7
+[18] R. Laraufie, S. Deck, Assessment of Reynolds stresses tensor reconstruc-
+tion methods for synthetic turbulent inflow conditions. Application to
+hybrid RANS/LES methods.
+International Journal of Heat and Fluid
+Flow 42, 68–78 (2013). https://doi.org/10.1016/j.ijheatfluidflow.2013.04.
+007
+[19] H.M. Nagib, K.A. Chauhan, P.A. Monkewitz, Approach to an asymptotic
+state for zero pressure gradient turbulent boundary layers. Philosoph-
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+Engineering Sciences 365(1852), 755–770 (2007)
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+tor for Hybrid RANS/LES Methods (TU Braunschweig-Nieders¨achsisches
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+Springer Nature 2021 LATEX template
+26
+Grey area in Embedded WMLES on a nacelle-aircraft configuration
+Forschungszentrum f¨ur Luftfahrt, 2020)
+[21] P.R. Spalart, C. Streett, Young-person’s guide to detached-eddy simula-
+tion grids. NASA Technical Reports Server (2001)
+[22] F.R. Menter, Best practice: scale-resolving simulations in ansys cfd.
+ANSYS Germany GmbH 1 (2012)
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+study of shock oscillation over a transonic supercritical profile.
+AIAA
+journal 47(9), 1985–1994 (2009)
+
diff --git a/79E4T4oBgHgl3EQf2g20/content/tmp_files/load_file.txt b/79E4T4oBgHgl3EQf2g20/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf,len=1088
+page_content='Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a  transonic nacelle-aircraft configuration  Marius Herr1*, Axel Probst2 and Rolf Radespiel1  1*Institute of Fluid Mechanics, TU Braunschweig,  Hermann-Blenk-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 37, Braunschweig, 38108, Lower Saxony,  Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  2Institute for Aerodynamics and Flow Technology, DLR,  Bunsenstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 10, G¨ottingen, 37073, Lower Saxony, Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Corresponding author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' E-mail(s): m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='herr@tu-bs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='de;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Contributing authors: axel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='probst@dlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='de;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='radespiel@tu-bs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='de;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Abstract  A scale resolving hybrid RANS-LES technique is applied to an air-  craft - nacelle configuration under transonic flow conditions using the  unstructured, compressible TAU solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore a wall modelled LES  methodology is locally applied to the nacelle lower surface in order to  examine shock induced separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In this context a synthetic turbu-  lence generator (STG) is used to shorten the adaption region at the  RANS – LES interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Prior to the actual examinations, fundamen-  tal features of the simulation technique are validated by simulations of  decaying isotropic turbulence as well as a flat plate flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For the aircraft  nacelle configuration at a Reynolds number of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 million a sophisti-  cated mesh with 420 million points was designed which refines 32 % of  the outer casing surface of the nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The results show a development  of a well resolved turbulent boundary layer with a broad spectrum of  turbulent scales which demonstrates the applicability of the mesh and  method for aircraft configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Furthermore, the necessity of a low  dissipation low dispersion scheme is demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' However, the dis-  tinct adaption region downstream of the STG limits the employment  of the method in case of shock buffet for the given flow conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Keywords: hybrid RANS-LES, wall-modelled LES, synthetic turbulence,  aircraft configuration, transonic flow, shock induced separation  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='05299v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='flu-dyn]  12 Jan 2023  Springer Nature 2021 LATEX template  2  Grey area in Embedded WMLES on a nacelle-aircraft configuration  1 Introduction  Transonic flows about aircraft configurations exhibit complex, instationary  flow phenomena such as oscillating shock fronts with boundary layer sepa-  ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This so-called buffet phenomenon causes unsteady aerodynamic loads  which might endanger the flight safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore a fundamental understand-  ing of the related flow physics is of particular interest to be able to find  specific technical solutions which control this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The present study  examines a XRF-1 aircraft model which represents a wide-body long-range con-  figuration and was designed by Airbus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' An Ultra High Bypass Ratio (UHBR)  nacelle is coupled to the model which represents a modern and efficient jet  engine that is modelled as flow-through nacelle for wind tunnel testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Due  to the large circumference of the nacelle, a close coupling by means of a pylon  to the wing lower side is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This channel-like arrangement of nacelle,  pylon, wing and fuselage causes the development of an accelerated flow which  triggers the formation of transonic shocks within this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Depending on the  exact flow conditions these shocks evolve into buffet with significant loads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Initial investigations in the framework of the DFG (Deutsche Forschungsge-  meinschaft) funded research group have shown a complex system of shock  fronts [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As a first step toward representing this complex system with a sophis-  ticated numerical method this study focuses on a single shock front located at  the lower side of the nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Numerous numerical investigations have investigated the problem of buf-  fet onset with well established unsteady Reynolds-averaged Navier-Stokes  (URANS) methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' However, it is well known that even highly developed  Reynolds stress based URANS models show deficiencies in describing the  dynamics of separated boundary layer as well as the aerodynamic effects of  large flow separations [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Also, due to high, flight relevant Reynolds numbers  a broad scale of turbulent structures arise for the given flow phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Therefore a simulation technique that provide both high spatial and temporal  resolution is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Direct Numerical Simulation (DNS) resolves all turbu-  lent scales but is so far restricted to simple geometries at low Reynolds numbers  due to its unfeasible computational effort for flight relevant flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore a  Large Eddy Simulation (LES) technique is required which only resolves large  turbulent scales whereas small, isotropic scales are modelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Since an appli-  cation of LES to the entire aircraft configuration is still computationally too  expensive a hybrid RANS - LES technique is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In the present study the  wall modelled LES (WMLES) method within the Improved Delayed Detached  Eddy Simulation (IDDES) methodology is used [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Depending on the spatial  discretisation, up to 5 % of the wall adjacent boundary layer is modelled by  the RANS equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Additionally, the area of WMLES is embedded around  the transonic shock such that all relevant flow areas are enclosed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This cor-  responds to 32 % of the outer casing surface of the nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The remaining  flow field of wing, body, pylon and nacelle is modelled with a URANS model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The embedded WMLES (EWMLES) requires an injection of synthetic turbu-  lence at the RANS-LES interface which is located at the leading edge of the  Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  3  nacelle for the present configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Otherwise, a so-called grey area would  arise which describes a region of underresolved turbulence directly downstream  of the RANS-LES boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' To this end the synthetic turbulence generator  (STG) devised by [4] is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Nevertheless, using this method, a transi-  tional region from modelled to fully resolved turbulence is still present and is  referred to as adaption region in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The analysis of this adaption region  with regard to its length and behaviour of relevant flow quantities in this area  are of major interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Thus, especially the transient establishment of resolved  turbulence within the WMLES area and the fundamental applicability of the  method to the aircraft configuration are the focus of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The study is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The employed WMLES model in  conjunction with the STG is described in detail in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Subsequently a thorough description of the employed low dissi-  pation low dispersion (LD2) numerical scheme is given in 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The following  section 3 provides a basic validation of the Embedded WMLES based on the  SST-RANS model by means of flows of decaying isotropic turbulence and a  flow about a flat plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The results of the application to the XRF-1 configu-  ration are presented in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' An extensive description of the mesh design  with regard to the extension of the WMLES area, the used refinement criteria  and its application to the actual mesh environment are presented (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Results of the transient WMLES establishment are then shown and assessed  in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The analysis of temporally and spatially averaged flow quanti-  ties in the area related to the STG is carried out (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Finally, sensitivity  studies with regard to the position of the RANS-LES boundary (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1)  and the effect of using a standard numerical scheme instead of the low dissipa-  tion scheme (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2) is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This paper is closed by a final summary  of all research findings (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  2 Numerical Methods  The flow simulations in this paper use the unstructured compressible DLR-  TAU code [5] which numerically solves the flow and model equations on  mixed-element grids (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' hexahedra, tetrahedra, prims) via the finite-volume  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It applies 2nd-order discretization schemes for both space and time,  together with low-Mach-number preconditioning for flows that are close to  the incompressible limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Implicit dual-time stepping allows adapting the time  step in unsteady simulation to the physical requirements (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' related to the  convective CFL-criterion), avoiding numerical stability restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The relevant methods for embedded wall-modelled LES, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' the overall  (hybrid) turbulence model, the method to generate and inject synthetic turbu-  lence and the required local adaptation of the numerical scheme, are outlined  in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  4  Grey area in Embedded WMLES on a nacelle-aircraft configuration  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 Hybrid RANS-LES Model  The present embedded wall-modelled LES approach relies on the Improved  Delayed Detached-Eddy Simulation (IDDES) [3] which combines local RANS,  DES (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' RANS-LES) and wall-modelled LES (WMLES) functionalities in a  seamless, automatic manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This is achieved by a single hybrid length scale  replacing the integral turbulent scale lRANS in the underlying RANS model,  which is the two-equation SST model [6] in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The hybrid length  scale reads:  lhyb = ˜fd (1 + fe) lRANS +  �  1 − ˜fd  �  lLES  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  (1)  Here, the function ˜fd = max {(1 − fdt) , fB} is the main blending switch  between the different modelling modes, where fdt and fB depend on local grid  and flow properties (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  In WMLES mode (fdt ≡ 1 and, thus, ˜fd ≡ fB), if resolved turbulent  content enters an attached boundary layer, a RANS layer is kept near the  wall and sized according to the local grid resolution, thus circumventing the  extreme grid requirements of wall-resolved LES at high Reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  However, since no wall-functions are applied in the present work, the equations  need to be solved down to the wall with a (normalized) near-wall grid spacing  of y+(1) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The additional elevating function fe is designed to reduce the  well-known log-layer mismatch in WMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  In the largest (outer) parts of the boundary layer, lhyb ≡ lLES = CDES∆,  which approximates the behaviour of a Smagorinsky-type sub-grid model for  LES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The model constant CDES is usually calibrated for canonical turbulent  flow, such as decaying isotropic turbulence (DIT), see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' However, since  wall-bounded flows typically require a different calibration than free turbu-  lence, another modification compared to standard DES/LES is introduced in  the filter width ∆:  ∆ = ∆IDDES = min {max [Cw · dw, Cw · hmax, hwn] , ∆DES}  ,  (2)  where Cw = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In essence, this near-wall limitation of the filter width  compensates for this flow-type dependency and allows using a unique CDES  value for both wall-bounded and off-wall turbulent flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' More details on this  modification are found in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  For embedded WMLES, the IDDES in TAU can be locally forced to  WMLES mode according to external user input, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' inside boxes or other suit-  able geometric sub-areas of the flow domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This is achieved by setting the  function fdt to 1 downstream of the desired RANS-WMLES interface, thus  safely reducing the eddy viscosity from RANS to WMLES level [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 Synthetic Turbulence Generation  In this work, synthetic turbulent fluctuations at the streamwise RANS-LES  interface are provided by the Synthetic Turbulence Generator (STG) of  Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  5  Adamian and Travin [8] with extensions for volumetric forcing by Francois [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  This STG generates local velocity fluctuations from a superimposed set of N  Fourier modes as:  ⃗u′  ST = ⃗A ·  √  6  N  �  n=1  √qn  �  ⃗σn cos  �  kn ⃗dn · ⃗r′ + φn + sn t′  τ  ��  ,  (3)  where the direction vectors ⃗dn and ⃗σn ⊥ ⃗dn, the mode phase φn, and the mode  frequency sn are randomly distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A realistic spectral energy distribution  of the mode amplitudes qn is achieved by constructing a von K´arm´an model  spectrum from RANS input data and a local grid cut-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The RANS data,  which is automatically extracted from just upstream the RANS/LES inter-  face, is also used to scale the fluctuations via the Cholesky-decomposed RANS  Reynolds-stress tensor ⃗A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  For realistic temporal correlations in a volumetric forcing domain, the posi-  tion vector ⃗r′ and the time t′ are modified in accordance with Taylor’s frozen  velocity hypothesis, see [9] for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Synthetic-Turbulence Injection  To inject the synthetic fluctuations from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' (3), a forcing volume with a  streamwise extent of about half the local boundary-layer thickness is marked  just downstream of the RANS/LES interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Inside this volume, a momentum  source term is added [10] which approximates the partial time derivative of  the synthetic fluctuations as:  ⃗Q = ∂ (ρ⃗u′  ST )  ∂t  ≈ 3 (ρ⃗u′  ST − ρ⃗u′n) −  �  ρ⃗u′n − ρ⃗u′n−1�  2∆t  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  (4)  This discretization corresponds to the 2nd-order backward difference scheme  used for unsteady simulations with TAU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' By computing the fluctuation values  of the previous time steps from the actual flow field, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' as ⃗u′n = ⃗un − ⟨⃗u⟩ and  ⃗u′n−1 = ⃗un−1 −⟨⃗u⟩, the synthetic target field (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 3) can be reproduced rather  accurately in the simulation, even though running time averages are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  An additional Gauss-like blending function with a maximum value of 1 around  the streamwise center of the forcing volume is multiplied to the source term  in order to prevent abrupt variation of the forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 Hybrid Low-Dissipation Low-Dispersion Scheme  Since scale-resolving simulation methods like IDDES involve explicit modelling  of the sub-grid stresses, the overall accuracy relies on low spatial discretization  errors in the LES regions of a given grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Concerning resolved turbulence, there  are two types of error that mainly stem from the discretized convection of  momentum: while numerical dissipation damps the turbulent fluctuations and  Springer Nature 2021 LATEX template  6  Grey area in Embedded WMLES on a nacelle-aircraft configuration  would lead to under-predicted Reynolds stress, numerical dispersion distorts  the shape of resolved turbulent structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  For that reason, the present simulations apply a hybrid low-dissipation  low-dispersion scheme (HLD2) [11], which combines different techniques to  optimize the convection scheme for local scale-resolving simulations using  unstructured finite-volume solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  To provide low numerical dissipation, the spatial fluxes are calculated  from Kok’s [12] skew-symmetric central convection operator, which allows for  kinetic-energy conservation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=', it is non-dissipative) on curvilinear grids in  the incompressible limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For compressible flow on general unstructured grids,  a classic blend of 2nd- / 4th-order artificial matrix-dissipation is added to  ensure stability around shocks and in smooth flow regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Compared to RANS  computations, however, the 4th-order dissipation has been strongly reduced  by manually optimizing its parameters in LES computations of the channel  flow, yielding e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' a global scaling factor of κ(4) = 1/1024 and a reduced  Mach-number cut-off in the low-Mach-number preconditioning matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Moreover, to minimize the dispersion error of the second-order scheme, the  skew-symmetric central fluxes are based on linearly-reconstructed face values  φL,ij, φR,ij using the local Green-Gauss gradients ∇0φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Exemplarily, a generic  central flux term reads:  φij,α = 1  2 (φL,ij + φR,ij) = 1  2 (φi + φj) + 1  2α (∇0φi − ∇0φj) · dij  ,  (5)  where dij is the distance between the points i and j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' With an extrapolation  parameter of α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='36 the scheme was found to minimize the required points  per wavelength for achieving a given error level in a 1-D wave problem, see  [13] for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Blended Scheme for Hybrid RANS-LES  While the low-error properties of the LD2 scheme are essential for accurate  LES and WMLES predictions with TAU [11], the pure RANS and outer flow  regions in hybrid RANS-LES are less dependent on such numerical accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Moreoever, although the LD2 scheme has been globally applied in hybrid  RANS-LES, complex geometries like the present XRF-1 configuration and cor-  responding unstructured grids may induce local numerical instabilities that  are not damped by low-dissipative schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For this reason, we apply the LD2  scheme in a hybrid form [11] where all parameters of the spatial scheme, Ψi,  are locally computed from a blending formula:  Ψi = (1 − σ) · Ψi,LD2 + σ · Ψi,Ref  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  (6)  Here, Ψi,LD2 are the parameter values of the LD2 scheme (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' κ(4) = 1/1024,  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='36), whereas Ψi,Ref corresponds to standard central-scheme parameters  typically used in RANS computations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' κ(4) = 1/64, α = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The blending  Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  7  function σ is adopted from [4] and discerns between the well-resolved vortex-  dominated flow regions (LD2) and coarse-grid irrotational regions (Ref ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  By now, the hybrid LD2 scheme (HLD2) has been successfully applied  in a number of hybrid RANS-LES computations ranging from canonical  flows on structured grids [11] to complex high-lift aircraft on mixed-element  unstructured meshes [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  3 Basic Validation of Embedded WMLES  Before analyzing the embedded WMLES approach from Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2 for a complex  transonic aircraft configuration with UHBR nacelle in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4, we investigate  and demonstrate its basic scale-resolving functionalities in fundamental test  cases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' decaying isotropic turbulence for pure LES and a developing flat-  plate boundary layer for WMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 Decaying Isotropic Turbulence  Although SST-based IDDES is a well-known hybrid model present in many  CFD codes, a proper verification for a given flow solver and the applied  numerical scheme requires fundamental tests of the different modelling modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  This includes the pure LES functionality, where the hybrid model acts  as Smagorinsky-type sub-grid model and mostly relies on the ”outer-flow”  calibration constant of SST-based IDDES, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' CDES = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1  For this reason, we present for the first time TAU simulations of decaying  isotropic turbulence (DIT) using SST-IDDES with the LD2 scheme and com-  pare the results with classic experimental data from [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In particular, the  turbulent-kinetic-energy (TKE) spectra at two different time levels after the  start of decay, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='87 s and t = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='0 s, are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Additionally, to  emphasize the effect of the LD2 scheme, further SST-IDDES simulations are  performed using a reference central-scheme with higher artificial dissipation  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 6 in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  As for the computational setup, a cubic domain with normalized edge  length of 2π is discretized by Cartesian meshes with 323, 643 and 1283 cells,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Periodic boundary conditions are applied in all three directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The initial velocity field has been generated by a Kraichnan-type synthetic  turbulence approach [16] and retains the TKE spectrum of the experiment at  t = 0 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Due to the compressible formulation of the DLR-TAU code, appropri-  ate initial density and pressure fields are derived from the isentropic relations of  compressible fluids, describing the change of state from stagnation (Ma∞ = 0)  to the local Mach number, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' ρ/ρ∞ = f (Ma) and p/p∞ = f (Ma).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Moreover,  the initial fields of modeled TKE and specific dissipation rate ω are computed  in a preliminary steady-state SST-IDDES computation, where all equations  except for the hybrid turbulence model are frozen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The temporal resolutions  1Note that the calibration constant in SST-based DES-variants takes a different value close to  walls, but this region is usually treated in RANS mode anyway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='.  Springer Nature 2021 LATEX template  8  Grey area in Embedded WMLES on a nacelle-aircraft configuration  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 1 TKE spectra of decaying isotropic turbulence (DIT) for two different times along  with experimental data [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Results for the LD2 scheme (left) and a reference central-scheme  (right) are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  of ∆t/s ∈ { 5·10−3, 5·10−3, 2·10−3} for the coarse, middle and fine grid were  determined in time-step convergence studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 1 (left) shows the results for the SST-IDDES with LD2 scheme which  demonstrate a good agreement with the experimental results for all spatial  resolutions and both time levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For the reference central-scheme however,  the picture is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Although there are agreements with the experimental  results for small wave numbers scales k+ ≤ 8 for all resolutions and time levels,  deviations arise for larger wave numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' These deviations are growing with  increasing wave number and finally result in a significant underestimation of  the TKE for all setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  As a result we successfully demonstrated the LES functionality of SST-  IDDES in conjunction with the LD2 scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The low dissipation feature of  the numerical scheme was confirmed and additionally emphasized by reference  simulations with higher artificial dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 Developing Flat Plate Boundary Layer  For a basic assessment of the full embedded WMLES functionality, we consider  the test case of a developing flat-plate boundary layer, which transitions from  RANS to WMLES at a fixed streamwise position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It starts with zero thickness  at the inflow and is computed in SST-RANS mode up to the position, where  the momentum-thickness Reynolds number reaches Reθ = 3040.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Here, a zonal  switch to WMLES within IDDES is placed, along with a synthetic-turbulence  forcing region of about half a boundary layer thickness in streamwise direction,  see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  A hybrid grid with 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='8 million points and hexahedral cells in the WMLES  area is used, which ensures ∆x+ ≈ 100 − 200, ∆y+ ≈ 1, ∆z+ ≈ 50 like the  structured grid used in [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' More relevant for WMLES, the streamwise spacing  fulfills ∆x ≤ δ/10 throughout the flow domain, where δ is the approximate  local boundary layer thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The normalized timestep (in wall units) is  E+  10-2  10  Experiment t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='84  Experiment t = 2  SST -- IDDES, 323, LD2  SST -- IDDES, 643, LD2  SST -- IDDES, 1283, LD2  k*  20  40  60E+  10  10  Experiment t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='84  Experiment t = 2  SST -- IDDES, 323, ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Scheme  SST -- IDDES, 643, ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' scheme  SST -- IDDES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 128, ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' scheme  k*  20  40  60Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  9  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2 Evolution of averaged skin friction along streamwise position x of the flat plate test  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  ∆t+ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4 and safely fulfills the convective CFL criterion (CFLconv < 1) in  the whole LES region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The statistical input data for the STG methods is given by external input  from a precursor RANS profile at Reθ = 3040 which has been augmented with  an anisotropic normal-stress approximation according to [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The spanwise and temporal averaged results of the skin friction distribu-  tion mean-cf are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2 along with the Coles-Fernholz correlation  [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' After an initial overshoot of mean-cf at the position of the STG, mean-cf  shows good agreement with the Coles-Fernholz correlation and remains within  an acceptable error margin of 5 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Note that the adaption region downstream  of the STG is hardly visible but still present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This region is defined as underpre-  diction of mean-cf compared to the previous mean-cf level directly upstream  of the STG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The adaption-length which respresents the distance between the  position of the STG and the first peak in mean-cf downstream of the overshoot  amounts 7 δST G where δST G is the boundary layer thickness at the position of  the STG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Within this adaption region the sum of modelled and resolved tur-  bulent stresses are lower than the previous level of modelled turbulence of the  RANS region which results in an underprediction of mean-cf [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Finally, this examination confirms the embedded WMLES functionality of  SST-IDDES with STG for a flat plate flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Thus this methodic is basically  verified for comparable geometry sections at the XRF-1-UHBR configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4 Grey-Area Investigation on Nacelle-Aircraft  Configuration  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 Geometry, Flow Conditions and RANS Mesh  The actual target configuration consists of a half model of a modern trans-  port aircraft configuration in conjunction with a through flow nacelle (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The employed XRF-1 aircraft model represents a wide-body long-range  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='003  mean-cf  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='001  Coles-Fernholz  SST - IDDES + STG (LD2)  0  20  40  60  X/Springer Nature 2021 LATEX template  10  Grey area in Embedded WMLES on a nacelle-aircraft configuration  research configuration and is designed by Airbus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A Ultra High Bypass Ratio  (UHBR) nacelle is integrated with the aid of a pylon and positioned close to  the wing lower side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The UHBR design consists of an outer casing and a core  body with plug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The casing is shaped circularly with a cross section similar to  an airfoil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Both, nacelle and a specifically designed pylon were developed by  DLR [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  In order to find a suitable flow condition with shock induced separation in  the surrounding of the nacelle surface a comprehensive numerical study was  performed where various high speed off-design conditions were assessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As  key parameter for the occurrence of transonic shocks at a Reynolds number  of Re = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 million a low angle of attack (α) was identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For a farfield  Mach number of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='84 and α = −4◦ shock induced separation is present at  the wing lower side, the pylon and the nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A single, locally separated  transonic shock could be found at the outer surface of the nacelle lower side  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Thus, a flow condition which allows to examine an isolated shock  with subsequent boundary layer separation in the context of a nacelle-aircraft  configuration was found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  In a prelinimary work a high quality RANS mesh for the XRF-1 - UHBR  half model was designed and constructed by projects partners of the research  unit at the University of Stuttgart and DLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The surface RANS mesh mainly  consists of structured areas which are extruded to hexahedral blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' These  are designed to contain the entire RANS boundary layer with a safety factor  of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The wall adjacent cell spacing fulfills y+(1) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4 and a growth rate of  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='12 is applied in wall normal direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A h-type mesh topology is employed  at the intersections of the aircraft components to be able to accurately resolve  flow features in these areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The farfield region is discreticed by tetrahedra  and extends to 50 wingspans in all coordinate directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The total grid size  before refinement amounts 112 million points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 Grid Design for Embedded WMLES  In the following the mesh design for the WMLES refinement region is intro-  duced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A sophisticated meshing strategy, that aims to reduce the grid size  as far as possible but follows basic refinement and extension constraints for  WMLES, is developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This is necessary in order to limit mesh size and result-  ing computing time to a reasonable level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Special care was taken to the mesh  resolution of all coordinate directions (∆x, ∆y and ∆z) which depend on the  local boundary layer thickness δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Additionally, a potential shock movement is  considered with regard to the refinement extension as well as mesh resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The refinement region is embedded within the previously described RANS  mesh with the aid of unstructured bands in the surface mesh (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This strategy allows to drastically increase the resolution within the  structured boundary layer such that the surrounding RANS region remains  unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' An unstructured nearfield block, which is also present in the pure  RANS mesh, serves as an interface between the hexahedral blocks and the  Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  11  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 3 Bottom view of XRF-1 - aircraft configuration with UHBR nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The nacelle  lower side includes the mesh refinement region for embedded WMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  farfield, exhibits a mesh decay rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The total mesh size of the combina-  tion of RANS mesh and refinement region for WMLES comprises 420 million  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 Extension of the refinement region  To describe locations on the nacelle surface more precisely a cylindrical coor-  dinate system r, ϕ and x/c is introduced, where c represents the nacelle chord  length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Its reference point r = 0, x/c = 0 is located in the nacelle center within  a cross section that includes the entire nacelle leading edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' ϕ is set to 0◦ at  the intersection between nacelle and pylon and increases in clockwise direction  that 90◦ points towards the fuselage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  According to [21] the first step in designing hybrid RANS LES mesh for  DES based algorithms is the definition of the RANS and LES regions for the  given configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Since the aim of this research topic is the application of a  WMLES methodology to a flow region with shock induced separation, all flow  regions directly related to this phenomenon are of interest and should be highly  resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The primary region is the area of recirculation (AOR) downstream  of the shock position (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4 left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Flow regions related to this are the  attached boundary layer upstream of the AOR and separated boundary layer  downstream of the AOR until the trailing edge of the nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' To this end the  average shock front position and extension of the AOR are calculated by a  preceding SST-RANS calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4 (left) shows a surface plot of the skin  friction coefficient (cf) where the cf is only plotted for cf < 0 which serves as  an indicator of the AOR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The refinement region in spanwise direction (ϕ) is  chosen such that the entire area of recirculation is included with some margins  in ϕ-direction and extends 105◦ starting from 120◦ until 225◦ (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  X  ZSpringer Nature 2021 LATEX template  12  Grey area in Embedded WMLES on a nacelle-aircraft configuration  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4  Bottom view of the UHBR-nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Left: Area of recirculation of SST-RANS solu-  tion for Ma∞ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='84 and α = −4◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The shown RANS surface mesh already includes the  boundaries for the refinement region in form of unstructured streaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Right: Extension of  refinement area with stepwise increase in streamwise direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The colorbar visualizes the  cell surface area where yellow and purple represent large and low areas, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Since the boundary layers thickness is not only a function of x but also  of ϕ we introduce the new variables δϕ,max(x) and δϕ,min(x) which refer to  the maximum and minimum boundary layer thickness for a given streamwise  position x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In x/c direction the refinement is applied between xa/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06  and xb/c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The choice of xa/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 as the most upstream position  is the result of the dependence of mesh resolution on the boundary layer  thickness δϕ,min(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The smaller the boundary layer thickness δϕ,min(x) at  location xa the smaller the required cell lengths ∆ζ(xa) for ζ ∈ {r, ϕ, x}  since ∆ζ(x) ≤ δϕ,min(x)/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The refinement in wall normal direction r is  applied for wall distances that hold dw(x) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 · δϕ,max(x) in the interval  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 ≤ x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 and dw ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 · δϕ,max(x) within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 ≤ x/c ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Thus dw/c  ranges from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2% at x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 to 15% at the trailing edge (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4 right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Although these distances are smaller than dw ≤ 2 · δ(x) suggested by [22] we  show in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 that the whole resolved boundary layer remains within the  refined area with distance drefined(x) over the entire simulated time period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Additionally, the extension of the refinement area in r-direction also consid-  ers a potential oscillation of the boundary layer separation point around its  average position at xs/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='13 (SST-RANS solution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' We assumed an oscil-  lation amplitude of ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='03 c which also allows to employ this mesh in case of  shock buffet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As a consequence, at position x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 a refinement distance  of drefined(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16c) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 · δϕ,max(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='19c) is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 Resolution of the refinement region  The resolution in x-direction depends on the local boundary layer thick-  ness and is set to a limit of ∆x(x) ≤ δϕ,min(x)/10 which leads to a total  number of 1350 points in x-direction from the leading edge to the trail-  ing edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Again an oscillation of separation due to shock buffet point is  considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Thus it is assumed to have a attached boundary layer until  C,<0  XZSpringer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  13  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 5 Surface mesh of refinement region on lower side of UHBR nacelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Left:  Discrete  coarsening of ∆ϕ is apparent which subdivides the refinement area into five subregions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Right:  Vertical unstructured (triangular based) streak enables to refine locally and keep  surrounding RANS resolution untouched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Horizontal unstructured stripe allows to coarsen  the refinement region in ϕ-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  xs/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='13 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='03 leading to reduced boundary layer thickness compared to  the preliminary SST-RANS solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore the boundary layer thickness  at x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 is estimated to δϕ,min(x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08) · 24/5 according to turbu-  lent boundary layer theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As before the resolution in ϕ-direction is limited  to r∆ϕ(x) ≤ δϕ,min(x)/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In contrast to the resolution in x-direction the  adaption of ∆ϕ(x) to δϕ,min(x) is realised in a discrete manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore the  refinement region is separated into five subregions with its boundaries located  at x/c ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='82;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 1} (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' ∆ϕ(x) remains con-  stant within each subregion Ωi and is set to r∆ϕ(x ∈ Ωi) = δϕ,min(xi)/10 with  xi defined as the most upstream position of Ωi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' With this protocol the res-  olution in ϕ-direction is always smaller than δϕ,min(x)/10 which results into  {4350;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 1660;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 870;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 603;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 250} points in ϕ-direction within the correspond-  ing subregion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Without this stepwise increase of ∆ϕ the total grid number  would increase by a factor of 3 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2 · 109 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Again a potential move-  ment of the boundary layer separation point is considered and therefore  r∆ϕ(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16c) =  1  10δϕ,min(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08c) · 24/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In r-direction the wall normal  spacing of the wall adjacent cells is limited to r+(1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The cells of the  entire refinement area are extruded geometrically with a growth factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='12  until ∆r = ∆x(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06c) is reached and ∆r is initially kept constant to obtain  locally isotropic cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Since the distance of the refinement region drefined(x)  increases in x-direction in a cascading manner (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4 (right) and 6) the  geometric growth is continued for refinement areas with larger wall distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Exemplarily, ∆r is further increased to ∆r = ∆x(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16c) for wall distances  in the interval drefined(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16c) ≤ r ≤ drefined(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25c) and applied  where 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 ≤ x/c ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Subsequently ∆r is again increased until ∆r = ∆x(x =  X  Y  ZSpringer Nature 2021 LATEX template  14  Grey area in Embedded WMLES on a nacelle-aircraft configuration  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 6 Cross section of nacelle lower side at ϕ = 180◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Subregion Ω1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 ≤ x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16)  of the refinement region includes 200 Mio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' cells which corresponds to 48% of the entire grid  size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25c) for wall distances in the intervall drefined(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25c) ≤ r ≤ drefined(x =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4c) and applied where 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25 ≤ x/c ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This protocol is repeated until ∆r  amounts ∆r = ∆x(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='82c) for drefined(x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='82c) ≤ r ≤ drefined(x = 1c)  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='82 ≤ x/c ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Finally, the total number of grid points in wall normal  direction comprises {113;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 168;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 183;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 230;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 258} points within the corresponding  subregion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 Results of Transient WMLES Establishment  As initial solution for the SST-IDDES a converged SST-RANS solution  was employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The physical time step size amounts ∆t = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 · 10−8 s =  1/16750 CTU where 1 CTU = u∞ · c represents a single convective time unit  (CTU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' ∆t is chosen that CFL < 1 is fulfilled for all grid cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 7 represents the temporal evolution of the Mach number in a cross  section at ϕ = 180◦ and four different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' With regard to the turbulent  boundary layer thickness δ it should be noted that δ is entirely located within  the refinement volume with sufficient distance to its boundary (indicated by  black lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' After the depicted maximal extension at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU the boundary  layer thickness significantly decreases at later times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This decrease appears  to be related with the shock movement in downstream direction since this  correlation is also observed for various transonic flows of wing profiles [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  As mentioned before the root of the shock front xs is moving from its initial  SST-RANS position xs(t0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='13c downstream to xs(t1 CTU) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='17c and  remains at the same position until xs(t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Although xs is located further  downstream as we assumed for the mesh design (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 ≤ xs/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16) one has  to note that such shock displacements are common in transient simulations  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' t ≤ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The shock position will most likely move upstream again  for more advanced simulation times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Another perspective on the temporal evolution is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Here the  cf-distribution is shown at four different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This figure confirms that the  resolved turbulence develops over the entire refinement area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The transonic  shock front is visible in form of a sudden decrease in cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 7 it can  be seen that the whole front is moving downstream until it remains in an area  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 ≤ xs/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A minor numerical effect appears at the lateral edge  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='6  X/cSpringer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  15  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 7  Ma-number fields within a cross section of the refinement volume at ϕ = 180◦ for  four different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  of the refined mesh in ϕ-direction where underresolved turbulence is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  This is due to the fact that the STG does not directly connect to the lateral  RANS zones at the edges of the refinement region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore two small gaps  appear where little resolved and significantly reduced modelled turbulence  exists which result in low values of cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This artefact can easily be circumvented  in future simulations by narrowing the LES zone in spanwise direction and  thus generate modelled turbulence in the respective regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Nevertheless, the  Ma 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='02 CTU  x/c-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='5 CTU  x/cSpringer Nature 2021 LATEX template  16  Grey area in Embedded WMLES on a nacelle-aircraft configuration  described phenomenon is limited to the boundaries and does not affect the  actual focus region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  To give an impression of the vortex structure of the resolved turbulence an  isosurface of the Q-criterion (Q = 1010) at t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As already observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 8 an extensive formation of turbulent struc-  tures within the refinement region is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' These structures are growing  with increasing streamwise position and partially evolve into horseshoe vortices  which corresponds to expected flow behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4 Investigation of grey area  In the following a quantitave analysis of the grey area / adaption region is  performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore the flow field was averaged with regard to time and  spanwise direction ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The temporal average was applied for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='42 ≤ t/CTU ≤  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The start time t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='42 is chosen such that the resolved turbulence is  completely established within the focus region (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 ≤ x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25) and no  remains of the initial RANS-solution are present in this area (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 8 at  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The spanwise average was applied over the refinement section  such that the areas of underresolved turbulence at its margins were omitted  (ϕ ∈ [125◦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 220◦]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 10 (top) shows the result of the EWMLES mean pressure distribution  (mean-cp) along with the initial RANS solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Good agreement between  these curves are present for x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='13 where x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='13 is the average location  of the shock front of the SST-RANS solution which results into a sudden rise in  mean-cp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It is apparent that this agreement also persists for positions upstream  of the STG (x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06) which indicates that no upstream effect of the STG  exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' With regard to the EWMLES shock position the already described  shift in downstream direction is also present in this depiction and located at  x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Due to the comparatively early start in the averaging of mean-cp  it is not reasonable to compare the curves for x/c ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 since transient effects  from the switch from RANS to EWMLES still exist in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  A further quantitive flow comparison between SST-RANS and EWMLES is  given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 10 (bottom) which shows mean skin friction distributions (mean-  cf).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In the flow region upstream of the STG (x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06) good agreement  are visible again which confirms the previously mentioned absence of potential  STG upstream effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' However, for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 ≤ x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 remarkable deviations  appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' One observes a significant drop in mean-cf directly downstream of  the STG and its increase with a peak value at x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='13 and a mean-cf-  level which is comparable to the mean-cf value at the STG position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Although  a similar behaviour is present for the flat plate flow as described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2  the flat plate variations in mean-cf are of significantly smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The adaption  length which measures the distance between STG position and subsequent  peak in mean-cf amounts 46 δST G where δST G represents the boundary layer  thickness at the STG position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In case of the flat plate flow this adaption  length only amounts 6 δST G (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A further analysis of these deviations  with reference to the flat plate flow are given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='5 CTU  X/CSpringer Nature 2021 LATEX template  18  Grey area in Embedded WMLES on a nacelle-aircraft configuration  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 9 Isosurface of Q-Criterion (Q = 1010) at nacelle lower surface for LD2 scheme at  t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  region where 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 ≤ x/c ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25 we observe that the region of recirculation has  disappeared, at least for this transient period of time averaging since mean-cf  is always positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Furthermore additional distortions in the EWMLES mean-  cf distribution appear at x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='25 and x/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='40 which corresponds to  locations of the ∆ϕ coarsening steps of the mesh (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This indicates  that the local mesh resolutions of r∆ϕ = δϕ,min/10 might be locally at the  lower limit at these positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 Sensitivity studies  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 Positioning of the RANS-LES interface  Preliminary grid number estimations for different locations of the RANS-LES  interface in x-direction (xST G) demonstrated a strong dependence of xST G  and the total grid number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A shift of this boundary in downstream direction  allows to reduce the total grid number significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Exemplarily, moving xST G  by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='02c enables to reduce the total grid size about 100 Mio points without  violating the applied extension and resolution constraints for the refinement  area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This dependence is a consequence of the shortening of the refinement area  in x-direction by which the subregion with the highest cell density is narrowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Also, due to the dependence of ∆ϕΩ1 on δϕ,min(xST G) in subregion Ω1 it is  possible to increase ∆ϕΩ1 in the entire interval x/c ∈ [xST G;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16] (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  This dependency on the STG position suggests to place the RANS-LES  boundary as close as possible to the shock front and examine its effect on the  flow solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Based on the original assumption that the adaption length of the  STG amounts less than 10 δST G we estimated xST G/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08 as latest possible  position in order to avoid direct interactions with the shock front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Additionally,  for this estimation a potential shock movement in upstream direction until  xs,min = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1 was taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For the following examinations we used  Ma 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='8Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  19  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 10 Quantitave comparison of time and spanwise averaged pressure - (top) and skin  friction distributions (bottom) between the initial RANS and EWMLES solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  the same mesh as before to verify a basic applicability of a late RANS-LES  interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 11 shows mean-cp and mean-cf distributions of the EWMLES results  for xST G/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08 (green curves) where the same averaging procedure as in  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4 is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It is striking that the mean-cp distribution is almost  identical to the previous xST G/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 result (red) with maximum deviations  of two line thicknesses for x/c ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' However, with respect to mean-cf and  its adaption area downstream of the STG distinct differences compared to the  xST G/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 result exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Firstly, the initial decay is significantly weaker than  before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Furthermore, its adaption length is reduced and only amounts 19 δST G  so that its peak is located at almost the same position as for the xST G/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06  result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The peak value though, is significantly reduced and corresponding to  the initial RANS solution directly upstream of the shock position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A further  discussion of these features of the adaption regions is given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It is  remarkable that for x/c ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='16 the subsequent mean-cf evolution is almost  identical to the xST G/c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06 result which demonstrates an independence of  the flow solution with regard to the location of the RANS-LES interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='2 Impact of Numerical Scheme  A further objective of our research was to compare the effect of different numer-  ical schemes for the central discretisation of viscous fluxes which is applied in  the refinement region (LES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' In addition to the already employed LD2 scheme  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' 6 in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' 11 Effect of positioning of the RANS-LES interface on averaged surface pressure and  skin friction distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  numerical setup as in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' Although the necessity of the high quality LD2  scheme against the reference scheme has been demonstrated with the aid of  the DIT-testcase in 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' To give a qualitative impression of the  flowfield the Q-Criterion at Q = 1010 for a snapshot at t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU is shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 12 which can directly compared to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The comparison shows that  the previous formation of turbulent structures is now partially interrupted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Especially the region directly downstream of the STG lacks turbulent struc-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It is striking that coarser structures such as the clearly visible horseshoe  vortexes are preserved whereas tiny structures are vanished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This is in direct  agreement with the results from the DIT testcase which demonstrates that  small turbulent scales are strongly damped by the reference scheme (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  These observations are also present in the analysis of the average skin fric-  tion distribution (blue curve in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Whereas the mean surface pressure  is hardly affected by the numerical scheme, mean-cf shows large deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Especially the decay downstream of the STG indicates a lack of resolved  turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' 12 of  underresolved turbulence throughout the entire refinement region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='6  x/cSpringer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  21  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 12 Isosurface of Q-Criterion (Q = 1010) for reference central-scheme at nacelle lower  at t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='5 CTU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 13 Effect of different numerical schemes on averaged surface pressure and skin friction  distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='6 Reynolds number and mesh resolution effect on STG  adaption region  In the following we address the so far unsound behaviour of the adaption  region downstream of the STG arising for all shown configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As already  described before the adaption region displays the largest deviations with regard  to adaption length as well as maximal and minimal mean-cf-deviations for the  Ma 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='8RANS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2  EWMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' STG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' LD2  EWMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' STG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' LD2  EWMLES, STG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06, Reference  1  mean-cp  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='006  RANS  EWMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' STG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' LD2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='005  EWMLES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' STG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' LD2  EWMLES, STG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06, Reference  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='004  mean-cf  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='001  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='6  x/cSpringer Nature 2021 LATEX template  22  Grey area in Embedded WMLES on a nacelle-aircraft configuration  nacelle at xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' These features reduce for xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08c and almost  vanish but are still present for the flat plate test case (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 2 and 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A  closer look into the flow properties and mesh resolution at the location of the  STG suggests a dependency on Reδ,ST G (Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Here, Reδ,ST G is defined as a  Reynolds number referring to the local boundary layer thickness δST G as well  as velocity and kinematic viscosity at the outer edge of δST G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This Reynolds  number, which directly impacts the input statistics of the STG, has its lowest  number for the nacelle case at xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06c (4989) and increases for xST G =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06c (6975) and the flat plate flow (24200).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The ratio of turbulent- and laminar  viscosity (max (µt/µl)) which serves as measure of modelled turbulence shows  a comparable trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Since low Reynolds numbers enhance the stability of the  boundary layer and hence suppress turbulent fluctuations, this might lead to a  damping of the injected turbulent structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' As a consequence the boundary  layer evolves into a flow with significantly reduced turbulence which is visible  in a strongly reduced level of mean-cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Thus, it appears that the distinct  adaption region can be traced back to a low-Reynolds number effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Another reason might be due to the mesh resolution ∆y which amounts  δ/20 for the flat plate flow and coarsens to δ/16 and δ/12 for xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08c  and xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06c, respectively (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Since a resolution of ∆y = δ/20 is  actually defined as coarsest resolution in this flow direction the here observed  somewhat coarser resolutions might perturb a proper development of the  turbulent boundary layer [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Therefore further examinations of the transonic nacelle flow for higher Re∞  (resulting in larger Reδ) as well as finer resolutions ∆y will be performed in  future work in order to provide a verification of the here detected limits of  synthetic turbulence generation at locally low Reynolds numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Re∞  δST G/m  Reδ,ST G  ∆x  ∆y  max (µt/µl)  Flat Plate  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='7 Mio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='006  24200  δ/10  δ/20  87  Nacelle  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 Mio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='00024  4989  δ/11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='2  δ/11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='76  9  xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='06c  Nacelle  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='3 Mio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='00033  6975  δ/13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='75  δ/16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='17  10  xST G = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='08c  Table 1 Comparison of several local flow quantities at the location of the synthetic  turbulence generator for all presented configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  5 Conclusions  A scale-resolving WMLES methodology in conjunction with the SST tur-  bulence model was applied to the XRF-1 aircraft configuration with UHBR  nacelle at transonic flow conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The method was applied locally at the  Springer Nature 2021 LATEX template  Grey area in Embedded WMLES on a nacelle-aircraft configuration  23  nacelle surface in order to examine shock induced separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' A Synthetic  Turbulence Generator (STG) was employed to enhance the transition from  modelled to resolved turbulence at the RANS-LES interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Prior to the actual examination on the aircraft configurations basic func-  tionalities of the methodology were successfully verified for flows of decaying  isotropic turbulence and a flow over a flat plate for Reθ = 3030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  With regard to the target configuration a sophisticated mesh which refines  32 % of the nacelle outer surfaces and comprises 420 million grid points was  constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The main features of the mesh design are the dependence of mesh  resolution (∆x, ∆y and ∆z) on the local boundary layer thickness and the  consideration of a potential shock movement due to buffet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Analysis of the transient process of the simulation showed a well resolved  formation of turbulent structures over almost the entire refinement region with  a broad spectrum of turbulent scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' It has been demonstrated that these  features are also the result of the employed LD2 scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For a reference central-  scheme with higher artificial dissipation, small turbulent scales are damped  leading to globally underresolved turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Another outcome of this study is the observation that the STG - adaption  region correlates to the local Reynolds number as well as mesh resolution in  spanwise direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' For decreasing Reynolds numbers and coarser mesh resolu-  tions an increasing adaption length and more distinct decay in the skin friction  distribution were observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' We note that the methodology is only applicable  if the STG adaption region does not interfere with the transonic shock front  and therefore sufficient distance to the shock is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' This distance might  not be given in case of an upstream moving shock which would arise for strong  shock buffet at the given Reynolds number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Therefore further research on the  transonic nacelle flow for higher Reynolds numbers as well as finer resolutions  will be performed in future work to verify a potential reduction of the adaption  length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The authors gratefully acknowledge the Deutsche  Forschungsgemeinschaft DFG (German Research Foundation) for funding this  work in the framework of the research unit FOR 2895.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' The authors thank the  Helmholtz Gemeinschaft HGF (Helmholtz Association), Deutsches Zentrum  f¨ur Luft- und Raumfahrt DLR (German AerospaceCenter) and Airbus for pro-  viding the wind tunnel model and financing the wind tunnel measurements  Additionally, the authors gratefully acknowledge the computing time granted  by the Resource Allocation Board and provided on the supercomputer Lise and  Emmy at NHR@ZIB and NHR@G¨ottingen as part of the NHR infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  The calculations for this research were conducted with computing resources  under the project nii00164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Declarations  Funding: This study was funded by DFG (German Research Foundation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  24  Grey area in Embedded WMLES on a nacelle-aircraft configuration  Competing interests: The authors have no competing interests to declare  that are relevant to the content of this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='  org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1007/978-3-319-70031-1 7  [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Laraufie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Deck, Assessment of Reynolds stresses tensor reconstruc-  tion methods for synthetic turbulent inflow conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Application to  hybrid RANS/LES methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='ijheatfluidflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  007  [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Nagib, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Chauhan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Monkewitz, Approach to an asymptotic  state for zero pressure gradient turbulent boundary layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Philosoph-  ical Transactions of the Royal Society A: Mathematical, Physical and  Engineering Sciences 365(1852), 755–770 (2007)  [20] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Fran¸cois, Development of an Efficient Synthetic Turbulence Genera-  tor for Hybrid RANS/LES Methods (TU Braunschweig-Nieders¨achsisches  Springer Nature 2021 LATEX template  26  Grey area in Embedded WMLES on a nacelle-aircraft configuration  Forschungszentrum f¨ur Luftfahrt, 2020)  [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Spalart, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Streett, Young-person’s guide to detached-eddy simula-  tion grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' NASA Technical Reports Server (2001)  [22] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+page_content=' Menter, Best practice: scale-resolving simulations in ansys cfd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  ANSYS Germany GmbH 1 (2012)  [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Jacquin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Molton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Deck, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Maury, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content=' Soulevant, Experimental  study of shock oscillation over a transonic supercritical profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
+page_content='  AIAA  journal 47(9), 1985–1994 (2009)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E4T4oBgHgl3EQf2g20/content/2301.05299v1.pdf'}
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+arXiv:2301.02633v1  [math.DG]  6 Jan 2023
+COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE
+COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS
+STEFANO BORGHINI AND LORENZO MAZZIERI
+Abstract. In [3] an estimate for suitable skew-symmetric 2-tensors was claimed.
+Soon after,
+this estimate has been exploited to claim powerful classification results: most notably, it has been
+employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes
+with positive scalar curvature [6] and in connection with the Besse Conjecture [8]. In the present
+note we point out an issue in the argument proposed in [3] and we provide a counterexample to
+the estimate.
+1. Introduction
+The Black Hole Uniqueness Theorem for three-dimensional static solutions with positive scalar
+curvature and the Besse Conjecture for solutions to the Critical Point Equation are two very
+famous and related open problems in contemporary geometric analysis. Very recently, some very
+remarkable advances have been claimed on both of these problems in a series of papers [1, 2, 3, 6,
+7, 8]. In this short note, we point out an issue in the approach proposed in the above mentioned
+papers, providing counterexamples.
+To introduce the problems of interest together with some notation, let us recall that a three-
+dimensional static solution is a triple (M, g, f) satisfying
+fRic = ∇2f + R
+2 f g ,
+∆f = −R
+2 f ,
+(1.1)
+where (M, g) is a Riemannian manifold, f is a smooth function and Ric and R denote the Ricci
+tensor and the scalar curvature of g, respectively. When R is positive, it is natural to suppose that
+(M, g) is a compact manifold with boundary and that f is vanishing on the boundary. A strictly
+related problem is the so called Critical Point Equation, which consists in the following system
+(1 + f)
+�
+Ric − R
+n g
+�
+= ∇2f +
+R
+n(n − 1) g ,
+∆f = −
+R
+n − 1f
+(1.2)
+where the unknowns are given by the triple (M, g, f), with (M, g) a closed Riemannian manifold
+and f a smooth function.
+In [3], the authors aim at classifying solutions to the Critical Point Equation subject to the
+condition of having Positive Isotropic Curvature. To this end, they consider the differential 2-form
+ω = df ∧ ι∇fz ,
+where z indicates the traceless Ricci tensor, and they claim that it must vanish. Notice that,
+using (1.2), the differential 2-form ω can be rewritten as
+ω =
+1
+2(1 + f)df ∧ d|∇f|2 ,
+where | · | is the norm computed with respect to the metric g. If ω ≡ 0, then, using again the
+equation (1.2), one can prove that the Cotton tensor of g must also vanish, by a direct computation.
+It follows that either n = 3 and g is Locally Conformally Flat, or else n ≥ 4 and g has harmonic
+Weyl tensor. In both cases, the classification follows easily. The same strategy is adopted in [6]1,
+1Notice that this reference has been withdrawn by the authors during the preparation of the present note.
+1
+
+2
+S. BORGHINI AND L. MAZZIERI
+where this time the differential 2-form ω is defined as
+ω =
+1
+2f df ∧ d|∇f|2 ,
+with g and f satisfying (1.1). In both cases, the vanishing of ω is deduced through an integration
+by parts argument – which we describe in Subsection 2.2 below, in the case of static metrics –
+making a substantial use of the key estimate
+|∇ω|2 ≥ |δω|2 ,
+(1.3)
+which the authors claim to hold at all points of M where ω is not vanishing (see Lemma 5.5 in [3]).
+The proposed proof of (1.3) does not make use of the full strength of either (1.1) or (1.2). In fact,
+it is based on a local computation, in which the global structure of M is not playing any role. As
+such, if correct, it should work for every differential 2-form having the structure
+ω = λ(f) df ∧ d|∇f|2 .
+(1.4)
+for some smooth function λ = λ(f), independently of the validity of (1.1) or (1.2). Aim of the
+present note is to disprove the claim that every ω as in (1.4), defined on an open subset of a
+Riemannian manifold (M, g), satisfies estimate (1.3).
+In Section 3 we point out the issue in the original proof of (1.3), given in [3, Lemma 5.5], whereas
+in Section 4 we provide effective counterexamples to the claim. Namely, we show that
+For every smooth real function λ ̸≡ 0, there exist a smooth Riemannian metric g and a smooth
+function f such that |∇ω|2 < |δω|2, with ω = λ(f) df ∧ d|∇f|2.
+For the sake of completeness, we discuss in Section 2 how the validity of an estimate like (1.3)
+can be exploited to deduce that ω must vanish everywhere.
+2. Analysis of a skew-symmetric 2-tensor field
+To make our computations more transparent, we prefer to work with the tensor-fields formalism.
+However one can also work with the formalism of differential forms as done in [3]. Instead of ω
+defined as in (2.1), we consider the skew-symmetric 2-tensor field P, given by
+P = λ(f)
+�
+df ⊗ d|∇f|2 − d|∇f|2 ⊗ df
+�
+,
+(2.1)
+with λ, f and g as above. In this formalism, we have that estimate (1.3) is equivalent to
+|∇P|2 ≥ 2 |divP|2 ,
+(2.2)
+as 2 |∇ω|2 = |∇P|2 (the factor two comes from the slight difference in the definition of norms on dif-
+ferential forms and tensor, namely |∇ω|2 = �
+j<k
+�
+i(∇iωjk)2, whereas |∇P|2 = �
+j,k
+�
+i(∇iPjk)2)
+and δω = −divP. Notice that, replacing the constant 2 with the smaller constant 1/n, one gets
+the always valid lower bound |∇P|2 ≥ (1/n) |divP|2. Furthermore, exploiting the special struc-
+ture (2.1) of P, one can significantly improve on this bound, obtaining (n − 1)|∇P|2 ≥ 2 |divP|2
+(see the appendix). On the other hand, estimate (2.2) is too strong and cannot hold in general, as
+we will discuss below.
+2.1. Two differential identities. Here we discuss some basic though fundamental properties of
+a skew-symmetric 2-tensor P having the form (2.1).
+Proposition 2.1. Let (M, g) be a n-dimensional Riemannian manifold and let f ∈ C ∞(M).
+Then, the skew-symmetric 2-tensor field P defined as in (2.1), for some smooth real function λ,
+satisfies the identity
+∇P(X, Y, Z) + ∇P(Y, Z, X) + ∇P(Z, X, Y ) = 0 .
+Remark 1. In terms of the differential 2-form ω defined as in (1.4), the above identity is telling
+us that ω is closed, as observed in [3, Lemma 5.4]. Observe that, if ω is as in (1.4), then it is
+straightforward to realize that dω = (dλ/df) df ∧ df ∧ d|∇f|2 = 0.
+
+COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS3
+Proof. For simplicity we work with normal coordinates {x1, . . . , xn}. A simple computation gives
+∇iPjk =
+˙λ
+λPjk∇if + λ
+�
+∇2
+ijf∇k|∇f|2 − ∇j|∇f|2∇2
+ikf
+�
++ λ
+�
+∇jf∇2
+ik|∇f|2 − ∇2
+ij|∇f|2∇kf
+�
+.
+It is now a matter of computation to check that the sums over rotating indexes of the three pieces
+on the right hand side give zero. We compute
+Pjk∇if + Pki∇jf + Pij∇kf = λ
+�
+∇if∇jf∇k|∇f|2 − ∇if∇j|∇f|2∇kf
++ ∇jf∇kf∇i|∇f|2 − ∇jf∇k|∇f|2∇if + ∇kf∇if∇j|∇f|2 − ∇kf∇i|∇f|2∇jf
+�
+= 0 .
+Similarly, one has
+∇2
+ijf∇k|∇f|2 − ∇j|∇f|2∇2
+ikf + ∇2
+jkf∇i|∇f|2 − ∇k|∇f|2∇2
+jif + ∇2
+kif∇j|∇f|2 − ∇i|∇f|2∇2
+kjf = 0 ,
+∇jf∇2
+ik|∇f|2 − ∇2
+ij|∇f|2∇kf + ∇kf∇2
+ji|∇f|2 − ∇2
+jk|∇f|2∇if + ∇if∇2
+kj|∇f|2 − ∇2
+ki|∇f|2∇jf = 0 .
+It follows then that
+∇iPjk + ∇jPki + ∇kPij = 0 ,
+as claimed.
+□
+Another interesting property of P is that it satisfies a Bochner-type formula, as it is established
+in the following proposition.
+Proposition 2.2. Let (M, g) be a n-dimensional Riemannian manifold and let f ∈ C ∞(M).
+Then, the skew-symmetric 2-tensor field P defined as in (2.1), for some smooth real function λ,
+satisfies the identity
+1
+2∆|P|2 = |∇P|2 + 2⟨P | ∇(div P)⟩ +
+2R
+(n − 1)(n − 2)|P|2 + 2n − 4
+n − 2RjsPskPjk + 2WijksPisPjk .
+Proof. We perform our computations with respect to normal coordinates.
+Exploiting Proposi-
+tion 2.1 and the skew-symmetry of P, we compute
+∆|P|2 = 2∇i(Pjk∇iPjk)
+= 2|∇P|2 + 2Pjk∆Pjk
+= 2|∇P|2 − 2Pjk∇2
+ijPki − 2Pjk∇2
+ikPij
+= 2|∇P|2 + 4Pjk∇2
+ijPik
+= 2|∇P|2 + 4Pjk
+�
+∇2
+jiPik + RijisPsk + RijksPis
+�
+= 2|∇P|2 + 4Pjk (∇j(div P)k + RjsPsk + RijksPis) .
+To obtain the claimed identity, it is now enough to substitute the general formula for the Riemann
+tensor
+Rijks = −
+R
+(n − 1)(n − 2)(gikgjs − gisgjk) +
+1
+n − 2 (Rikgjs − Risgjk + gikRjs − gisRjk) + Wijks
+in the computation above.
+□
+The differential identity obtained in the previous proposition simplifies significantly when n = 3,
+since in this case the Weyl tensor vanishes and we get
+1
+2∆|P|2 = |∇P|2 + 2⟨P | ∇(div P)⟩ + R|P|2 − 2RjsPskPjk .
+(2.3)
+
+4
+S. BORGHINI AND L. MAZZIERI
+2.2. Application to 3-dimensional static solutions. In [6] a classification result for 3-dimensional
+static metrics with positive scalar curvature was proposed, building on the above Bochner-type
+formula and on the validity of estimate (3.4). For completeness, here we retrace their proof.
+Using formula (1.1), we can substitute the Ricci tensor in (2.3), getting
+1
+2∆|P|2 = |∇P|2 + 2⟨P | ∇(div P)⟩ + R
+2 |P|2 + 2
+f P(∇f, div P) − 1
+2f ⟨∇f | ∇|P|2⟩ ,
+(2.4)
+which can be rewritten as
+1
+2div(f|P|2) = f|∇P|2 + 2f⟨P | ∇(div P)⟩ + R
+2 f |P|2 + 2P(∇f, div P) .
+Since M is compact and f = 0 on ∂M, integrating by parts we obtain then
+0 =
+ˆ
+M
+�
+f|∇P|2 − 2f|div P|2 + R
+2 f |P|2
+�
+dµ .
+Here one can appreciate the strength of estimate (2.2). Indeed, if (2.2) is in force and R > 0, then
+|P|2 must vanish identically and we obtain the following
+Proposition 2.3. Let (M, g, f) be a compact three-dimensional static solution with positive scalar
+curvature and nonempty boundary. Assume that f = 0 on ∂M and positive in the interior. If
+estimate (2.2) holds for some P as in (2.1), then P must vanish identically and one has
+df ⊗ d|∇f|2 = d|∇f|2 ⊗ df .
+This is a crucial step in the strategy outlined in [6]. As anticipated, they exploit the identity
+P = 0 in combination with the static equation to deduce that the Cotton tensor must vanish. The
+classification follows, invoking a well known result by Kobayashi [4] and Lafontaine [5].
+As we are going to see in the next sections, it is not clear how to establish the validity of (2.2)
+in general, however we will prove in the appendix that the weaker lower bound |∇P|2 ≥ |divP|2
+holds true. This leads to
+ˆ
+M
+f|div P|2dµ ≥
+ˆ
+M
+R
+2 f |P|2dµ .
+Building on this integral inequality, one might classify three-dimensional static metrics with posi-
+tive scalar curvature admitting a divergence-free P-tensor.
+3. The issue in the proof of the estimate
+Here we retrace the proof of estimate (1.3) originally proposed in [3, Lemma 5.5], pointing out
+the main issue in the argument.
+As a first step, the authors find a local orthonormal frame with respect to which the tensor P
+has a nice structure. This part of the proof appears to be correct and it is an interesting fact
+on its own that will also be helpful in the appendix, so we include it here as a lemma. In the
+following statement it is helpful to consider the vector valued 1-form A : TM → TM defined by
+P(X, Y ) = g(AX, Y ). In coordinates: Aj
+i = gjmPim.
+Lemma 3.1. Let (M, g) be a n-dimensional Riemannian manifold. Let f ∈ C ∞(M) and let P be
+the tensor defined by (2.1). Let x ∈ M be a point with |P|(x) ̸= 0. Then in a small neighborhood
+U of x it holds |P| ̸= 0, |∇f| ̸= 0, |A∇f| ̸= 0 and there exists a smooth orthonormal frame
+{E1, . . . , En} with E1 = ∇f/|∇f| and E2 = AE1/|AE1|. With respect to this frame, the tensor P
+rewrites as
+P = u
+�
+θ1 ⊗ θ2 − θ2 ⊗ θ1�
+,
+(3.1)
+where u is a smooth function and {θ1, . . . , θn} is the dual coframe of {E1, . . . , En} (namely,
+θi(Ej) = δi
+j at any point in U).
+
+COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS5
+Proof. A proof of this fact is given in [3], however we write here a shorter self contained version.
+We first construct the orthonormal frame in the lemma.
+Consider a neighborhood U of x
+in which |P| ̸= 0.
+From the definition (2.1) of P, it is clear that |∇f| ̸= 0 in U as well.
+In
+particular the vector E1 = ∇f/|∇f| is well defined in U. We complete E1 to an orthonormal
+frame {E1, �E2, . . . , �En} in U. Since g(E1, �Ei) = 0 for i ≥ 2, we have ∇ �
+Eif = 0 for any i ≥ 2, hence
+P( �Ei, �Ej) = λ(f)
+�
+∇ �
+Eif ∇ �
+Ej|∇f|2 − ∇ �
+Ei|∇f|2 ∇ �
+Ejf
+�
+= 0 ,
+(3.2)
+for any i, j ≥ 2. Since |P| ̸= 0 in U, then at any point in U it holds g(AE1, �Ej) = P(E1, �Ej) ̸= 0
+for some j. In particular AE1 ̸= 0 in U. Since g(AE1, E1) = P(E1, E1) = 0, it follows that AE1 is
+orthogonal to E1. In particular, the vector E2 = AE1/|AE1| is well defined and orthonormal to E1
+on the whole U. We can then complete E1, E2 to an orthonormal frame {E1, . . . , En} in U. This
+is precisely the orthonormal frame described in the statement of the lemma. Notice in particular
+that
+P(E1, Ej) = g(AE1, Ej) = |AE1| g(E2, Ej) = |AE1| δ2j .
+In view of (3.2), we deduce that the only nonzero entries of P are P(E1, E2) = −P(E2, E1).
+Formula (3.1) follows.
+□
+Next, the authors compute |∇P|2 and |div P|2 with respect to this frame. The computations
+regarding |∇P|2 appear to be correct. On the other hand, it seems to us that the expression of
+the divergence term worked out by the authors contains a mistake. A simple calculation (see the
+appendix for more details) gives
+(div P)(E1) = −E2(u) +
+n
+�
+i=3
+⟨∇EiEi | E2⟩ u = −E2(u) +
+n
+�
+i=3
+⟨Ei | [E2, Ei]⟩ u ,
+(div P)(E2) = E1(u) −
+n
+�
+i=3
+⟨∇EiEi | E1⟩ u = E1(u) +
+n
+�
+i=3
+⟨Ei | [E1, Ei]⟩ u ,
+(div P)(Ek) = ⟨Ek | [E1, E2]⟩ u ,
+k ≥ 3 .
+(3.3)
+It is worth pointing out that the frame {E1, . . . , En} was constructed with a pointwise argument.
+The frame is easily seen to be smooth, but it is important to observe that it is not necessarily
+induced from a local coordinate system. In particular, the Lie brackets [Ei, Ej] are not necessarily
+vanishing. This seems to be the core of the issue: in fact, the authors claim that
+div P = −E2(u)θ1 + E1(u)θ2 .
+(3.4)
+In view of (3.3), this formula appears to be incorrect whenever the Lie brackets do not vanish.
+Remark 2. In [3], and more precisely in the final page of the proof of [3, Lemma 5.5] this formula is
+written as δω = E2(u)θ1 − E1(u)θ2. As already observed, ω corresponds to our P in the formalism
+of the differential forms, and the codifferential δ is clearly related to the divergence through the
+formula δω = −divP.
+4. Counterexamples to estimate (1.3)
+We work in dimension 3 for simplicity, but similar counterexamples might be constructed in
+higher dimension as well. Consider local coordinates {r, x1, x2} defined on an open set, a positive
+smooth function φ = φ(r) and the warped product metric
+g = dr ⊗ dr + φ2(dx1 ⊗ dx1 + dx2 ⊗ dx2) .
+Let then f ∈ C ∞(M) be a smooth function of the form f = ψ ◦ x1, for some smooth nonconstant
+real function ψ. Let us consider then a skew-symmetric 2-tensor field P as in (2.1), for some choice
+of λ. In local coordinates, we have that the components of P are given by
+Pαβ = λ
+�
+∇αf∇2
+βηf − ∇βf∇2
+αηf
+�
+gησ∇σf = λ ψ′
+φ2
+�
+∇αf∇2
+1βf − ∇βf∇2
+1αf
+�
+,
+
+6
+S. BORGHINI AND L. MAZZIERI
+where the greek indexes are running in {r, 1, 2}. Here and in what follows we will denote with ′
+the derivatives with respect to x1 and with a dot the derivatives with respect to r. The Christoffel
+symbols of the metric g are as follows
+Γr
+rr = Γr
+ri = Γi
+rr = Γk
+ij = 0 ,
+Γr
+ij = −φ ˙φδij ,
+Γj
+ri =
+˙φ
+φδj
+i ,
+where the latin indexes are running in {1, 2}. It then follows easily that the only nonzero compo-
+nents of the Hessian are
+∇2
+11f = ψ′′ ,
+∇2
+1rf = −
+˙φ
+φ ψ′ ,
+and that
+P = λ
+˙φ
+φ3 (ψ′)3 �
+dr ⊗ dx1 − dx1 ⊗ dr
+�
+.
+Notice that we are in a setting similar to the one of Section 3, except that our frame
+{∂/∂r, ∂/∂x1, ∂/∂x2}
+is not orthonormal. Hence, to check that our P has the structure prescribed in (3.1), one should
+write its local expression, with respect to an orthonormal frame.
+This latter can be obtained
+setting E1 = (1/φ)∂/∂x1, E2 = ∂/∂r, E3 = (1/φ)∂/∂x2. Its dual orthonormal co-frame is then
+given by θ1 = φdx1, θ2 = dr, θ3 = φdx2. It is easy to check that this frame satisfies the properties
+described in Lemma 3.1 and that
+P = −λ
+˙φ
+φ4 (ψ′)3 �
+θ1 ⊗ θ2 − θ2 ⊗ θ1�
+.
+However, we prefer to perform our computations with respect to the frame fields induced by the
+local coordinates (r, x1, x2). In this framework, it is easy to show that the only nonzero components
+of ∇P are
+∇rP1r = −
+� ¨φ
+φ3 − 4
+˙φ2
+φ4
+�
+λ (ψ′)3 ,
+∇1P1r = −
+˙φ
+φ3 (λ (ψ′)3)′ ,
+∇2P12 = −
+˙φ2
+φ2 λ (ψ′)3 .
+It easily follows that
+divP = −
+˙φ
+φ5 (λ (ψ′)3)′ dr + λ (ψ′)3
+� ¨φ
+φ3 − 3
+˙φ2
+φ4
+�
+dx1 .
+Here it is possible to notice the discrepancy between our computations and formula (3.4), as
+computing the right hand side of that formula would give
+−
+˙φ
+φ5 (λ (ψ′)3)′ dr + λ (ψ′)3
+� ¨φ
+φ3 − 4
+˙φ2
+φ4
+�
+dx1 ,
+which looks very similar, but does not correspond to the correct value of divP. Computing the
+squared norms of ∇P and divP, one finally arrives at
+|∇P|2 − 2|divP|2 = 4λ2 ˙φ2(ψ′)6
+φ8
+�
+4
+˙φ2
+φ2 −
+¨φ
+φ
+�
+.
+To make this difference negative, it is then sufficient to specify a choice of the functions λ, ψ and
+φ such that the right hand side is negative. In particular, it is sufficient to choose φ in such a way
+that the quantity in round brackets is negative. This can be achieved, for example, setting
+φ = (r + c)−1/k,
+for some k > 3 and some c > 0 .
+
+COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS7
+It follows that, with this choice of φ, for any λ and any f = ψ ◦ x1, the estimate (2.2) does not
+hold. Hence, the lower bound (1.3) is false as well.
+Appendix
+For completeness, let us point out the correct relation always holding between |∇P| and |divP|.
+Let (M, g) be a n-dimensional Riemannian manifold, n ≥ 3. As in Section 3, we take a point x with
+|P|(x) ̸= 0 and we consider the local orthonormal frame {E1, . . . , En} provided by Lemma 3.1. We
+recall that, with respect to this frame, the tensor P takes the following form
+P = u
+�
+θ1 ⊗ θ2 − θ2 ⊗ θ1�
+.
+(4.1)
+Exploiting the compatibility of ∇ with the metric g, for any i, j, k we have
+0 = Ei (g(Ej, Ek)) = g(∇EiEj, Ek) + g(Ej, ∇EiEk) ,
+and in particular
+g(∇EiEk, Ek) = 0 ,
+g(∇EiEi, Ek) = −g(Ei, ∇EiEk) = −g(Ei, [Ei, Ek]) .
+We are now ready to compute the components of ∇P. Since P(Ei, Ej) = 0 whenever {i, j} ̸= {1, 2},
+we have
+∇EiP(E1, E2) = Ei (P(E1, E2)) − P(∇EiE1, E2) − P(E1, ∇EiE2)
+= Ei(u) − g(∇EiE1, E1)P(E1, E2) − g(∇EiE2, E2)P(E1, E2)
+= Ei(u) .
+Similarly, for any k ≥ 3, we have
+∇EiP(E1, Ek) = Ei(P(E1, Ek)) − P(∇EiE1, Ek) − P(E1, ∇EiEk)
+= − g(∇EiEk, E2)P(E1, E2)
+= − g(∇EiEk, E2) u ,
+and
+∇EiP(E2, Ek) = Ei(P(E2, Ek)) − P(∇EiE2, Ek) − P(E2, ∇EiEk)
+= − g(∇EiEk, E1)P(E2, E1)
+= g(∇EiEk, E1) u .
+Similarly, one computes ∇EiP(E1, E1) = ∇EiP(E2, E2) = 0 and ∇EiP(Ej, Ek) = 0 whenever j, k
+are ≥ 3. It is now easy to compute the divergence of P:
+(div P)(E1) = −E2(u) +
+n
+�
+i=3
+⟨∇EiEi | E2⟩ u = −E2(u) +
+n
+�
+i=3
+⟨Ei | [E2, Ei]⟩ u ,
+(div P)(E2) = E1(u) −
+n
+�
+i=3
+⟨∇EiEi | E1⟩ u = E1(u) −
+n
+�
+i=3
+⟨Ei | [E1, Ei]⟩ u ,
+(div P)(Ei) = −g(∇E1Ei, E2) u + g(∇E2Ei, E1) u ,
+i ≥ 3 .
+Using the inequality (�k
+i=1 xi)2 ≤ k �k
+i=1 x2
+i , a simple calculation then gives
+|divP|2
+n − 1
+≤
+2
+�
+k=1
+�
+Ek(u)2 +
+n
+�
+i=3
+⟨Ei | [Ei, Ek]⟩2u2
+�
++
+2
+n − 1
+n
+�
+i=3
+�
+⟨∇E1Ei | E2⟩2 + ⟨∇E2Ei | E1⟩2�
+u2
+≤
+2
+�
+k=1
+�
+Ek(u)2 +
+n
+�
+i=3
+⟨Ei | [Ei, Ek]⟩2u2
+�
++
+n
+�
+i=3
+�
+⟨∇E1Ei | E2⟩2 + ⟨∇E2Ei | E1⟩2�
+u2 .
+
+8
+S. BORGHINI AND L. MAZZIERI
+On the other hand
+1
+2|∇P|2 ≥
+2
+�
+k=1
+�
+(∇EkP(E1, E2))2 +
+n
+�
+i=3
+(∇EiP(Ek, Ei))2 +
+n
+�
+i=3
+(∇EkP(Ek, Ei))2
+�
+=
+2
+�
+k=1
+�
+Ek(u)2 +
+n
+�
+i=3
+⟨Ei | [Ei, Ek]⟩2u2
+�
++
+n
+�
+i=3
+�
+⟨∇E1Ei | E2⟩2 + ⟨∇E2Ei | E1⟩2�
+u2 .
+In conclusion, we have shown the following.
+Proposition 4.1. Let (M, g) be a n-dimensional Riemannian manifold, n ≥ 3. Let f ∈ C ∞(M)
+and let P be the tensor defined by (2.1). Then, at any point of M it holds
+|∇P|2 ≥
+2
+n − 1 |divP|2 .
+(4.2)
+Proof. Estimate (4.2) follows immediately from the computations above at any point where P has
+the form (2.1), that is, at any point where |P| ̸= 0. Let then x be a point where |P| = 0. If |P|
+vanishes identically in a neighborhood of x, then |∇P| = |div P| = 0 in that neighborhood, and
+inequality (4.2) is trivially satisfied. Otherwise there exists a sequence of points xi converging to
+x with |P|(xi) ̸= 0. Since estimate (4.2) holds at the points xi, then it must hold at x as well by
+continuity.
+□
+Acknowledgements. The authors would like to thank R. Beig, P. T. Chru´sciel and W. Simon
+for stimulating discussions about the classification of static vacuum spacetimes. The authors are
+members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilit`a e le loro Applicazioni
+(GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
+References
+[1] S. Hwang, M. Santos, and G. Yun. Closed generalized Einstein manifolds with positive isotropic curvature. arXiv
+preprint arXiv:2108.10675, 2021.
+[2] S. Hwang and G. Yun. Vacuum static spaces with positive isotropic curvature. arXiv preprint arXiv:2103.15818,
+2021.
+[3] S. Hwang and G. Yun. Besse conjecture with positive isotropic curvature. Annals of Global Analysis and Geometry,
+pages 1–26, 2022.
+[4] O. Kobayashi. A differential equation arising from scalar curvature function. J. Math. Soc. Japan, 34(4):665–675,
+1982.
+[5] J. Lafontaine. Sur la g´eom´etrie d’une g´en´eralisation de l’´equation diff´erentielle d’Obata. J. Math. Pures Appl.
+(9), 62(1):63–72, 1983.
+[6] X. Xu and J. Ye. Closed three-dimensional vacuum static spaces. Inventiones mathematicae, pages 1–17, 2022.
+[7] G. Yun and S. Hwang. V-static spaces with positive isotropic curvature. arXiv preprint arXiv:2103.16039, 2021.
+[8] G. Yun and S. Hwang. Critical point equation on three-dimensional manifolds and the Besse conjecture. arXiv
+preprint arXiv:2208.10887, 2022.
+S. Borghini, Universit`a degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy
+Email address: stefano.borghini@unitn.it
+L. Mazzieri, Universit`a degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy
+Email address: lorenzo.mazzieri@unitn.it
+
diff --git a/8tE0T4oBgHgl3EQfwgFY/content/tmp_files/load_file.txt b/8tE0T4oBgHgl3EQfwgFY/content/tmp_files/load_file.txt
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@@ -0,0 +1,340 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf,len=339
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='02633v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='DG]  6 Jan 2023  COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE  COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS  STEFANO BORGHINI AND LORENZO MAZZIERI  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In [3] an estimate for suitable skew-symmetric 2-tensors was claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Soon after,  this estimate has been exploited to claim powerful classification results: most notably, it has been  employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes  with positive scalar curvature [6] and in connection with the Besse Conjecture [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In the present  note we point out an issue in the argument proposed in [3] and we provide a counterexample to  the estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Introduction  The Black Hole Uniqueness Theorem for three-dimensional static solutions with positive scalar  curvature and the Besse Conjecture for solutions to the Critical Point Equation are two very  famous and related open problems in contemporary geometric analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Very recently, some very  remarkable advances have been claimed on both of these problems in a series of papers [1, 2, 3, 6,  7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In this short note, we point out an issue in the approach proposed in the above mentioned  papers, providing counterexamples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  To introduce the problems of interest together with some notation, let us recall that a three-  dimensional static solution is a triple (M, g, f) satisfying  fRic = ∇2f + R  2 f g ,  ∆f = −R  2 f ,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1)  where (M, g) is a Riemannian manifold, f is a smooth function and Ric and R denote the Ricci  tensor and the scalar curvature of g, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' When R is positive, it is natural to suppose that  (M, g) is a compact manifold with boundary and that f is vanishing on the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' A strictly  related problem is the so called Critical Point Equation, which consists in the following system  (1 + f)  �  Ric − R  n g  �  = ∇2f +  R  n(n − 1) g ,  ∆f = −  R  n − 1f  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2)  where the unknowns are given by the triple (M, g, f), with (M, g) a closed Riemannian manifold  and f a smooth function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  In [3], the authors aim at classifying solutions to the Critical Point Equation subject to the  condition of having Positive Isotropic Curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' To this end, they consider the differential 2-form  ω = df ∧ ι∇fz ,  where z indicates the traceless Ricci tensor, and they claim that it must vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Notice that,  using (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2), the differential 2-form ω can be rewritten as  ω =  1  2(1 + f)df ∧ d|∇f|2 ,  where | · | is the norm computed with respect to the metric g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' If ω ≡ 0, then, using again the  equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2), one can prove that the Cotton tensor of g must also vanish, by a direct computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  It follows that either n = 3 and g is Locally Conformally Flat, or else n ≥ 4 and g has harmonic  Weyl tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In both cases, the classification follows easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The same strategy is adopted in [6]1,  1Notice that this reference has been withdrawn by the authors during the preparation of the present note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  1  2  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' BORGHINI AND L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' MAZZIERI  where this time the differential 2-form ω is defined as  ω =  1  2f df ∧ d|∇f|2 ,  with g and f satisfying (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In both cases, the vanishing of ω is deduced through an integration  by parts argument – which we describe in Subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2 below, in the case of static metrics –  making a substantial use of the key estimate  |∇ω|2 ≥ |δω|2 ,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3)  which the authors claim to hold at all points of M where ω is not vanishing (see Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='5 in [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  The proposed proof of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3) does not make use of the full strength of either (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1) or (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In fact,  it is based on a local computation, in which the global structure of M is not playing any role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' As  such, if correct, it should work for every differential 2-form having the structure  ω = λ(f) df ∧ d|∇f|2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4)  for some smooth function λ = λ(f), independently of the validity of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1) or (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Aim of the  present note is to disprove the claim that every ω as in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4), defined on an open subset of a  Riemannian manifold (M, g), satisfies estimate (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  In Section 3 we point out the issue in the original proof of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3), given in [3, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='5], whereas  in Section 4 we provide effective counterexamples to the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Namely, we show that  For every smooth real function λ ̸≡ 0, there exist a smooth Riemannian metric g and a smooth  function f such that |∇ω|2 < |δω|2, with ω = λ(f) df ∧ d|∇f|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  For the sake of completeness, we discuss in Section 2 how the validity of an estimate like (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3)  can be exploited to deduce that ω must vanish everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Analysis of a skew-symmetric 2-tensor field  To make our computations more transparent, we prefer to work with the tensor-fields formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  However one can also work with the formalism of differential forms as done in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Instead of ω  defined as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), we consider the skew-symmetric 2-tensor field P, given by  P = λ(f)  �  df ⊗ d|∇f|2 − d|∇f|2 ⊗ df  �  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1)  with λ, f and g as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In this formalism, we have that estimate (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3) is equivalent to  |∇P|2 ≥ 2 |divP|2 ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2)  as 2 |∇ω|2 = |∇P|2 (the factor two comes from the slight difference in the definition of norms on dif-  ferential forms and tensor, namely |∇ω|2 = �  j<k  �  i(∇iωjk)2, whereas |∇P|2 = �  j,k  �  i(∇iPjk)2)  and δω = −divP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Notice that, replacing the constant 2 with the smaller constant 1/n, one gets  the always valid lower bound |∇P|2 ≥ (1/n) |divP|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Furthermore, exploiting the special struc-  ture (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1) of P, one can significantly improve on this bound, obtaining (n − 1)|∇P|2 ≥ 2 |divP|2  (see the appendix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' On the other hand, estimate (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) is too strong and cannot hold in general, as  we will discuss below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Two differential identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Here we discuss some basic though fundamental properties of  a skew-symmetric 2-tensor P having the form (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let (M, g) be a n-dimensional Riemannian manifold and let f ∈ C ∞(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Then, the skew-symmetric 2-tensor field P defined as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), for some smooth real function λ,  satisfies the identity  ∇P(X, Y, Z) + ∇P(Y, Z, X) + ∇P(Z, X, Y ) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In terms of the differential 2-form ω defined as in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4), the above identity is telling  us that ω is closed, as observed in [3, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Observe that, if ω is as in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4), then it is  straightforward to realize that dω = (dλ/df) df ∧ df ∧ d|∇f|2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS3  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' For simplicity we work with normal coordinates {x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , xn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' A simple computation gives  ∇iPjk =  ˙λ  λPjk∇if + λ  �  ∇2  ijf∇k|∇f|2 − ∇j|∇f|2∇2  ikf  �  + λ  �  ∇jf∇2  ik|∇f|2 − ∇2  ij|∇f|2∇kf  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  It is now a matter of computation to check that the sums over rotating indexes of the three pieces  on the right hand side give zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' We compute  Pjk∇if + Pki∇jf + Pij∇kf = λ  �  ∇if∇jf∇k|∇f|2 − ∇if∇j|∇f|2∇kf  + ∇jf∇kf∇i|∇f|2 − ∇jf∇k|∇f|2∇if + ∇kf∇if∇j|∇f|2 − ∇kf∇i|∇f|2∇jf  �  = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Similarly, one has  ∇2  ijf∇k|∇f|2 − ∇j|∇f|2∇2  ikf + ∇2  jkf∇i|∇f|2 − ∇k|∇f|2∇2  jif + ∇2  kif∇j|∇f|2 − ∇i|∇f|2∇2  kjf = 0 ,  ∇jf∇2  ik|∇f|2 − ∇2  ij|∇f|2∇kf + ∇kf∇2  ji|∇f|2 − ∇2  jk|∇f|2∇if + ∇if∇2  kj|∇f|2 − ∇2  ki|∇f|2∇jf = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  It follows then that  ∇iPjk + ∇jPki + ∇kPij = 0 ,  as claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  □  Another interesting property of P is that it satisfies a Bochner-type formula, as it is established  in the following proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let (M, g) be a n-dimensional Riemannian manifold and let f ∈ C ∞(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Then, the skew-symmetric 2-tensor field P defined as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), for some smooth real function λ,  satisfies the identity  1  2∆|P|2 = |∇P|2 + 2⟨P | ∇(div P)⟩ +  2R  (n − 1)(n − 2)|P|2 + 2n − 4  n − 2RjsPskPjk + 2WijksPisPjk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' We perform our computations with respect to normal coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Exploiting Proposi-  tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1 and the skew-symmetry of P, we compute  ∆|P|2 = 2∇i(Pjk∇iPjk)  = 2|∇P|2 + 2Pjk∆Pjk  = 2|∇P|2 − 2Pjk∇2  ijPki − 2Pjk∇2  ikPij  = 2|∇P|2 + 4Pjk∇2  ijPik  = 2|∇P|2 + 4Pjk  �  ∇2  jiPik + RijisPsk + RijksPis  �  = 2|∇P|2 + 4Pjk (∇j(div P)k + RjsPsk + RijksPis) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  To obtain the claimed identity, it is now enough to substitute the general formula for the Riemann  tensor  Rijks = −  R  (n − 1)(n − 2)(gikgjs − gisgjk) +  1  n − 2 (Rikgjs − Risgjk + gikRjs − gisRjk) + Wijks  in the computation above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  □  The differential identity obtained in the previous proposition simplifies significantly when n = 3,  since in this case the Weyl tensor vanishes and we get  1  2∆|P|2 = |∇P|2 + 2⟨P | ∇(div P)⟩ + R|P|2 − 2RjsPskPjk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3)  4  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' BORGHINI AND L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' MAZZIERI  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Application to 3-dimensional static solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In [6] a classification result for 3-dimensional  static metrics with positive scalar curvature was proposed, building on the above Bochner-type  formula and on the validity of estimate (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' For completeness, here we retrace their proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Using formula (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), we can substitute the Ricci tensor in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3), getting  1  2∆|P|2 = |∇P|2 + 2⟨P | ∇(div P)⟩ + R  2 |P|2 + 2  f P(∇f, div P) − 1  2f ⟨∇f | ∇|P|2⟩ ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4)  which can be rewritten as  1  2div(f|P|2) = f|∇P|2 + 2f⟨P | ∇(div P)⟩ + R  2 f |P|2 + 2P(∇f, div P) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Since M is compact and f = 0 on ∂M, integrating by parts we obtain then  0 =  ˆ  M  �  f|∇P|2 − 2f|div P|2 + R  2 f |P|2  �  dµ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Here one can appreciate the strength of estimate (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Indeed, if (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) is in force and R > 0, then  |P|2 must vanish identically and we obtain the following  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let (M, g, f) be a compact three-dimensional static solution with positive scalar  curvature and nonempty boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Assume that f = 0 on ∂M and positive in the interior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' If  estimate (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) holds for some P as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), then P must vanish identically and one has  df ⊗ d|∇f|2 = d|∇f|2 ⊗ df .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  This is a crucial step in the strategy outlined in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' As anticipated, they exploit the identity  P = 0 in combination with the static equation to deduce that the Cotton tensor must vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The  classification follows, invoking a well known result by Kobayashi [4] and Lafontaine [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  As we are going to see in the next sections, it is not clear how to establish the validity of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2)  in general, however we will prove in the appendix that the weaker lower bound |∇P|2 ≥ |divP|2  holds true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' This leads to  ˆ  M  f|div P|2dµ ≥  ˆ  M  R  2 f |P|2dµ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Building on this integral inequality, one might classify three-dimensional static metrics with posi-  tive scalar curvature admitting a divergence-free P-tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The issue in the proof of the estimate  Here we retrace the proof of estimate (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3) originally proposed in [3, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='5], pointing out  the main issue in the argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  As a first step, the authors find a local orthonormal frame with respect to which the tensor P  has a nice structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' This part of the proof appears to be correct and it is an interesting fact  on its own that will also be helpful in the appendix, so we include it here as a lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In the  following statement it is helpful to consider the vector valued 1-form A : TM → TM defined by  P(X, Y ) = g(AX, Y ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In coordinates: Aj  i = gjmPim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let (M, g) be a n-dimensional Riemannian manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let f ∈ C ∞(M) and let P be  the tensor defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let x ∈ M be a point with |P|(x) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Then in a small neighborhood  U of x it holds |P| ̸= 0, |∇f| ̸= 0, |A∇f| ̸= 0 and there exists a smooth orthonormal frame  {E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , En} with E1 = ∇f/|∇f| and E2 = AE1/|AE1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' With respect to this frame, the tensor P  rewrites as  P = u  �  θ1 ⊗ θ2 − θ2 ⊗ θ1�  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1)  where u is a smooth function and {θ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , θn} is the dual coframe of {E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , En} (namely,  θi(Ej) = δi  j at any point in U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS5  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' A proof of this fact is given in [3], however we write here a shorter self contained version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  We first construct the orthonormal frame in the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Consider a neighborhood U of x  in which |P| ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  From the definition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1) of P, it is clear that |∇f| ̸= 0 in U as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  In  particular the vector E1 = ∇f/|∇f| is well defined in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' We complete E1 to an orthonormal  frame {E1, �E2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , �En} in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Since g(E1, �Ei) = 0 for i ≥ 2, we have ∇ �  Eif = 0 for any i ≥ 2, hence  P( �Ei, �Ej) = λ(f)  �  ∇ �  Eif ∇ �  Ej|∇f|2 − ∇ �  Ei|∇f|2 ∇ �  Ejf  �  = 0 ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2)  for any i, j ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Since |P| ̸= 0 in U, then at any point in U it holds g(AE1, �Ej) = P(E1, �Ej) ̸= 0  for some j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In particular AE1 ̸= 0 in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Since g(AE1, E1) = P(E1, E1) = 0, it follows that AE1 is  orthogonal to E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In particular, the vector E2 = AE1/|AE1| is well defined and orthonormal to E1  on the whole U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' We can then complete E1, E2 to an orthonormal frame {E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , En} in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' This  is precisely the orthonormal frame described in the statement of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Notice in particular  that  P(E1, Ej) = g(AE1, Ej) = |AE1| g(E2, Ej) = |AE1| δ2j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  In view of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2), we deduce that the only nonzero entries of P are P(E1, E2) = −P(E2, E1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  □  Next, the authors compute |∇P|2 and |div P|2 with respect to this frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The computations  regarding |∇P|2 appear to be correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' On the other hand, it seems to us that the expression of  the divergence term worked out by the authors contains a mistake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' A simple calculation (see the  appendix for more details) gives  (div P)(E1) = −E2(u) +  n  �  i=3  ⟨∇EiEi | E2⟩ u = −E2(u) +  n  �  i=3  ⟨Ei | [E2, Ei]⟩ u ,  (div P)(E2) = E1(u) −  n  �  i=3  ⟨∇EiEi | E1⟩ u = E1(u) +  n  �  i=3  ⟨Ei | [E1, Ei]⟩ u ,  (div P)(Ek) = ⟨Ek | [E1, E2]⟩ u ,  k ≥ 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3)  It is worth pointing out that the frame {E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , En} was constructed with a pointwise argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  The frame is easily seen to be smooth, but it is important to observe that it is not necessarily  induced from a local coordinate system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In particular, the Lie brackets [Ei, Ej] are not necessarily  vanishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' This seems to be the core of the issue: in fact, the authors claim that  div P = −E2(u)θ1 + E1(u)θ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4)  In view of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3), this formula appears to be incorrect whenever the Lie brackets do not vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In [3], and more precisely in the final page of the proof of [3, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='5] this formula is  written as δω = E2(u)θ1 − E1(u)θ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' As already observed, ω corresponds to our P in the formalism  of the differential forms, and the codifferential δ is clearly related to the divergence through the  formula δω = −divP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Counterexamples to estimate (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3)  We work in dimension 3 for simplicity, but similar counterexamples might be constructed in  higher dimension as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Consider local coordinates {r, x1, x2} defined on an open set, a positive  smooth function φ = φ(r) and the warped product metric  g = dr ⊗ dr + φ2(dx1 ⊗ dx1 + dx2 ⊗ dx2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Let then f ∈ C ∞(M) be a smooth function of the form f = ψ ◦ x1, for some smooth nonconstant  real function ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let us consider then a skew-symmetric 2-tensor field P as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), for some choice  of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In local coordinates, we have that the components of P are given by  Pαβ = λ  �  ∇αf∇2  βηf − ∇βf∇2  αηf  �  gησ∇σf = λ ψ′  φ2  �  ∇αf∇2  1βf − ∇βf∇2  1αf  �  ,  6  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' BORGHINI AND L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' MAZZIERI  where the greek indexes are running in {r, 1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Here and in what follows we will denote with ′  the derivatives with respect to x1 and with a dot the derivatives with respect to r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The Christoffel  symbols of the metric g are as follows  Γr  rr = Γr  ri = Γi  rr = Γk  ij = 0 ,  Γr  ij = −φ ˙φδij ,  Γj  ri =  ˙φ  φδj  i ,  where the latin indexes are running in {1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' It then follows easily that the only nonzero compo-  nents of the Hessian are  ∇2  11f = ψ′′ ,  ∇2  1rf = −  ˙φ  φ ψ′ ,  and that  P = λ  ˙φ  φ3 (ψ′)3 �  dr ⊗ dx1 − dx1 ⊗ dr  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Notice that we are in a setting similar to the one of Section 3, except that our frame  {∂/∂r, ∂/∂x1, ∂/∂x2}  is not orthonormal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Hence, to check that our P has the structure prescribed in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), one should  write its local expression, with respect to an orthonormal frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  This latter can be obtained  setting E1 = (1/φ)∂/∂x1, E2 = ∂/∂r, E3 = (1/φ)∂/∂x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Its dual orthonormal co-frame is then  given by θ1 = φdx1, θ2 = dr, θ3 = φdx2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' It is easy to check that this frame satisfies the properties  described in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1 and that  P = −λ  ˙φ  φ4 (ψ′)3 �  θ1 ⊗ θ2 − θ2 ⊗ θ1�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  However, we prefer to perform our computations with respect to the frame fields induced by the  local coordinates (r, x1, x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In this framework, it is easy to show that the only nonzero components  of ∇P are  ∇rP1r = −  � ¨φ  φ3 − 4  ˙φ2  φ4  �  λ (ψ′)3 ,  ∇1P1r = −  ˙φ  φ3 (λ (ψ′)3)′ ,  ∇2P12 = −  ˙φ2  φ2 λ (ψ′)3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  It easily follows that  divP = −  ˙φ  φ5 (λ (ψ′)3)′ dr + λ (ψ′)3  � ¨φ  φ3 − 3  ˙φ2  φ4  �  dx1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Here it is possible to notice the discrepancy between our computations and formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='4), as  computing the right hand side of that formula would give  −  ˙φ  φ5 (λ (ψ′)3)′ dr + λ (ψ′)3  � ¨φ  φ3 − 4  ˙φ2  φ4  �  dx1 ,  which looks very similar, but does not correspond to the correct value of divP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Computing the  squared norms of ∇P and divP, one finally arrives at  |∇P|2 − 2|divP|2 = 4λ2 ˙φ2(ψ′)6  φ8  �  4  ˙φ2  φ2 −  ¨φ  φ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  To make this difference negative, it is then sufficient to specify a choice of the functions λ, ψ and  φ such that the right hand side is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' In particular, it is sufficient to choose φ in such a way  that the quantity in round brackets is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' This can be achieved, for example, setting  φ = (r + c)−1/k,  for some k > 3 and some c > 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  COUNTEREXAMPLES TO A DIVERGENCE LOWER BOUND FOR THE COVARIANT DERIVATIVE OF SKEW-SYMMETRIC 2-TENSOR FIELDS7  It follows that, with this choice of φ, for any λ and any f = ψ ◦ x1, the estimate (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) does not  hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Hence, the lower bound (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='3) is false as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Appendix  For completeness, let us point out the correct relation always holding between |∇P| and |divP|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Let (M, g) be a n-dimensional Riemannian manifold, n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' As in Section 3, we take a point x with  |P|(x) ̸= 0 and we consider the local orthonormal frame {E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' , En} provided by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' We  recall that, with respect to this frame, the tensor P takes the following form  P = u  �  θ1 ⊗ θ2 − θ2 ⊗ θ1�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1)  Exploiting the compatibility of ∇ with the metric g, for any i, j, k we have  0 = Ei (g(Ej, Ek)) = g(∇EiEj, Ek) + g(Ej, ∇EiEk) ,  and in particular  g(∇EiEk, Ek) = 0 ,  g(∇EiEi, Ek) = −g(Ei, ∇EiEk) = −g(Ei, [Ei, Ek]) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  We are now ready to compute the components of ∇P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Since P(Ei, Ej) = 0 whenever {i, j} ̸= {1, 2},  we have  ∇EiP(E1, E2) = Ei (P(E1, E2)) − P(∇EiE1, E2) − P(E1, ∇EiE2)  = Ei(u) − g(∇EiE1, E1)P(E1, E2) − g(∇EiE2, E2)P(E1, E2)  = Ei(u) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Similarly, for any k ≥ 3, we have  ∇EiP(E1, Ek) = Ei(P(E1, Ek)) − P(∇EiE1, Ek) − P(E1, ∇EiEk)  = − g(∇EiEk, E2)P(E1, E2)  = − g(∇EiEk, E2) u ,  and  ∇EiP(E2, Ek) = Ei(P(E2, Ek)) − P(∇EiE2, Ek) − P(E2, ∇EiEk)  = − g(∇EiEk, E1)P(E2, E1)  = g(∇EiEk, E1) u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Similarly, one computes ∇EiP(E1, E1) = ∇EiP(E2, E2) = 0 and ∇EiP(Ej, Ek) = 0 whenever j, k  are ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' It is now easy to compute the divergence of P:  (div P)(E1) = −E2(u) +  n  �  i=3  ⟨∇EiEi | E2⟩ u = −E2(u) +  n  �  i=3  ⟨Ei | [E2, Ei]⟩ u ,  (div P)(E2) = E1(u) −  n  �  i=3  ⟨∇EiEi | E1⟩ u = E1(u) −  n  �  i=3  ⟨Ei | [E1, Ei]⟩ u ,  (div P)(Ei) = −g(∇E1Ei, E2) u + g(∇E2Ei, E1) u ,  i ≥ 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Using the inequality (�k  i=1 xi)2 ≤ k �k  i=1 x2  i , a simple calculation then gives  |divP|2  n − 1  ≤  2  �  k=1  �  Ek(u)2 +  n  �  i=3  ⟨Ei | [Ei, Ek]⟩2u2  �  +  2  n − 1  n  �  i=3  �  ⟨∇E1Ei | E2⟩2 + ⟨∇E2Ei | E1⟩2�  u2  ≤  2  �  k=1  �  Ek(u)2 +  n  �  i=3  ⟨Ei | [Ei, Ek]⟩2u2  �  +  n  �  i=3  �  ⟨∇E1Ei | E2⟩2 + ⟨∇E2Ei | E1⟩2�  u2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  8  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' BORGHINI AND L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' MAZZIERI  On the other hand  1  2|∇P|2 ≥  2  �  k=1  �  (∇EkP(E1, E2))2 +  n  �  i=3  (∇EiP(Ek, Ei))2 +  n  �  i=3  (∇EkP(Ek, Ei))2  �  =  2  �  k=1  �  Ek(u)2 +  n  �  i=3  ⟨Ei | [Ei, Ek]⟩2u2  �  +  n  �  i=3  �  ⟨∇E1Ei | E2⟩2 + ⟨∇E2Ei | E1⟩2�  u2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  In conclusion, we have shown the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let (M, g) be a n-dimensional Riemannian manifold, n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let f ∈ C ∞(M)  and let P be the tensor defined by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Then, at any point of M it holds  |∇P|2 ≥  2  n − 1 |divP|2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) follows immediately from the computations above at any point where P has  the form (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='1), that is, at any point where |P| ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Let then x be a point where |P| = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' If |P|  vanishes identically in a neighborhood of x, then |∇P| = |div P| = 0 in that neighborhood, and  inequality (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) is trivially satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Otherwise there exists a sequence of points xi converging to  x with |P|(xi) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Since estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='2) holds at the points xi, then it must hold at x as well by  continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  □  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The authors would like to thank R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Beig, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Chru´sciel and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Simon  for stimulating discussions about the classification of static vacuum spacetimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' The authors are  members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilit`a e le loro Applicazioni  (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Hwang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Santos, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Yun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+page_content=' arXiv  preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='10675, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Hwang and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Yun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Vacuum static spaces with positive isotropic curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='15818,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+page_content=' Yun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Besse conjecture with positive isotropic curvature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Annals of Global Analysis and Geometry,  pages 1–26, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+page_content=' Hwang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Critical point equation on three-dimensional manifolds and the Besse conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' arXiv  preprint arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='10887, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+page_content=' Borghini, Universit`a degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy  Email address: stefano.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='borghini@unitn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='it  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content=' Mazzieri, Universit`a degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy  Email address: lorenzo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='mazzieri@unitn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
+page_content='it' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQfwgFY/content/2301.02633v1.pdf'}
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+Indistinguishable telecom band photons from a single erbium ion in the solid state
+Salim Ourari,1, ∗ Łukasz Dusanowski,1, ∗ Sebastian P. Horvath,1, ∗ Mehmet T. Uysal,1, ∗
+Christopher M. Phenicie,1 Paul Stevenson,1, † Mouktik Raha,1 Songtao Chen,1, ‡
+Robert J. Cava,2 Nathalie P. de Leon,1 and Jeff D. Thompson1, §
+1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA
+2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
+Atomic defects in the solid state are a key component of quantum repeater networks for long-
+distance quantum communication [1]. Recently, there has been significant interest in rare earth ions
+[2–4], in particular Er3+ for its telecom-band optical transition [5–7], but their application has been
+hampered by optical spectral diffusion precluding indistinguishable single photon generation. In
+this work we implant Er3+ into CaWO4, a material that combines a non-polar site symmetry, low
+decoherence from nuclear spins [8], and is free of background rare earth ions, to realize significantly
+reduced optical spectral diffusion. For shallow implanted ions coupled to nanophotonic cavities with
+large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral
+diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz. This enables
+the observation of Hong-Ou-Mandel interference [9] between successively emitted photons with high
+visibility, measured after a 36 km delay line. We also observe spin relaxation times T1 = 3.7 s and
+T2 > 200 µs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear
+spins. This represents a significant step towards the construction of telecom-band quantum repeater
+networks with single Er3+ ions.
+Long-distance quantum networks are an enabling technology for quantum communication, distributed quantum
+computing and entanglement-enhanced sensing and metrology [10]. The rate of direct entanglement transmission with
+photons decreases exponentially with distance, but this can be overcome using quantum repeaters with memories
+[11].
+In particular, single atom-like defects in the solid state [1] have been used to demonstrate key milestones
+including spin-photon entanglement [12, 13] and single-photon transistors [14], remote entanglement of spins [15],
+entanglement purification [16] and memory-enhanced quantum communication [17]. A challenge to deploying these
+techniques in long-distance networks is that atomic systems typically operate at transition frequencies outside of the
+low-loss window of optical fibers, requiring wavelength conversion for long-distance propagation [18, 19].
+The rare earth ion Er3+ has a telecom-band optical transition at a wavelength of 1.5 µm that is widely exploited
+for solid-state optical amplifiers, and in dilute ensembles, as a quantum memory for light [20, 21]. Er3+ ions can
+have long spin [8, 22] and optical [23] coherence in a variety of host crystals, a property shared with other rare earth
+ions [24–26]. In recent years, micro- and nano-scale optical resonators have enabled the observation of enhanced
+single photon emission from Er3+ and other rare earth ions [3–5, 7, 27], which has subsequently enabled single-shot
+spin readout [4, 28] and coupling to nearby nuclear spins that could serve as ancilla qubits [29–31]. However, a
+central challenge to the development of quantum repeaters with single rare earth ions is spectral diffusion, which
+is particularly pronounced in nanophotonic devices used to achieve fast optical emission from single rare earth ions
+[4, 5, 7]. To date, indistinguishable single photon emission from a single rare earth ion has not been observed.
+Rare earth ions also provide a unique opportunity for materials engineering, as they can be incorporated into a
+wide range of host crystals while preserving their basic properties, including the optical transition wavelength and
+spin configuration [32–35]. An ideal host material would incorporate Er3+ on a non-polar site to suppress linear
+electric field shifts of the optical transition, and have a low concentration of nuclear spins, other magnetic impurities
+and particularly trace rare earth ions to allow long spin coherence and low fluorescence background [36].
+In this work, we demonstrate indistinguishable single photon emission from a single Er3+ ion coupled to a
+nanophotonic optical cavity. This is enabled by shallow ion implantation of Er3+ into CaWO4, a host material
+satisfying the above criteria and for which long electron spin coherence has recently been demonstrated in Er3+
+ensembles at millikelvin temperatures [8]. By coupling the ions to silicon nanophotonic circuits, we observe individual
+ions with single-scan optical linewidths of 150 kHz, and emission rate enhancement by a factor of P = 850 via the
+Purcell effect. Using a 36 km delay line, we observe Hong-Ou-Mandel (HOM) interference between successively
+emitted photons with a visibility of V = 80(4)%. We also demonstrate spin initialization and single-shot readout
+with a fidelity F = 0.972, as well as the preservation of electron spin coherence for more than 200 µs, limited by
+paramagnetic impurities in the sample. This demonstration is a key step for the development of quantum repeaters
+based on single rare earth ions, and Er3+ in particular.
+Our samples are produced by introducing erbium into commercially available high purity CaWO4 using ion
+implantation with an energy of 35 keV, targeting a depth of 10 nm. In a test sample implanted with a high Er3+
+fluence of 1×1012 ions/cm2, we observe an ensemble optical spectrum at T = 4 K consistent with substitutional Er3+
+arXiv:2301.03564v1  [quant-ph]  9 Jan 2023
+
+2
+on the Ca2+ site with S4 symmetry (Fig. 1a) [37, 38]. After annealing at 300 ◦C in air, the inhomogeneous optical
+linewidth of the Z1-Y1 transition at 1532.63 nm is 730 MHz (Fig. 1b). This is comparable to previously reported
+linewidths in bulk-doped samples (approximately 0.5-1 GHz [35, 39]), suggesting that the implantation damage is
+effectively removed by annealing.
+To resolve individual ions, we implant a second sample at a lower fluence of 5 × 109 ions/cm2. Single ions are
+probed using a silicon photonic crystal cavity that is fabricated on a separate silicon-on-insulator wafer, and then
+bonded to the top surface of the CaWO4 substrate (Fig. 1c-d) [5]. The device and sample are cooled to T = 0.47 K
+in a 3He cryostat, with optical and microwave access provided with a scanning probe head [40]. We probe single
+ions in the device using photoluminescence excitation (PLE) spectroscopy, by sweeping the frequency of a pulsed
+laser and observing the time-delayed fluorescence through the cavity with a superconducting nanowire single photon
+detector (SNSPD). The spectrum contains clearly resolved lines from individual Er3+ ions (Fig. 1e). The number
+of lines is roughly consistent with the expected number of ions in the cavity area A = 1.3 µm2, suggesting a high
+conversion efficiency. The following experiments are performed on the ion indicated by the arrow.
+Coupling the Er3+ ion to the cavity allows for optical preparation and measurement of the electron spin. We apply
+a magnetic field of |B| = 600 G to lift the degeneracy of the S = 1/2 ground and excited states, resulting in two spin-
+conserving transitions (A,B) and two spin-flip transitions (C,D) as shown in Fig. 2a-b (the magnetic moments for the
+ground and excited state are described in the supplementary information [41]). Tuning the cavity to the A transition
+enhances the decay rate of the excited state, shortening the lifetime from 6.3 ms to τ = 7.4 µs, corresponding to a
+Purcell factor of P = 850 (Fig. 2c). To enable spin readout, we engineer a cycling transition by selectively enhancing
+the A transition relative to D by a combination of detuning from the cavity and preferential orientation of the
+transition dipole moment with respect to the cavity polarization [28], resulting in ΓA/ΓD ≈ 1030(10) [41]. Spin
+initialization is performed by optical pumping on the A or B transitions while simultaneously driving the excited
+state MWe transition [42]. In Fig. 2d, we demonstrate spin initialization and readout with an average fidelity of
+F = 0.972 (Fig. 2d). The combination of high collection efficiency and low background from other Er3+ ions allows
+for high-contrast optical Rabi oscillations (Fig. 2e). After a π pulse, a single photon is detected with a probability
+P1 = 0.035, on top of a background count rate of Pb = P1/117. Both P1 and the signal-to-background ratio are
+larger than what is obtained with frequency converted NV centers by more than an order of magnitude [19], enabled
+by the high quantum efficiency and collection efficiency of the Er-cavity system.
+The linewidth of the spin-conserving transitions is determined using PLE spectroscopy. To avoid optical pumping,
+the excitation laser has two tones separated by approximately 1 GHz to drive the A and B transitions simultaneously.
+The typical linewidth of a single scan (1 minute) is approximately 150 kHz, while the line center has an r.m.s.
+fluctuation of 63 kHz over 12 hours (Fig. 2f). This represents a 100-fold improvement over previously reported
+linewidths for individual Er3+ ions in nanophotonic cavities [5, 7, 42], and is to our knowledge the narrowest optical
+transition observed for a solid-state defect in a nanophotonic device. We note that similar linewidths have been
+observed for single Er3+ ions in 19 µm thick Y2SiO5 membranes [6]. The single-scan linewidth is 7 times larger
+than the Purcell-enhanced radiative linewidth of the A transition, Γr = 1/τ = 2π × 21.4 kHz, however, photon
+echo experiments suggest that this linewidth is dominated by slow dynamics [41], such that indistinguishable photon
+emission may be possible on short timescales or with active feedback.
+We perform HOM two-photon interference measurements [9] on time-delayed photons using an unbalanced Mach-
+Zehnder interferometer (MZI) with a ∆L = 36 km delay line in one arm (Fig. 3a). By tuning the repetition rate of
+the excitation pulses to match the delay time of the long arm (∆t = 175 µs), successive photons may arrive at the
+final beamsplitter simultaneously, and HOM interference will suppress the probability of detecting one photon at each
+output if the photons are indistinguishable. Experimentally, we observe strongly suppressed coincidences (Fig. 3b),
+indicating a high degree of indistinguishability. In a control experiment, we artificially broaden the photon in the
+short arm using a fiber stretcher driven by a noise source, restoring the coincidence rate expected for distinguishable
+photons (Fig. 3c). We measure an HOM coincidence rate of R = 2 min−1, defined as the rate of simultaneous photon
+detection in the distinguishable photon case, corresponding to a per-shot coincidence probability of Pc = 8.5 × 10−6.
+The indistinguishability is quantified by the visibility V [43], given by V = 1 − 2A0/A|i|≥2, where A0 is the
+integrated counts under the central peak and A|i|≥2 is the average integrated counts in each side peak (Fig. 3b). The
+visibility is maximized for a coincidence window approaching zero, however the number of photons within this window
+(the acceptance fraction) will also be small (Fig. 3e). For coincidences with photon detection times t1, t2 separated
+by |t2 − t1| < 2τ (corresponding to an acceptance fraction of 63%), the raw visibility is over 70%, rising to 90% when
+the accidental coincidences from dark counts and ambient background are subtracted. Integrating under the entire
+peak in Fig. 3d and subtracting accidental coincidences gives V = 80(4)%. The residual distinguishability has a
+significant contribution (4%) due to the MZI output beamsplitter ratio deviating from 50:50. Therefore, we conclude
+that the effective linewidth over hundreds of microseconds is only slightly larger than the radiative linewidth [41].
+Lastly, we study the properties of the Er3+ spin, which has the potential to serve as a quantum memory for spin-
+
+3
+photon entanglement. In bulk Er3+:CaWO4 , the magnetic moment is anisotropic with gc = 1.25 and ga = 8.38 [38].
+However, for the individual ions studied in this work, we observe significantly distorted magnetic moments, including
+a variation of g in the aa-plane. These deviations can be reproduced with the inclusion of a small axial crystal field
+term [41], which may arise from proximity to the surface or the presence of a nearby defect.
+The spin relaxation time is T1 = 3.7 s, in line with previous reports [8], and is limited by the direct process with
+a T1 ∝ 1/B5 dependence [41]. Ramsey and Hahn echo experiments give T ∗
+2 = 247 ns and T2 = 44 µs, respectively
+(Fig. 4c-d). An XY64 dynamical decoupling sequence allows coherence to be preserved for longer than 200 µs (Fig. 4e),
+while also showing collapses and revivals due to the 183W nuclear spin bath.
+The Hahn echo T2 is improved by one order of magnitude from Er3+:Y2SiO5 under similar conditions [42], but the
+coherence is still significantly shorter than predictions based on CCE simulations accounting for the 183W nuclear
+spin bath (I = 1/2, 14.3% abundance). This implicates paramagnetic impurities in the host crystal or on the surface
+as the primary source of decoherence, with an inferred density of approximately 3 × 1016 cm−3 [41]. Indeed, longer
+spin echo coherence times of T2 = 23 ms were observed for bulk Er3+ ensembles in CaWO4 in Ref [8] by operating
+at dilution refrigerator temperatures to freeze out paramagnetic impurities. Although the coherence is not limited
+by the nuclear spin bath, dips in coherence due to a single strongly coupled 183W spin are observed in Fig. 4d.
+The results demonstrated in this work will enable spin-photon entanglement and HOM interference between
+multiple Er3+ emitters with postselection using a narrow coincidence window or active tracking of the transition
+frequencies. In future work, the radiative linewidth can be further increased using cavities with higher Q [44] or
+smaller mode volume [45].
+Furthermore, more careful annealing or surface preparation may reduce the spectral
+diffusion.
+The flexibility to incorporate Er3+ via ion implantation, instead of during growth, will allow future
+exploration of CaWO4 samples produced and refined using diverse techniques. Reducing the impurity concentration
+may also improve the optical linewidth: scaling the ground state magnetic linewidth 1/T ∗
+2 to the optical transition
+implies a significant magnetic noise contribution of 2π × 46 kHz.
+In this work, we have demonstrated an engineered material, ion-implanted Er3+:CaWO4, that enables indistin-
+guishable single photon generation from a single rare earth ion in the telecom band. We attribute the improved
+performance to the higher Er3+ site symmetry (compared to previous observations of single Er3+ ions [5, 7, 27]).
+Spectral multiplexing of many ions per node [42], using quantum eraser techniques to overcome static frequency
+differences [46], will enable higher repetition rates over long fiber segments, while simultaneously reducing the co-
+herence time requirements [47]. Additional storage capacity and functionality may be obtained from ancilla nuclear
+spin registers, as recently demonstrated for several rare-earth ion systems [30, 31], and ion implantation may allow
+for the creation of spatially modulated density profiles with strong magnetic ion-ion interactions.
+Acknowledgements:
+We acknowledge helpful conversations with Charles Thiel, Philippe Goldner, and Miloš
+Rančić. This work was primarily supported by the U.S. Department of Energy, Office of Science, National Quantum
+Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number
+DE-SC0012704.
+We also acknowledge support from the DOE Early Career award (for modeling of decoherence
+mechanisms and spin interactions), as well as AFOSR (FA9550-18-1-0334 and YIP FA9550-18-1-0081), the Eric
+and Wendy Schmidt Transformative Technology Fund, and DARPA DRINQS (D18AC00015) for establishing the
+materials spectroscopy pipeline and developing integrated nanophotonic devices.
+We acknowledge the use of
+Princeton’s Imaging and Analysis Center, which is partially supported by the PCCM, an NSF MRSEC (DMR-
+1420541), as well as the Princeton Micro-Nano Fabrication Center.
+Note: While finalizing this manuscript, we became aware of recent reporting the detection of single Er3+ ions in
+CaWO4 using magnetic resonance techniques [48].
+
+4
+−500 −250
+0
+250
+500
+Laser frequency (MHz)
+0.000
+0.005
+0.010
+Counts per pulse
+~10 nm
+CaWO4
+implanted Er3+ 
+Z
+X
+silicon cavity
+a
+b
+d
+e
+c
+20 µm
+Y X
+5 µm
+2 µm
+Y
+X
+Y
+X
+(i)
+(i)
+(ii)
+(ii)
+e
+Ca
+W
+O
+Er
+a = 5.2 Å
+c = 11.4 Å
+a
+−6
+−3
+0
+3
+6
+Laser frequency (GHz) 
+- 1532.62 nm
+Fluorescence (a.u.)
+Z
+Y
+X
+FIG. 1. Er3+:CaWO4 device architecture. a CaWO4 crystal structure, with a substitutional Er3+ impurity in an S4 Ca2+
+site. b A dense implanted Er3+:CaWO4 ensemble has an inhomogeneous optical linewidth of 730 MHz on the Z1-Y1 transition.
+In addition to the central peak, we observe hyperfine structure from 167Er with nuclear spin I = 7/2. c Scanning electron
+microscope image of a representative silicon nanophotonic device, consisting of a photonic crystal grating coupler [inset (i)]
+that tapers adiabatically into a bus waveguide connected to a photonic crystal nanobeam cavity [inset (ii)]. d Erbium ions
+are implanted targeting a depth of 10 nm, and couple evanescently to the silicon photonic crystal on the surface. e PLE
+spectrum of Er3+ ions coupled to the cavity, with resolved single ion lines. The red arrow indicates the ion used for subsequent
+experiments.
+−500 −250
+0
+250
+500
+Detuning (kHz)
+4.50
+4.75
+5.00
+Time (hours)
+−500 −250
+0
+250 500
+Detuning (kHz)
+0
+2
+4
+6
+8
+10
+12
+Time (hours)
+A
+B
+D
+C
+MWg
+MWe
+|↑e⟩ 
+|↓e⟩
+|↑g⟩
+|↓g⟩
+1532 nm
+7 GHz
+6 GHz
+−10
+−5
+0
+5
+10
+Frequency (GHz)
+Reflection
+A
+B
+C
+D
+a
+b
+c
+d
+e
+f
+0
+300
+600
+Optical pulse width (ns)
+0.000
+0.018
+0.035
+Counts per pulse
+init. |↑g⟩
+init. |↓g⟩
+10
+0 10
+1 10
+2 10
+3 10
+4
+Time (µs)
+Fluorescence (a.u.)
+0
+5
+10
+15
+Number of photons
+10
+−4
+10
+−3
+10
+−2
+10
+−1
+10
+0
+Probability
+FIG. 2. Efficient photon collection from a cavity-coupled ion. a Er3+ level structure. In a magnetic field, Er3+ has
+four distinct optical transitions. The field strength is |B| = 600 G, oriented in the aa-plane, 22o from the X-axis. b Reflection
+spectrum of the cavity showing a full-width, half-maximum linewidth of κ = 1.0 GHz (Q = 1.9 × 105), which is tuned into
+resonance with the A transition. c The lifetime of the |↑e⟩ excited state is reduced to 7.4 µs (blue), which is 850 times shorter
+than the bulk lifetime of 6.3 ms (orange). d Histogram of photon counts obtained during spin readout after initializing in
+|↑g⟩ and |↓g⟩. The average readout fidelity is F = 0.972, using a threshold of one photon. The solid line is a fit to a Poisson
+distribution with average photon number ¯n = 6.4. e Optical Rabi oscillation on transition A. The peak single photon emission
+probability is P1 = 0.035. f Repeated PLE scans show an average single-scan linewidth of 150 kHz, and long-term diffusion
+of the line center of 63 kHz.
+
+8888
+888888888888888888888888885
+c
+75:25
+BS
+50:50
+BS
+36 km
+fiber
+SNSPD
+SNSPD
+fiber
+stretcher
+PC
+PC
+∆t
+VOA
+FG
+d
+a
+e
+−525
+−350
+−175
+0
+175
+350
+525
+0
+20
+40
+60
+80
+HOM coincidences
+−525
+−350
+−175
+0
+175
+350
+525
+Detection time difference t1 − t2 (μs)
+0
+20
+40
+60
+80
+HOM coincidences
+b
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Visibility
+0.0
+0.5
+1.0
+1.5
+2.0
+Coincidence window / (2T1)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Acceptance fraction
+A0
+A1
+A-1
+A-2
+A-3
+A2
+A3
+−30
+−15
+0
+15
+30
+Detection time difference t1 − t2 (μs)
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Norm. HOM coincidences
+FIG. 3. Generation of indistinguishable photons. a Schematic of the HOM interferometer, indicating beamsplitters (BS),
+a variable optical attenuator (VOA), polarization controllers (PC) and a fiber stretcher driven by a noise source (FG) to tune the
+distinguishability. b Histogram of coincidences detected in a 4 hour measurement period. The Hong-Ou-Mandel effect results
+in a suppressed probability of coincidences at zero delay, indicating indistinguishable single-photon emission. c Histogram
+of coincidences in a control experiment with a noise source applied to the fiber stretcher, destroying the indistinguishability
+and Hong–Ou–Mandel interference. d Zoom-in around the zero time delay HOM interference pattern. The red line shows
+a model including background counts (black dashed line) and pure dephasing of the optical transition.
+The blue dashed
+line shows a simple model for the control experiment assuming perfect distinguishability, while the solid blue line shows a
+model incorporating the finite bandwidth of the noise source [41]. e Interference visibility (top) and relative coincidence rate
+(bottom) as a function of the coincidence window, before (green) and after (red) subtracting the accidental coincidences from
+the detector and ambient background dark counts.
+
+6
+c
+e
+a
+b
+0.0
+0.4
+0.8
+Free evolution time (µs) 
+0.50
+0.75
+1.00
+Population |↑g⟩
+0
+5
+10
+Wait time (s)
+0.50
+0.75
+1.00
+Population |↑g⟩
+0
+150
+300
+MWg pulse width (ns)
+0.0
+0.5
+1.0
+Population |↑g⟩
+d
+0
+200
+400
+600
+800
+1000
+1200
+Free evolution time (µs) 
+0.4
+0.6
+0.8
+1.0
+Population |↑g⟩
+0
+50
+100
+Free evolution time (µs) 
+0.50
+0.75
+1.00
+Population |↓g⟩
+FIG. 4. Spin dynamics. a Rabi oscillations after initializing into |↑g⟩ (blue) or |↓g⟩ (orange). The spin transition frequency
+fMWg = 7.0 GHz.
+b Spin relaxation after initialization into |↑g⟩.
+An exponential fit yields T1 = 3.7(3) s.
+c Ramsey
+measurement. Fitting to e−(t/T ∗
+2 )n reveals a T ∗
+2 = 247(9) ns with n = 2.2(3). d A Hahn echo measurement shows dips
+in coherence resulting from the 183W nuclear spin bath. The grey lines show CCE simulations for randomly selected 183W
+configurations, where each configuration includes a single strongly coupled 183W spin required to reproduce the dips. The blue
+lines include an additional, phenomenological stretched decay with T2 = 44 µs. e Applying an XY64 dynamical decoupling
+sequence extends the spin coherence to longer times. Here, the grey lines show CCE simulations for the same 183W bath
+configurations in panel (d), while the blue lines have an additional phenomenological decay of 460 µs.
+
+7
+∗ These authors contributed equally to this work.
+† Present address: Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
+‡ Present address: Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA
+§ jdthompson@princeton.edu
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+Supplementary information for indistinguishable telecom band photons from a single
+erbium ion in the solid state
+Salim Ourari,1, ∗ Łukasz Dusanowski,1, ∗ Sebastian P. Horvath,1, ∗ Mehmet T. Uysal,1, ∗ Christopher M. Phenicie,1
+Paul Stevenson,1 Mouktik Raha,1 Songtao Chen,1 Robert J. Cava,2 Nathalie P. de Leon,1 and Jeff D. Thompson1, †
+1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA
+2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
+CONTENTS
+I. Photon collection efficiency
+1
+II. CaWO4 sample preparation
+2
+III. Site-selective excitation spectroscopy
+2
+IV. Spin state initialization and readout
+3
+V. Engineering an optical cycling transition
+3
+VI. Photon echo investigation of the optical coherence
+4
+VII. HOM fit functions
+4
+VIII. Distortion of the magnetic moment tensor
+7
+IX. Dependence of T1 on magnetic field
+8
+X. Spin coherence modeling
+8
+XI. Estimating concentration of paramagnetic impurities
+10
+References
+12
+I.
+PHOTON COLLECTION EFFICIENCY
+This section details the efficiency of components in our photonic circuit that impact the total photon collection
+efficiency. We group these losses into four terms: internal losses in the cavity, in the grating coupler and waveguide
+taper, transmission through passive optical components, and the quantum efficiency of the SNSPDs.
+The internal losses in the cavity are determined from the reflection spectrum. In particular, the contrast of the
+reflection on and off cavity resonance C = (Roff − Ron)/Roff has the form [1]:
+C = (1 − 2ηcav)2.
+(1)
+The photon extraction efficiency from the cavity ηcav = κwg/κtot is the ratio of cavity outcoupling rate κwg to the total
+loss κtot = κwg +κint, including internal cavity losses κint. For the device used in this work, we find ηcav = 0.26. The
+grating coupler and waveguide efficiency is estimated by measuring the round-trip optical losses away from the cavity
+resonance. We compute the efficiency as ηGC =
+�
+Pout/Pin, and find ηGC = 0.36 for the device used in this work.
+The transmission through passive optical components (beamsplitters, splices, etc.) is measured independently to be
+ηnet = 0.61 (the HOM interferometer has additional losses, discussed below). The detection efficiency of the SNSPD
+is ηdet = 0.85. This gives a combined predicted photon detection probability of P1 = ηcav ×ηGC ×ηnet ×ηdet = 0.049.
+We lose an additional 7% of the single-ion emission from the finite time required to switch on the SNSPD bias current
+(≈ 900 ns), which is turned off during the optical excitation pulse to avoid saturating the detector. The predicted
+photon detection probability is then P1 = 0.045, close to the measured value of 0.035.
+arXiv:2301.03564v1  [quant-ph]  9 Jan 2023
+
+2
+In the HOM experiment, the two-photon coincidence probability is decreased by the losses of the MZI delay line.
+We measured the optical transmission in the 36 km fiber spool to be T = 0.2, consistent with an attenuation length
+La = 21.7 km. To maximize the coincidence probability and balance the power in the two arms of the interferometer,
+we use a 75 : 25 ratio beamsplitter at the input, such that 0.75 of the power is directed into the long MZI arm,
+while 0.25 is directed into the short one. In the shorter arm, we utilize a variable optical attenuator set to match
+the powers before the final MZI beamsplitter input ports. Accounting for both the losses in the fiber spool in the
+long interferometer arm (matched with a VOA on the short arm), as well as the beamsplitter ratio, the two-photon
+coincidence probability at |t1 − t2| = 0 is PHOM = 0.5 × (0.75P1T)2 = 0.01P 2
+1 . Here, the factor of 0.5 accounts for
+the requirement that the early (late) photon must pass through the long (short) interferometer arm. For P1 = 0.035
+we get PHOM = 1.4 × 10−5, close to the measured value of 8.5 × 10−6.
+II.
+CAWO4 SAMPLE PREPARATION
+The CaWO4 substrates used in this study were procured from SurfaceNet GmbH with a single sided epi polish and
+(100) orientation (i.e., with a surface spanned by a and c axes). According to the vendor, the crystals were grown
+using 99.9999% purity precursors and sold as “high purity CaWO4.” Polished samples were implanted with erbium
+(II-VI Inc.) using an energy of 35 keV which corresponds to a target depth of 10 nm (calculated by Stopping-Range
+of Ions in Matter simulations [2]). Samples were prepared using two different Er3+ concentrations, a high density
+sample used for ensemble spectroscopy utilizing a fluence of 1 × 1012 ions/cm2 and a low density sample used for
+single ion spectroscopy implanted with a fluence of 5 × 109 ions/cm2. Subsequent to implantation, samples were
+annealed in air at a temperature of T = 300 ◦C for 1 hour, with a heating rate of T = 300 ◦C/hour. Annealing
+healed implantation damage and improved site occupation of the S4 point-group symmetry substitutional site.
+Silicon photonic crystal cavities are prepared as described previously [3]. The cavities are oriented on the substrate
+such that the predominant electric field polarization is parallel to the CaWO4 c-axis.
+III.
+SITE-SELECTIVE EXCITATION SPECTROSCOPY
+In order to confirm that implanted Er3+ ions substitute at a site with S4 symmetry we performed a site-selective
+excitation spectroscopy measurement using the high density sample cooled to 4 K. A tunable narrowband laser was
+employed in conjunction with an optical chopper to generate a train of excitation pulses. Using a second chopper,
+fluorescence was collected out of phase with the excitation laser, dispersed using a monochromator, and detected
+with an InGaAs detector array. By performing a fluorescence measurement while sweeping the excitation laser a
+map of site-specific excitation and emission frequencies was obtained (Fig. S1a). Table S1 summarizes the measured
+transition energies of four 4I15/2 and three 4I13/2 levels. The resulting energy level structure is shown in Fig. S1b, and
+found to be in close agreement with the transition energies previously reported for bulk doped samples [4], confirming
+the S4 site assignment. The spectrum does not show any detectable fluorescence at other wavelengths within our
+scan range, suggesting that this is the only Er3+ incorporation site.
+TABLE S1.
+Transition energies of implanted Er3+:CaWO4 determined using site-selective excitation spectroscopy. All values
+are in cm−1. Transitions to Zn and Yn for n greater than what is shown were not observed due to limitations in detection
+sensitivity. The observed transition energies are in close agreement with values obtained for bulk doped samples [4].
+n
+4I15/2Zn
+4I13/2Yn
+1
+0
+6524.4
+2
+20.3
+6532.9
+3
+25.9
+6573.2
+4
+52.0
+*
+We note that compared to the optical excited state lifetime of 6.3 ms the Yn crystal field levels thermalize rapidly,
+such that an identical fluorescence spectrum is obtained independent of which 4I13/2 level is excited (green arrows
+in Fig. S1). Furthermore, while the fluorescence spectrum is dominated by decay from the 4I13/2Y1 level, a small
+fraction of fluorescence originates from the 4I13/2Y2 level. This leads to two sets of fluorescence patterns with identical
+energy splittings (but different intensities), overlaid with an offset given by the 4I13/2Y1-4I13/2Y2 splitting (indicated
+using dashed arrows in Fig. S1).
+
+3
+Y1
+Y2
+Y3
+Z2
+Z3
+Z1
+Z4
+2 3
+1
+2
+3
+1
+1 2 3
+5
+6
+4
+3
+1
+2 & 6
+4
+7
+5
+7
+4I15/2
+4I13/2
+a
+b
+1520
+1522
+1524
+1526
+1528
+1530
+1532
+Excitation wavelength (nm)
+1510
+1515
+1520
+1525
+1530
+1535
+1540
+1545
+1550
+Fluorescence wavelength (nm)
+Y7
+Z8
+FIG. S1. Ensemble spectroscopy of Er3+:CaWO4. a Site-selective excitation spectrum of Er3+:CaWO4. Green arrows
+indicate when the excitation laser is resonant with different excited state crystal-field levels, where the corresponding excitation
+path is labeled using the matching number in (b). Solid orange arrows denote the fluorescence energies due to decay from
+the 4I13/2Y1 level, whereas the dashed arrows denote decay from the 4I13/2Y2 level. The prominent line with unity gradient
+corresponds to laser scatter and has been re-scaled in intensity for clarity. b The inferred energy level structure of Er3+:CaWO4.
+In total, the performed spectroscopy yielded energies of four 4I15/2 and three 4I13/2 levels.
+IV.
+SPIN STATE INITIALIZATION AND READOUT
+To achieve fast and efficient spin state initialization we follow the approach used in Ref. [5]. This initialization
+scheme consists of using optical π pulses resonant with either the A or B transition, each followed by a microwave
+pulse resonant with the excited state spin transition, MWe. For example, to initialize into the |↓g⟩ state we alternate
+π pulses resonant with the optical A and MWe transitions. The number of pulse pairs used for the HOM and spin
+dynamics experiments was 1 and 10, respectively.
+For spin state readout, we used a sequence of n optical π pulses resonant with the A transition each followed by a
+fluorescence collection window. By varying the number of readout pulses we found that the spin state readout fidelity
+is maximized for n = 195, and applying further pulses would reduce the readout fidelity due to optical pumping.
+After optimizing the number of readout pulses, a threshold was set for the total number of photons collected after n
+pulses (Nthresh) to discriminate between the |↓g⟩ and |↑g⟩ states. We found that a threshold of Nthresh = 1 gives the
+highest readout fidelity; that is, if we obtained on average one photon or more after the n pulses then the spin state
+was assigned to |↑g⟩, and if we obtained no photon then the spin state was assigned to |↓g⟩.
+V.
+ENGINEERING AN OPTICAL CYCLING TRANSITION
+As noted in Ref. [6] for Er3+:YSO, the cyclicity of the optical transition depends strongly on the magnetic
+field orientation since changing the field changes the atomic transition dipole moment with respect to the cavity
+polarization. For the case where the cavity linewidth is large compared to the Zeeman splitting, the cyclicity is
+maximized when the spin-flip transitions C, D are orthogonal to the cavity polarization. In this work, by combining
+a larger C-D splitting and a narrower optical cavity than in Ref. [6] we were able to tune the A transition into
+resonance with the cavity while simultaneously keeping the spin-flip transitions C and D detuned from the cavity
+(see Fig. 2b). Consequently we optimize the magnetic field orientation to maximize cyclicity. From this we found
+the optimal field orientation to be in the aa-plane, rotated 22o from the X-axis.
+To probe the cyclicity, the ion was initialized into |↑g⟩ and subsequently read out using 400 pulses. Each readout
+pulse consisted of an optical π pulse resonant with the A transition followed by a fluorescence collection window.
+Due to the finite cyclicity, the fluorescence count rate decays with increasing readout pulse number. This yielded a
+cyclicity of C = ΓA/ΓD = 1030(10) (Fig. S2a).
+To establish the single photon emission we calculate the intensity autocorrelation g(2)(τ) as shown in Fig. S2b. At
+
+4
+zero offset pulse delay, we observe g(2)(0) = 0.018(3), showing strong suppression of multi-photon emission events
+and thus a high purity of single photon emission.
+0
+100
+200
+300
+400
+Readout pulse number
+0.00
+0.01
+0.02
+0.03
+Counts per pulse
+b
+a
+−20
+−10
+0
+10
+20
+Pulse offset n
+10
+−2
+10
+−1
+10
+0
+g(2)(τ)
+FIG. S2. Measuring the cyclicity. a Decay of the A transition fluorescence count rate from optical pumping after initializing
+into |↑g⟩ (blue). The count rate decays as e−n/C revealing a cyclicity of C = 1030(10). The orange trace corresponds to the
+same readout pulse sequence after initializing into |↓g⟩. b Intensity autocorrelation g(2)(τ) of the A transition showing strong
+suppression of the zero-delay peak with g(2)(0) = 0.018(3).
+VI.
+PHOTON ECHO INVESTIGATION OF THE OPTICAL COHERENCE
+We probe the coherence of the optical A transition using the photon echo technique. After initialization of the
+spin state, we utilized an excitation sequence consisting of three optical pulses π/2 - π - π/2 separated by a waiting
+time τ (for a total free evolution time 2τ), followed by a fluorescence collection window. The refocusing π pulse
+in the middle of the sequence removes the slowly varying inhomogeneous dephasing. For each evolution time, we
+swept the phase of the last π/2 pulse and fitted the fluorescence intensity change against the phase angle using a sine
+function. The fitted oscillation amplitude is proportional to the two-level coherence. This yielded a coherence time
+of T2 = 10.2 µs for a Hahn echo sequence (Fig. S3a blue points). To further filter out higher frequency noise, we
+increased the number of refocusing pulses using an XY N dynamical decoupling sequence (see Fig. S3b) and reached a
+radiatively limited coherence time of 18 µs for N = 32 (see Fig. S3a orange points). We note that in this experiment
+the emission lifetime is T1 = 9.1 µs, different from 7.4 µs recorded using time-resolved PLE shown in the main text.
+The results of this experiment implicate slow spectral diffusion as the main source of decoherence in our system. In
+the case of the Hahn echo sequence, the recorded T2 time is approximately a factor of two from the lifetime limit
+T2/(2T1) = 0.56.
+VII.
+HOM FIT FUNCTIONS
+In this section, we derive the two-photon interference functions used to model the HOM histograms in the main
+text. In particular, we consider two dephasing mechanisms, which allow us to estimate the possible bounds on the
+emission linewidth based on the photon visibility determined from the HOM experiment. Finally, we extend the
+model to simulate the reference HOM measurement, where the photons are made distinguishable by periodically
+changing the phase of one of the two interfering photons.
+To model the HOM zero-delay time peak shape, we follow the derivation of Ref [7]. We assume that single photon
+spatio-temporal wave functions have an exponential form:
+ζ(t) = H(t) · exp
+�
+− t
+2T1
+− i[ω(t)t + φ(t)]
+�
+,
+(2)
+where H(t) is the Heaviside function, T1 is the radiative lifetime, ω(t) is the photon frequency and φ(t) is the
+phase. In an ideal case, the frequency and phase of the photon are constant over time, so the photon coherence is
+lifetime limited. A time-dependent frequency and phase noise lead to decoherence. Typically it is assumed that such
+perturbations yield random walks in phase and frequency at two distinct timescales leading to two different physical
+descriptions. The first regime is pure dephasing, caused by fast frequency jumps accumulating phase on a timescale
+
+5
+b
+a
+0
+10
+20
+30
+40
+50
+Free evolution time (μs)
+10
+−1
+10
+0
+Coherence
+0
+5
+10
+15
+20
+25
+30
+ Number of π pulses
+5
+10
+15
+20
+ Coherence time (μs)
+FIG. S3. Optical coherence of Er3+:CaWO4. a An optical Hahn echo measurement (green) reveals an optical coherence
+of T2 = 10.2 µs. Applying XY 32 dynamical decoupling sequence (orange) extends the optical coherence to the radiative limit
+(blue dashed line) T2 = 18 µs, at a field where the optical T1 = 9.1(3) µs. b Optical coherence scaling with the number of
+refocusing pulses of XY dynamical decoupling sequences (red) compared to the lifetime limit (blue).
+shorter than T1. The second regime is described by spectral diffusion, primarily attributed to slow frequency drift on
+a timescale considerably longer than T1. It is worth noting that this time-scale distinction is somewhat artificial, as
+it is known that different noise sources have continuous power spectral densities [8]. Still, we perform this analysis to
+study limiting cases. It can be shown that for single photons passing through an unbalanced MZI with a delay equal
+to the photon generation rate, the HOM histogram peak areas An will be given by: A|i|≥2 = A, A1 = A(1 − R2),
+A−1 = A(1 − T 2) and A0 = A(R2 + T 2 − 2RTVint) [9]. Here, A is the Poissionian peak coincidence level, R/T is the
+reflection/transmission coefficient of the output MZI beamsplitter, and Vint is the emitter visibility. In such cases,
+the HOM two-photon interference coincidence probability function can be described by
+P(τ) =Pdc + A
+N
+�
+k=2
+e−
+|τ±ktrep|
+T1
++ A(1 − R2)e−
+|τ+trep|
+T1
++ A(1 − T 2)e−
+|τ−trep|
+T1
++ Ae− |τ|
+T1 (R2 + T 2 − 2RT · F(τ)),
+(3)
+where Pdc is the coincidence level related to SNSPD dark counts and ambient light counts, and trep is the pulse
+repetition period. Further, F(τ) is an integral defined as [7]
+F(τ) =
+� ∞
+−∞
+dt0 cos [∆ω(τ, t0)τ + ∆φ(τ, t0)] ,
+(4)
+where ∆φ(τ, t0) is a the phase difference and ∆ω(τ, t0) is the frequency difference between two interfering photons.
+If frequency and phase fluctuations are assumed to follow Gaussian distribution functions, F(τ) is given by [7]
+F(τ) = exp
+�
+− 2|τ|
+Tdep
+− σ2τ 2
+�
+,
+(5)
+where Tdep is the dephasing time 1/Tdep = 1/T2 −1/(2T1), and σ is the inhomogeneous linewidth broadening related
+to slow spectral diffusion.
+First, we consider the case where fast spectral diffusion dominates (Lorentzian broadening), for which
+Flor(τ) = exp
+�
+− 2|τ|
+Tdep
+�
+.
+(6)
+This allows for the evaluation of the HOM histogram central peak area
+A0 = A
+� ∞
+−∞
+dτ
+�
+R2 + T 2 − 2RTe
+− 2|τ|
+Tdep
+�
+e− |τ|
+T1 = A
+�
+2T1(R2 + T 2) − 4RT
+T1Tdep
+2T1 + Tdep
+�
+,
+(7)
+
+6
+and the off-center peak area A|i|≥2
+A|i|≥2 = A
+� ∞
+−∞
+dτe− |τ|
+T1 = 2AT1,
+(8)
+giving a visibility of
+V = 1 − 2A0
+A|i|≥2
+= 1 − 2
+�
+R2 + T 2�
++ 4RT
+Tdep
+2T1 + Tdep
+= 1 − 2
+�
+R2 + T 2�
++ 4RT T2
+2T1
+.
+(9)
+Note that this definition of visibility contains information about both the MZI interferometer imperfections (BS R : T)
+and the intrinsic indistinguishability of the emitted photons Vint = T2/(2T1). In our experiment R : T = 0.43 : 0.57
+is determined from the imbalance between A−1 and A1 peak areas in the HOM histogram (see Fig. 3b in the main
+text), contributing to a decrease in visibility of around 4%. By evaluating the integrated counts A0 and A|n|≥2 in
+the HOM experiment, we obtain a visibility of 80% after the dark and ambient light counts are subtracted. This
+allows us to estimate Vint = 0.84, and further T2 = 0.84 × 2T1 = 15.3 µs. Using Eqs. (3) and (6) with T2 = 15.3 µs
+we model the HOM histogram in the main text (Fig. 3b,d). Furthermore, using this model, we can estimate the
+bound on the emission linewidth at the timescale of 100 − 200 µs following
+νL =
+1
+πT2
+=
+1
+2πT1Vint
+,
+(10)
+which yields Lorentzian broadening of νL = 20.6 kHz. Note that in the case of Fourier limited photons, one obtains
+νLF = 1/(2πT1) = 17.3 kHz.
+In the case where slow dynamics dominate decoherence (Gaussian broadening), the function F(τ) is simplified to
+Fgau(τ) = exp
+�
+−σ2τ 2�
+, such that
+A0 = A
+�
+��2T1(R2 + T 2) − 2RT
+√πe
+1
+4σ2T 2
+1 erfc
+�
+1
+2σT1
+�
+σ
+�
+�� .
+(11)
+This leads to a visibility given by
+V = 1 − 2
+�
+R2 + T 2�
++ 2RT
+√πe
+1
+4σ2T 2
+1 erfc
+�
+1
+2σT1
+�
+σT1
+,
+(12)
+where the intrinsic emitter visibility is given by
+Vint =
+√πe
+1
+4σ2T 2
+1 erfc
+�
+1
+2σT1
+�
+2σT1
+.
+(13)
+Using Vint = 0.84 we get σ equal to 0.039 MHz, which corresponds to a Gaussian broadening of νG = 2
+√
+2ln2
+√
+2σ =
+21 kHz. Note that the estimated νG is on the order of the Fourier limit of 17.3 kHz, such that the resultant emission
+line-shape will be described by a Voigt profile with a total width of
+νV = 0.535
+2πT1
++
+�
+0.217
+(2πT1)2 + ν2
+G,
+(14)
+equal to a linewidth of 31.4 kHz. This bounds the emission linewidth to be in the range 20.6 − 31.4 kHz for a
+timescale of 175.2 µs.
+Next, we consider the case of the reference HOM measurement in Fig. 3c. Typically, the distinguishability in
+HOM experiments is tuned by rotating the polarization of one of the photons. However, our SNSPDs have a strongly
+polarization-dependent detection efficiency, which complicates the interpretation of such a measurement. Therefore,
+we instead make the photons distinguishable by artificial spectral broadening, achieved by rapidly modulating the
+path length of one of the interferometer arms with a large amplitude. Specifically, the phase of the photons traveling
+through the shorter MZI arm is modulated using a triangle wave with frequency
+ωm
+2π = 43 kHz and amplitude
+Am = 0.75π. Consequently, the phase difference can be described directly by
+∆φ(τ, t0) = 2Am
+π
+[arcsin (sin (ωm(τ + t0))) − arcsin (sin (ωmt0))] .
+(15)
+
+7
+In this case we can assume that the HOM zero-delay peak area will be dominated by the external phase modulation
+so that we can omit the ∆ω term, and F(τ) will only depend on ∆φ(t0, τ)
+Fmod(τ) =
+� ∞
+−∞
+dt0 cos
+�2Am
+π
+[arcsin (sin (ωm(τ + t0))) − arcsin (sin (ωmt0))]
+�
+.
+(16)
+The periodic modulation of the phase difference with τ will translate into a quantum-beat-like signal with a distinct
+dip at zero detection time difference. To fit the HOM data in Fig. 3c,d of the main text, we evaluate Fmod(τ)
+numerically. The best fit to the experimental data is obtained for a modulation amplitude of 0.73(5)π where the
+modulation frequency was fixed to the value used in the experiment, 43 kHz.
+VIII.
+DISTORTION OF THE MAGNETIC MOMENT TENSOR
+The magnetic moments of individual single ions changed appreciably from ion-to-ion as well as from the previously
+recorded ground state g-tensor [4]. To investigate this, the magnetic response of two single ions (different from the
+single ion investigated in the main text) was fully characterized by probing the optical transition frequencies of the
+four transitions A, B, C, and D for a range of field orientations using a magnetic field magnitude of 50 G, with the
+results shown in Tab. S2.
+TABLE S2. Single-ion g-tensors measured for two separate ions. Due to a small distortion of the S4 point-group site, the
+single-ion magnetic moments do not satisfy gx = gy = g⊥. We note that in this and subsequent sections we use the convention
+where the z axis points along the crystallographic c axis, which is different to the coordinate system used in the main text.
+Ground state
+Excited state
+gx
+gy
+gz
+gx
+gy
+gz
+Ion 1
+8.5
+7.6
+1.7
+7.3
+6.9
+1.8
+Ion 2
+8.6
+7.9
+2.5
+7.6
+6.9
+2.3
+In order to gain a deeper understanding of the g-tensor anisotropy, an effective crystal-field Hamiltonian was used
+to model the intra-4f transitions of Er3+:CaWO4. The complete Hamiltonian has the form
+H = HFI + HCF + HZ,
+(17)
+where HFI corresponds to the free-ion components of the Hamiltonian, HCF accounts for the interaction of the
+valance electrons with the host material, and HZ is the Zeeman Hamiltonian. The free-ion Hamiltonian used is [10]
+HFI = EAVG +
+�
+1,2,3
+F kfk + ζ4fASO + αL(L + 1) + βG(G2) + γG(R7) +
+�
+i=2,3,4,6,7,8
+T iti.
+(18)
+Noting only the most significant contributions, EAVG accounts for the spherically symmetric one-electron component,
+F k are the Slater parameters, f k are the electrostatic repulsion with angular dependence, ζ4f is the spin-orbit coupling
+term, and ASO is the spin-orbit coupling operator. The remaining contributions are higher-order and the reader is
+referred to Ref. [11] for details. To model the contribution of the S4 point-group symmetry crystal-field the following
+Hamiltonian was used
+HCF = B2
+0C(2)
+0
++ B4
+0C(4)
+0
++ B6
+0C(6)
+0
++ B4
+4(C(4)
+4
++ C(4)
+−4) + B6
+4(C(6)
+4
++ C(6)
+−4),
+(19)
+with the coefficients Bk
+q the crystal-field parameters and C(k)
+q
+spherical-tensor operators in Wybourne’s normalization.
+We note that the above Bk
+q are all real with the exception of B6
+4, which is complex. The above Hamiltonian was
+fitted to data obtained using site-selective fluorescence spectroscopy of the 4I13/2 →4I15/2 transitions as well as the
+barycenter of higher-energy transitions up to 4S3/2 obtained from literature [4]. Furthermore, the fit was optimized
+to reproduce the ensemble 4I15/2Z1 and 4I13/2Y1 g-tensors.
+Using the crystal-field parameters obtained via the method outlined above as a starting point, a fit was then
+performed to the g-tensor of both Ion 1 and Ion 2 to determine the crystal-field environment local to each ion. We
+hypothesize that the perturbation of the S4 point-group symmetry was caused by a single dominant defect, potentially
+due to the substrate surface or some form of remote charge compensation. Consequently, an axial term ¯B2
+0 oriented
+at an arbitrary angle with respect to the crystal-field quantization axis was introduced, and both the magnitude as
+
+8
+well as the orientation were varied to reproduce the observed ground and excited state g-tensors. This assumed that
+the crystal-field potential due to the defect is superposable with the nominal crystal-field potential [12].
+For Ion 1, the observed g-tensor was reproduced by an axial term ¯B2
+0 = 9.3 cm−1, rotated by an Euler rotation
+from the quantization axis with α = 90.4◦, β = 265◦ and γ = 0◦, following the Euler angle convention of Messiah [13].
+Similarly, Ion 2 required an axial term ¯B2
+0 = 10.7 cm−1, rotated by an Euler rotation from the quantization axis with
+α = 270.2◦, β = 98.0◦ and γ = 0◦. We note that the unperturbed rank 2 crystal-field parameter has a magnitude
+of B2
+0 = 578 cm−1, such that the observed change in the rank 2 crystal-field potential consisted of around ∼ 2% for
+both of the ions. This amounts to a frequency shift of 3.5 GHz for Ion 1 and 3.9 GHz for Ion 2 for the 4I15/2Z1
+to 4I13/2Y1 transition when compared to the crystal-field model not including any perturbation, which is somewhat
+larger than, but comparable to, the observed inhomogeneous linewidth for single ions coupled to the nanophotonic
+device. Therefore, the observed g-value anisotropy is consistent with a small amount of strain near the ion, potentially
+due to proximity to the surface or a charge compensation mechanism.
+In order to perform the initial crystal-field Hamiltonian fit we independently measured the 4I15/2Z1 and 4I13/2Y1
+ensemble magnetic moments using optical spectroscopy by utilizing the high density implanted sample. From this we
+obtain g⊥ = 8.6 and g∥ = 1.4 for the ground state, and g⊥ = 7.6 and g∥ = 1.3 for the excited state. The fitted ground
+state g-values deviate from the literature values measured by electron-spin resonance [4]; however, the deviation is
+within the uncertainty of our vector magnet calibration due to magnetic field gradients within the sample space. We
+note that the above conclusion about the mechanism for the anisotropy of single ion g-values does not depend on the
+precise magnetic moments assumed for bulk Er3+:CaWO4. Additionally, in the above fit we have constrained that
+gx = gy, and our data was also consistent with a fit for which gx ̸= gy at the 5% level. This suggests that some of
+the observed distortion of the magnetic moment tensor may also be present in an ensemble average.
+IX.
+DEPENDENCE OF T1 ON MAGNETIC FIELD
+To understand the observed spin lifetime, we performed a lifetime measurement at a second magnetic field strength,
+|B| = 950 G, obtaining T1 = 0.393 s. At low temperatures, Raman and Orbach processes are slow and the spin
+relaxation rate is dominated by the direct process. This has the following functional form with respect to an applied
+magnetic field [14]:
+T −1
+1
+= Ad
+�gµBB
+h
+�5
+coth
+�gµBB
+2kbT
+�
+.
+(20)
+Fitting the above equation to the observed spin lifetime data (Fig. S4) yielded a direct process constant Ad =
+6.4(2) × 10−6 s−1 GHz−5, with the expected T1 ∝ 1/B5 scaling. The spin T1 has previously been measured for
+CaWO4 at low temperatures, and the zero-temperature extrapolated lifetime was found to be 4.8 s at a frequency
+of 7.881 GHz [15]. This corresponds to Ad = 7.2 × 10−6 s−1GHz−5, approximately consistent with our value.
+X.
+SPIN COHERENCE MODELING
+In order to explain the observed spin coherence, we consider the magnetic environment of the Er3+ ion in the
+CaWO4 host crystal, consisting of the 183W nuclear spin bath and paramagnetic impurities. While the concentration
+and dynamics of paramagnetic impurities is not well known, the dynamics of the nuclear spin bath under decoupling
+sequences can be understood using standard CCE (Cluster Correlation Expansion) techniques [16]. First, we describe
+the Er3+ spin coupling to the nuclear spin bath and explain features observed in the Hahn experiment at short times.
+Then, we apply our understanding of the nuclear spin bath to find the expected decoherence rates for the Hahn and
+Ramsey experiments and observe that it cannot explain the observed rates in either. This leads us to conjecture the
+existence of an appreciable concentration of paramagnetic impurities, which we discuss in the next section.
+To form the nuclear spin bath, we generate random configurations of nuclear spins by allowing each W atom to
+be an 183W isotope (I = 1/2) with probability 14.3%. Under the secular approximation for the electron spin, this
+bath can be described by the following Hamiltonian in the rotating frame of the Er3+ spin:
+H = 2Sz
+�
+i
+(A(i)
+|| Ii
+z + A(i)
+⊥ Ii
+x) +
+�
+i
+ωL,W Ii
+z +
+�
+i,j
+H(i,j)
+nn ,
+(21)
+where Ii
+z/x are the nuclear spin operators of the ith spin, A(i)
+||
+and A(i)
+⊥ are the parallel and perpendicular hyperfine
+interaction terms, ωL,W is the Larmor frequency of the W nuclear spin (107.7 kHz at |B| = 600 G) and H(i,j)
+nn
+is the
+dipolar interaction Hamiltonian between W nuclear spins.
+
+9
+10
+2
+10
+3
+|B| (G)
+10
+−1
+10
+0
+10
+1
+10
+2
+Spin T1 (s)
+FIG. S4. Spin lifetime as a function of magnetic field strength. Solid line is a fit to Eq.(20) as is predicted for the
+spin-lattice relaxation time.
+This implies that there can be considerable variation in ESEEM (Electron Spin Echo Envelope Modulation) features
+observed for an Er3+ ion, depending on whether a nearby W nuclear spin is present. We observe such features as
+dips in coherence in the Hahn experiment (Fig. 4d). In contrast to decay envelopes, these sharp features occur at
+particular pulse spacings and indicate coherent coupling to a W nuclear spin occupying one of the nearest sites.
+Since we are working under the assumption that there is only one nearby W nuclear spin, we do not allow another
+nuclear spin within the first ten nearest W sites when generating the random nuclear spin baths. We find hyperfine
+parameters of the strongly coupled W nuclear spin by minimizing over the following cost function:
+C(A||, A⊥) =
+�
+k
+�
+j
+(Ssim,k(τj) − Sexp(τj))2;
+Ssim,k(τj) = e−(2τj/T2)n · Sbath,k(τj) · S(τj, A||, A⊥).
+(22)
+Here, τj are the time units that were sampled in the Hahn experiment, Ssim,k(τj) is the simulated signal for the
+kth bath and Sexp(τj) is the experimentally measured contrast for the experiment. Ssim,k(τj) is calculated by taking
+a product of three factors: a stretched exponential decay, with decay constants T2 = 44 µs and n = 1.4 used in
+Fig. 4d, the CCE simulation for the nuclear spin bath, Sbath,k(τj), and simulation for a single W nuclear spin coupled
+to Er3+, S(τj, A||, A⊥). The form of Ssim,k(τj) is justified as a first order CCE expansion, which does not take
+interactions between constituents of the bath into account. The envelope e−(2τj/T2)n is assumed to come from a
+source independent of the nuclear spin bath.
+The minimization yields the hyperfine parameters, (A||, A⊥) = (25.2, 31.7) kHz. These values are within range of
+expected interaction strengths for nearby W nuclear spin. In particular, for the W nuclear spin coordinates given as
+rW = ±a/2 + c/2, where a = aˆx and c = cˆz are CaWO4 lattice vectors, we calculate (A||, A⊥) = (15.5, 30.5) kHz at
+our field orientation. The discrepancy could be due to uncertainty in the field alignment or the Er3+ spin g-tensor,
+which can lead to rotations as discussed in Sec. VIII.
+Finally, ignoring the contribution from the phenomenological decay, we simulate longer time delays to extract the
+W bath limited coherence times for the Hahn and Ramsey experiments. We perform a second order CCE simulation
+for the simulation of the Hahn experiment, which takes into account the dipolar coupling between nuclear spins.
+Noting that ESEEM features will persist as observed in Fig. 4d, we find that the interaction between nuclear spin
+pairs leads to an envelope which decays in 22.6 ms (Fig. S5a). We also perform a Ramsey simulation and show
+that the expected T ∗
+2 decoherence due to the W-bath is about 4 µs (Fig. S5b). Both of these coherence values are
+significantly longer than the observed values for T2 and T ∗
+2 . We attribute the difference to paramagnetic impurities
+and explore the expected concentration in the next section.
+
+10
+a
+b
+|  g
+Free evolution time 2τ (µs)
+ 
+ 
+Population 
+0
+5
+10
+15
+20
+25
+30
+0
+0.5
+1
+Population |  g
+ 
+Free evolution time τ (µs)
+0
+10
+20
+30
+40
+50
+60
+70
+80
+0
+0.5
+1
+FIG. S5. W bath limited coherence. a The second order contribution to the CCE simulation for the Hahn experiment
+for 10 random W-bath configurations, where we assume that the nearest W nuclear spin is located at rW. Fitting each of
+the curves to a stretched exponential yields T2 = 22.7(4) ms with n = 2.7(1). We note that this is only the envelope and
+faster ESEEM features, obtained from the first order CCE simulation, persist as seen in Fig. 4d. This simulation considers
+W nuclear spins within an 11 nm radius of the Er3+ spin. b CCE simulation of Ramsey experiment for the same W bath
+configurations. Fitting each of the curves to a Gaussian decay yields T ∗
+2 = 4.0(4) µs. Both simulations are performed at our
+experimental field configuration.
+XI.
+ESTIMATING CONCENTRATION OF PARAMAGNETIC IMPURITIES
+In order to estimate the concentration of paramagnetic impurities, we use the Ramsey experiment as a probe of
+the static magnetic noise experienced by the Er3+ ion. As stated in the previous sections, the W bath limited T ∗
+2
+(Fig. S5b) is significantly longer than the measured T ∗
+2 of 247 ns. This indicates that the measured T ∗
+2 is limited
+by paramagnetic impurities. Therefore, we can use the measured T ∗
+2 to roughly estimate the concentration of these
+impurities.
+Without loss of generality, we can assume that the interaction between the Er3+ spin and the paramagnetic impurity
+will be of the Ising form under the secular approximation, forbidding exchanges that do not conserve magnetization.
+Under these assumptions, we can write down the Hamiltonian concerning the Er3+ spin and the paramagnetic bath
+in the frame rotating at Er3+ and the impurity frequency for a single impurity species
+H = Sz
+�
+i
+J(i)
+I Si
+z +
+�
+i,j
+J(i,j)
+I
+Si
+zSj
+z + J(i,j)
+S,k (Si
+xSj
+x + Si
+ySj
+y) +
+�
+i
+∆iSi
+z.
+(23)
+Here, J(i)
+I
+is the Ising interaction strength between the Er3+ spin and the impurity, while J(i,j)
+I
+and J(i,j)
+S
+are the Ising
+and Symmetric interaction strengths between the two impurities and ∆i is the disorder in the precession frequency
+of each impurity. While the bath interaction and disorder terms become important for decoupling sequences, these
+processes do not contribute on the timescale of the Ramsey experiment, which is dominated by the static noise
+represented by the first term. Based on this understanding, we can compute the net frequency, in the rotating frame,
+of the Er3+ spin given the state of the bath. For the purposes of this calculation, we take this bath to consist of
+S = 1/2 electrons with g = 2 and represent its state by the bitstring k of length N. We can then write down the
+Hamiltonian projected by the state k of the bath
+Hk = ⟨k|Sz
+�
+i
+J(i)
+I Si
+z|k⟩ = Sz
+�
+i
+J(i)
+I
+(−1)ki
+2
+= ωkSz;
+ωk =
+�
+i
+(−1)kiJ(i)
+I
+2
+.
+(24)
+Here, ωk is the precession frequency of the Er3+ spin given the state k of the bath. We can then calculate the Ramsey
+
+11
+coherence as T ∗
+2 = π/∆ω, where ∆ω2 is the variance over the set {ωk}:
+∆ω2 = 1
+2N
+�
+k
+ω2
+k = 1
+2N
+�
+k
+�
+i
+�(−1)kiJ(i)
+I
+2
+�2
++ 1
+2N
+�
+k
+�
+i<j
+(−1)ki+kjJ(i)
+I J(j)
+I
+=
+�
+i
+�J(i)
+I
+2
+�2
+,
+(25)
+where we have used the fact that the distribution is centered at zero and the summations can be reordered. We
+observe that the frequency standard deviation can be interpreted as the norm of the vector of Ising interaction
+strengths.
+In order to estimate the concentration based on this expression, we generate 2000 instances of randomly distributed
+electron spin baths across a range of concentrations, calculate the resultant T ∗
+2 of each configuration and use Bayes
+rule to infer a probability density, P(ρ|T ∗
+2 ), for the concentration, ρ, given our observation of T ∗
+2
+P(ρ|T ∗
+2 ) =
+P(T ∗
+2 |ρ)
+� ∞
+0
+P(T ∗
+2 |ρ′)dρ′ .
+(26)
+Here, P(T ∗
+2 |ρ′) is the probability to obtain a given T ∗
+2 for the bath concentration ρ. In practice, we calculate this
+expression by counting the number of instances for each concentration that yields a value of T ∗
+2 within 3 standard
+deviations of the observed value. We perform this estimate for both a 3D geometry of electron spins located in the
+bulk and a 2D geometry of spins located on the sample surface, estimated to be 10 nm away. We obtain concentrations
+of 1.6 − 5.7 × 1016 cm−3 and 0.5 − 1.3 nm−2 for the bulk and surface concentration estimates respectively with 70%
+confidence (Fig. S6). As both of these are plausible concentrations, we note that both may be playing a non-negligible
+role. We are not able to make a calculation of how this concentration of paramagnetic impurities affects the Hahn
+coherence because it depends on the dynamics of this paramagnetic impurity bath, which is not well known. Doing
+this calculation would require further information such as the species and spin-lifetime of impurities, as well as the
+disorder of the bath.
+a
+b
+0
+5
+10
+15
+20
+0.0
+0.1
+0.2
+Prob. density (10-16 cm3)
+0.0
+0.5
+1.0
+1.5
+0.0
+1.0
+2.0
+3.0
+Prob. density (nm2)
+ρ (1016 cm-3)
+ρΑ (nm-2)
+FIG. S6. Probability density of paramagnetic impurity concentration. a Assuming a 3D uniform distribution of
+impurities, we estimate that the bath concentration is in the range 1.6×1016 – 5.7×1016 cm−3 with 70% confidence, with the
+likeliest concentration at 3.7×1016 cm−3. b Assuming a 2D distribution on the surface of our crystal, assumed to be located
+10 nm away from the Er3+ spin, we estimate an area concentration in the range of 0.5 – 1.3 nm−2 with 70% confidence, with
+the likeliest concentration at 0.77 nm−2. Dashed lines indicate the confidence ranges for the impurity concentrations.
+
+12
+∗ These authors contributed equally to this work.
+† jdthompson@princeton.edu
+[1] Dibos, A. M., Raha, M., Phenicie, C. M. & Thompson, J. D. Atomic Source of Single Photons in the Telecom Band.
+Physical Review Letters 120, 243601 (2018).
+[2] Ziegler, J. F., Ziegler, M. D. & Biersack, J. P.
+SRIM – The stopping and range of ions in matter (2010).
+Nuclear
+Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 268, 1818–1823
+(2010).
+[3] Chen, S. et al. Hybrid microwave-optical scanning probe for addressing solid-state spins in nanophotonic cavities. Optics
+Express 29, 4902 (2021).
+[4] Enrique, B. G. Optical spectrum and magnetic properties of Er3+ in CaWO4. The Journal of Chemical Physics 55,
+2538–2549 (1971).
+[5] Chen, S., Raha, M., Phenicie, C. M., Ourari, S. & Thompson, J. D. Parallel single-shot measurement and coherent control
+of solid-state spins below the diffraction limit. Science 370, 592–595 (2020).
+[6] Raha, M. et al. Optical quantum nondemolition measurement of a single rare earth ion qubit. Nature Communications
+11, 1605 (2020).
+[7] Kambs, B. & Becher, C. Limitations on the indistinguishability of photons from remote solid state sources. New Journal
+of Physics 20, 115003 (2018).
+[8] Kuhlmann, A. V. et al. Transform-limited single photons from a single quantum dot. Nature Communications 6, 8204
+(2015).
+[9] Loredo, J. C. et al. Scalable performance in solid-state single-photon sources. Optica 3, 433 (2016).
+[10] Carnall, W. T., Goodman, G. L., Rajnak, K. & Rana, R. S. A systematic analysis of the spectra of the lanthanides doped
+into single crystal LaF3. The Journal of Chemical Physics 90, 3443–3457 (1989).
+[11] Wybourne, B. G. Spectroscopic properties of rare earths (Interscience Publishers, 1965).
+[12] Newman, D. Theory of lanthanide crystal fields. Advances in Physics 20, 197–256 (1971).
+[13] Messiah, A. Quantum mechanics (Dover Publications, 1961).
+[14] Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (OUP Oxford, 1970).
+[15] LeDantec, M. et al. Twenty-three–millisecond electron spin coherence of erbium ions in a natural-abundance crystal.
+Science Advances 7, eabj9786 (2021).
+[16] Yang, W. & Liu, R.-B. Quantum many-body theory of qubit decoherence in a finite-size spin bath. ii. ensemble dynamics.
+Physical Review B 79, 115320 (2009).
+
diff --git a/DdE1T4oBgHgl3EQf-Abs/content/tmp_files/load_file.txt b/DdE1T4oBgHgl3EQf-Abs/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,1041 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf,len=1040
+page_content='Indistinguishable telecom band photons from a single erbium ion in the solid state  Salim Ourari,1, ∗ Łukasz Dusanowski,1, ∗ Sebastian P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Horvath,1, ∗ Mehmet T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Uysal,1, ∗  Christopher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Phenicie,1 Paul Stevenson,1, † Mouktik Raha,1 Songtao Chen,1, ‡  Robert J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Cava,2 Nathalie P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' de Leon,1 and Jeff D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Thompson1, §  1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA  2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA  Atomic defects in the solid state are a key component of quantum repeater networks for long-  distance quantum communication [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Recently, there has been significant interest in rare earth ions  [2–4], in particular Er3+ for its telecom-band optical transition [5–7], but their application has been  hampered by optical spectral diffusion precluding indistinguishable single photon generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In  this work we implant Er3+ into CaWO4, a material that combines a non-polar site symmetry, low  decoherence from nuclear spins [8], and is free of background rare earth ions, to realize significantly  reduced optical spectral diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For shallow implanted ions coupled to nanophotonic cavities with  large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral  diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This enables  the observation of Hong-Ou-Mandel interference [9] between successively emitted photons with high  visibility, measured after a 36 km delay line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We also observe spin relaxation times T1 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7 s and  T2 > 200 µs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear  spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This represents a significant step towards the construction of telecom-band quantum repeater  networks with single Er3+ ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Long-distance quantum networks are an enabling technology for quantum communication, distributed quantum  computing and entanglement-enhanced sensing and metrology [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The rate of direct entanglement transmission with  photons decreases exponentially with distance, but this can be overcome using quantum repeaters with memories  [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In particular, single atom-like defects in the solid state [1] have been used to demonstrate key milestones  including spin-photon entanglement [12, 13] and single-photon transistors [14], remote entanglement of spins [15],  entanglement purification [16] and memory-enhanced quantum communication [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' A challenge to deploying these  techniques in long-distance networks is that atomic systems typically operate at transition frequencies outside of the  low-loss window of optical fibers, requiring wavelength conversion for long-distance propagation [18, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The rare earth ion Er3+ has a telecom-band optical transition at a wavelength of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 µm that is widely exploited  for solid-state optical amplifiers, and in dilute ensembles, as a quantum memory for light [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Er3+ ions can  have long spin [8, 22] and optical [23] coherence in a variety of host crystals, a property shared with other rare earth  ions [24–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In recent years, micro- and nano-scale optical resonators have enabled the observation of enhanced  single photon emission from Er3+ and other rare earth ions [3–5, 7, 27], which has subsequently enabled single-shot  spin readout [4, 28] and coupling to nearby nuclear spins that could serve as ancilla qubits [29–31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' However, a  central challenge to the development of quantum repeaters with single rare earth ions is spectral diffusion, which  is particularly pronounced in nanophotonic devices used to achieve fast optical emission from single rare earth ions  [4, 5, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To date, indistinguishable single photon emission from a single rare earth ion has not been observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Rare earth ions also provide a unique opportunity for materials engineering, as they can be incorporated into a  wide range of host crystals while preserving their basic properties, including the optical transition wavelength and  spin configuration [32–35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' An ideal host material would incorporate Er3+ on a non-polar site to suppress linear  electric field shifts of the optical transition, and have a low concentration of nuclear spins, other magnetic impurities  and particularly trace rare earth ions to allow long spin coherence and low fluorescence background [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In this work, we demonstrate indistinguishable single photon emission from a single Er3+ ion coupled to a  nanophotonic optical cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This is enabled by shallow ion implantation of Er3+ into CaWO4, a host material  satisfying the above criteria and for which long electron spin coherence has recently been demonstrated in Er3+  ensembles at millikelvin temperatures [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' By coupling the ions to silicon nanophotonic circuits, we observe individual  ions with single-scan optical linewidths of 150 kHz, and emission rate enhancement by a factor of P = 850 via the  Purcell effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Using a 36 km delay line, we observe Hong-Ou-Mandel (HOM) interference between successively  emitted photons with a visibility of V = 80(4)%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We also demonstrate spin initialization and single-shot readout  with a fidelity F = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='972, as well as the preservation of electron spin coherence for more than 200 µs, limited by  paramagnetic impurities in the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This demonstration is a key step for the development of quantum repeaters  based on single rare earth ions, and Er3+ in particular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Our samples are produced by introducing erbium into commercially available high purity CaWO4 using ion  implantation with an energy of 35 keV, targeting a depth of 10 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In a test sample implanted with a high Er3+  fluence of 1×1012 ions/cm2, we observe an ensemble optical spectrum at T = 4 K consistent with substitutional Er3+  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='03564v1  [quant-ph]  9 Jan 2023  2  on the Ca2+ site with S4 symmetry (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 1a) [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' After annealing at 300 ◦C in air, the inhomogeneous optical  linewidth of the Z1-Y1 transition at 1532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='63 nm is 730 MHz (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This is comparable to previously reported  linewidths in bulk-doped samples (approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5-1 GHz [35, 39]), suggesting that the implantation damage is  effectively removed by annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  To resolve individual ions, we implant a second sample at a lower fluence of 5 × 109 ions/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Single ions are  probed using a silicon photonic crystal cavity that is fabricated on a separate silicon-on-insulator wafer, and then  bonded to the top surface of the CaWO4 substrate (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 1c-d) [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The device and sample are cooled to T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='47 K  in a 3He cryostat, with optical and microwave access provided with a scanning probe head [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We probe single  ions in the device using photoluminescence excitation (PLE) spectroscopy, by sweeping the frequency of a pulsed  laser and observing the time-delayed fluorescence through the cavity with a superconducting nanowire single photon  detector (SNSPD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The spectrum contains clearly resolved lines from individual Er3+ ions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 1e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The number  of lines is roughly consistent with the expected number of ions in the cavity area A = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 µm2, suggesting a high  conversion efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The following experiments are performed on the ion indicated by the arrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Coupling the Er3+ ion to the cavity allows for optical preparation and measurement of the electron spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We apply  a magnetic field of |B| = 600 G to lift the degeneracy of the S = 1/2 ground and excited states, resulting in two spin-  conserving transitions (A,B) and two spin-flip transitions (C,D) as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2a-b (the magnetic moments for the  ground and excited state are described in the supplementary information [41]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Tuning the cavity to the A transition  enhances the decay rate of the excited state, shortening the lifetime from 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 ms to τ = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 µs, corresponding to a  Purcell factor of P = 850 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To enable spin readout, we engineer a cycling transition by selectively enhancing  the A transition relative to D by a combination of detuning from the cavity and preferential orientation of the  transition dipole moment with respect to the cavity polarization [28], resulting in ΓA/ΓD ≈ 1030(10) [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Spin  initialization is performed by optical pumping on the A or B transitions while simultaneously driving the excited  state MWe transition [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2d, we demonstrate spin initialization and readout with an average fidelity of  F = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='972 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The combination of high collection efficiency and low background from other Er3+ ions allows  for high-contrast optical Rabi oscillations (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' After a π pulse, a single photon is detected with a probability  P1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='035, on top of a background count rate of Pb = P1/117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Both P1 and the signal-to-background ratio are  larger than what is obtained with frequency converted NV centers by more than an order of magnitude [19], enabled  by the high quantum efficiency and collection efficiency of the Er-cavity system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The linewidth of the spin-conserving transitions is determined using PLE spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To avoid optical pumping,  the excitation laser has two tones separated by approximately 1 GHz to drive the A and B transitions simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The typical linewidth of a single scan (1 minute) is approximately 150 kHz, while the line center has an r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  fluctuation of 63 kHz over 12 hours (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This represents a 100-fold improvement over previously reported  linewidths for individual Er3+ ions in nanophotonic cavities [5, 7, 42], and is to our knowledge the narrowest optical  transition observed for a solid-state defect in a nanophotonic device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We note that similar linewidths have been  observed for single Er3+ ions in 19 µm thick Y2SiO5 membranes [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The single-scan linewidth is 7 times larger  than the Purcell-enhanced radiative linewidth of the A transition, Γr = 1/τ = 2π × 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 kHz, however, photon  echo experiments suggest that this linewidth is dominated by slow dynamics [41], such that indistinguishable photon  emission may be possible on short timescales or with active feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  We perform HOM two-photon interference measurements [9] on time-delayed photons using an unbalanced Mach-  Zehnder interferometer (MZI) with a ∆L = 36 km delay line in one arm (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' By tuning the repetition rate of  the excitation pulses to match the delay time of the long arm (∆t = 175 µs), successive photons may arrive at the  final beamsplitter simultaneously, and HOM interference will suppress the probability of detecting one photon at each  output if the photons are indistinguishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Experimentally, we observe strongly suppressed coincidences (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3b),  indicating a high degree of indistinguishability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In a control experiment, we artificially broaden the photon in the  short arm using a fiber stretcher driven by a noise source, restoring the coincidence rate expected for distinguishable  photons (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We measure an HOM coincidence rate of R = 2 min−1, defined as the rate of simultaneous photon  detection in the distinguishable photon case, corresponding to a per-shot coincidence probability of Pc = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 × 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The indistinguishability is quantified by the visibility V [43], given by V = 1 − 2A0/A|i|≥2, where A0 is the  integrated counts under the central peak and A|i|≥2 is the average integrated counts in each side peak (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The  visibility is maximized for a coincidence window approaching zero, however the number of photons within this window  (the acceptance fraction) will also be small (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For coincidences with photon detection times t1, t2 separated  by |t2 − t1| < 2τ (corresponding to an acceptance fraction of 63%), the raw visibility is over 70%, rising to 90% when  the accidental coincidences from dark counts and ambient background are subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Integrating under the entire  peak in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3d and subtracting accidental coincidences gives V = 80(4)%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The residual distinguishability has a  significant contribution (4%) due to the MZI output beamsplitter ratio deviating from 50:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Therefore, we conclude  that the effective linewidth over hundreds of microseconds is only slightly larger than the radiative linewidth [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Lastly, we study the properties of the Er3+ spin, which has the potential to serve as a quantum memory for spin-  3  photon entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In bulk Er3+:CaWO4 , the magnetic moment is anisotropic with gc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='25 and ga = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='38 [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  However, for the individual ions studied in this work, we observe significantly distorted magnetic moments, including  a variation of g in the aa-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' These deviations can be reproduced with the inclusion of a small axial crystal field  term [41], which may arise from proximity to the surface or the presence of a nearby defect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The spin relaxation time is T1 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7 s, in line with previous reports [8], and is limited by the direct process with  a T1 ∝ 1/B5 dependence [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Ramsey and Hahn echo experiments give T ∗  2 = 247 ns and T2 = 44 µs, respectively  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4c-d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' An XY64 dynamical decoupling sequence allows coherence to be preserved for longer than 200 µs (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4e),  while also showing collapses and revivals due to the 183W nuclear spin bath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The Hahn echo T2 is improved by one order of magnitude from Er3+:Y2SiO5 under similar conditions [42], but the  coherence is still significantly shorter than predictions based on CCE simulations accounting for the 183W nuclear  spin bath (I = 1/2, 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3% abundance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This implicates paramagnetic impurities in the host crystal or on the surface  as the primary source of decoherence, with an inferred density of approximately 3 × 1016 cm−3 [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Indeed, longer  spin echo coherence times of T2 = 23 ms were observed for bulk Er3+ ensembles in CaWO4 in Ref [8] by operating  at dilution refrigerator temperatures to freeze out paramagnetic impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Although the coherence is not limited  by the nuclear spin bath, dips in coherence due to a single strongly coupled 183W spin are observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The results demonstrated in this work will enable spin-photon entanglement and HOM interference between  multiple Er3+ emitters with postselection using a narrow coincidence window or active tracking of the transition  frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In future work, the radiative linewidth can be further increased using cavities with higher Q [44] or  smaller mode volume [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Furthermore, more careful annealing or surface preparation may reduce the spectral  diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The flexibility to incorporate Er3+ via ion implantation, instead of during growth, will allow future  exploration of CaWO4 samples produced and refined using diverse techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Reducing the impurity concentration  may also improve the optical linewidth: scaling the ground state magnetic linewidth 1/T ∗  2 to the optical transition  implies a significant magnetic noise contribution of 2π × 46 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In this work, we have demonstrated an engineered material, ion-implanted Er3+:CaWO4, that enables indistin-  guishable single photon generation from a single rare earth ion in the telecom band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We attribute the improved  performance to the higher Er3+ site symmetry (compared to previous observations of single Er3+ ions [5, 7, 27]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Spectral multiplexing of many ions per node [42], using quantum eraser techniques to overcome static frequency  differences [46], will enable higher repetition rates over long fiber segments, while simultaneously reducing the co-  herence time requirements [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Additional storage capacity and functionality may be obtained from ancilla nuclear  spin registers, as recently demonstrated for several rare-earth ion systems [30, 31], and ion implantation may allow  for the creation of spatially modulated density profiles with strong magnetic ion-ion interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Acknowledgements:  We acknowledge helpful conversations with Charles Thiel, Philippe Goldner, and Miloš  Rančić.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This work was primarily supported by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Department of Energy, Office of Science, National Quantum  Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number  DE-SC0012704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  We also acknowledge support from the DOE Early Career award (for modeling of decoherence  mechanisms and spin interactions), as well as AFOSR (FA9550-18-1-0334 and YIP FA9550-18-1-0081), the Eric  and Wendy Schmidt Transformative Technology Fund, and DARPA DRINQS (D18AC00015) for establishing the  materials spectroscopy pipeline and developing integrated nanophotonic devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  We acknowledge the use of  Princeton’s Imaging and Analysis Center, which is partially supported by the PCCM, an NSF MRSEC (DMR-  1420541), as well as the Princeton Micro-Nano Fabrication Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Note: While finalizing this manuscript, we became aware of recent reporting the detection of single Er3+ ions in  CaWO4 using magnetic resonance techniques [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  4  −500 −250  0  250  500  Laser frequency (MHz)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='010  Counts per pulse  ~10 nm  CaWO4  implanted Er3+  Z  X  silicon cavity  a  b  d  e  c  20 µm  Y X  5 µm  2 µm  Y  X  Y  X  (i)  (i)  (ii)  (ii)  e  Ca  W  O  Er  a = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2 Å  c = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 Å  a  −6  −3  0  3  6  Laser frequency (GHz)  1532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='62 nm  Fluorescence (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=')  Z  Y  X  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Er3+:CaWO4 device architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a CaWO4 crystal structure, with a substitutional Er3+ impurity in an S4 Ca2+  site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b A dense implanted Er3+:CaWO4 ensemble has an inhomogeneous optical linewidth of 730 MHz on the Z1-Y1 transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In addition to the central peak, we observe hyperfine structure from 167Er with nuclear spin I = 7/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' c Scanning electron  microscope image of a representative silicon nanophotonic device, consisting of a photonic crystal grating coupler [inset (i)]  that tapers adiabatically into a bus waveguide connected to a photonic crystal nanobeam cavity [inset (ii)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' d Erbium ions  are implanted targeting a depth of 10 nm, and couple evanescently to the silicon photonic crystal on the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' e PLE  spectrum of Er3+ ions coupled to the cavity, with resolved single ion lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The red arrow indicates the ion used for subsequent  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  −500 −250  0  250  500  Detuning (kHz)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='50  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='75  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='00  Time (hours)  −500 −250  0  250 500  Detuning (kHz)  0  2  4  6  8  10  12  Time (hours)  A  B  D  C  MWg  MWe  |↑e⟩  |↓e⟩  |↑g⟩  |↓g⟩  1532 nm  7 GHz  6 GHz  −10  −5  0  5  10  Frequency (GHz)  Reflection  A  B  C  D  a  b  c  d  e  f  0  300  600  Optical pulse width (ns)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='035  Counts per pulse  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' |↑g⟩  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' |↓g⟩  10  0 10  1 10  2 10  3 10  4  Time (µs)  Fluorescence (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=')  0  5  10  15  Number of photons  10  −4  10  −3  10  −2  10  −1  10  0  Probability  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Efficient photon collection from a cavity-coupled ion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a Er3+ level structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In a magnetic field, Er3+ has  four distinct optical transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The field strength is |B| = 600 G, oriented in the aa-plane, 22o from the X-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b Reflection  spectrum of the cavity showing a full-width, half-maximum linewidth of κ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0 GHz (Q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9 × 105), which is tuned into  resonance with the A transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' c The lifetime of the |↑e⟩ excited state is reduced to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 µs (blue), which is 850 times shorter  than the bulk lifetime of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 ms (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' d Histogram of photon counts obtained during spin readout after initializing in  |↑g⟩ and |↓g⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The average readout fidelity is F = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='972, using a threshold of one photon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The solid line is a fit to a Poisson  distribution with average photon number ¯n = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' e Optical Rabi oscillation on transition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The peak single photon emission  probability is P1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' f Repeated PLE scans show an average single-scan linewidth of 150 kHz, and long-term diffusion  of the line center of 63 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  8888  888888888888888888888888885  c  75:25  BS  50:50  BS  36 km  fiber  SNSPD  SNSPD  fiber  stretcher  PC  PC  ∆t  VOA  FG  d  a  e  −525  −350  −175  0  175  350  525  0  20  40  60  80  HOM coincidences  −525  −350  −175  0  175  350  525  Detection time difference t1 − t2 (μs)  0  20  40  60  80  HOM coincidences  b  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  Visibility  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  Coincidence window / (2T1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  Acceptance fraction  A0  A1  A-1  A-2  A-3  A2  A3  −30  −15  0  15  30  Detection time difference t1 − t2 (μs)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content='5  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' HOM coincidences  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Generation of indistinguishable photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a Schematic of the HOM interferometer, indicating beamsplitters (BS),  a variable optical attenuator (VOA), polarization controllers (PC) and a fiber stretcher driven by a noise source (FG) to tune the  distinguishability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b Histogram of coincidences detected in a 4 hour measurement period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The Hong-Ou-Mandel effect results  in a suppressed probability of coincidences at zero delay, indicating indistinguishable single-photon emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' c Histogram  of coincidences in a control experiment with a noise source applied to the fiber stretcher, destroying the indistinguishability  and Hong–Ou–Mandel interference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' d Zoom-in around the zero time delay HOM interference pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The red line shows  a model including background counts (black dashed line) and pure dephasing of the optical transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The blue dashed  line shows a simple model for the control experiment assuming perfect distinguishability, while the solid blue line shows a  model incorporating the finite bandwidth of the noise source [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' e Interference visibility (top) and relative coincidence rate  (bottom) as a function of the coincidence window, before (green) and after (red) subtracting the accidental coincidences from  the detector and ambient background dark counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  6  c  e  a  b  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content='8  Free evolution time (µs)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='00  Population |↑g⟩  0  5  10  Wait time (s)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content='00  Population |↑g⟩  0  150  300  MWg pulse width (ns)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  Population |↑g⟩  d  0  200  400  600  800  1000  1200  Free evolution time (µs)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  Population |↑g⟩  0  50  100  Free evolution time (µs)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='00  Population |↓g⟩  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Spin dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a Rabi oscillations after initializing into |↑g⟩ (blue) or |↓g⟩ (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The spin transition frequency  fMWg = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  b Spin relaxation after initialization into |↑g⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  An exponential fit yields T1 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7(3) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  c Ramsey  measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Fitting to e−(t/T ∗  2 )n reveals a T ∗  2 = 247(9) ns with n = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' d A Hahn echo measurement shows dips  in coherence resulting from the 183W nuclear spin bath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The grey lines show CCE simulations for randomly selected 183W  configurations, where each configuration includes a single strongly coupled 183W spin required to reproduce the dips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The blue  lines include an additional, phenomenological stretched decay with T2 = 44 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' e Applying an XY64 dynamical decoupling  sequence extends the spin coherence to longer times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Here, the grey lines show CCE simulations for the same 183W bath  configurations in panel (d), while the blue lines have an additional phenomenological decay of 460 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  7  ∗ These authors contributed equally to this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  † Present address: Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA  ‡ Present address: Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA  § jdthompson@princeton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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+page_content=' URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  org/abs/2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='02653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Supplementary information for indistinguishable telecom band photons from a single  erbium ion in the solid state  Salim Ourari,1, ∗ Łukasz Dusanowski,1, ∗ Sebastian P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Horvath,1, ∗ Mehmet T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Uysal,1, ∗ Christopher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Phenicie,1  Paul Stevenson,1 Mouktik Raha,1 Songtao Chen,1 Robert J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Cava,2 Nathalie P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' de Leon,1 and Jeff D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Thompson1, †  1Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA  2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA  CONTENTS  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Photon collection efficiency  1  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' CaWO4 sample preparation  2  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Site-selective excitation spectroscopy  2  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Spin state initialization and readout  3  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Engineering an optical cycling transition  3  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Photon echo investigation of the optical coherence  4  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' HOM fit functions  4  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Distortion of the magnetic moment tensor  7  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Dependence of T1 on magnetic field  8  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Spin coherence modeling  8  XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Estimating concentration of paramagnetic impurities  10  References  12  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  PHOTON COLLECTION EFFICIENCY  This section details the efficiency of components in our photonic circuit that impact the total photon collection  efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We group these losses into four terms: internal losses in the cavity, in the grating coupler and waveguide  taper, transmission through passive optical components, and the quantum efficiency of the SNSPDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The internal losses in the cavity are determined from the reflection spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In particular, the contrast of the  reflection on and off cavity resonance C = (Roff − Ron)/Roff has the form [1]:  C = (1 − 2ηcav)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (1)  The photon extraction efficiency from the cavity ηcav = κwg/κtot is the ratio of cavity outcoupling rate κwg to the total  loss κtot = κwg +κint, including internal cavity losses κint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For the device used in this work, we find ηcav = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The  grating coupler and waveguide efficiency is estimated by measuring the round-trip optical losses away from the cavity  resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We compute the efficiency as ηGC =  �  Pout/Pin, and find ηGC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='36 for the device used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The transmission through passive optical components (beamsplitters, splices, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=') is measured independently to be  ηnet = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='61 (the HOM interferometer has additional losses, discussed below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The detection efficiency of the SNSPD  is ηdet = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This gives a combined predicted photon detection probability of P1 = ηcav ×ηGC ×ηnet ×ηdet = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  We lose an additional 7% of the single-ion emission from the finite time required to switch on the SNSPD bias current  (≈ 900 ns), which is turned off during the optical excitation pulse to avoid saturating the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The predicted  photon detection probability is then P1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='045, close to the measured value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='03564v1  [quant-ph]  9 Jan 2023  2  In the HOM experiment, the two-photon coincidence probability is decreased by the losses of the MZI delay line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  We measured the optical transmission in the 36 km fiber spool to be T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2, consistent with an attenuation length  La = 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To maximize the coincidence probability and balance the power in the two arms of the interferometer,  we use a 75 : 25 ratio beamsplitter at the input, such that 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='75 of the power is directed into the long MZI arm,  while 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='25 is directed into the short one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In the shorter arm, we utilize a variable optical attenuator set to match  the powers before the final MZI beamsplitter input ports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Accounting for both the losses in the fiber spool in the  long interferometer arm (matched with a VOA on the short arm), as well as the beamsplitter ratio, the two-photon  coincidence probability at |t1 − t2| = 0 is PHOM = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 × (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='75P1T)2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='01P 2  1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Here, the factor of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 accounts for  the requirement that the early (late) photon must pass through the long (short) interferometer arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For P1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='035  we get PHOM = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 × 10−5, close to the measured value of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 × 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  CAWO4 SAMPLE PREPARATION  The CaWO4 substrates used in this study were procured from SurfaceNet GmbH with a single sided epi polish and  (100) orientation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=', with a surface spanned by a and c axes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' According to the vendor, the crystals were grown  using 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9999% purity precursors and sold as “high purity CaWO4.” Polished samples were implanted with erbium  (II-VI Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=') using an energy of 35 keV which corresponds to a target depth of 10 nm (calculated by Stopping-Range  of Ions in Matter simulations [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Samples were prepared using two different Er3+ concentrations, a high density  sample used for ensemble spectroscopy utilizing a fluence of 1 × 1012 ions/cm2 and a low density sample used for  single ion spectroscopy implanted with a fluence of 5 × 109 ions/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Subsequent to implantation, samples were  annealed in air at a temperature of T = 300 ◦C for 1 hour, with a heating rate of T = 300 ◦C/hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Annealing  healed implantation damage and improved site occupation of the S4 point-group symmetry substitutional site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Silicon photonic crystal cavities are prepared as described previously [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The cavities are oriented on the substrate  such that the predominant electric field polarization is parallel to the CaWO4 c-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  SITE-SELECTIVE EXCITATION SPECTROSCOPY  In order to confirm that implanted Er3+ ions substitute at a site with S4 symmetry we performed a site-selective  excitation spectroscopy measurement using the high density sample cooled to 4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' A tunable narrowband laser was  employed in conjunction with an optical chopper to generate a train of excitation pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Using a second chopper,  fluorescence was collected out of phase with the excitation laser, dispersed using a monochromator, and detected  with an InGaAs detector array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' By performing a fluorescence measurement while sweeping the excitation laser a  map of site-specific excitation and emission frequencies was obtained (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Table S1 summarizes the measured  transition energies of four 4I15/2 and three 4I13/2 levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The resulting energy level structure is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S1b, and  found to be in close agreement with the transition energies previously reported for bulk doped samples [4], confirming  the S4 site assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The spectrum does not show any detectable fluorescence at other wavelengths within our  scan range, suggesting that this is the only Er3+ incorporation site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  TABLE S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Transition energies of implanted Er3+:CaWO4 determined using site-selective excitation spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' All values  are in cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Transitions to Zn and Yn for n greater than what is shown were not observed due to limitations in detection  sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The observed transition energies are in close agreement with values obtained for bulk doped samples [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  n  4I15/2Zn  4I13/2Yn  1  0  6524.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4  2  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3  6532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9  3  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9  6573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2  4  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0 We note that compared to the optical excited state lifetime of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 ms the Yn crystal field levels thermalize rapidly,  such that an identical fluorescence spectrum is obtained independent of which 4I13/2 level is excited (green arrows  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Furthermore, while the fluorescence spectrum is dominated by decay from the 4I13/2Y1 level, a small  fraction of fluorescence originates from the 4I13/2Y2 level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This leads to two sets of fluorescence patterns with identical  energy splittings (but different intensities), overlaid with an offset given by the 4I13/2Y1-4I13/2Y2 splitting (indicated  using dashed arrows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  3  Y1  Y2  Y3  Z2  Z3  Z1  Z4  2 3  1  2  3  1  1 2 3  5  6  4  3  1  2 & 6  4  7  5  7  4I15/2  4I13/2  a  b  1520  1522  1524  1526  1528  1530  1532  Excitation wavelength (nm)  1510  1515  1520  1525  1530  1535  1540  1545  1550  Fluorescence wavelength (nm)  Y7  Z8  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Ensemble spectroscopy of Er3+:CaWO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a Site-selective excitation spectrum of Er3+:CaWO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Green arrows  indicate when the excitation laser is resonant with different excited state crystal-field levels, where the corresponding excitation  path is labeled using the matching number in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Solid orange arrows denote the fluorescence energies due to decay from  the 4I13/2Y1 level, whereas the dashed arrows denote decay from the 4I13/2Y2 level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The prominent line with unity gradient  corresponds to laser scatter and has been re-scaled in intensity for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b The inferred energy level structure of Er3+:CaWO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In total, the performed spectroscopy yielded energies of four 4I15/2 and three 4I13/2 levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  SPIN STATE INITIALIZATION AND READOUT  To achieve fast and efficient spin state initialization we follow the approach used in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This initialization  scheme consists of using optical π pulses resonant with either the A or B transition, each followed by a microwave  pulse resonant with the excited state spin transition, MWe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For example, to initialize into the |↓g⟩ state we alternate  π pulses resonant with the optical A and MWe transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The number of pulse pairs used for the HOM and spin  dynamics experiments was 1 and 10, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  For spin state readout, we used a sequence of n optical π pulses resonant with the A transition each followed by a  fluorescence collection window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' By varying the number of readout pulses we found that the spin state readout fidelity  is maximized for n = 195, and applying further pulses would reduce the readout fidelity due to optical pumping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  After optimizing the number of readout pulses, a threshold was set for the total number of photons collected after n  pulses (Nthresh) to discriminate between the |↓g⟩ and |↑g⟩ states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We found that a threshold of Nthresh = 1 gives the  highest readout fidelity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' that is, if we obtained on average one photon or more after the n pulses then the spin state  was assigned to |↑g⟩, and if we obtained no photon then the spin state was assigned to |↓g⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  ENGINEERING AN OPTICAL CYCLING TRANSITION  As noted in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' [6] for Er3+:YSO, the cyclicity of the optical transition depends strongly on the magnetic  field orientation since changing the field changes the atomic transition dipole moment with respect to the cavity  polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For the case where the cavity linewidth is large compared to the Zeeman splitting, the cyclicity is  maximized when the spin-flip transitions C, D are orthogonal to the cavity polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In this work, by combining  a larger C-D splitting and a narrower optical cavity than in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' [6] we were able to tune the A transition into  resonance with the cavity while simultaneously keeping the spin-flip transitions C and D detuned from the cavity  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Consequently we optimize the magnetic field orientation to maximize cyclicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' From this we found  the optimal field orientation to be in the aa-plane, rotated 22o from the X-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  To probe the cyclicity, the ion was initialized into |↑g⟩ and subsequently read out using 400 pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Each readout  pulse consisted of an optical π pulse resonant with the A transition followed by a fluorescence collection window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Due to the finite cyclicity, the fluorescence count rate decays with increasing readout pulse number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This yielded a  cyclicity of C = ΓA/ΓD = 1030(10) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  To establish the single photon emission we calculate the intensity autocorrelation g(2)(τ) as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' At  4  zero offset pulse delay, we observe g(2)(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='018(3), showing strong suppression of multi-photon emission events  and thus a high purity of single photon emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  0  100  200  300  400  Readout pulse number  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='03  Counts per pulse  b  a  −20  −10  0  10  20  Pulse offset n  10  −2  10  −1  10  0  g(2)(τ)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Measuring the cyclicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a Decay of the A transition fluorescence count rate from optical pumping after initializing  into |↑g⟩ (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The count rate decays as e−n/C revealing a cyclicity of C = 1030(10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The orange trace corresponds to the  same readout pulse sequence after initializing into |↓g⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b Intensity autocorrelation g(2)(τ) of the A transition showing strong  suppression of the zero-delay peak with g(2)(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='018(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  PHOTON ECHO INVESTIGATION OF THE OPTICAL COHERENCE  We probe the coherence of the optical A transition using the photon echo technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' After initialization of the  spin state, we utilized an excitation sequence consisting of three optical pulses π/2 - π - π/2 separated by a waiting  time τ (for a total free evolution time 2τ), followed by a fluorescence collection window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The refocusing π pulse  in the middle of the sequence removes the slowly varying inhomogeneous dephasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For each evolution time, we  swept the phase of the last π/2 pulse and fitted the fluorescence intensity change against the phase angle using a sine  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The fitted oscillation amplitude is proportional to the two-level coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This yielded a coherence time  of T2 = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2 µs for a Hahn echo sequence (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S3a blue points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To further filter out higher frequency noise, we  increased the number of refocusing pulses using an XY N dynamical decoupling sequence (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S3b) and reached a  radiatively limited coherence time of 18 µs for N = 32 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S3a orange points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We note that in this experiment  the emission lifetime is T1 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='1 µs, different from 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 µs recorded using time-resolved PLE shown in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The results of this experiment implicate slow spectral diffusion as the main source of decoherence in our system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In  the case of the Hahn echo sequence, the recorded T2 time is approximately a factor of two from the lifetime limit  T2/(2T1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  HOM FIT FUNCTIONS  In this section, we derive the two-photon interference functions used to model the HOM histograms in the main  text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In particular, we consider two dephasing mechanisms, which allow us to estimate the possible bounds on the  emission linewidth based on the photon visibility determined from the HOM experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Finally, we extend the  model to simulate the reference HOM measurement, where the photons are made distinguishable by periodically  changing the phase of one of the two interfering photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  To model the HOM zero-delay time peak shape, we follow the derivation of Ref [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We assume that single photon  spatio-temporal wave functions have an exponential form:  ζ(t) = H(t) · exp  �  − t  2T1  − i[ω(t)t + φ(t)]  �  ,  (2)  where H(t) is the Heaviside function, T1 is the radiative lifetime, ω(t) is the photon frequency and φ(t) is the  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In an ideal case, the frequency and phase of the photon are constant over time, so the photon coherence is  lifetime limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' A time-dependent frequency and phase noise lead to decoherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Typically it is assumed that such  perturbations yield random walks in phase and frequency at two distinct timescales leading to two different physical  descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The first regime is pure dephasing, caused by fast frequency jumps accumulating phase on a timescale  5  b  a  0  10  20  30  40  50  Free evolution time (μs)  10  −1  10  0  Coherence  0  5  10  15  20  25  30  Number of π pulses  5  10  15  20  Coherence time (μs)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Optical coherence of Er3+:CaWO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a An optical Hahn echo measurement (green) reveals an optical coherence  of T2 = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Applying XY 32 dynamical decoupling sequence (orange) extends the optical coherence to the radiative limit  (blue dashed line) T2 = 18 µs, at a field where the optical T1 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='1(3) µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b Optical coherence scaling with the number of  refocusing pulses of XY dynamical decoupling sequences (red) compared to the lifetime limit (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  shorter than T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The second regime is described by spectral diffusion, primarily attributed to slow frequency drift on  a timescale considerably longer than T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' It is worth noting that this time-scale distinction is somewhat artificial, as  it is known that different noise sources have continuous power spectral densities [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Still, we perform this analysis to  study limiting cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' It can be shown that for single photons passing through an unbalanced MZI with a delay equal  to the photon generation rate, the HOM histogram peak areas An will be given by: A|i|≥2 = A, A1 = A(1 − R2),  A−1 = A(1 − T 2) and A0 = A(R2 + T 2 − 2RTVint) [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Here, A is the Poissionian peak coincidence level, R/T is the  reflection/transmission coefficient of the output MZI beamsplitter, and Vint is the emitter visibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In such cases,  the HOM two-photon interference coincidence probability function can be described by  P(τ) =Pdc + A  N  �  k=2  e−  |τ±ktrep|  T1  + A(1 − R2)e−  |τ+trep|  T1  + A(1 − T 2)e−  |τ−trep|  T1  + Ae− |τ|  T1 (R2 + T 2 − 2RT · F(τ)),  (3)  where Pdc is the coincidence level related to SNSPD dark counts and ambient light counts, and trep is the pulse  repetition period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Further, F(τ) is an integral defined as [7]  F(τ) =  � ∞  −∞  dt0 cos [∆ω(τ, t0)τ + ∆φ(τ, t0)] ,  (4)  where ∆φ(τ, t0) is a the phase difference and ∆ω(τ, t0) is the frequency difference between two interfering photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  If frequency and phase fluctuations are assumed to follow Gaussian distribution functions, F(τ) is given by [7]  F(τ) = exp  �  − 2|τ|  Tdep  − σ2τ 2  �  ,  (5)  where Tdep is the dephasing time 1/Tdep = 1/T2 −1/(2T1), and σ is the inhomogeneous linewidth broadening related  to slow spectral diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  First, we consider the case where fast spectral diffusion dominates (Lorentzian broadening), for which  Flor(τ) = exp  �  − 2|τ|  Tdep  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (6)  This allows for the evaluation of the HOM histogram central peak area  A0 = A  � ∞  −∞  dτ  �  R2 + T 2 − 2RTe  − 2|τ|  Tdep  �  e− |τ|  T1 = A  �  2T1(R2 + T 2) − 4RT  T1Tdep  2T1 + Tdep  �  ,  (7)  6  and the off-center peak area A|i|≥2  A|i|≥2 = A  � ∞  −∞  dτe− |τ|  T1 = 2AT1,  (8)  giving a visibility of  V = 1 − 2A0  A|i|≥2  = 1 − 2  �  R2 + T 2�  + 4RT  Tdep  2T1 + Tdep  = 1 − 2  �  R2 + T 2�  + 4RT T2  2T1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (9)  Note that this definition of visibility contains information about both the MZI interferometer imperfections (BS R : T)  and the intrinsic indistinguishability of the emitted photons Vint = T2/(2T1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In our experiment R : T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='43 : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='57  is determined from the imbalance between A−1 and A1 peak areas in the HOM histogram (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3b in the main  text), contributing to a decrease in visibility of around 4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' By evaluating the integrated counts A0 and A|n|≥2 in  the HOM experiment, we obtain a visibility of 80% after the dark and ambient light counts are subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This  allows us to estimate Vint = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='84, and further T2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='84 × 2T1 = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' (3) and (6) with T2 = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 µs  we model the HOM histogram in the main text (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3b,d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Furthermore, using this model, we can estimate the  bound on the emission linewidth at the timescale of 100 − 200 µs following  νL =  1  πT2  =  1  2πT1Vint  ,  (10)  which yields Lorentzian broadening of νL = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Note that in the case of Fourier limited photons, one obtains  νLF = 1/(2πT1) = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In the case where slow dynamics dominate decoherence (Gaussian broadening), the function F(τ) is simplified to  Fgau(τ) = exp  �  −σ2τ 2�  , such that  A0 = A  �  ��2T1(R2 + T 2) − 2RT  √πe  1  4σ2T 2  1 erfc  �  1  2σT1  �  σ  �  �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (11)  This leads to a visibility given by  V = 1 − 2  �  R2 + T 2�  + 2RT  √πe  1  4σ2T 2  1 erfc  �  1  2σT1  �  σT1  ,  (12)  where the intrinsic emitter visibility is given by  Vint =  √πe  1  4σ2T 2  1 erfc  �  1  2σT1  �  2σT1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (13)  Using Vint = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='84 we get σ equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='039 MHz, which corresponds to a Gaussian broadening of νG = 2  √  2ln2  √  2σ =  21 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Note that the estimated νG is on the order of the Fourier limit of 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 kHz, such that the resultant emission  line-shape will be described by a Voigt profile with a total width of  νV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='535  2πT1  +  �  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='217  (2πT1)2 + ν2  G,  (14)  equal to a linewidth of 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This bounds the emission linewidth to be in the range 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6 − 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 kHz for a  timescale of 175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2 µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Next, we consider the case of the reference HOM measurement in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Typically, the distinguishability in  HOM experiments is tuned by rotating the polarization of one of the photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' However, our SNSPDs have a strongly  polarization-dependent detection efficiency, which complicates the interpretation of such a measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Therefore,  we instead make the photons distinguishable by artificial spectral broadening, achieved by rapidly modulating the  path length of one of the interferometer arms with a large amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Specifically, the phase of the photons traveling  through the shorter MZI arm is modulated using a triangle wave with frequency  ωm  2π = 43 kHz and amplitude  Am = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='75π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Consequently, the phase difference can be described directly by  ∆φ(τ, t0) = 2Am  π  [arcsin (sin (ωm(τ + t0))) − arcsin (sin (ωmt0))] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (15)  7  In this case we can assume that the HOM zero-delay peak area will be dominated by the external phase modulation  so that we can omit the ∆ω term, and F(τ) will only depend on ∆φ(t0, τ)  Fmod(τ) =  � ∞  −∞  dt0 cos  �2Am  π  [arcsin (sin (ωm(τ + t0))) − arcsin (sin (ωmt0))]  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (16)  The periodic modulation of the phase difference with τ will translate into a quantum-beat-like signal with a distinct  dip at zero detection time difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To fit the HOM data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 3c,d of the main text, we evaluate Fmod(τ)  numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The best fit to the experimental data is obtained for a modulation amplitude of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='73(5)π where the  modulation frequency was fixed to the value used in the experiment, 43 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  DISTORTION OF THE MAGNETIC MOMENT TENSOR  The magnetic moments of individual single ions changed appreciably from ion-to-ion as well as from the previously  recorded ground state g-tensor [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To investigate this, the magnetic response of two single ions (different from the  single ion investigated in the main text) was fully characterized by probing the optical transition frequencies of the  four transitions A, B, C, and D for a range of field orientations using a magnetic field magnitude of 50 G, with the  results shown in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  TABLE S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Single-ion g-tensors measured for two separate ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Due to a small distortion of the S4 point-group site, the  single-ion magnetic moments do not satisfy gx = gy = g⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We note that in this and subsequent sections we use the convention  where the z axis points along the crystallographic c axis, which is different to the coordinate system used in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Ground state  Excited state  gx  gy  gz  gx  gy  gz  Ion 1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='8  Ion 2  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3  In order to gain a deeper understanding of the g-tensor anisotropy, an effective crystal-field Hamiltonian was used  to model the intra-4f transitions of Er3+:CaWO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The complete Hamiltonian has the form  H = HFI + HCF + HZ,  (17)  where HFI corresponds to the free-ion components of the Hamiltonian, HCF accounts for the interaction of the  valance electrons with the host material, and HZ is the Zeeman Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The free-ion Hamiltonian used is [10]  HFI = EAVG +  �  1,2,3  F kfk + ζ4fASO + αL(L + 1) + βG(G2) + γG(R7) +  �  i=2,3,4,6,7,8  T iti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (18)  Noting only the most significant contributions, EAVG accounts for the spherically symmetric one-electron component,  F k are the Slater parameters, f k are the electrostatic repulsion with angular dependence, ζ4f is the spin-orbit coupling  term, and ASO is the spin-orbit coupling operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The remaining contributions are higher-order and the reader is  referred to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' [11] for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' To model the contribution of the S4 point-group symmetry crystal-field the following  Hamiltonian was used  HCF = B2  0C(2)  0  + B4  0C(4)  0  + B6  0C(6)  0  + B4  4(C(4)  4  + C(4)  −4) + B6  4(C(6)  4  + C(6)  −4),  (19)  with the coefficients Bk  q the crystal-field parameters and C(k)  q  spherical-tensor operators in Wybourne’s normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  We note that the above Bk  q are all real with the exception of B6  4, which is complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The above Hamiltonian was  fitted to data obtained using site-selective fluorescence spectroscopy of the 4I13/2 →4I15/2 transitions as well as the  barycenter of higher-energy transitions up to 4S3/2 obtained from literature [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Furthermore, the fit was optimized  to reproduce the ensemble 4I15/2Z1 and 4I13/2Y1 g-tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Using the crystal-field parameters obtained via the method outlined above as a starting point, a fit was then  performed to the g-tensor of both Ion 1 and Ion 2 to determine the crystal-field environment local to each ion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We  hypothesize that the perturbation of the S4 point-group symmetry was caused by a single dominant defect, potentially  due to the substrate surface or some form of remote charge compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Consequently, an axial term ¯B2  0 oriented  at an arbitrary angle with respect to the crystal-field quantization axis was introduced, and both the magnitude as  8  well as the orientation were varied to reproduce the observed ground and excited state g-tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This assumed that  the crystal-field potential due to the defect is superposable with the nominal crystal-field potential [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  For Ion 1, the observed g-tensor was reproduced by an axial term ¯B2  0 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 cm−1, rotated by an Euler rotation  from the quantization axis with α = 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4◦, β = 265◦ and γ = 0◦, following the Euler angle convention of Messiah [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Similarly, Ion 2 required an axial term ¯B2  0 = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7 cm−1, rotated by an Euler rotation from the quantization axis with  α = 270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2◦, β = 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0◦ and γ = 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We note that the unperturbed rank 2 crystal-field parameter has a magnitude  of B2  0 = 578 cm−1, such that the observed change in the rank 2 crystal-field potential consisted of around ∼ 2% for  both of the ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This amounts to a frequency shift of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 GHz for Ion 1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='9 GHz for Ion 2 for the 4I15/2Z1  to 4I13/2Y1 transition when compared to the crystal-field model not including any perturbation, which is somewhat  larger than, but comparable to, the observed inhomogeneous linewidth for single ions coupled to the nanophotonic  device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Therefore, the observed g-value anisotropy is consistent with a small amount of strain near the ion, potentially  due to proximity to the surface or a charge compensation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In order to perform the initial crystal-field Hamiltonian fit we independently measured the 4I15/2Z1 and 4I13/2Y1  ensemble magnetic moments using optical spectroscopy by utilizing the high density implanted sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' From this we  obtain g⊥ = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6 and g∥ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 for the ground state, and g⊥ = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6 and g∥ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 for the excited state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The fitted ground  state g-values deviate from the literature values measured by electron-spin resonance [4];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' however, the deviation is  within the uncertainty of our vector magnet calibration due to magnetic field gradients within the sample space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We  note that the above conclusion about the mechanism for the anisotropy of single ion g-values does not depend on the  precise magnetic moments assumed for bulk Er3+:CaWO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Additionally, in the above fit we have constrained that  gx = gy, and our data was also consistent with a fit for which gx ̸= gy at the 5% level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This suggests that some of  the observed distortion of the magnetic moment tensor may also be present in an ensemble average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  DEPENDENCE OF T1 ON MAGNETIC FIELD  To understand the observed spin lifetime, we performed a lifetime measurement at a second magnetic field strength,  |B| = 950 G, obtaining T1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='393 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' At low temperatures, Raman and Orbach processes are slow and the spin  relaxation rate is dominated by the direct process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This has the following functional form with respect to an applied  magnetic field [14]:  T −1  1  = Ad  �gµBB  h  �5  coth  �gµBB  2kbT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (20)  Fitting the above equation to the observed spin lifetime data (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S4) yielded a direct process constant Ad =  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4(2) × 10−6 s−1 GHz−5, with the expected T1 ∝ 1/B5 scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The spin T1 has previously been measured for  CaWO4 at low temperatures, and the zero-temperature extrapolated lifetime was found to be 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='8 s at a frequency  of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='881 GHz [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This corresponds to Ad = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2 × 10−6 s−1GHz−5, approximately consistent with our value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  SPIN COHERENCE MODELING  In order to explain the observed spin coherence, we consider the magnetic environment of the Er3+ ion in the  CaWO4 host crystal, consisting of the 183W nuclear spin bath and paramagnetic impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' While the concentration  and dynamics of paramagnetic impurities is not well known, the dynamics of the nuclear spin bath under decoupling  sequences can be understood using standard CCE (Cluster Correlation Expansion) techniques [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' First, we describe  the Er3+ spin coupling to the nuclear spin bath and explain features observed in the Hahn experiment at short times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Then, we apply our understanding of the nuclear spin bath to find the expected decoherence rates for the Hahn and  Ramsey experiments and observe that it cannot explain the observed rates in either.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This leads us to conjecture the  existence of an appreciable concentration of paramagnetic impurities, which we discuss in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  To form the nuclear spin bath, we generate random configurations of nuclear spins by allowing each W atom to  be an 183W isotope (I = 1/2) with probability 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Under the secular approximation for the electron spin, this  bath can be described by the following Hamiltonian in the rotating frame of the Er3+ spin:  H = 2Sz  �  i  (A(i)  || Ii  z + A(i)  ⊥ Ii  x) +  �  i  ωL,W Ii  z +  �  i,j  H(i,j)  nn ,  (21)  where Ii  z/x are the nuclear spin operators of the ith spin, A(i)  ||  and A(i)  ⊥ are the parallel and perpendicular hyperfine  interaction terms, ωL,W is the Larmor frequency of the W nuclear spin (107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7 kHz at |B| = 600 G) and H(i,j)  nn  is the  dipolar interaction Hamiltonian between W nuclear spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  9  10  2  10  3  |B| (G)  10  −1  10  0  10  1  10  2  Spin T1 (s)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Spin lifetime as a function of magnetic field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Solid line is a fit to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' (20) as is predicted for the  spin-lattice relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  This implies that there can be considerable variation in ESEEM (Electron Spin Echo Envelope Modulation) features  observed for an Er3+ ion, depending on whether a nearby W nuclear spin is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We observe such features as  dips in coherence in the Hahn experiment (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In contrast to decay envelopes, these sharp features occur at  particular pulse spacings and indicate coherent coupling to a W nuclear spin occupying one of the nearest sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Since we are working under the assumption that there is only one nearby W nuclear spin, we do not allow another  nuclear spin within the first ten nearest W sites when generating the random nuclear spin baths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We find hyperfine  parameters of the strongly coupled W nuclear spin by minimizing over the following cost function:  C(A||, A⊥) =  �  k  �  j  (Ssim,k(τj) − Sexp(τj))2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Ssim,k(τj) = e−(2τj/T2)n · Sbath,k(τj) · S(τj, A||, A⊥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (22)  Here, τj are the time units that were sampled in the Hahn experiment, Ssim,k(τj) is the simulated signal for the  kth bath and Sexp(τj) is the experimentally measured contrast for the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Ssim,k(τj) is calculated by taking  a product of three factors: a stretched exponential decay, with decay constants T2 = 44 µs and n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='4 used in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4d, the CCE simulation for the nuclear spin bath, Sbath,k(τj), and simulation for a single W nuclear spin coupled  to Er3+, S(τj, A||, A⊥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The form of Ssim,k(τj) is justified as a first order CCE expansion, which does not take  interactions between constituents of the bath into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The envelope e−(2τj/T2)n is assumed to come from a  source independent of the nuclear spin bath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  The minimization yields the hyperfine parameters, (A||, A⊥) = (25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2, 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7) kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' These values are within range of  expected interaction strengths for nearby W nuclear spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In particular, for the W nuclear spin coordinates given as  rW = ±a/2 + c/2, where a = aˆx and c = cˆz are CaWO4 lattice vectors, we calculate (A||, A⊥) = (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5, 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5) kHz at  our field orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' The discrepancy could be due to uncertainty in the field alignment or the Er3+ spin g-tensor,  which can lead to rotations as discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Finally, ignoring the contribution from the phenomenological decay, we simulate longer time delays to extract the  W bath limited coherence times for the Hahn and Ramsey experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We perform a second order CCE simulation  for the simulation of the Hahn experiment, which takes into account the dipolar coupling between nuclear spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Noting that ESEEM features will persist as observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4d, we find that the interaction between nuclear spin  pairs leads to an envelope which decays in 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6 ms (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S5a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We also perform a Ramsey simulation and show  that the expected T ∗  2 decoherence due to the W-bath is about 4 µs (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S5b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Both of these coherence values are  significantly longer than the observed values for T2 and T ∗  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We attribute the difference to paramagnetic impurities  and explore the expected concentration in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  10  a  b  |  g  Free evolution time 2τ (µs)  Population  0  5  10  15  20  25  30  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  1  Population |  g  Free evolution time τ (µs)  0  10  20  30  40  50  60  70  80  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' W bath limited coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a The second order contribution to the CCE simulation for the Hahn experiment  for 10 random W-bath configurations, where we assume that the nearest W nuclear spin is located at rW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Fitting each of  the curves to a stretched exponential yields T2 = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7(4) ms with n = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We note that this is only the envelope and  faster ESEEM features, obtained from the first order CCE simulation, persist as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This simulation considers  W nuclear spins within an 11 nm radius of the Er3+ spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b CCE simulation of Ramsey experiment for the same W bath  configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Fitting each of the curves to a Gaussian decay yields T ∗  2 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0(4) µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Both simulations are performed at our  experimental field configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  ESTIMATING CONCENTRATION OF PARAMAGNETIC IMPURITIES  In order to estimate the concentration of paramagnetic impurities, we use the Ramsey experiment as a probe of  the static magnetic noise experienced by the Er3+ ion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' As stated in the previous sections, the W bath limited T ∗  2  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S5b) is significantly longer than the measured T ∗  2 of 247 ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' This indicates that the measured T ∗  2 is limited  by paramagnetic impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Therefore, we can use the measured T ∗  2 to roughly estimate the concentration of these  impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Without loss of generality, we can assume that the interaction between the Er3+ spin and the paramagnetic impurity  will be of the Ising form under the secular approximation, forbidding exchanges that do not conserve magnetization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  Under these assumptions, we can write down the Hamiltonian concerning the Er3+ spin and the paramagnetic bath  in the frame rotating at Er3+ and the impurity frequency for a single impurity species  H = Sz  �  i  J(i)  I Si  z +  �  i,j  J(i,j)  I  Si  zSj  z + J(i,j)  S,k (Si  xSj  x + Si  ySj  y) +  �  i  ∆iSi  z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (23)  Here, J(i)  I  is the Ising interaction strength between the Er3+ spin and the impurity, while J(i,j)  I  and J(i,j)  S  are the Ising  and Symmetric interaction strengths between the two impurities and ∆i is the disorder in the precession frequency  of each impurity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' While the bath interaction and disorder terms become important for decoupling sequences, these  processes do not contribute on the timescale of the Ramsey experiment, which is dominated by the static noise  represented by the first term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Based on this understanding, we can compute the net frequency, in the rotating frame,  of the Er3+ spin given the state of the bath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' For the purposes of this calculation, we take this bath to consist of  S = 1/2 electrons with g = 2 and represent its state by the bitstring k of length N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We can then write down the  Hamiltonian projected by the state k of the bath  Hk = ⟨k|Sz  �  i  J(i)  I Si  z|k⟩ = Sz  �  i  J(i)  I  (−1)ki  2  = ωkSz;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  ωk =  �  i  (−1)kiJ(i)  I  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (24)  Here, ωk is the precession frequency of the Er3+ spin given the state k of the bath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We can then calculate the Ramsey  11  coherence as T ∗  2 = π/∆ω, where ∆ω2 is the variance over the set {ωk}:  ∆ω2 = 1  2N  �  k  ω2  k = 1  2N  �  k  �  i  �(−1)kiJ(i)  I  2  �2  + 1  2N  �  k  �  i<j  (−1)ki+kjJ(i)  I J(j)  I  =  �  i  �J(i)  I  2  �2  ,  (25)  where we have used the fact that the distribution is centered at zero and the summations can be reordered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We  observe that the frequency standard deviation can be interpreted as the norm of the vector of Ising interaction  strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  In order to estimate the concentration based on this expression, we generate 2000 instances of randomly distributed  electron spin baths across a range of concentrations, calculate the resultant T ∗  2 of each configuration and use Bayes  rule to infer a probability density, P(ρ|T ∗  2 ), for the concentration, ρ, given our observation of T ∗  2  P(ρ|T ∗  2 ) =  P(T ∗  2 |ρ)  � ∞  0  P(T ∗  2 |ρ′)dρ′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  (26)  Here, P(T ∗  2 |ρ′) is the probability to obtain a given T ∗  2 for the bath concentration ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' In practice, we calculate this  expression by counting the number of instances for each concentration that yields a value of T ∗  2 within 3 standard  deviations of the observed value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We perform this estimate for both a 3D geometry of electron spins located in the  bulk and a 2D geometry of spins located on the sample surface, estimated to be 10 nm away.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We obtain concentrations  of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7 × 1016 cm−3 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 nm−2 for the bulk and surface concentration estimates respectively with 70%  confidence (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' As both of these are plausible concentrations, we note that both may be playing a non-negligible  role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' We are not able to make a calculation of how this concentration of paramagnetic impurities affects the Hahn  coherence because it depends on the dynamics of this paramagnetic impurity bath, which is not well known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Doing  this calculation would require further information such as the species and spin-lifetime of impurities, as well as the  disorder of the bath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  a  b  0  5  10  15  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='2  Prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' density (10-16 cm3)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='0  Prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' density (nm2)  ρ (1016 cm-3)  ρΑ (nm-2)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Probability density of paramagnetic impurity concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' a Assuming a 3D uniform distribution of  impurities, we estimate that the bath concentration is in the range 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='6×1016 – 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7×1016 cm−3 with 70% confidence, with the  likeliest concentration at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='7×1016 cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' b Assuming a 2D distribution on the surface of our crystal, assumed to be located  10 nm away from the Er3+ spin, we estimate an area concentration in the range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='5 – 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='3 nm−2 with 70% confidence, with  the likeliest concentration at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='77 nm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content=' Dashed lines indicate the confidence ranges for the impurity concentrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  12  ∗ These authors contributed equally to this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
+page_content='  † jdthompson@princeton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DdE1T4oBgHgl3EQf-Abs/content/2301.03564v1.pdf'}
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diff --git a/F9E4T4oBgHgl3EQfHQxB/content/tmp_files/2301.04901v1.pdf.txt b/F9E4T4oBgHgl3EQfHQxB/content/tmp_files/2301.04901v1.pdf.txt
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@@ -0,0 +1,2015 @@
+Pylon: Table Union Search through Contrastive Representation
+Learning
+Tianji Cong
+University of Michigan
+Ann Arbor, Michigan, USA
+congtj@umich.edu
+H. V. Jagadish
+University of Michigan
+Ann Arbor, Michigan, USA
+jag@umich.edu
+ABSTRACT
+The large size and fast growth of data repositories, such as data
+lakes, has spurred the need for data discovery to help analysts find
+related data. The problem has become challenging as (i) a user
+typically does not know what datasets exist in an enormous data
+repository; and (ii) there is usually a lack of a unified data model to
+capture the interrelationships between heterogeneous datasets from
+disparate sources. The common practice in production is to provide
+a keyword search interface over the metadata of datasets but users
+often have discovery needs that cannot be precisely expressed by
+keywords. In this work, we address one important class of discovery
+needs: finding union-able tables.
+The task is to find tables in the repository (or on the web) that
+can be unioned with a given query table. The challenge is to rec-
+ognize union-able columns that may be represented differently. In
+this paper, we propose a data-driven learning approach: specifically,
+an unsupervised representation learning and embedding retrieval
+task. Our key idea is to exploit self-supervised contrastive learn-
+ing to learn an embedding model that produces close embeddings
+for columns with semantically similar values while pushing apart
+columns with semantically dissimilar values. We then find union-
+able tables based on similarities between their constituent columns
+in embedding space. On a real-world dataset, we demonstrate that
+our best-performing model achieves significant improvements in
+precision (16% ↑), recall (17% ↑), and query response time (7x faster)
+compared to the state-of-the-art.
+CCS CONCEPTS
+• Information systems → Information integration.
+KEYWORDS
+data discovery, data integration, table union search, contrastive
+learning, embeddings
+Permission to make digital or hard copies of all or part of this work for personal or
+classroom use is granted without fee provided that copies are not made or distributed
+for profit or commercial advantage and that copies bear this notice and the full citation
+on the first page. Copyrights for components of this work owned by others than ACM
+must be honored. Abstracting with credit is permitted. To copy otherwise, or republish,
+to post on servers or to redistribute to lists, requires prior specific permission and/or a
+fee. Request permissions from permissions@acm.org.
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+© 2018 Association for Computing Machinery.
+ACM ISBN 978-1-4503-XXXX-X/18/06...$15.00
+https://doi.org/XXXXXXX.XXXXXXX
+ACM Reference Format:
+Tianji Cong and H. V. Jagadish. 2018. Pylon: Table Union Search through
+Contrastive Representation Learning. In Proceedings of Make sure to en-
+ter the correct conference title from your rights confirmation emai (Confer-
+ence acronym ’XX). ACM, New York, NY, USA, 13 pages. https://doi.org/
+XXXXXXX.XXXXXXX
+1
+INTRODUCTION
+Recent years have witnessed a vast growth in the amount of data
+available to the public, particularly from data markets, open data
+portals, and data communities (e.g., Wikidata and Kaggle) [7]. To
+benefit from the many new opportunities for data analytics and
+data science, the user first usually has to find related datasets in
+a large repository (e.g., data lakes). The challenge for a system is
+to support users with varying discovery needs, without the help
+of a unified data model capturing the interrelationships between
+datasets.
+In response to the challenge, there are many ongoing efforts
+under the umbrella of data discovery. One task of the interest in
+data discovery is to find union-able tables [1, 5, 10, 27] with the
+aim of adding additional relevant rows to a user-provided table.
+Figure 1 shows an example of two tables union-able over four pairs
+of attributes. In general, the literature considers two tables union-
+able if they share attributes from the same domain and assumes the
+union-ability of two attributes can be implied by some notion of
+similarity. We refer to the problem of finding union-able tables as
+table union search (termed in [27]) in the rest of the paper.
+The typical solution path is to first identify union-able attributes
+(or columns in the tables) and then aggregate column-level results
+to obtain candidate union-able tables. To uncover the union-ability
+of attributes, both syntactic and semantic methods have been em-
+ployed in the literature. Syntactic methods are the easiest, and have
+been used the longest. While they are robust at catching small
+changes, such as capitalization or the use of a hyphen, they are
+unable to address the use of common synonyms. Semantic methods
+offer the possibility of finding union-able columns of semantically
+similar values despite their syntactic dissimilarity (e.g., the "venue"
+column and the "platform" column in figure 1). [10, 27] link cell val-
+ues to entity classes in an external ontology and compare similarity
+of entity sets. [1, 27] use off-the-shelf word embeddings to measure
+semantics. Both methods have notable limitations. [27] observed
+that only 13% of attribute values of their collected Open Data ta-
+bles can be mapped to entities in YAGO [32], one of the largest
+and publicly available ontologies. Although word embeddings can
+provide more semantic coverage of attributes, they are subject to
+the training text corpus and may not generalize well to textual data
+in tables [18, 23].
+arXiv:2301.04901v1  [cs.DB]  12 Jan 2023
+
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+Tianji Cong and H. V. Jagadish
+id
+title
+authors
+venue
+year
+671167
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+Fg-index: towards verification-free query proc...
+J Cheng, Y Ke, W Ng, A Lu
+Proceedings of the 2007 ACM SIGMOD internation...
+https://scholar.google.com/scholar?oi=bibs&hl=...
+286
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+...
+Figure 1: An example of two tables union-able over four pairs of attributes: title - Title, authors - Authors, venue - Platform,
+and year - Year.
+Instead of relying on low-coverage ontologies or pre-trained
+word embeddings, a data-driven learning approach seems more
+promising to capture semantics as shown in many data manage-
+ment tasks such as entity resolution [24, 25], data cleaning [34], and
+table interpretation [11]. A large part of their success requires la-
+beled data for supervised learning. However, there is no large-scale
+labeled dataset for table union search. The only publicly available
+benchmark [27] with table- and column-level ground truth con-
+tains limited number of tables synthesized from only 32 base tables,
+which is far from being representative for training purposes. Ad-
+ditionally, labeling new datasets could be very laborious and time
+consuming as curators need to examine every pair of columns in
+every pair of tables in a collection. Even if the training data prob-
+lem were resolved, we would only be able to determine column
+matches pairwise. It would still be very inefficient to exhaustively
+consider every query column and every column in the corpus pair-
+wise to predict union-ability. In short, the inherent search nature
+of the problem makes it unsuitable to formulate it as a supervised
+classification problem.
+In this work, we overcome the aforementioned difficulties by
+casting table union search as an unsupervised representation learn-
+ing and embedding retrieval task. Our goal is to learn column-level
+embeddings into a high-dimensional feature space. Locality search
+in this feature space can then directly be used for union-able table
+search. To achieve this goal, our key idea is to exploit self-supervised
+contrastive learning to learn an embedding model that produces
+close embeddings for columns with semantically similar values
+and pushes away columns with semantically dissimilar values. We
+propose Pylon, a novel contrastive learning framework that learns
+column representations for tabular data and serves the table union
+search problem without relying on labeled data.
+There are two main challenges in the development of Pylon,
+specifically, on how to adapt contrastive learning for tabular data.
+(1) How to create training data without human labeling? The
+self-supervised contrastive learning technique requires con-
+structing positive and negative examples from the data itself.
+In the field of computer vision where contrastive learning
+first took off, [9] applies a series of random data augmen-
+tation of crop, flip, color jitter, and grayscale to generate
+stochastic views of an image. These views preserve the se-
+mantic class label of the image and so make positive exam-
+ples for training. They further consider any two views not
+from the same image as a negative example. However, the
+tabular data modality is dramatically different from images
+and it remains unclear how to create different views of tables
+while keeping the semantics.
+(2) What is a feasible feature encoder for tabular data? Another
+key component in contrastive learning is a pre-trained base
+encoder that gives initial embeddings for raw data. Both
+computer vision (CV) and natural language processing (NLP)
+communities have widely recognized models for feature ex-
+tractions (e.g., ResNet [19] in CV and BERT [12] in NLP).
+On the contrary, there is no generally accepted feature ex-
+traction model for tables despite the recent progress in Web
+table modeling (which we discuss in subsection 2.2).
+In summary, we make the following contributions:
+• We formulate semantic table union search as an unsuper-
+vised representation learning and embedding retrieval prob-
+lem, and propose to use self-supervised contrastive learning
+to avoid the labeling issue.
+• We present Pylon, to the best of our knowledge, the first con-
+trastive learning framework for learning semantic column
+representations from large collections of tables. We also ex-
+plore the design of each component in contrastive learning
+and take an initiative in adapting contrastive learning for
+tabular data.
+• We empirically show that our embedding approach is both
+more effective and efficient than existing embedding meth-
+ods on a self-curated real-world dataset and a synthetic pub-
+lic benchmark. On the real-world dataset, two of our model
+variants outperform their corresponding baseline version by
+14% and 6% respectively on both precision and recall. We
+also observe that they speed up the query response time by
+2.7x and 9x respectively. We (plan to) open-source the new
+benchmark for future research study.
+• We demonstrate that our embedding approach can be further
+augmented by syntactic measures and that our best ensemble
+model has significant advantages over the state-of-the-art
+(namely, 𝐷3𝐿 [1]), more than 15% improvement in precision
+and recall, and 7x faster in query response time.
+We give a formal problem setup and background about embed-
+ding models in Section 2. We describe our framework Pylon includ-
+ing embedding training and search in Section 3. Section 4 reports
+experiments that validate our approach. We discuss related work
+in Section 5 and conclude in Section 6.
+
+Pylon: Table Union Search through Contrastive Representation Learning
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+2
+PROBLEM DEFINITION & BACKGROUND
+In this section, we start by describing the formal problem setup
+in section 2.1, and then provide an overview of existing embed-
+ding models for tabular data. We also discuss the challenges of
+representation learning for table union search.
+2.1
+Table Union Search
+The table union search problem [27] is motivated by the need to
+augment a (target) table at hand with additional data from other
+tables containing similar information. For example, starting with
+a table about traffic accidents in one state for a particular year, an
+analyst may wish to find similar traffic accident data for other states
+and years. Ideally, these tables would have the same schema (e.g.
+data from the same state agency for two different years) so that
+we could simply union the row-sets. However, this is typically not
+the case for data recorded independently (e.g. data from different
+states). We consider two tables union-able if they share attributes
+from the same domain. Also, as in prior work on this topic, we
+assume the union-ability of attributes can be quantified by some
+notion of similarity.
+Definition 1 (Attribute Union-ability). Given two attributes 𝐴 and
+𝐵, the attribute union-ability U𝑎𝑡𝑡𝑟 (𝐴, 𝐵) is defined as
+U𝑎𝑡𝑡𝑟 (𝐴, 𝐵) = M(T (𝐴), T (𝐵))
+where T (·) is a feature extraction technique that transforms raw
+columns (attribute names, attribute values, or both) to a feature
+space and M(·, ·) is a similarity measure between two instances in
+the feature space.
+With the definition of attribute union-ability, we can define table
+uniona-bility as a bipartite graph matching problem where the
+disjoint sets of vertices are attributes of the target table and the
+source table respectively, and edges can be defined by attribute
+union-ability. In this paper, we restrict ourselves to the class of
+greedy solutions. Therefore, we formalize the definition table union-
+ability as a greedy matching problem as follows:
+Definition 2 (Union-able Tables). A source table 𝑆 with attributes
+B = {𝐵𝑗 }𝑛
+𝑗=1 is union-able to a target table 𝑇 with attributes A =
+{𝐴𝑖}𝑚
+𝑖=1 if there exists a one-to-one mapping 𝑔 : A′(≠ ∅) ⊆ A →
+B′ ⊆ B such that
+(1) |A′| = |B′|;
+(2) ∀𝐴𝑖 ∈ A′, U𝑎𝑡𝑡𝑟 (𝐴𝑖,𝑔(𝐴𝑖)) ≥ 𝜏 where
+𝑔(𝐴𝑖) = arg max
+𝐵𝑗
+{U𝑎𝑡𝑡𝑟 (𝐴𝑖, 𝐵𝑗) : 1 ≤ 𝑗 ≤ 𝑛}
+and 𝜏 is a pre-defined similarity threshold.
+Definition 3 (Table Union-ability). Following notations in Defini-
+tion 2, the table union-ability U(𝑆,𝑇) is defined as
+U(𝑆,𝑇) =
+�𝑙
+𝑖=1 𝑤𝑖 · U𝑎𝑡𝑡𝑟 (𝐴𝑖,𝑔(𝐴𝑖))
+�𝑙
+𝑖=1 𝑤𝑖
+where 𝑙 is the number of union-able attribute pairs between the
+target table 𝑇 and a source table 𝑆, and 𝑤𝑖 weights the contribution
+of the attribute pair (𝐴𝑖,𝑔(𝐴𝑖)) to the table union-ability.
+Considering the scale of the dataset repository, we also follow
+the common practice[1, 10, 27] of performing top-𝑘 search. The
+table union search problem is formally defined as below.
+Definition 4 (Top-𝑘 Table Union Search). Given a table corpus
+S, a target table 𝑇, and a constant 𝑘, find up to 𝑘 candidate tables
+𝑆1,𝑆2, ...,𝑆𝑘 ∈ S in descending order of table union-ability with
+respect to the query table 𝑇 such that 𝑆1,𝑆2, ...,𝑆𝑘 are most likely
+to be union-able with 𝑇.
+2.2
+Embedding Models for Tabular Data
+The advance of language modeling in the field of NLP has sparked
+its adoption in many applications of data management such as
+semantic queries in relational databases [3, 17], entity resolution [24,
+25], and data cleaning [34]. We give an (non-exhaustive) overview
+of embedding models that have been used for tabular data.
+Word Embeddings. Word embeddings are vector representa-
+tions of words in a low-dimension space where words that share the
+common context are close to each other. Most popular word embed-
+ding models include Word2Vec [26], GloVe [30], and fastText [2].
+Unlike Word2Vec and GloVe that learn embeddings directly for
+words, fastText represents a word as an n-gram of characters (i.e.,
+subwords) and generate word embeddings based on subwords. In
+this way, fastText is able to handle out-of-vocabulary words that
+do not appear in the training corpus. In the context of table union
+search, both [27] and [1] employed off-the-shelf fastText embed-
+dings to measure the semantic relatedness between two columns,
+which implies union-ability. One issue with pre-trained word em-
+beddings is that the text value distribution in tables is different
+from what models capture in the training corpus consisting of un-
+structured documents. To generate embeddings for textual values
+in tables, [18] serialized tables to sequences of tokens and trained
+a fastText model on a text corpus extracted from Web tables. The
+resulting web table embedding models demonstrated better perfor-
+mance as compared to off-the-shelf fastText embeddings in a task
+of ranking union-able columns pairs.
+Transformer-based Language Models. Another well-known
+issue with word embedding models is that they assign a fixed em-
+bedding for each word regardless of various meanings a word could
+have and different linguistic contexts in which a word could appear.
+This (partly) motivates the development of contextual language
+models (LMs) such as BERT [12]. The underlying Transformer ar-
+chitecture empowered by the attention mechanism [35] enables
+LMs to represent any word relative to all other words in the context
+(i.e., surrounding words in the same sentence). Note that these LMs
+are first pre-trained on a large text corpus with a general-purpose
+objective (e.g., masked language model (MLM), which predicts ran-
+domly masked words based on their contexts) and fine-tuned with
+supervision (labeled data) for downstream tasks. This pre-training
+and fine-tuning paradigm has become the de facto practice in many
+NLP tasks.
+The tremendous success of Transformer-based LMs has inspired
+their counterparts on tabular data. TAPAS [20] extended the BERT
+architecture to answer questions over tables by pre-training the
+model on text-table pairs using the MLM objective and fine-tuning
+it on downstream task datasets in a weakly supervised manner.
+In addition to MLM, TURL [11] proposed a new Masked Entity
+
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+Tianji Cong and H. V. Jagadish
+Recovery objective for pre-training on entity-rich relational tables
+from Web. Their pre-trained contextualized representations were
+shown to generalize well to six downstream table understanding
+tasks with fine-tuning. TaBERT [38] jointly learned semi-structured
+Web tables and their surrounding texts in pre-training and was fine-
+tuned for semantic parsing tasks. TUTA [36] devised a tree-based
+Transformer and expanded pre-training to generally structured
+tables including entity and matrix tables, and spreadsheet tables.
+They fine-tuned the model for cell-type classification and table-type
+classification tasks.
+2.3
+Challenges
+Representation learning for tables has achieved excellent results
+for many table-centric tasks. We hypothesize that the table union
+search problem can also benefit from advances in table modeling.
+However, several challenges remain to be addressed.
+(1) To the best of our knowledge, no prior work has taken the
+learning approach for table union search. We argue that this
+is mainly because neither the supervised learning setting nor
+the popular pre-training and fine-tuning paradigm is directly
+applicable for the problem. It is inefficient to formulate the
+underlying search of union-able columns as a classification
+problem. In a supervised learning setting, one can attempt to
+train a classifier to predict whether two columns are union-
+able, but it will quickly become computationally prohibitive
+in the search phase to classify every pair of target column
+in a query table with every column in a large corpus.
+(2) The scarcity of table union search datasets is another severe
+bottleneck of applying a learning approach and studying
+the problem in general. The only publicly available bench-
+mark [27] with table- and column-level ground truth is syn-
+thesized from only 32 base tables, which is barely enough for
+evaluation. It is also very laborious and time consuming to
+label such datasets, as curators need to examine every pair
+of columns for every pair of tables in a collection.
+(3) How to encode non-Web tables? Transformer-based mod-
+els surveyed above are primarily designed for Web tables
+and assume access to abundant metadata such as table cap-
+tions, surrounding text, and topic entities. In contrast, non-
+Web tables like Open Data tables and tables extracted from
+GitHub [21] do not have such information available in gen-
+eral. We can reasonably assume access to data values and
+table headers but not much more. Even informative schema
+is not always available.
+In the next section, we present our design that contributes a
+representation learning approach to table union search while effec-
+tively mitigating the challenges we point out here.
+3
+PYLON: A SELF-SUPERVISED
+CONTRASTIVE LEARNING FRAMEWORK
+FOR TABULAR DATA
+Our key idea is to leverage self-supervised contrastive learning
+that provides a feasible training objective for learning effective
+column representations for the table union search problem while
+not requiring any labeled data (corresp. to challenge 1 and 2). Within
+the framework of contrastive learning, we propose two strategies
+that arithmetically construct training data from unlabeled data to
+tackle challenge 2. We also experiment with several encoders to
+gain empirical insights into challenge 3.
+3.1
+Contrastive Learning
+The high-level goal of contrastive learning is to learn to distin-
+guish (so called "contrast") between pairs of similar and dissimilar
+instances. Ideally, in the learned representation space, similar in-
+stances stay close to each other whereas dissimilar ones are pushed
+far away. A pair of instances is considered similar and labeled a
+positive example in training if it comprises different views of the
+same object; otherwise, they are considered dissimilar and make a
+negative example. Contrastive learning has been used extensively
+in computer vision [9], where a positive example consists of a pair
+of augmented images transformed from the same image (e.g., by
+applying cropping or color distortion).
+We introduce, Pylon, our self-supervised contrastive learning
+framework for learning representations from large collections of
+tables. As table union search begins by finding union-able columns,
+Pylon is designed to generate a vector representation for each
+column of input tables where columns containing semantically
+similar values have embeddings closer to one another.
+3.2
+Pylon Workflow
+Figure 2 shows the training workflow of the framework that consists
+of the following major components.
+Training Data Construction. Without labeled data, the suc-
+cess of contrastive learning hinges on the construction of positive
+and negative examples from the data itself. To make positive ex-
+amples, it requires an operation to transform a data instance in a
+way that introduces variations while preserving the semantics. As
+table union search builds on union-able column search, we propose
+two strategies to construct positive and negative examples at the
+column level.
+(1) Online sampling strategy. Consider a training batch of 𝑁
+tables {𝑇𝑖}𝑁
+𝑖=1 where each table 𝑇𝑖 has 𝑚𝑖 columns {𝐶𝑖
+𝑗 }𝑚𝑖
+𝑗=1,
+giving 𝑀 = �𝑁
+𝑖=1 𝑚𝑖 columns in total. We obtain a positive
+example of column pairs (𝑥𝑘,𝑥𝑘+𝑀) (1 ≤ 𝑘 ≤ 𝑀) by ran-
+domly sampling values from each column 𝐶𝑖
+𝑗 of each table𝑇𝑖.
+Since both 𝑥𝑘 and 𝑥𝑘+𝑀 are samples from the same column
+of the same table, we consider they share semantics and
+make a positive example. The sampling process yields 2𝑀
+column instances, and we treat the other 2(𝑀 − 1) samples
+as negatives with respect to 𝑥𝑘. In other words, considering
+(𝑥𝑘,𝑥𝑘+𝑀) and (𝑥𝑘+𝑀,𝑥𝑘) as distinct positive examples, we
+construct 2𝑀 positive examples and 2𝑀(𝑀 − 1) negative
+examples from each training batch.
+(2) Offline approximate matching strategy. An alternative is to
+construct positive examples ahead of training. Instead of
+relying on ad-hoc sampling, we can leverage existing ap-
+proaches to find a union-able candidate for each column,
+which in turn makes positive examples in training. Based
+on the observation that top-𝑘 union-able column search of
+existing techniques is highly precise when 𝑘 is small (e.g.,
+
+Pylon: Table Union Search through Contrastive Representation Learning
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+r1
+r2
+r3
+r4
+r5
+r6
+Online Training
+Data 
+Construction
+Base Encoder f & 
+Projection Head g 
+f
+g
+f
+g
+e1
+e2
+e3
+e1+M
+e2+M
+e3+M
+Projected column embeddings 
+Table Samples
+c1 c2 c3
+r1
+r2
+r5
+r2
+r3
+r6
+Figure 2: Training workflow of Pylon (with online training data construction).
+𝑘 = 1), we are able to use this approximate matching without
+human involvement. We find that it produces valid results
+and does not suffer the issue of false positives.
+Base Encoder & Projection Head. We pass column instances
+{𝑥𝑘}2𝑀
+𝑘=1 through a base encoder 𝑓 (·) to get initial column embed-
+dings {𝑒𝑘}2𝑀
+𝑘=1. Note that our contrastive learning framework is
+flexible about the choice of the base encoder. The encoder can give
+embeddings at token/cell/column level, and if necessary, we can
+apply aggregation (e.g, average or max) to obtain column-level
+embeddings. Our framework has the flexibility to benefit from the
+advance of modeling techniques in NLP over time without being
+tied to a specific model. We describe the choices of 𝑓 (·) we experi-
+ment with in subsection 3.3.
+Following the encoder, a small multi-layer neural network 𝑔(·),
+called projection head, maps the representations from the encoder
+to a latent space through linear transformations and non-linear
+activation in between. Note that unlike the practice in CV which
+discards projection head in inference and uses encoder outputs for
+downstream tasks, we preserve projection head and use projected
+embeddings for table union search. This is because we found pro-
+jected embeddings yield better performance in initial experiments,
+and for encoders like word embedding models, only projection head
+is trainable and has to be preserved for inference. For simplicity,
+we keep using the notations {𝑒𝑘}2𝑀
+𝑘=1 for projection outputs.
+Contrastive Loss. One common setting of contrastive learning
+defines a prediction task of identifying positive examples from the
+training batch. Given embedded columns {𝑒𝑘}2𝑀
+𝑘=1, the model learns
+to predict 𝑒𝑘+𝑀 as the most similar one to 𝑒𝑘 and vice versa for
+each 𝑒𝑘 (1 ≤ 𝑘 ≤ 𝑀). The similarity between any two instances 𝑒𝑖
+and 𝑒𝑗 is measured by their cosine similarity as
+𝑠𝑖𝑚(𝑖, 𝑗) =
+𝑒𝑇
+𝑖 𝑒𝑗
+∥𝑒𝑖 ∥∥𝑒𝑗 ∥
+and the loss is calculated as
+𝑙(𝑘,𝑘 + 𝑀) = − log
+exp (𝑠𝑖𝑚(𝑘,𝑘 + 𝑀) / 𝜏)
+�2𝑀
+𝑙=1,𝑙≠𝑘 exp (𝑠𝑖𝑚(𝑘,𝑙) / 𝜏)
+where 𝜏 > 0 is a scaling hyper-parameter called temperature. Mini-
+mizing 𝑙(𝑘,𝑘 + 𝑀) is equivalent to maximizing the probability of
+𝑒𝑘+𝑀 being the most similar to 𝑒𝑘 among all the embedded columns
+except 𝑒𝑘 itself.
+Finally, the loss over all the 2𝑀 positive column pairs in a training
+batch is computed as
+𝐿 =
+1
+2𝑀
+𝑀
+∑︁
+𝑘=1
+[𝑙(𝑘,𝑘 + 𝑀),𝑙(𝑘 + 𝑀,𝑘)]
+This loss formulation is called InfoNCE loss [28] (also known as
+the normalized temperature-scaled cross entropy loss [9]), which
+approximately maximizes the mutual information (i.e., a measure
+of how dependent two random variables are to each other) between
+two views of the same object.
+3.3
+Choices of the Base Encoder
+Although we expect the input to the contrastive loss function to be
+column embeddings, the base encoder does not necessarily need to
+give column embeddings directly. It is possible for the encoder
+model to generate embeddings at different granularity (i.e., to-
+ken/cell/column) because we can apply aggregation if necessary.
+We describe the basic encoding process of embedding models we
+experimented with in section 4.
+Word Embedding Models (WEM). As a WEM assigns a fix
+representation to a token, WEM-based encoders treat each column
+independently as a document where a standard text parser tokenizes
+data values in a column. With a fastText embedding model, we first
+get cell embeddings by averaging token embeddings in each cell and
+then aggregate cell embeddings to get a column embedding. More
+
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+Tianji Cong and H. V. Jagadish
+interestingly, web table embedding models [18] consider each cell as
+a single token (they concatenate tokens in a cell with underscores)
+and output embeddings at cell level. Nevertheless, we aggregate
+cell embeddings to derive the column embedding.
+Language Models (LM). Since a table is a cohesive structure
+for storing data, considering values in neighboring columns could
+integrate context into the embeddings and help mitigate ambiguity
+in unionable column search. For example, encoding column "year"
+in figure 1 individually loses the context that this column refers to
+the publication year of research papers. In this case, the embeddings
+of "Year" columns in the corpus are less distinguishable (in terms of
+cosine similarity) even though they may refer to different concepts
+of year such as the birth year of people or the release year of movies.
+With context provided by other columns like "Title" and "Venue", it
+is more likely that "Year" columns appearing in tables about papers
+are more close to each other than "Year" columns in tables about
+other topics, which helps find more related tables.
+We leverage LMs to derive contextual column embeddings. We
+first serialize each row in 𝑇𝑖 as a sequence by concatenating tok-
+enized cell values. For example, the first row of the table at the top
+in Figure 1 will be encoded as follows
+[𝐶𝐿𝑆] title | A Database ... [SEP] authors | Jerry... [SEP] ...[𝐸𝑁𝐷]
+The sequence is annotated with special tokens in the LM where
+[𝐶𝐿𝑆] token indicates the beginning of the sequence, [𝐸𝑁𝐷] token
+indicates the end, and [𝑆𝐸𝑃] tokens separate cell values in different
+columns. Then the LM takes in each sequence and generates a con-
+textual representation for each token in the sequence (essentially
+taking into account the relation between values in the same row).
+We apply mean pooling to tokens in the same cell and get cell em-
+beddings. To consider the relation of values in the same column, we
+adopt the vertical attention mechanism in [38] to have weighted
+column embeddings by attending to all of the sampled cells in the
+same column.
+Word embedding models have previously been used to find
+union-able tables. Two state-of-the-art choices are fastText and
+WTE (web table embeddings [18]). Language models have not thus
+far been used for the union-ability problem. BERT[12] is a lead-
+ing language model used for many purposes today. We develop
+three versions of Pylon, one for each of these three encoder choices:
+fastText, WTE, and a BERT-based language model, and refer to the
+derived models as Pylon-fastText, Pylon-WTE, Pylon-LM respectively.
+We evaluate the effect of encoder choices in subsection 4.5.
+3.4
+Embedding Indexing and Search
+To avoid exhaustive comparisons of column embeddings over a
+large corpus at query time, we use locality-sensitive hashing (LSH) [22]
+for approximate nearest neighbor search and treat union-able col-
+umn search as an LSH-index lookup task [1, 27]. LSH utilizes a
+family of hash functions that maximize collisions for similar inputs.
+The result of LSH indexing is that similar inputs produce the same
+hash value and are bucketed together whereas dissimilar inputs are
+ideally placed in different buckets. Algorithm 1 gives the indexing
+procedure. For approximate search with respect to the cosine simi-
+larity, we index all column embeddings in a random projection LSH
+index [8]. The idea of random projection is to separate data points
+Algorithm 1: Embedding Inference and Indexing
+Input
+:
+S, a corpus of tables;
+𝑔 ◦ 𝑓 , a Pylon model;
+𝑝, a list of LSH index parameters.
+Output:
+I, a random projection LSH index.
+1 I ← create_index(𝑝);
+2 for 𝑡 ∈ S do
+3
+𝑡_𝑠𝑒𝑟𝑖𝑎𝑙𝑖𝑧𝑒𝑑 ← preprocess(𝑡);
+4
+𝑐𝑜𝑙𝑢𝑚𝑛_𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔𝑠 ← 𝑔 ◦ 𝑓 (𝑡_𝑠𝑒𝑟𝑖𝑎𝑙𝑖𝑧𝑒𝑑);
+5
+for 𝑒 ∈ 𝑐𝑜𝑙𝑢𝑚𝑛_𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔𝑠 do
+6
+I.insert(𝑒);
+7
+end
+8 end
+9 return I;
+Algorithm 2: Top-𝑘 Table Union Search
+Input
+:
+I, a LSH index;
+𝑄, a query table;
+𝑘, a constant.
+Output:
+top-𝑘 union-able tables.
+1 𝑐𝑜𝑙𝑢𝑚𝑛_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 ← {};
+2 𝑐𝑜𝑙𝑢𝑚𝑛_𝑠𝑐𝑜𝑟𝑒𝑠 ← {};
+3 for 𝑐 ∈ 𝑄.𝑐𝑜𝑙𝑢𝑚𝑛𝑠 do
+4
+𝑐_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠,𝑐_𝑠𝑐𝑜𝑟𝑒𝑠 ← I.lookup(𝑐);
+5
+𝑐𝑜𝑙𝑢𝑚𝑛_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠[𝑐].add(𝑐_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠);
+6
+𝑐𝑜𝑙𝑢𝑚𝑛_𝑠𝑐𝑜𝑟𝑒𝑠[𝑐].add(𝑐_𝑠𝑐𝑜𝑟𝑒𝑠);
+7 end
+8 𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 ← group_by(𝑐𝑜𝑙𝑢𝑚𝑛_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠);
+9 𝑟𝑎𝑛𝑘𝑒𝑑_𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 ←
+cmpt_table_unionability(𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠,𝑐𝑜𝑙𝑢𝑚𝑛_𝑠𝑐𝑜𝑟𝑒𝑠);
+10 return 𝑟𝑎𝑛𝑘𝑒𝑑_𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠[: 𝑘];
+in a high-dimensional vector space by inserting hyper-planes. Em-
+beddings with high cosine similarity tend to lie on the same side of
+many hyper-planes.
+Algorithm 2 summarizes the top-𝑘 table union search. Following
+Definition 1, we instantiate the union-ability of two attributes as
+the cosine similarity of their embeddings (𝑐_𝑠𝑐𝑜𝑟𝑒𝑠 in line 4 of
+Algorithm 2). Line 8 groups retrieved column candidates across
+query columns by their table sources. To decide on the table union-
+ability from Definition 3 (𝑐𝑚𝑝𝑡_𝑡𝑎𝑏𝑙𝑒_𝑢𝑛𝑖𝑜𝑛𝑎𝑏𝑖𝑙𝑖𝑡𝑦 in line 9), we
+use the same weighting strategy as [1] over query attributes and
+corresponding matching attributes in candidate tables. For a target
+attribute 𝐴, let 𝑅𝐴 denote the distribution of all similarity (union-
+ability) scores between 𝐴 and any attribute 𝐵 returned by the LSH
+index. The weight𝑤 of a similarity score U𝑎𝑡𝑡𝑟 (𝐴, 𝐵) is given by the
+cumulative distribution function of 𝑅𝐴 evaluated at U𝑎𝑡𝑡𝑟 (𝐴, 𝐵):
+𝑤 = Pr(U𝑎𝑡𝑡𝑟 (𝐴, 𝐵′) ≤ U𝑎𝑡𝑡𝑟 (𝐴, 𝐵)), ∀ U𝑎𝑡𝑡𝑟 (𝐴, 𝐵′) ∈ 𝑅𝐴
+In other words, a similarity score is weighted by its percentile in
+the distribution. This weighting scheme helps balance between a
+
+Pylon: Table Union Search through Contrastive Representation Learning
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+candidate table with a few union-able attributes of high similarity
+scores and another candidate table with more union-able attributes
+but of lower similarity scores.
+Using the same index and search structure as previous works
+makes it transparent to compare our embedding approach with
+theirs in effectiveness and efficiency.
+3.5
+Integrating Syntactic Methods
+Thus far, we have focused purely on semantic methods to unify
+similar attributes. It makes sense to prefer semantic methods to
+syntactic ones because of their potential robustness to many differ-
+ent types of variation. However, we note that syntactic methods
+are based on measures of similarity very different from semantic
+methods. Intuitively, one should expect to be able to do better if we
+can integrate the two.
+Indeed, some previous work [1, 27] has made this observation
+as well, and shown that an ensemble of semantic and syntactic
+methods can do better than either on its own. The Pylon semantic
+method permits the use of an additional complementary syntactic
+method. As in [1], we independently obtain scores from the two
+methods and then use the average of the two as our final score.
+4
+EXPERIMENTS
+We first evaluate the effectiveness and efficiency of three model vari-
+ants from our contrastive learning framework and compare them
+with their corresponding base encoders. We then demonstrate that
+our embedding approach is orthogonal to existing syntactic mea-
+sures, which can further improve the results. We finally compare
+our best model with the state-of-the-art 𝐷3𝐿 [1].
+4.1
+Datasets and Metrics
+TUS Benchmark1. [27] compiled the first benchmark with ground
+truth out of Canadian and UK Open Data. They synthesized around
+5, 000 tables from 32 base tables by performing random projection
+and selection. They also generated a smaller benchmark consisting
+of around 1, 5002 tables from 10 base tables. We refer to them as
+TUS-Large and TUS-Small respectively.
+Pylon Benchmark. We create a new dataset from GitTables [21],
+a corpus of 1.7𝑀 tables extracted from CSV files on GitHub3. The
+benchmark comprises 1,746 tables including union-able table sub-
+sets under topics selected from Schema.org [16]: scholarly article,
+job posting, and music playlist. We end up with these three topics
+since we can find a fair number of union-able tables of them from
+diverse sources in the corpus (we can easily find union-able tables
+from a single source but they are less interesting for table union
+search as simple syntactic methods can identify all of them because
+of the same schema and consistent value representations).
+Cleaning and Construction. We download three largest sub-
+sets of GitTables ("object", "thing", and "whole") and preprocess them
+by removing HTML files, tables without headers, rows with foreign
+languages, and finally small tables with fewer than four rows or
+four columns. We cluster the resulting tables by their schema and
+1TUS benchmark can be accessed from https://github.com/RJMillerLab/table-union-
+search-benchmark.
+2We export 1, 530 tables from the small benchmark although the paper and the website
+claim ∼1, 300 tables.
+3GitTables 1.7𝑀 is available from https://zenodo.org/record/4943312#.Ylm2ftPMJxZ.
+perform a keyword search over schema with keywords related to
+three topics. We manually select 35 union-able tables of topic schol-
+arly article, 41 tables of topic job posting, and 48 tables of topic
+music playlist. We then randomly sample 100,000 tables4 for train-
+ing, 5,000 tables for validation, and put the rest of tables as noise5
+in a pool with union-able table subsets for the search evaluation.
+Table 1 provides an overview of basic statistics of tables in each
+evaluation dataset.
+Table 1: Basic statistics of evaluation datasets.
+Pylon
+TUS-Small
+TUS-Large
+# Tables
+1,746
+1,530
+5,043
+# Base Tables
+1,746
+10
+32
+Avg. # Rows
+115
+4,466
+1,915
+Avg. # Columns
+10
+10
+11
+# Queries
+124
+1,327
+4,296
+Avg. # Answers
+42
+174
+280
+Metrics. For effectiveness, we report both precision and recall
+of top-𝑘 search with varying 𝑘. At each value of 𝑘, we average the
+precision and recall numbers over all the queries. We consider a
+table candidate as a true positive with respect to the target table as
+long as it is in the corresponding ground truth. We do not require
+perfect attribute pair matching as it is a more challenging setting
+and requires laborious column-level labeling.
+As to efficiency, we report indexing time (i.e., total amount of
+time in minutes to index all columns in a dataset) and query re-
+sponse time (i.e., average amount of time in seconds for the LSH
+index to return results over all queries in a dataset).
+In evaluation, we randomly sample 1000 queries from TUS-Large
+for efficient experiment purposes. The query subset has an average
+answer size of 277, which is very close to that of the full query set
+(i.e., 280). We use all the queries in Pylon and TUS-Small datasets.
+4.2
+Baselines
+We consider two embedding methods and one full approach as
+baselines for comparison.
+fastText. Many data discovery tasks [15, 27] not limited to table
+union search have adopted fastText in their approach, which is a
+popular word embedding model trained on Wikipedia documents.
+WTE. [18] devised a word embedding-based technique to rep-
+resent text values in Web tables. They generated text sequences
+from tables for training by serializing tables in two different ways
+that capture row-wise relations and relations between schema and
+data values respectively. It is reported that the model using both
+serialization obtained the best performance in a task of ranking
+unionable columns. We use this model6 in comparison and refer to
+it as WTE (for web table embeddings).
+4We noticed that a few schemas have an overwhelming number of tables (because
+some GitHub repositories publish hundreds and thousands of tables with the same
+schema). In sampling, we take at most 200 tables from each schema to increase the
+diversity of the training set.
+5we filtered these tables using their schema to reduce the chance of them being union-
+able to selected tables in the union-able subsets (i.e., true noise).
+6𝑊𝑐𝑜𝑚𝑏𝑜 150dim: https://github.com/guenthermi/table-embeddings/tree/main#pre-
+trained-models
+
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+Tianji Cong and H. V. Jagadish
+D3L. [1] proposed a distance-based framework 𝐷3𝐿 that uses
+five types of evidence to decide on column unionability: (i) attribute
+name similarity; (ii) attribute extent overlap; (iii) word-embedding
+similarity; (iv) format representation similarity; (v) domain distri-
+bution similarity for numerical attributes. Their aggregated ap-
+proach is shown to be more effective and efficient than previous
+work [13, 27] on the TUS benchmark and another self-curated
+dataset of Open Data tables. To the best of our knowledge, 𝐷3𝐿 is
+the current state-of-the-art of the table union search problem.
+4.3
+Comparisons of Interest
+We have 5 variants of Pylon to compare against baseline systems for
+both effectiveness and efficiency in identifying union-able tables
+using semantic similarity methods: 3 variants from the online train-
+ing data construction strategy and 2 variants from the offline data
+construction strategy. In addition, we have 3 syntactic similarity
+measures that could be used to augment each of these 5 variants.
+Finally, we have 3 baselines, two of which are semantic word embed-
+ding based, and hence could also be augmented with the syntactic
+similarity measures. The third baseline (D3L) already integrates
+both syntactic and semantic similarity, and hence does not benefit
+from additional augmentation with syntactic techniques.
+Since there are a very large number of alternatives to compare,
+we break up the comparisons into four sets, as follows, and present
+the results for each set separately. For the first three sets, we restrict
+ourselves to the online training data construction strategy for Pylon.
+We refer to the derived models as Pylon-fastText, Pylon-WTE, Pylon-
+LM respectively based on the corresponding encoder choice. Results
+for the offline data construction strategy show generally similar
+trends, and the most interesting are shown in the fourth set.
+The first set of comparisons look purely at semantic methods,
+considering the 3 variants of Pylon and comparing them to the first
+two baselines. We leave out D3L because it already incorporates
+syntactic methods as well. The second set of comparisons look
+purely at the benefit obtained when semantic methods are enhanced
+with syntactic measures. We do so for all methods evaluated in the
+first set. Finally, we bring everything together by comparing the
+best methods of the second set with the best integrated baseline,
+D3L. This is the final top line "take away" from the experiments,
+eliding details from the first two sets of comparisons.
+4.4
+Experiment Details
+As to model training, we train Pylon-fastText for 50 epochs with a
+batch size of 16 on 2 NVIDIA GeForce RTX 2080 Ti GPUs; Pylon-
+WTE for 20 epochs with a batch size of 32 on a single NVIDIA
+Tesla P100 GPU; Pylon-LM for 20 epochs with a batch size of 8
+on 4 NVIDIA Tesla P100 GPUs from Google Cloud Platform. As
+seen in table 2, the training is especially efficient for simple word
+embedding encoders (as only parameters in projection head are
+updated) and the offline data construction strategy (as embeddings
+are pre-computed before training). We save the models with the
+smallest validation loss. The model training is implemented in
+PyTorch [29] and PyTorch Lightning7.
+For evaluation of table union search, we set the similarity thresh-
+old of LSH index to 0.7 in all experiments and use the default hash
+7https://www.pytorchlightning.ai/
+Table 2: Model training time (min / epoch) where each model
+is defined by the encoder choice and the training data con-
+struction strategy.
+Online Sampling
+Offline Approximate Matching
+Pylon-fastText
+6.5
+0.42
+Pylon-WTE
+0.99
+0.13
+Pylon-LM
+33
+-
+size (a MinHash size of 256 and a random projection size of 1024) as
+D3L. We run all evaluation on a Ubuntu 20.04.4 LTS machine with
+128 GiB RAM and Intel(R) Xeon(R) Bronze 3106 CPU @ 1.70GHz.
+4.5
+Results
+As Pylon is an embedding-based approach, we first evaluate Pylon
+model variants against embedding baselines fastText and WTE, and
+inspect what effects contrastive learning have on them.
+Experiment 1(a): Comparison of effectiveness between Py-
+lon model variants and their corresponding base encoders.
+Figure 3 shows the precision and recall of each embedding measure
+on the Pylon dataset. Both Pylon-WTE and Pylon-fastText outper-
+form their corresponding base models with a notable margin. When
+𝑘 = 40, around the average answer size, Pylon-WTE is 6% better
+than WTE on both metrics, and Pylon-fastText performs better than
+fastText by 15% on precision and 14% on recall.
+Overall, our Pylon-WTE model consistently achieves the highest
+precision and recall as 𝑘 increases. We also note that Pylon-LM
+has strong performance up until 𝑘 = 30 but degrades after that.
+This is because Pylon-LM only samples 10 rows from each table to
+construct embeddings (for indexing efficiency) while other word-
+embedding methods can afford to encode the entire table at low
+indexing time, which we demonstrate in experiment 1(b).
+Experiment 1(b): Comparison of efficiency between Pylon
+model variants and their corresponding base encoders. In fig-
+ure 4, we see both embedding baselines are very efficient in index
+construction and it takes less than 2 minutes to index the entire
+Pylon dataset. Unlike fixed embeddings, our models need to infer
+embeddings at runtime. For Pylon-fastText and Pylon-WTE, since
+the encoder is fixed, the inference cost is exclusively from projec-
+tion head. It takes both less than 3.5 minutes to build the index. In
+contrast, the runtime inference cost of Pylon-LM is more expensive
+as the language model has much more complex architecture and has
+130M parameters versus 35.8K parameters in projection head. We
+also acknowledge the less efficient implementation of embedding
+inference at this point (e.g., run inference for each column with-
+out batch predictions). Nevertheless, indexing time, as a one-time
+overhead, can be amortized among queries.
+On the other hand, all of our models are considerably more
+efficient in query response time. Pylon-fastText is 2.7x faster than
+fastText and Pylon-WTE is 9x faster than WTE. The significant
+speedup of query response time is attributed to contrastive learning
+where embeddings of attribute values occurring in the same context
+are pushed close to each other whereas embeddings of two random
+columns are pushed apart. As the embedding similarity between
+two random columns is suppressed, this dramatically reduces the
+chance of two random columns sharing many LSH buckets. In
+
+Pylon: Table Union Search through Contrastive Representation Learning
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+10
+20
+30
+40
+50
+60
+70
+80
+90
+100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+fastText
+Pylon-fastText
+WTE
+Pylon-WTE
+Pylon-LM
+10
+20
+30
+40
+50
+60
+70
+80
+90
+100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+fastText
+Pylon-fastText
+WTE
+Pylon-WTE
+Pylon-LM
+Figure 3: Top-k precision and recall of embedding mea-
+sures on the Pylon dataset.
+fastText
+Pylon-fastText
+WTE
+Pylon-WTE
+Pylon-LM
+Model
+0
+5
+10
+15
+20
+25
+30
+Indexing Time (min)
+1.8
+2.4
+1.3
+3.4
+23.8
+fastText
+Pylon-fastText
+WTE
+Pylon-WTE
+Pylon-LM
+Model
+0
+5
+10
+15
+20
+25
+Query Response Time (s / query)
+15.8
+4.3
+24.7
+2.4
+3.0
+Figure 4: Indexing time and query response time on the
+Pylon dataset.
+0
+20 40 60 80 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-fastText
+Pylon-fastText-NVF
+Pylon-fastText-NV
+0
+20 40 60 80 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-WTE
+Pylon-WTE-NVF
+Pylon-WTE-NV
+0
+20 40 60 80 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-LM
+Pylon-LM-NVF
+Pylon-LM-NV
+0
+20 40 60 80 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+0
+20 40 60 80 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+0
+20 40 60 80 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+(a) Pylon dataset
+10
+50
+90
+130
+170
+210
+250
+290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-fastText
+Pylon-fastText-NVF
+Pylon-fastText-NV
+10
+50
+90
+130
+170
+210
+250
+290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-WTE
+Pylon-WTE-NVF
+Pylon-WTE-NV
+10
+50
+90
+130
+170
+210
+250
+290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-LM
+Pylon-LM-NVF
+Pylon-LM-NV
+10
+50
+90
+130
+170
+210
+250
+290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+10
+50
+90
+130
+170
+210
+250
+290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+10
+50
+90
+130
+170
+210
+250
+290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+(b) TUS-Small dataset
+Figure 5: Precision and recall (w.r.t. varying 𝑘) of the ensemble of Pylon embedding models and syntactic measures.
+other words, LSH index can process much fewer candidates at the
+configured similarity threshold.
+To illustrate the suppression effect of contrastive learning, we
+compare heatmaps of pairwise cosine similarity of column em-
+beddings encoded by WTE and Pylon-WTE respectively. Consider
+the three text columns of the first table in Figure 1. As shown in
+Figure 6(a), the pairwise cosine similarity of WTE embeddings is
+mostly above 0.5. There is a very high similarity (0.87) between the
+"title" column and the "venue" column and they will be mistakenly
+viewed as unionable. But this is not an issue for Pylon-WTE embed-
+dings as shown in Figure 6(b) where the pairwise similarity between
+different columns are much lower (below 0.51) and the LSH index
+will not return the "venue" column as a unionable candidate of the
+"title" column.
+Figure 6: Pairwise cosine similarity of column embeddings:
+(a) WTE embeddings; (b) Pylon-WTE embeddings.
+
+title
+authors
+venue
+title
+authors
+venue
+1.0
+1.0
+0.5203
+0.8675
+1.0
+0.0182
+0.5095
+title -
+title -
+0.8
+0.6
+0.5203
+1.0
+0.492
+0.0182
+1.0
+authors - 
+0.0063
+authors -
+0.4
+0.2
+0.8675
+0.492
+1.0
+0.5095
+0.0063
+1.0
+venue
+venue -
+0.0Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+Tianji Cong and H. V. Jagadish
+In the next set of experiments, we consider three syntactic mea-
+sures used by D3L and evaluate how much they can augment our
+embedding measures.
+(1) Name (𝑁): Jaccard similarity between q-gram sets of at-
+tribute names.
+(2) Value (𝑉 ): Jaccard similarity between the TF-IDF sets of
+attribute values.
+(3) Format (𝐹): Jaccard similarity between regular-expression
+sets of attribute values.
+Experiment 2: Effectiveness of the ensemble of Pylon model
+variants and syntactic measures. Figure 5(a) and (b) show the
+precision and recall of the ensemble of Pylon embedding models and
+syntactic measures on Pylon and TUS-Small datasets respectively.
+We consistently observe from both datasets that adding syntactic
+measures can further enhance the performance. In particular, name
+(𝑁) and value (𝑉 ) similarity are most effective syntactic measures.
+Around the average answer size of the Pylon dataset (𝑘 = 40), 𝑁
+and 𝑉 together raise up the precision and recall of Pylon-fastText
+by nearly 20%, of Pylon-WTE by 10%, and of Pylon-LM by over 5%.
+Similarly, around the average answer size of the TUS-Small dataset
+(𝑘 = 170), there is an increase of about 10% in both precision and
+recall for Pylon-fastText, about 5% for Pylon-WTE, and more than
+10% for Pylon-LM.
+We also observe that adding additional format measure (𝐹) hurts
+the performance (notably on the Pylon dataset and slightly on TUS-
+small). This is because tables in the Pylon dataset are mostly from
+disparate sources and so the value format tends to be inconsistent
+across tables whereas tables in TUS-Small are synthesized from
+only 8 base tables and it is much more likely for many tables to share
+format similarity. Even worse, including format index imposes non-
+trivial runtime cost (see figure 7). For example, compared to model
+Pylon-WTE-NV, the query response time of Pylon-WTE-NVF (with
+the extra format measure) surges by 66.7% on the Pylon dataset and
+by 32.2% on TUS-Small.
+Pylon-fastText
+Pylon-WTE
+Pylon-LM
+0
+1
+2
+3
+4
+5
+6
+7
+Query Response Time (s / query)
+7.2
+3.9
+4.2
+4.7
+2.3
+3.3
+NVF
+NV
+(a) Pylon dataset
+Pylon-fastText
+Pylon-WTE
+Pylon-LM
+0
+5
+10
+15
+20
+25
+30
+35
+Query Response Time (s / query)
+34.9
+27.3
+16.2
+28.7
+20.6
+11.1
+NVF
+NV
+(b) TUS-Small dataset
+Figure 7: Comparison of query response time between in-
+cluding and excluding the format measure.
+Finally, we compare our best-performing model Pylon-WTE-NV
+with the state-of-the-art D3L. As Pylon-WTE-NV does not use for-
+mat and domain measures in D3L, for fair comparison, we consider
+three versions of D3L. We refer to the full version of D3L as D3L-5,
+the one without the format measure as D3L-4, and the one without
+format and domain measures as D3L-3.
+Experiment 3: Comparison of effectiveness and efficiency
+between our best model and D3L. Figure 8 shows the perfor-
+mance of Pylon-WTE-NV and three D3L variants on Pylon , TUS-
+Small, TUS-Large datasets respectively. Around the average answer
+size (𝑘 = 40) of the Pylon dataset, Pylon-WTE-NV is around 15%
+better than the strongest D3L instance (i.e., D3L-3) in both precision
+and recall. Pylon-WTE-NV performs much better than D3L in this
+case because our embedding model using contrastive learning was
+trained on a dataset of a distribution similar to the test set and can
+capture more semantics than the off-the-shelf fastText embedding
+model used in D3L.
+On TUS-Small and TUS-Large, we observe all instances have
+relatively competitive performance while Pylon-WTE-NV performs
+marginally better compared to all D3L variants. On TUS-Small,
+around the average answer size (𝑘 = 170), Pylon-WTE-NV is 2%
+better than D3L-3 and 5% better than D3L-5 in both precision and
+recall. On TUS-Large, around the average answer size (𝑘 = 290),
+Pylon-WTE-NV is more than 2% better than D3L variants in both
+metrics. The small performance gap is due to the synthetic nature
+of TUS benchmark where most of union-able tables are generated
+from the same base table and share common attribute names and
+many attribute values. So syntactic measures (𝑁 and𝑉 ) can capture
+most of similarity signals and obtain high precision and recall even
+without support of semantic evidence.
+Additional to the performance gain, the biggest advantage of
+Pylon-WTE-NV is the fast query response time. On the Pylon dataset,
+our model is nearly 9x faster than the full version D3L-5 and 7x
+faster than D3L-3. Even on TUS-Small and TUS-Large, which are
+datasets of a different data distribution (Open Data tables), we still
+save runtime by 44% and 32% respectively compared to D3L-5, and
+by 35.5% and 21.9% respectively compared to D3L-3.
+Experiment 4: Effectiveness and efficiency of Pylon model
+variants from the offline training data construction strategy.
+Figure 10 shows the precision and recall of 4 Pylon variants from
+two training data construction strategies and their baselines. On the
+Pylon dataset, around the average answer size (𝑘 = 40), two Pylon
+models from the alternative data construction strategy, Pylon-WTE-
+offline and Pylon-fastText-offline, retain strong performance and
+outperform the corresponding baseline by 3% and 9% respectively.
+Note that Pylon models derived from the sampling data construc-
+tion strategy have consistently better performance as 𝑘 increases.
+We also observe a similar trend on the TUS benchmark while the
+performance gap of all instances is smaller.
+As shown in figure 11, both new models are efficient in index-
+ing time and query response time. Compared to the correspond-
+ing baseline, Pylon-WTE-offline is 12x faster and Pylon-fastText-
+offline is 14.5x faster in query response time. Again, this signifi-
+cant speedup demonstrates the distinguishing power of contrastive
+learning, which enables the LSH index to work more efficiently
+with embeddings.
+4.6
+Discussion
+Although this paper mainly focuses on the novel learning approach
+for the table union search problem, we also leave and discuss a few
+clues for future extensions.
+
+Pylon: Table Union Search through Contrastive Representation Learning
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+0
+20
+40
+60
+80
+100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+Precision
+Pylon-WTE-NV
+D3L-3
+D3L-4
+D3L-5
+0
+20
+40
+60
+80
+100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+Recall
+Pylon-WTE-NV
+D3L-3
+D3L-4
+D3L-5
+(a) Pylon dataset
+10
+50
+90 130 170 210 250 290
+k
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-WTE-NV
+D3L-3
+D3L-4
+D3L-5
+10
+50
+90 130 170 210 250 290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+Pylon-WTE-NV
+D3L-3
+D3L-4
+D3L-5
+(b) TUS-Small dataset
+10
+50
+90 130 170 210 250 290
+k
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-WTE-NV
+D3L-3
+D3L-4
+D3L-5
+10
+50
+90 130 170 210 250 290
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+Pylon-WTE-NV
+D3L-3
+D3L-4
+D3L-5
+(c) TUS-Large dataset
+Figure 8: Comparison of precision and recall between D3L instances and our best model Pylon-WTE-NV.
+D3L-5
+D3L-4
+D3L-3
+Pylon-WTE-NV
+Model
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+20.0
+Query Response Time (s / query)
+19.6
+17.1
+16.1
+2.3
+(a) Pylon dataset
+D3L-5
+D3L-4
+D3L-3
+Pylon-WTE-NV
+Model
+0
+5
+10
+15
+20
+25
+30
+35
+40
+Query Response Time (s / query)
+41.2
+42.2
+32
+20.6
+(b) TUS-Small dataset
+D3L-5
+D3L-4
+D3L-3
+Pylon-WTE-NV
+Model
+0
+20
+40
+60
+80
+100
+Query Response Time (s / query)
+110
+110.5
+95.6
+74.6
+(c) TUS-Large dataset
+Figure 9: Comparison of query response time between D3L instances and Pylon-WTE-NV.
+10 20 30 40 50 60 70 80 90 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Precision
+Pylon-WTE
+Pylon-WTE-offline
+WTE
+Pylon-fastText
+Pylon-fastText-offline
+fastText
+10 20 30 40 50 60 70 80 90 100
+k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+Recall
+Pylon-WTE
+Pylon-WTE-offline
+WTE
+Pylon-fastText
+Pylon-fastText-offline
+fastText
+Figure 10: Top-k precision and recall of 6 embedding
+measures on the Pylon dataset.
+fastText
+Pylon-fastText
+Pylon-fastText-offline
+WTE
+Pylon-WTE
+Pylon-WTE-offline
+Model
+0
+1
+2
+3
+4
+Indexing Time (min)
+1.8
+2.4
+2.2
+1.3
+3.4
+1.7
+fastText
+Pylon-fastText
+Pylon-fastText-offline
+WTE
+Pylon-WTE
+Pylon-WTE-offline
+Model
+0
+5
+10
+15
+20
+25
+Query Response Time (s / query)
+15.8
+4.3
+1.2
+24.7
+2.4
+1.7
+Figure 11: Indexing time and query response time on the
+Pylon dataset.
+Alternative Contrastive Loss. While InfoNCE (used in this
+project) is a popular and effective loss function, it is not the only
+feasible training objective for self-supervised contrastive learning.
+For example, triplet loss [31] considers a triplet (𝑥,𝑥+,𝑥−) as a
+training example where 𝑥 is an input, 𝑥+ is a positive sample (be-
+longing to the same class as 𝑥 or semantically similar to 𝑥) and
+
+Conference acronym ’XX, June 03–05, 2018, Woodstock, NY
+Tianji Cong and H. V. Jagadish
+𝑥− is a negative sample. Additionally, what considers as negative
+examples and "hardness" of negative examples are also interesting
+perspectives to explore.
+Verification of Column Union-ability. Besides quantitative
+evaluation, we also manually inspect results of a few queries for
+each dataset. We observe that even in correct table matches, there
+are false positives of union-able column candidates. To mitigate
+this issue, we believe that progress in column semantic type pre-
+diction [33, 39] can be beneficial for verifying the union-ability of
+columns as a post-processing step.
+5
+RELATED WORK
+Our work is most related to data integration in the Web context
+and data discovery over enterprise and Open Data repositories.
+Web Table Search. [4] presents OCTOPUS that integrate rel-
+evant data tables from relational sources on the Web. OCTOPUS
+includes operators that perform a search-style keyword query over
+extracted relations and their context, and cluster results into groups
+of union-able tables using column-to-column mean string length
+similarity and TF-IDF cosine similarity. [37] defines three infor-
+mation gathering tasks on Web tables: augmentation by attribute
+names, augmentation by example, and attribute discovery. The task
+of augmentation by example essentially involves finding union-able
+tables that can be used to fill in the missing values in a given table.
+Their Infogather system leverages indirectly matching tables in
+addition to directly matching ones to augment a user input. [10]
+formalizes the problem of detecting related Web tables. At the log-
+ical level, the work considers two tables related to each other if
+they can be viewed as results to queries over the same (possibly
+hypothetical) original table. In particular, one type of relatedness
+they define is Entity Complement where two tables with coherent
+and complementary subject entities can be unioned over the com-
+mon attributes. This definition requires each table to have a subject
+column of entities indicating what the table is about and that the
+subject column can be detected. Following the definition, the work
+captures entity consistency and expansion by measuring the relat-
+edness of detected sets of entities with signals mined from external
+ontology sources. Finally, they perform schema mapping of two
+complement tables by computing a schema consistency score made
+up of the similarity in attribute names, data types, and values.
+Data Discovery in the Enterprise. [14] identifies data discov-
+ery challenges in the enterprise environment. The position paper
+describes a data discovery system including enrichment primitives
+that allow a user to perform entity and schema complement opera-
+tions. Building on top of the vision in [14], [13] presents AURUM,
+a system that models syntactic relationships between datasets in
+a graph data structure. With a two-step process of profiling and
+indexing data, AURUM constructs a graph with nodes representing
+column signatures and weighted edges indicating the similarity be-
+tween two nodes (e.g., content and schema similarity). By framing
+queries as graph traverse problems, AURUM can support varied
+discovery needs of a user such as keyword search and similar con-
+tent search (which can be used for finding union-able columns
+and tables). [15] further employs word embeddings in AURUM to
+identify semantically related objects in the graph.
+Data Discovery over Open Data Repositories. [27] defines
+the table union search problem on open data and decomposes it as
+finding union-able attributes. They propose three statistical tests to
+determine the attribute union-ability: (1) set union-ability measure
+based on value overlap; (2) semantic union-ability measure based
+on ontology class overlap; and (3) natural language union-ability
+measure based on word embeddings, where union-ability is the esti-
+mated probability that the text values contained in two columns are
+drawn from the same domain. A synthesized benchmark consisting
+of original tables from Canadian and UK Open Data shows that nat-
+ural language union-ability works best for larger 𝑘 in top-𝑘 search.
+In the meantime, set union-ability is decent when 𝑘 = 1 for each
+query but vulnerable to value overlap in attributes of non-unionable
+tables, and semantic union-ability stays competitive to find some
+union-able tables for most queries despite incomplete coverage of
+external ontologies. The ensemble of three measures further im-
+proves the evaluation metrics. [1] adopts more types of similarity
+measures based on schema- and instance-level fine-grained features.
+Without relying on any external sources, their D3L framework is
+shown effective and efficient on Open Data Lakes. EMBDI [6] pro-
+poses a graph model to capture relationships across relational tables
+and derives training sequences from random walks over the graph.
+They further take advantage of embedding training algorithms like
+fastText to construct embedding models. Their relational embed-
+dings demonstrate promising results for data integration tasks such
+as schema matching and entity resolution.
+For a broader overview of the literature, we refer readers to the
+survey of dataset search [7].
+6
+CONCLUSION
+In this work, we present Pylon, a self-supervised contrastive learn-
+ing framework for learning semantic column representations from
+large collections of tables. We demonstrate that contrastive learning
+is a feasible way of learning effective representations for the table
+union search problem without relying on labeled data or being
+restricted to off-the-shelf embedding models. In comparison with
+embedding baselines and the state-of-the-art, we observe that (i)
+on the real-world dataset of a data distribution similar to the train-
+ing data, our models consistently achieve significant gain in both
+effectiveness and efficiency; (ii) on the synthetic benchmark of a
+different data distribution, our models have marginal performance
+improvement while staying more efficient.
+We hypothesize that the contrastive learning paradigm can also
+benefit other data discovery and table understanding problems that
+do not fit into the classification formulation or lack large scale
+of labeled data (e.g., join-path discovery). It is also worth noting
+that contrastive learning does not contradict supervision. It will be
+interesting to see if contrastive learning can also enhance existing
+supervised learning solutions for entity resolution and many table
+understanding tasks such as semantic column type annotation.
+ACKNOWLEDGMENTS
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+page_content='Pylon: Table Union Search through Contrastive Representation  Learning  Tianji Cong  University of Michigan  Ann Arbor, Michigan, USA  congtj@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='edu  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  University of Michigan  Ann Arbor, Michigan, USA  jag@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='edu  ABSTRACT  The large size and fast growth of data repositories, such as data  lakes, has spurred the need for data discovery to help analysts find  related data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The problem has become challenging as (i) a user  typically does not know what datasets exist in an enormous data  repository;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' and (ii) there is usually a lack of a unified data model to  capture the interrelationships between heterogeneous datasets from  disparate sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The common practice in production is to provide  a keyword search interface over the metadata of datasets but users  often have discovery needs that cannot be precisely expressed by  keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In this work, we address one important class of discovery  needs: finding union-able tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  The task is to find tables in the repository (or on the web) that  can be unioned with a given query table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The challenge is to rec-  ognize union-able columns that may be represented differently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In  this paper, we propose a data-driven learning approach: specifically,  an unsupervised representation learning and embedding retrieval  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Our key idea is to exploit self-supervised contrastive learn-  ing to learn an embedding model that produces close embeddings  for columns with semantically similar values while pushing apart  columns with semantically dissimilar values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We then find union-  able tables based on similarities between their constituent columns  in embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' On a real-world dataset, we demonstrate that  our best-performing model achieves significant improvements in  precision (16% ↑), recall (17% ↑), and query response time (7x faster)  compared to the state-of-the-art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  CCS CONCEPTS  Information systems → Information integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  KEYWORDS  data discovery, data integration, table union search, contrastive  learning, embeddings  Permission to make digital or hard copies of all or part of this work for personal or  classroom use is granted without fee provided that copies are not made or distributed  for profit or commercial advantage and that copies bear this notice and the full citation  on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Copyrights for components of this work owned by others than ACM  must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Abstracting with credit is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To copy otherwise, or republish,  to post on servers or to redistribute to lists, requires prior specific permission and/or a  fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Request permissions from permissions@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  © 2018 Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  ACM ISBN 978-1-4503-XXXX-X/18/06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='$15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='00  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='org/XXXXXXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='XXXXXXX  ACM Reference Format:  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Pylon: Table Union Search through  Contrastive Representation Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of Make sure to en-  ter the correct conference title from your rights confirmation emai (Confer-  ence acronym ’XX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' ACM, New York, NY, USA, 13 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='org/  XXXXXXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='XXXXXXX  1  INTRODUCTION  Recent years have witnessed a vast growth in the amount of data  available to the public, particularly from data markets, open data  portals, and data communities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', Wikidata and Kaggle) [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To  benefit from the many new opportunities for data analytics and  data science, the user first usually has to find related datasets in  a large repository (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', data lakes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The challenge for a system is  to support users with varying discovery needs, without the help  of a unified data model capturing the interrelationships between  datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In response to the challenge, there are many ongoing efforts  under the umbrella of data discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' One task of the interest in  data discovery is to find union-able tables [1, 5, 10, 27] with the  aim of adding additional relevant rows to a user-provided table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Figure 1 shows an example of two tables union-able over four pairs  of attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In general, the literature considers two tables union-  able if they share attributes from the same domain and assumes the  union-ability of two attributes can be implied by some notion of  similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We refer to the problem of finding union-able tables as  table union search (termed in [27]) in the rest of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  The typical solution path is to first identify union-able attributes  (or columns in the tables) and then aggregate column-level results  to obtain candidate union-able tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To uncover the union-ability  of attributes, both syntactic and semantic methods have been em-  ployed in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Syntactic methods are the easiest, and have  been used the longest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' While they are robust at catching small  changes, such as capitalization or the use of a hyphen, they are  unable to address the use of common synonyms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Semantic methods  offer the possibility of finding union-able columns of semantically  similar values despite their syntactic dissimilarity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', the "venue"  column and the "platform" column in figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [10, 27] link cell val-  ues to entity classes in an external ontology and compare similarity  of entity sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [1, 27] use off-the-shelf word embeddings to measure  semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Both methods have notable limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [27] observed  that only 13% of attribute values of their collected Open Data ta-  bles can be mapped to entities in YAGO [32], one of the largest  and publicly available ontologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Although word embeddings can  provide more semantic coverage of attributes, they are subject to  the training text corpus and may not generalize well to textual data  in tables [18, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='04901v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='DB]  12 Jan 2023  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  id  title  authors  venue  year  671167  A Database System for Real-Time Event Aggregat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Jerry Baulier, Stephen Blott, Henry F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Korth, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Very Large Data Bases  1998  672964  Integrating a Structured-Text Retrieval System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Tak W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Yan, Jurgen Annevelink  Very Large Data Bases  1994  872823  Evaluating probabilistic queries over imprecis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Reynold Cheng, Dmitri V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Kalashnikov, Sunil Pr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  International Conference on Management of Data  2003  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='  66  2009  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='  Figure 1: An example of two tables union-able over four pairs of attributes: title - Title, authors - Authors, venue - Platform,  and year - Year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Instead of relying on low-coverage ontologies or pre-trained  word embeddings, a data-driven learning approach seems more  promising to capture semantics as shown in many data manage-  ment tasks such as entity resolution [24, 25], data cleaning [34], and  table interpretation [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' A large part of their success requires la-  beled data for supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' However, there is no large-scale  labeled dataset for table union search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The only publicly available  benchmark [27] with table- and column-level ground truth con-  tains limited number of tables synthesized from only 32 base tables,  which is far from being representative for training purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Ad-  ditionally, labeling new datasets could be very laborious and time  consuming as curators need to examine every pair of columns in  every pair of tables in a collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Even if the training data prob-  lem were resolved, we would only be able to determine column  matches pairwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It would still be very inefficient to exhaustively  consider every query column and every column in the corpus pair-  wise to predict union-ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In short, the inherent search nature  of the problem makes it unsuitable to formulate it as a supervised  classification problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In this work, we overcome the aforementioned difficulties by  casting table union search as an unsupervised representation learn-  ing and embedding retrieval task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Our goal is to learn column-level  embeddings into a high-dimensional feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Locality search  in this feature space can then directly be used for union-able table  search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To achieve this goal, our key idea is to exploit self-supervised  contrastive learning to learn an embedding model that produces  close embeddings for columns with semantically similar values  and pushes away columns with semantically dissimilar values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We  propose Pylon, a novel contrastive learning framework that learns  column representations for tabular data and serves the table union  search problem without relying on labeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  There are two main challenges in the development of Pylon,  specifically, on how to adapt contrastive learning for tabular data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (1) How to create training data without human labeling?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The  self-supervised contrastive learning technique requires con-  structing positive and negative examples from the data itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In the field of computer vision where contrastive learning  first took off, [9] applies a series of random data augmen-  tation of crop, flip, color jitter, and grayscale to generate  stochastic views of an image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' These views preserve the se-  mantic class label of the image and so make positive exam-  ples for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' They further consider any two views not  from the same image as a negative example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' However, the  tabular data modality is dramatically different from images  and it remains unclear how to create different views of tables  while keeping the semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (2) What is a feasible feature encoder for tabular data?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Another  key component in contrastive learning is a pre-trained base  encoder that gives initial embeddings for raw data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Both  computer vision (CV) and natural language processing (NLP)  communities have widely recognized models for feature ex-  tractions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', ResNet [19] in CV and BERT [12] in NLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  On the contrary, there is no generally accepted feature ex-  traction model for tables despite the recent progress in Web  table modeling (which we discuss in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In summary, we make the following contributions:  We formulate semantic table union search as an unsuper-  vised representation learning and embedding retrieval prob-  lem, and propose to use self-supervised contrastive learning  to avoid the labeling issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We present Pylon, to the best of our knowledge, the first con-  trastive learning framework for learning semantic column  representations from large collections of tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We also ex-  plore the design of each component in contrastive learning  and take an initiative in adapting contrastive learning for  tabular data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We empirically show that our embedding approach is both  more effective and efficient than existing embedding meth-  ods on a self-curated real-world dataset and a synthetic pub-  lic benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' On the real-world dataset, two of our model  variants outperform their corresponding baseline version by  14% and 6% respectively on both precision and recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We  also observe that they speed up the query response time by  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7x and 9x respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We (plan to) open-source the new  benchmark for future research study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We demonstrate that our embedding approach can be further  augmented by syntactic measures and that our best ensemble  model has significant advantages over the state-of-the-art  (namely, 𝐷3𝐿 [1]), more than 15% improvement in precision  and recall, and 7x faster in query response time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We give a formal problem setup and background about embed-  ding models in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We describe our framework Pylon includ-  ing embedding training and search in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Section 4 reports  experiments that validate our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We discuss related work  in Section 5 and conclude in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Pylon: Table Union Search through Contrastive Representation Learning  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  2  PROBLEM DEFINITION & BACKGROUND  In this section, we start by describing the formal problem setup  in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1, and then provide an overview of existing embed-  ding models for tabular data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We also discuss the challenges of  representation learning for table union search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  Table Union Search  The table union search problem [27] is motivated by the need to  augment a (target) table at hand with additional data from other  tables containing similar information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For example, starting with  a table about traffic accidents in one state for a particular year, an  analyst may wish to find similar traffic accident data for other states  and years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Ideally, these tables would have the same schema (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  data from the same state agency for two different years) so that  we could simply union the row-sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' However, this is typically not  the case for data recorded independently (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' data from different  states).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We consider two tables union-able if they share attributes  from the same domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Also, as in prior work on this topic, we  assume the union-ability of attributes can be quantified by some  notion of similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Definition 1 (Attribute Union-ability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Given two attributes 𝐴 and  𝐵, the attribute union-ability U𝑎𝑡𝑡𝑟 (𝐴, 𝐵) is defined as  U𝑎𝑡𝑡𝑟 (𝐴, 𝐵) = M(T (𝐴), T (𝐵))  where T (·) is a feature extraction technique that transforms raw  columns (attribute names, attribute values, or both) to a feature  space and M(·, ·) is a similarity measure between two instances in  the feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  With the definition of attribute union-ability, we can define table  uniona-bility as a bipartite graph matching problem where the  disjoint sets of vertices are attributes of the target table and the  source table respectively, and edges can be defined by attribute  union-ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In this paper, we restrict ourselves to the class of  greedy solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Therefore, we formalize the definition table union-  ability as a greedy matching problem as follows:  Definition 2 (Union-able Tables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' A source table 𝑆 with attributes  B = {𝐵𝑗 }𝑛  𝑗=1 is union-able to a target table 𝑇 with attributes A =  {𝐴𝑖}𝑚  𝑖=1 if there exists a one-to-one mapping 𝑔 : A′(≠ ∅) ⊆ A →  B′ ⊆ B such that  (1) |A′| = |B′|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (2) ∀𝐴𝑖 ∈ A′, U𝑎𝑡𝑡𝑟 (𝐴𝑖,𝑔(𝐴𝑖)) ≥ 𝜏 where  𝑔(𝐴𝑖) = arg max  𝐵𝑗  {U𝑎𝑡𝑡𝑟 (𝐴𝑖, 𝐵𝑗) : 1 ≤ 𝑗 ≤ 𝑛}  and 𝜏 is a pre-defined similarity threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Definition 3 (Table Union-ability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Following notations in Defini-  tion 2, the table union-ability U(𝑆,𝑇) is defined as  U(𝑆,𝑇) =  �𝑙  𝑖=1 𝑤𝑖 · U𝑎𝑡𝑡𝑟 (𝐴𝑖,𝑔(𝐴𝑖))  �𝑙  𝑖=1 𝑤𝑖  where 𝑙 is the number of union-able attribute pairs between the  target table 𝑇 and a source table 𝑆, and 𝑤𝑖 weights the contribution  of the attribute pair (𝐴𝑖,𝑔(𝐴𝑖)) to the table union-ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Considering the scale of the dataset repository, we also follow  the common practice[1, 10, 27] of performing top-𝑘 search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The  table union search problem is formally defined as below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Definition 4 (Top-𝑘 Table Union Search).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Given a table corpus  S, a target table 𝑇, and a constant 𝑘, find up to 𝑘 candidate tables  𝑆1,𝑆2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=',𝑆𝑘 ∈ S in descending order of table union-ability with  respect to the query table 𝑇 such that 𝑆1,𝑆2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=',𝑆𝑘 are most likely  to be union-able with 𝑇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  Embedding Models for Tabular Data  The advance of language modeling in the field of NLP has sparked  its adoption in many applications of data management such as  semantic queries in relational databases [3, 17], entity resolution [24,  25], and data cleaning [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We give an (non-exhaustive) overview  of embedding models that have been used for tabular data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Word Embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Word embeddings are vector representa-  tions of words in a low-dimension space where words that share the  common context are close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Most popular word embed-  ding models include Word2Vec [26], GloVe [30], and fastText [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Unlike Word2Vec and GloVe that learn embeddings directly for  words, fastText represents a word as an n-gram of characters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=',  subwords) and generate word embeddings based on subwords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In  this way, fastText is able to handle out-of-vocabulary words that  do not appear in the training corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In the context of table union  search, both [27] and [1] employed off-the-shelf fastText embed-  dings to measure the semantic relatedness between two columns,  which implies union-ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' One issue with pre-trained word em-  beddings is that the text value distribution in tables is different  from what models capture in the training corpus consisting of un-  structured documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To generate embeddings for textual values  in tables, [18] serialized tables to sequences of tokens and trained  a fastText model on a text corpus extracted from Web tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The  resulting web table embedding models demonstrated better perfor-  mance as compared to off-the-shelf fastText embeddings in a task  of ranking union-able columns pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Transformer-based Language Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Another well-known  issue with word embedding models is that they assign a fixed em-  bedding for each word regardless of various meanings a word could  have and different linguistic contexts in which a word could appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  This (partly) motivates the development of contextual language  models (LMs) such as BERT [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The underlying Transformer ar-  chitecture empowered by the attention mechanism [35] enables  LMs to represent any word relative to all other words in the context  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', surrounding words in the same sentence).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Note that these LMs  are first pre-trained on a large text corpus with a general-purpose  objective (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', masked language model (MLM), which predicts ran-  domly masked words based on their contexts) and fine-tuned with  supervision (labeled data) for downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' This pre-training  and fine-tuning paradigm has become the de facto practice in many  NLP tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  The tremendous success of Transformer-based LMs has inspired  their counterparts on tabular data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' TAPAS [20] extended the BERT  architecture to answer questions over tables by pre-training the  model on text-table pairs using the MLM objective and fine-tuning  it on downstream task datasets in a weakly supervised manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In addition to MLM, TURL [11] proposed a new Masked Entity  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  Recovery objective for pre-training on entity-rich relational tables  from Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Their pre-trained contextualized representations were  shown to generalize well to six downstream table understanding  tasks with fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' TaBERT [38] jointly learned semi-structured  Web tables and their surrounding texts in pre-training and was fine-  tuned for semantic parsing tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' TUTA [36] devised a tree-based  Transformer and expanded pre-training to generally structured  tables including entity and matrix tables, and spreadsheet tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  They fine-tuned the model for cell-type classification and table-type  classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  Challenges  Representation learning for tables has achieved excellent results  for many table-centric tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We hypothesize that the table union  search problem can also benefit from advances in table modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  However, several challenges remain to be addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (1) To the best of our knowledge, no prior work has taken the  learning approach for table union search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We argue that this  is mainly because neither the supervised learning setting nor  the popular pre-training and fine-tuning paradigm is directly  applicable for the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It is inefficient to formulate the  underlying search of union-able columns as a classification  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In a supervised learning setting, one can attempt to  train a classifier to predict whether two columns are union-  able, but it will quickly become computationally prohibitive  in the search phase to classify every pair of target column  in a query table with every column in a large corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (2) The scarcity of table union search datasets is another severe  bottleneck of applying a learning approach and studying  the problem in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The only publicly available bench-  mark [27] with table- and column-level ground truth is syn-  thesized from only 32 base tables, which is barely enough for  evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It is also very laborious and time consuming to  label such datasets, as curators need to examine every pair  of columns for every pair of tables in a collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (3) How to encode non-Web tables?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Transformer-based mod-  els surveyed above are primarily designed for Web tables  and assume access to abundant metadata such as table cap-  tions, surrounding text, and topic entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In contrast, non-  Web tables like Open Data tables and tables extracted from  GitHub [21] do not have such information available in gen-  eral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We can reasonably assume access to data values and  table headers but not much more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Even informative schema  is not always available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In the next section, we present our design that contributes a  representation learning approach to table union search while effec-  tively mitigating the challenges we point out here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3  PYLON: A SELF-SUPERVISED  CONTRASTIVE LEARNING FRAMEWORK  FOR TABULAR DATA  Our key idea is to leverage self-supervised contrastive learning  that provides a feasible training objective for learning effective  column representations for the table union search problem while  not requiring any labeled data (corresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' to challenge 1 and 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Within  the framework of contrastive learning, we propose two strategies  that arithmetically construct training data from unlabeled data to  tackle challenge 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We also experiment with several encoders to  gain empirical insights into challenge 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  Contrastive Learning  The high-level goal of contrastive learning is to learn to distin-  guish (so called "contrast") between pairs of similar and dissimilar  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Ideally, in the learned representation space, similar in-  stances stay close to each other whereas dissimilar ones are pushed  far away.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' A pair of instances is considered similar and labeled a  positive example in training if it comprises different views of the  same object;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' otherwise, they are considered dissimilar and make a  negative example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Contrastive learning has been used extensively  in computer vision [9], where a positive example consists of a pair  of augmented images transformed from the same image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', by  applying cropping or color distortion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We introduce, Pylon, our self-supervised contrastive learning  framework for learning representations from large collections of  tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As table union search begins by finding union-able columns,  Pylon is designed to generate a vector representation for each  column of input tables where columns containing semantically  similar values have embeddings closer to one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  Pylon Workflow  Figure 2 shows the training workflow of the framework that consists  of the following major components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Training Data Construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Without labeled data, the suc-  cess of contrastive learning hinges on the construction of positive  and negative examples from the data itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To make positive ex-  amples, it requires an operation to transform a data instance in a  way that introduces variations while preserving the semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As  table union search builds on union-able column search, we propose  two strategies to construct positive and negative examples at the  column level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (1) Online sampling strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Consider a training batch of 𝑁  tables {𝑇𝑖}𝑁  𝑖=1 where each table 𝑇𝑖 has 𝑚𝑖 columns {𝐶𝑖  𝑗 }𝑚𝑖  𝑗=1,  giving 𝑀 = �𝑁  𝑖=1 𝑚𝑖 columns in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We obtain a positive  example of column pairs (𝑥𝑘,𝑥𝑘+𝑀) (1 ≤ 𝑘 ≤ 𝑀) by ran-  domly sampling values from each column 𝐶𝑖  𝑗 of each table𝑇𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Since both 𝑥𝑘 and 𝑥𝑘+𝑀 are samples from the same column  of the same table, we consider they share semantics and  make a positive example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The sampling process yields 2𝑀  column instances, and we treat the other 2(𝑀 − 1) samples  as negatives with respect to 𝑥𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In other words, considering  (𝑥𝑘,𝑥𝑘+𝑀) and (𝑥𝑘+𝑀,𝑥𝑘) as distinct positive examples, we  construct 2𝑀 positive examples and 2𝑀(𝑀 − 1) negative  examples from each training batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (2) Offline approximate matching strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' An alternative is to  construct positive examples ahead of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Instead of  relying on ad-hoc sampling, we can leverage existing ap-  proaches to find a union-able candidate for each column,  which in turn makes positive examples in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Based  on the observation that top-𝑘 union-able column search of  existing techniques is highly precise when 𝑘 is small (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=',  Pylon: Table Union Search through Contrastive Representation Learning  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  r1  r2  r3  r4  r5  r6  Online Training  Data  Construction  Base Encoder f &  Projection Head g  f  g  f  g  e1  e2  e3  e1+M  e2+M  e3+M  Projected column embeddings  Table Samples  c1 c2 c3  r1  r2  r5  r2  r3  r6  Figure 2: Training workflow of Pylon (with online training data construction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  𝑘 = 1), we are able to use this approximate matching without  human involvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We find that it produces valid results  and does not suffer the issue of false positives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Base Encoder & Projection Head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We pass column instances  {𝑥𝑘}2𝑀  𝑘=1 through a base encoder 𝑓 (·) to get initial column embed-  dings {𝑒𝑘}2𝑀  𝑘=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Note that our contrastive learning framework is  flexible about the choice of the base encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The encoder can give  embeddings at token/cell/column level, and if necessary, we can  apply aggregation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g, average or max) to obtain column-level  embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Our framework has the flexibility to benefit from the  advance of modeling techniques in NLP over time without being  tied to a specific model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We describe the choices of 𝑓 (·) we experi-  ment with in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Following the encoder, a small multi-layer neural network 𝑔(·),  called projection head, maps the representations from the encoder  to a latent space through linear transformations and non-linear  activation in between.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Note that unlike the practice in CV which  discards projection head in inference and uses encoder outputs for  downstream tasks, we preserve projection head and use projected  embeddings for table union search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' This is because we found pro-  jected embeddings yield better performance in initial experiments,  and for encoders like word embedding models, only projection head  is trainable and has to be preserved for inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For simplicity,  we keep using the notations {𝑒𝑘}2𝑀  𝑘=1 for projection outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Contrastive Loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' One common setting of contrastive learning  defines a prediction task of identifying positive examples from the  training batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Given embedded columns {𝑒𝑘}2𝑀  𝑘=1, the model learns  to predict 𝑒𝑘+𝑀 as the most similar one to 𝑒𝑘 and vice versa for  each 𝑒𝑘 (1 ≤ 𝑘 ≤ 𝑀).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The similarity between any two instances 𝑒𝑖  and 𝑒𝑗 is measured by their cosine similarity as  𝑠𝑖𝑚(𝑖, 𝑗) =  𝑒𝑇  𝑖 𝑒𝑗  ∥𝑒𝑖 ∥∥𝑒𝑗 ∥  and the loss is calculated as  𝑙(𝑘,𝑘 + 𝑀) = − log  exp (𝑠𝑖𝑚(𝑘,𝑘 + 𝑀) / 𝜏)  �2𝑀  𝑙=1,𝑙≠𝑘 exp (𝑠𝑖𝑚(𝑘,𝑙) / 𝜏)  where 𝜏 > 0 is a scaling hyper-parameter called temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Mini-  mizing 𝑙(𝑘,𝑘 + 𝑀) is equivalent to maximizing the probability of  𝑒𝑘+𝑀 being the most similar to 𝑒𝑘 among all the embedded columns  except 𝑒𝑘 itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Finally, the loss over all the 2𝑀 positive column pairs in a training  batch is computed as  𝐿 =  1  2𝑀  𝑀  ∑︁  𝑘=1  [𝑙(𝑘,𝑘 + 𝑀),𝑙(𝑘 + 𝑀,𝑘)]  This loss formulation is called InfoNCE loss [28] (also known as  the normalized temperature-scaled cross entropy loss [9]), which  approximately maximizes the mutual information (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', a measure  of how dependent two random variables are to each other) between  two views of the same object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  Choices of the Base Encoder  Although we expect the input to the contrastive loss function to be  column embeddings, the base encoder does not necessarily need to  give column embeddings directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It is possible for the encoder  model to generate embeddings at different granularity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', to-  ken/cell/column) because we can apply aggregation if necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We describe the basic encoding process of embedding models we  experimented with in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Word Embedding Models (WEM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As a WEM assigns a fix  representation to a token, WEM-based encoders treat each column  independently as a document where a standard text parser tokenizes  data values in a column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' With a fastText embedding model, we first  get cell embeddings by averaging token embeddings in each cell and  then aggregate cell embeddings to get a column embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' More  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  interestingly, web table embedding models [18] consider each cell as  a single token (they concatenate tokens in a cell with underscores)  and output embeddings at cell level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Nevertheless, we aggregate  cell embeddings to derive the column embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Language Models (LM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Since a table is a cohesive structure  for storing data, considering values in neighboring columns could  integrate context into the embeddings and help mitigate ambiguity  in unionable column search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For example, encoding column "year"  in figure 1 individually loses the context that this column refers to  the publication year of research papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In this case, the embeddings  of "Year" columns in the corpus are less distinguishable (in terms of  cosine similarity) even though they may refer to different concepts  of year such as the birth year of people or the release year of movies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  With context provided by other columns like "Title" and "Venue", it  is more likely that "Year" columns appearing in tables about papers  are more close to each other than "Year" columns in tables about  other topics, which helps find more related tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We leverage LMs to derive contextual column embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We  first serialize each row in 𝑇𝑖 as a sequence by concatenating tok-  enized cell values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For example, the first row of the table at the top  in Figure 1 will be encoded as follows  [𝐶𝐿𝑆] title | A Database .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [SEP] authors | Jerry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [SEP] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='[𝐸𝑁𝐷]  The sequence is annotated with special tokens in the LM where  [𝐶𝐿𝑆] token indicates the beginning of the sequence, [𝐸𝑁𝐷] token  indicates the end, and [𝑆𝐸𝑃] tokens separate cell values in different  columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Then the LM takes in each sequence and generates a con-  textual representation for each token in the sequence (essentially  taking into account the relation between values in the same row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We apply mean pooling to tokens in the same cell and get cell em-  beddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To consider the relation of values in the same column, we  adopt the vertical attention mechanism in [38] to have weighted  column embeddings by attending to all of the sampled cells in the  same column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Word embedding models have previously been used to find  union-able tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Two state-of-the-art choices are fastText and  WTE (web table embeddings [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Language models have not thus  far been used for the union-ability problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' BERT[12] is a lead-  ing language model used for many purposes today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We develop  three versions of Pylon, one for each of these three encoder choices:  fastText, WTE, and a BERT-based language model, and refer to the  derived models as Pylon-fastText, Pylon-WTE, Pylon-LM respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We evaluate the effect of encoder choices in subsection 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  Embedding Indexing and Search  To avoid exhaustive comparisons of column embeddings over a  large corpus at query time, we use locality-sensitive hashing (LSH) [22]  for approximate nearest neighbor search and treat union-able col-  umn search as an LSH-index lookup task [1, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' LSH utilizes a  family of hash functions that maximize collisions for similar inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  The result of LSH indexing is that similar inputs produce the same  hash value and are bucketed together whereas dissimilar inputs are  ideally placed in different buckets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Algorithm 1 gives the indexing  procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For approximate search with respect to the cosine simi-  larity, we index all column embeddings in a random projection LSH  index [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The idea of random projection is to separate data points  Algorithm 1: Embedding Inference and Indexing  Input  :  S, a corpus of tables;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  𝑔 ◦ 𝑓 , a Pylon model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  𝑝, a list of LSH index parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Output:  I, a random projection LSH index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  1 I ← create_index(𝑝);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2 for 𝑡 ∈ S do  3  𝑡_𝑠𝑒𝑟𝑖𝑎𝑙𝑖𝑧𝑒𝑑 ← preprocess(𝑡);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4  𝑐𝑜𝑙𝑢𝑚𝑛_𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔𝑠 ← 𝑔 ◦ 𝑓 (𝑡_𝑠𝑒𝑟𝑖𝑎𝑙𝑖𝑧𝑒𝑑);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  5  for 𝑒 ∈ 𝑐𝑜𝑙𝑢𝑚𝑛_𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔𝑠 do  6  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='insert(𝑒);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  7  end  8 end  9 return I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Algorithm 2: Top-𝑘 Table Union Search  Input  :  I, a LSH index;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  𝑄, a query table;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  𝑘, a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Output:  top-𝑘 union-able tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  1 𝑐𝑜𝑙𝑢𝑚𝑛_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 ← {};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2 𝑐𝑜𝑙𝑢𝑚𝑛_𝑠𝑐𝑜𝑟𝑒𝑠 ← {};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3 for 𝑐 ∈ 𝑄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='𝑐𝑜𝑙𝑢𝑚𝑛𝑠 do  4  𝑐_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠,𝑐_𝑠𝑐𝑜𝑟𝑒𝑠 ← I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='lookup(𝑐);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  5  𝑐𝑜𝑙𝑢𝑚𝑛_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠[𝑐].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='add(𝑐_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  6  𝑐𝑜𝑙𝑢𝑚𝑛_𝑠𝑐𝑜𝑟𝑒𝑠[𝑐].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='add(𝑐_𝑠𝑐𝑜𝑟𝑒𝑠);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  7 end  8 𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 ← group_by(𝑐𝑜𝑙𝑢𝑚𝑛_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  9 𝑟𝑎𝑛𝑘𝑒𝑑_𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠 ←  cmpt_table_unionability(𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠,𝑐𝑜𝑙𝑢𝑚𝑛_𝑠𝑐𝑜𝑟𝑒𝑠);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  10 return 𝑟𝑎𝑛𝑘𝑒𝑑_𝑡𝑎𝑏𝑙𝑒_𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠[: 𝑘];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  in a high-dimensional vector space by inserting hyper-planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Em-  beddings with high cosine similarity tend to lie on the same side of  many hyper-planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Algorithm 2 summarizes the top-𝑘 table union search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Following  Definition 1, we instantiate the union-ability of two attributes as  the cosine similarity of their embeddings (𝑐_𝑠𝑐𝑜𝑟𝑒𝑠 in line 4 of  Algorithm 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Line 8 groups retrieved column candidates across  query columns by their table sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To decide on the table union-  ability from Definition 3 (𝑐𝑚𝑝𝑡_𝑡𝑎𝑏𝑙𝑒_𝑢𝑛𝑖𝑜𝑛𝑎𝑏𝑖𝑙𝑖𝑡𝑦 in line 9), we  use the same weighting strategy as [1] over query attributes and  corresponding matching attributes in candidate tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For a target  attribute 𝐴, let 𝑅𝐴 denote the distribution of all similarity (union-  ability) scores between 𝐴 and any attribute 𝐵 returned by the LSH  index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The weight𝑤 of a similarity score U𝑎𝑡𝑡𝑟 (𝐴, 𝐵) is given by the  cumulative distribution function of 𝑅𝐴 evaluated at U𝑎𝑡𝑡𝑟 (𝐴, 𝐵):  𝑤 = Pr(U𝑎𝑡𝑡𝑟 (𝐴, 𝐵′) ≤ U𝑎𝑡𝑡𝑟 (𝐴, 𝐵)), ∀ U𝑎𝑡𝑡𝑟 (𝐴, 𝐵′) ∈ 𝑅𝐴  In other words, a similarity score is weighted by its percentile in  the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' This weighting scheme helps balance between a  Pylon: Table Union Search through Contrastive Representation Learning  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  candidate table with a few union-able attributes of high similarity  scores and another candidate table with more union-able attributes  but of lower similarity scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Using the same index and search structure as previous works  makes it transparent to compare our embedding approach with  theirs in effectiveness and efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  Integrating Syntactic Methods  Thus far, we have focused purely on semantic methods to unify  similar attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It makes sense to prefer semantic methods to  syntactic ones because of their potential robustness to many differ-  ent types of variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' However, we note that syntactic methods  are based on measures of similarity very different from semantic  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Intuitively, one should expect to be able to do better if we  can integrate the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Indeed, some previous work [1, 27] has made this observation  as well, and shown that an ensemble of semantic and syntactic  methods can do better than either on its own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The Pylon semantic  method permits the use of an additional complementary syntactic  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As in [1], we independently obtain scores from the two  methods and then use the average of the two as our final score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4  EXPERIMENTS  We first evaluate the effectiveness and efficiency of three model vari-  ants from our contrastive learning framework and compare them  with their corresponding base encoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We then demonstrate that  our embedding approach is orthogonal to existing syntactic mea-  sures, which can further improve the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We finally compare  our best model with the state-of-the-art 𝐷3𝐿 [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  Datasets and Metrics  TUS Benchmark1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [27] compiled the first benchmark with ground  truth out of Canadian and UK Open Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' They synthesized around  5, 000 tables from 32 base tables by performing random projection  and selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' They also generated a smaller benchmark consisting  of around 1, 5002 tables from 10 base tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We refer to them as  TUS-Large and TUS-Small respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Pylon Benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We create a new dataset from GitTables [21],  a corpus of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7𝑀 tables extracted from CSV files on GitHub3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The  benchmark comprises 1,746 tables including union-able table sub-  sets under topics selected from Schema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='org [16]: scholarly article,  job posting, and music playlist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We end up with these three topics  since we can find a fair number of union-able tables of them from  diverse sources in the corpus (we can easily find union-able tables  from a single source but they are less interesting for table union  search as simple syntactic methods can identify all of them because  of the same schema and consistent value representations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Cleaning and Construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We download three largest sub-  sets of GitTables ("object", "thing", and "whole") and preprocess them  by removing HTML files, tables without headers, rows with foreign  languages, and finally small tables with fewer than four rows or  four columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We cluster the resulting tables by their schema and  1TUS benchmark can be accessed from https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='com/RJMillerLab/table-union-  search-benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2We export 1, 530 tables from the small benchmark although the paper and the website  claim ∼1, 300 tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  3GitTables 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7𝑀 is available from https://zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='org/record/4943312#.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='Ylm2ftPMJxZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  perform a keyword search over schema with keywords related to  three topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We manually select 35 union-able tables of topic schol-  arly article, 41 tables of topic job posting, and 48 tables of topic  music playlist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We then randomly sample 100,000 tables4 for train-  ing, 5,000 tables for validation, and put the rest of tables as noise5  in a pool with union-able table subsets for the search evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Table 1 provides an overview of basic statistics of tables in each  evaluation dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Table 1: Basic statistics of evaluation datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Pylon  TUS-Small  TUS-Large  # Tables  1,746  1,530  5,043  # Base Tables  1,746  10  32  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' # Rows  115  4,466  1,915  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' # Columns  10  10  11  # Queries  124  1,327  4,296  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' # Answers  42  174  280  Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For effectiveness, we report both precision and recall  of top-𝑘 search with varying 𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' At each value of 𝑘, we average the  precision and recall numbers over all the queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We consider a  table candidate as a true positive with respect to the target table as  long as it is in the corresponding ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We do not require  perfect attribute pair matching as it is a more challenging setting  and requires laborious column-level labeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  As to efficiency, we report indexing time (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', total amount of  time in minutes to index all columns in a dataset) and query re-  sponse time (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', average amount of time in seconds for the LSH  index to return results over all queries in a dataset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In evaluation, we randomly sample 1000 queries from TUS-Large  for efficient experiment purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The query subset has an average  answer size of 277, which is very close to that of the full query set  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', 280).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We use all the queries in Pylon and TUS-Small datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  Baselines  We consider two embedding methods and one full approach as  baselines for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  fastText.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Many data discovery tasks [15, 27] not limited to table  union search have adopted fastText in their approach, which is a  popular word embedding model trained on Wikipedia documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  WTE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [18] devised a word embedding-based technique to rep-  resent text values in Web tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' They generated text sequences  from tables for training by serializing tables in two different ways  that capture row-wise relations and relations between schema and  data values respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It is reported that the model using both  serialization obtained the best performance in a task of ranking  unionable columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We use this model6 in comparison and refer to  it as WTE (for web table embeddings).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4We noticed that a few schemas have an overwhelming number of tables (because  some GitHub repositories publish hundreds and thousands of tables with the same  schema).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In sampling, we take at most 200 tables from each schema to increase the  diversity of the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  5we filtered these tables using their schema to reduce the chance of them being union-  able to selected tables in the union-able subsets (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', true noise).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  6𝑊𝑐𝑜𝑚𝑏𝑜 150dim: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='com/guenthermi/table-embeddings/tree/main#pre-  trained-models  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [1] proposed a distance-based framework 𝐷3𝐿 that uses  five types of evidence to decide on column unionability: (i) attribute  name similarity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (ii) attribute extent overlap;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (iii) word-embedding  similarity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (iv) format representation similarity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (v) domain distri-  bution similarity for numerical attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Their aggregated ap-  proach is shown to be more effective and efficient than previous  work [13, 27] on the TUS benchmark and another self-curated  dataset of Open Data tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To the best of our knowledge, 𝐷3𝐿 is  the current state-of-the-art of the table union search problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  Comparisons of Interest  We have 5 variants of Pylon to compare against baseline systems for  both effectiveness and efficiency in identifying union-able tables  using semantic similarity methods: 3 variants from the online train-  ing data construction strategy and 2 variants from the offline data  construction strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In addition, we have 3 syntactic similarity  measures that could be used to augment each of these 5 variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Finally, we have 3 baselines, two of which are semantic word embed-  ding based, and hence could also be augmented with the syntactic  similarity measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The third baseline (D3L) already integrates  both syntactic and semantic similarity, and hence does not benefit  from additional augmentation with syntactic techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Since there are a very large number of alternatives to compare,  we break up the comparisons into four sets, as follows, and present  the results for each set separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For the first three sets, we restrict  ourselves to the online training data construction strategy for Pylon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We refer to the derived models as Pylon-fastText, Pylon-WTE, Pylon-  LM respectively based on the corresponding encoder choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Results  for the offline data construction strategy show generally similar  trends, and the most interesting are shown in the fourth set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  The first set of comparisons look purely at semantic methods,  considering the 3 variants of Pylon and comparing them to the first  two baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We leave out D3L because it already incorporates  syntactic methods as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The second set of comparisons look  purely at the benefit obtained when semantic methods are enhanced  with syntactic measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We do so for all methods evaluated in the  first set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Finally, we bring everything together by comparing the  best methods of the second set with the best integrated baseline,  D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' This is the final top line "take away" from the experiments,  eliding details from the first two sets of comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  Experiment Details  As to model training, we train Pylon-fastText for 50 epochs with a  batch size of 16 on 2 NVIDIA GeForce RTX 2080 Ti GPUs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Pylon-  WTE for 20 epochs with a batch size of 32 on a single NVIDIA  Tesla P100 GPU;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Pylon-LM for 20 epochs with a batch size of 8  on 4 NVIDIA Tesla P100 GPUs from Google Cloud Platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As  seen in table 2, the training is especially efficient for simple word  embedding encoders (as only parameters in projection head are  updated) and the offline data construction strategy (as embeddings  are pre-computed before training).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We save the models with the  smallest validation loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The model training is implemented in  PyTorch [29] and PyTorch Lightning7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  For evaluation of table union search, we set the similarity thresh-  old of LSH index to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7 in all experiments and use the default hash  7https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='pytorchlightning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='ai/  Table 2: Model training time (min / epoch) where each model  is defined by the encoder choice and the training data con-  struction strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Online Sampling  Offline Approximate Matching  Pylon-fastText  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='42  Pylon-WTE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='13  Pylon-LM  33 size (a MinHash size of 256 and a random projection size of 1024) as  D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We run all evaluation on a Ubuntu 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4 LTS machine with  128 GiB RAM and Intel(R) Xeon(R) Bronze 3106 CPU @ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='70GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  Results  As Pylon is an embedding-based approach, we first evaluate Pylon  model variants against embedding baselines fastText and WTE, and  inspect what effects contrastive learning have on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Experiment 1(a): Comparison of effectiveness between Py-  lon model variants and their corresponding base encoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Figure 3 shows the precision and recall of each embedding measure  on the Pylon dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Both Pylon-WTE and Pylon-fastText outper-  form their corresponding base models with a notable margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' When  𝑘 = 40, around the average answer size, Pylon-WTE is 6% better  than WTE on both metrics, and Pylon-fastText performs better than  fastText by 15% on precision and 14% on recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Overall, our Pylon-WTE model consistently achieves the highest  precision and recall as 𝑘 increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We also note that Pylon-LM  has strong performance up until 𝑘 = 30 but degrades after that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  This is because Pylon-LM only samples 10 rows from each table to  construct embeddings (for indexing efficiency) while other word-  embedding methods can afford to encode the entire table at low  indexing time, which we demonstrate in experiment 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Experiment 1(b): Comparison of efficiency between Pylon  model variants and their corresponding base encoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In fig-  ure 4, we see both embedding baselines are very efficient in index  construction and it takes less than 2 minutes to index the entire  Pylon dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Unlike fixed embeddings, our models need to infer  embeddings at runtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For Pylon-fastText and Pylon-WTE, since  the encoder is fixed, the inference cost is exclusively from projec-  tion head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It takes both less than 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5 minutes to build the index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In  contrast, the runtime inference cost of Pylon-LM is more expensive  as the language model has much more complex architecture and has  130M parameters versus 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8K parameters in projection head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We  also acknowledge the less efficient implementation of embedding  inference at this point (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', run inference for each column with-  out batch predictions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Nevertheless, indexing time, as a one-time  overhead, can be amortized among queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  On the other hand, all of our models are considerably more  efficient in query response time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Pylon-fastText is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7x faster than  fastText and Pylon-WTE is 9x faster than WTE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The significant  speedup of query response time is attributed to contrastive learning  where embeddings of attribute values occurring in the same context  are pushed close to each other whereas embeddings of two random  columns are pushed apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As the embedding similarity between  two random columns is suppressed, this dramatically reduces the  chance of two random columns sharing many LSH buckets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In  Pylon: Table Union Search through Contrastive Representation Learning  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  10  20  30  40  50  60  70  80  90  100  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Precision  fastText  Pylon-fastText  WTE  Pylon-WTE  Pylon-LM  10  20  30  40  50  60  70  80  90  100  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Precision  Pylon-LM  Pylon-LM-NVF  Pylon-LM-NV  10  50  90  130  170  210  250  290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Recall  10  50  90  130  170  210  250  290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Recall  10  50  90  130  170  210  250  290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Recall  (b) TUS-Small dataset  Figure 5: Precision and recall (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' varying 𝑘) of the ensemble of Pylon embedding models and syntactic measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  other words, LSH index can process much fewer candidates at the  configured similarity threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  To illustrate the suppression effect of contrastive learning, we  compare heatmaps of pairwise cosine similarity of column em-  beddings encoded by WTE and Pylon-WTE respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Consider  the three text columns of the first table in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As shown in  Figure 6(a), the pairwise cosine similarity of WTE embeddings is  mostly above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' There is a very high similarity (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='87) between the  "title" column and the "venue" column and they will be mistakenly  viewed as unionable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' But this is not an issue for Pylon-WTE embed-  dings as shown in Figure 6(b) where the pairwise similarity between  different columns are much lower (below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='51) and the LSH index  will not return the "venue" column as a unionable candidate of the  "title" column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Figure 6: Pairwise cosine similarity of column embeddings:  (a) WTE embeddings;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (b) Pylon-WTE embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  title  authors  venue  title  authors  venue  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='0  authors -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0063  authors -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='0063  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  venue  venue -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  In the next set of experiments, we consider three syntactic mea-  sures used by D3L and evaluate how much they can augment our  embedding measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (1) Name (𝑁): Jaccard similarity between q-gram sets of at-  tribute names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (2) Value (𝑉 ): Jaccard similarity between the TF-IDF sets of  attribute values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  (3) Format (𝐹): Jaccard similarity between regular-expression  sets of attribute values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Experiment 2: Effectiveness of the ensemble of Pylon model  variants and syntactic measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Figure 5(a) and (b) show the  precision and recall of the ensemble of Pylon embedding models and  syntactic measures on Pylon and TUS-Small datasets respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We consistently observe from both datasets that adding syntactic  measures can further enhance the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In particular, name  (𝑁) and value (𝑉 ) similarity are most effective syntactic measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Around the average answer size of the Pylon dataset (𝑘 = 40), 𝑁  and 𝑉 together raise up the precision and recall of Pylon-fastText  by nearly 20%, of Pylon-WTE by 10%, and of Pylon-LM by over 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Similarly, around the average answer size of the TUS-Small dataset  (𝑘 = 170), there is an increase of about 10% in both precision and  recall for Pylon-fastText, about 5% for Pylon-WTE, and more than  10% for Pylon-LM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We also observe that adding additional format measure (𝐹) hurts  the performance (notably on the Pylon dataset and slightly on TUS-  small).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' This is because tables in the Pylon dataset are mostly from  disparate sources and so the value format tends to be inconsistent  across tables whereas tables in TUS-Small are synthesized from  only 8 base tables and it is much more likely for many tables to share  format similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Even worse, including format index imposes non-  trivial runtime cost (see figure 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' For example, compared to model  Pylon-WTE-NV, the query response time of Pylon-WTE-NVF (with  the extra format measure) surges by 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7% on the Pylon dataset and  by 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2% on TUS-Small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Pylon-fastText  Pylon-WTE  Pylon-LM  0  1  2  3  4  5  6  7  Query Response Time (s / query)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  NVF  NV  (a) Pylon dataset  Pylon-fastText  Pylon-WTE  Pylon-LM  0  5  10  15  20  25  30  35  Query Response Time (s / query)  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='6  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  NVF  NV  (b) TUS-Small dataset  Figure 7: Comparison of query response time between in-  cluding and excluding the format measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Finally, we compare our best-performing model Pylon-WTE-NV  with the state-of-the-art D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' As Pylon-WTE-NV does not use for-  mat and domain measures in D3L, for fair comparison, we consider  three versions of D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We refer to the full version of D3L as D3L-5,  the one without the format measure as D3L-4, and the one without  format and domain measures as D3L-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Experiment 3: Comparison of effectiveness and efficiency  between our best model and D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Figure 8 shows the perfor-  mance of Pylon-WTE-NV and three D3L variants on Pylon , TUS-  Small, TUS-Large datasets respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Around the average answer  size (𝑘 = 40) of the Pylon dataset, Pylon-WTE-NV is around 15%  better than the strongest D3L instance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', D3L-3) in both precision  and recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Pylon-WTE-NV performs much better than D3L in this  case because our embedding model using contrastive learning was  trained on a dataset of a distribution similar to the test set and can  capture more semantics than the off-the-shelf fastText embedding  model used in D3L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  On TUS-Small and TUS-Large, we observe all instances have  relatively competitive performance while Pylon-WTE-NV performs  marginally better compared to all D3L variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' On TUS-Small,  around the average answer size (𝑘 = 170), Pylon-WTE-NV is 2%  better than D3L-3 and 5% better than D3L-5 in both precision and  recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' On TUS-Large, around the average answer size (𝑘 = 290),  Pylon-WTE-NV is more than 2% better than D3L variants in both  metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The small performance gap is due to the synthetic nature  of TUS benchmark where most of union-able tables are generated  from the same base table and share common attribute names and  many attribute values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' So syntactic measures (𝑁 and𝑉 ) can capture  most of similarity signals and obtain high precision and recall even  without support of semantic evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Additional to the performance gain, the biggest advantage of  Pylon-WTE-NV is the fast query response time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' On the Pylon dataset,  our model is nearly 9x faster than the full version D3L-5 and 7x  faster than D3L-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Even on TUS-Small and TUS-Large, which are  datasets of a different data distribution (Open Data tables), we still  save runtime by 44% and 32% respectively compared to D3L-5, and  by 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5% and 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9% respectively compared to D3L-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Experiment 4: Effectiveness and efficiency of Pylon model  variants from the offline training data construction strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Figure 10 shows the precision and recall of 4 Pylon variants from  two training data construction strategies and their baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' On the  Pylon dataset, around the average answer size (𝑘 = 40), two Pylon  models from the alternative data construction strategy, Pylon-WTE-  offline and Pylon-fastText-offline, retain strong performance and  outperform the corresponding baseline by 3% and 9% respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Note that Pylon models derived from the sampling data construc-  tion strategy have consistently better performance as 𝑘 increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We also observe a similar trend on the TUS benchmark while the  performance gap of all instances is smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  As shown in figure 11, both new models are efficient in index-  ing time and query response time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Compared to the correspond-  ing baseline, Pylon-WTE-offline is 12x faster and Pylon-fastText-  offline is 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5x faster in query response time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Again, this signifi-  cant speedup demonstrates the distinguishing power of contrastive  learning, which enables the LSH index to work more efficiently  with embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='6  Discussion  Although this paper mainly focuses on the novel learning approach  for the table union search problem, we also leave and discuss a few  clues for future extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Pylon: Table Union Search through Contrastive Representation Learning  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  0  20  40  60  80  100  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='9  Precision  Pylon-WTE-NV  D3L-3  D3L-4  D3L-5  0  20  40  60  80  100  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='9  Recall  Pylon-WTE-NV  D3L-3  D3L-4  D3L-5  (a) Pylon dataset  10  50  90 130 170 210 250 290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Precision  Pylon-WTE-NV  D3L-3  D3L-4  D3L-5  10  50  90 130 170 210 250 290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='0  Recall  Pylon-WTE-NV  D3L-3  D3L-4  D3L-5  (b) TUS-Small dataset  10  50  90 130 170 210 250 290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='0  Precision  Pylon-WTE-NV  D3L-3  D3L-4  D3L-5  10  50  90 130 170 210 250 290  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='0  Recall  Pylon-WTE-NV  D3L-3  D3L-4  D3L-5  (c) TUS-Large dataset  Figure 8: Comparison of precision and recall between D3L instances and our best model Pylon-WTE-NV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  D3L-5  D3L-4  D3L-3  Pylon-WTE-NV  Model  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='0  Query Response Time (s / query)  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='3  (a) Pylon dataset  D3L-5  D3L-4  D3L-3  Pylon-WTE-NV  Model  0  5  10  15  20  25  30  35  40  Query Response Time (s / query)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='6  (b) TUS-Small dataset  D3L-5  D3L-4  D3L-3  Pylon-WTE-NV  Model  0  20  40  60  80  100  Query Response Time (s / query)  110  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='6  (c) TUS-Large dataset  Figure 9: Comparison of query response time between D3L instances and Pylon-WTE-NV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  10 20 30 40 50 60 70 80 90 100  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Precision  Pylon-WTE  Pylon-WTE-offline  WTE  Pylon-fastText  Pylon-fastText-offline  fastText  10 20 30 40 50 60 70 80 90 100  k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='0  Recall  Pylon-WTE  Pylon-WTE-offline  WTE  Pylon-fastText  Pylon-fastText-offline  fastText  Figure 10: Top-k precision and recall of 6 embedding  measures on the Pylon dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  fastText  Pylon-fastText  Pylon-fastText-offline  WTE  Pylon-WTE  Pylon-WTE-offline  Model  0  1  2  3  4  Indexing Time (min)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  fastText  Pylon-fastText  Pylon-fastText-offline  WTE  Pylon-WTE  Pylon-WTE-offline  Model  0  5  10  15  20  25  Query Response Time (s / query)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='2  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='7  Figure 11: Indexing time and query response time on the  Pylon dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Alternative Contrastive Loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' While InfoNCE (used in this  project) is a popular and effective loss function, it is not the only  feasible training objective for self-supervised contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  For example, triplet loss [31] considers a triplet (𝑥,𝑥+,𝑥−) as a  training example where 𝑥 is an input, 𝑥+ is a positive sample (be-  longing to the same class as 𝑥 or semantically similar to 𝑥) and  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  Tianji Cong and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Jagadish  𝑥− is a negative sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Additionally, what considers as negative  examples and "hardness" of negative examples are also interesting  perspectives to explore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Verification of Column Union-ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Besides quantitative  evaluation, we also manually inspect results of a few queries for  each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We observe that even in correct table matches, there  are false positives of union-able column candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' To mitigate  this issue, we believe that progress in column semantic type pre-  diction [33, 39] can be beneficial for verifying the union-ability of  columns as a post-processing step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  5  RELATED WORK  Our work is most related to data integration in the Web context  and data discovery over enterprise and Open Data repositories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Web Table Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [4] presents OCTOPUS that integrate rel-  evant data tables from relational sources on the Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' OCTOPUS  includes operators that perform a search-style keyword query over  extracted relations and their context, and cluster results into groups  of union-able tables using column-to-column mean string length  similarity and TF-IDF cosine similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [37] defines three infor-  mation gathering tasks on Web tables: augmentation by attribute  names, augmentation by example, and attribute discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The task  of augmentation by example essentially involves finding union-able  tables that can be used to fill in the missing values in a given table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Their Infogather system leverages indirectly matching tables in  addition to directly matching ones to augment a user input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [10]  formalizes the problem of detecting related Web tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' At the log-  ical level, the work considers two tables related to each other if  they can be viewed as results to queries over the same (possibly  hypothetical) original table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In particular, one type of relatedness  they define is Entity Complement where two tables with coherent  and complementary subject entities can be unioned over the com-  mon attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' This definition requires each table to have a subject  column of entities indicating what the table is about and that the  subject column can be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Following the definition, the work  captures entity consistency and expansion by measuring the relat-  edness of detected sets of entities with signals mined from external  ontology sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Finally, they perform schema mapping of two  complement tables by computing a schema consistency score made  up of the similarity in attribute names, data types, and values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Data Discovery in the Enterprise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [14] identifies data discov-  ery challenges in the enterprise environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The position paper  describes a data discovery system including enrichment primitives  that allow a user to perform entity and schema complement opera-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Building on top of the vision in [14], [13] presents AURUM,  a system that models syntactic relationships between datasets in  a graph data structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' With a two-step process of profiling and  indexing data, AURUM constructs a graph with nodes representing  column signatures and weighted edges indicating the similarity be-  tween two nodes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', content and schema similarity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' By framing  queries as graph traverse problems, AURUM can support varied  discovery needs of a user such as keyword search and similar con-  tent search (which can be used for finding union-able columns  and tables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [15] further employs word embeddings in AURUM to  identify semantically related objects in the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Data Discovery over Open Data Repositories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [27] defines  the table union search problem on open data and decomposes it as  finding union-able attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' They propose three statistical tests to  determine the attribute union-ability: (1) set union-ability measure  based on value overlap;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (2) semantic union-ability measure based  on ontology class overlap;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' and (3) natural language union-ability  measure based on word embeddings, where union-ability is the esti-  mated probability that the text values contained in two columns are  drawn from the same domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' A synthesized benchmark consisting  of original tables from Canadian and UK Open Data shows that nat-  ural language union-ability works best for larger 𝑘 in top-𝑘 search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  In the meantime, set union-ability is decent when 𝑘 = 1 for each  query but vulnerable to value overlap in attributes of non-unionable  tables, and semantic union-ability stays competitive to find some  union-able tables for most queries despite incomplete coverage of  external ontologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' The ensemble of three measures further im-  proves the evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' [1] adopts more types of similarity  measures based on schema- and instance-level fine-grained features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Without relying on any external sources, their D3L framework is  shown effective and efficient on Open Data Lakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' EMBDI [6] pro-  poses a graph model to capture relationships across relational tables  and derives training sequences from random walks over the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  They further take advantage of embedding training algorithms like  fastText to construct embedding models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Their relational embed-  dings demonstrate promising results for data integration tasks such  as schema matching and entity resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  For a broader overview of the literature, we refer readers to the  survey of dataset search [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  6  CONCLUSION  In this work, we present Pylon, a self-supervised contrastive learn-  ing framework for learning semantic column representations from  large collections of tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' We demonstrate that contrastive learning  is a feasible way of learning effective representations for the table  union search problem without relying on labeled data or being  restricted to off-the-shelf embedding models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In comparison with  embedding baselines and the state-of-the-art, we observe that (i)  on the real-world dataset of a data distribution similar to the train-  ing data, our models consistently achieve significant gain in both  effectiveness and efficiency;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' (ii) on the synthetic benchmark of a  different data distribution, our models have marginal performance  improvement while staying more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  We hypothesize that the contrastive learning paradigm can also  benefit other data discovery and table understanding problems that  do not fit into the classification formulation or lack large scale  of labeled data (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=', join-path discovery).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It is also worth noting  that contrastive learning does not contradict supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' It will be  interesting to see if contrastive learning can also enhance existing  supervised learning solutions for entity resolution and many table  understanding tasks such as semantic column type annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  REFERENCES  [1] Alex Bogatu, Alvaro AA Fernandes, Norman W Paton, and Nikolaos Konstantinou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Dataset discovery in data lakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In 2020 IEEE 36th International Conference  on Data Engineering (ICDE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' IEEE, 709–720.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Pylon: Table Union Search through Contrastive Representation Learning  Conference acronym ’XX, June 03–05, 2018, Woodstock, NY  [2] Piotr Bojanowski, Edouard Grave, Armand Joulin, and Tomas Mikolov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Enriching word vectors with subword information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Transactions of the association  for computational linguistics 5 (2017), 135–146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [3] Rajesh Bordawekar and Oded Shmueli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='  In Proceedings of the 2020 ACM SIGMOD International Conference on Management  of Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content=' IEEE,  468–479.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content='cc/paper/9015-pytorch-  an-imperative-style-high-performance-deep-learning-library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Glove:  Global vectors for word representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of the 2014 conference on  empirical methods in natural language processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 1532–1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [31] Florian Schroff, Dmitry Kalenichenko, and James Philbin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Facenet: A  unified embedding for face recognition and clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of the IEEE  conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 815–823.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [32] Fabian M Suchanek, Gjergji Kasneci, and Gerhard Weikum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Yago: a core of  semantic knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of the 16th international conference on World  Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 697–706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [33] Yoshihiko Suhara, Jinfeng Li, Yuliang Li, Dan Zhang, Çağatay Demiralp, Chen  Chen, and Wang-Chiew Tan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Annotating columns with pre-trained lan-  guage models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of the 2022 International Conference on Management  of Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 1493–1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [34] Nan Tang, Ju Fan, Fangyi Li, Jianhong Tu, Xiaoyong Du, Guoliang Li, Sam Madden,  and Mourad Ouzzani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' RPT: relational pre-trained transformer is almost  all you need towards democratizing data preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Proceedings of the VLDB  Endowment 14, 8 (2021), 1254–1261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [35] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones,  Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Attention is all  you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Advances in neural information processing systems 30 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [36] Zhiruo Wang, Haoyu Dong, Ran Jia, Jia Li, Zhiyi Fu, Shi Han, and Dongmei  Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' TUTA: Tree-based Transformers for Generally Structured Table  Pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of the 27th ACM SIGKDD Conference on Knowledge  Discovery & Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 1780–1790.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [37] Mohamed Yakout, Kris Ganjam, Kaushik Chakrabarti, and Surajit Chaudhuri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Infogather: entity augmentation and attribute discovery by holistic match-  ing with web tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In Proceedings of the 2012 ACM SIGMOD International Con-  ference on Management of Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 97–108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  [38] Pengcheng Yin, Graham Neubig, Wen-tau Yih, and Sebastian Riedel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  TaBERT: Pretraining for Joint Understanding of Textual and Tabular Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' In  Proceedings of the 58th Annual Meeting of the Association for Computational Lin-  guistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' 8413–8426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content=' Sato: Contextual Semantic Type Detection in Tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
+page_content='  Proceedings of the VLDB Endowment 13, 11 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/F9E4T4oBgHgl3EQfHQxB/content/2301.04901v1.pdf'}
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+Coupling multi-fluid dynamics equipped with Landau closures to the
+particle-in-cell method
+Rouven Lemmerz,1,2 ★ Mohamad Shalaby,1 † Timon Thomas,1 Christoph Pfrommer1
+1 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
+2 University of Potsdam, Institute of Physics and Astronomy, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany
+Accepted XXX. Received YYY; in original form ZZZ
+ABSTRACT
+The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational
+costs and limits simulations to short physical run-times and often to setups in less than three spatial dimensions. Tradition-
+ally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC
+methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid). Because both methods
+preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-
+conservative multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell’s
+equations. This avoids simplifications typically adopted for Ohm’s Law and enables us to fully resolve the electron temporal
+and spatial scales while retaining the versatility of initializing any number of ion, electron, or neutral species with arbitrary
+velocity distributions. The fluid solver includes closures emulating Landau damping so that we can account for this important
+kinetic process in our fluid species. Our fluid-PIC code is second-order accurate in space and time. The code is successfully
+validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping
+rates of waves in unmagnetized and magnetized plasmas. It also matches growth rates and saturation levels of the gyro-scale and
+intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison
+to linear theory and PIC simulations. This new fluid-SHARP code is specially designed for studying high-energy cosmic rays
+interacting with thermal plasmas over macroscopic timescales.
+Key words: plasmas – hydrodynamics – methods: numerical – cosmic rays
+1 INTRODUCTION
+The PIC method (Dawson 1962; Langdon & Birdsall 1970; Hockney
+1988; Birdsall & Langdon 1991) has become one of the most used
+methods for studying plasmas from laboratory to astrophysical scales.
+Due to its ability to resolve kinetic processes, it became one of the
+most successful research tools in computational plasma physics. Ex-
+amples of that include revolutionizing our understanding of the rich
+physics found in collisionless shocks (Spitkovsky 2008; Marcowith
+et al. 2016), magnetic reconnection (Daughton et al. 2006, 2011;
+Sironi & Spitkovsky 2014), instabilities driven by highly relativis-
+tic electron-positron beams (Bret et al. 2010; Shalaby et al. 2017b;
+Shalaby et al. 2018, 2020), as well as the transport of non-thermal
+particle populations like cosmic rays (Holcomb & Spitkovsky 2019;
+Shalaby et al. 2021). However, the PIC method needs to advance nu-
+merous particles per cell each time step, and thus it is quick to reach
+its computational limit. Even one-dimensional simulations usually
+only capture dynamics on very short physical times and the extent
+to which two or three-dimensional simulations can be performed is
+very limited.
+The time-gap between the inverse of the electron plasma frequency,
+★ E-mail: rlemmerz@aip.de (RL)
+† E-mail: mshalaby@live.ca (MS)
+𝜔−1
+e , (which is necessary to ensure the stability of the PIC algorithm)
+and that of the ion plasma frequency, 𝜔−1
+i , depends on the ion-to-
+electron mass ratio, since 𝜔−1
+i /𝜔−1
+e
+= (𝑚i/𝑚e)1/2, assuming charge
+neutrality, i.e. that the electron and ion densities are equal. There-
+fore, one frequently used trick to increase the computational effi-
+ciency in PIC simulations is to adopt a reduced ion-to-electron mass
+ratio to bridge the gap between the smallest timescale in the simula-
+tion and the larger timescale on which interesting physical processes
+occur/evolve. However, this might lead to artificial suppression of
+physical effects (Bret & Dieckmann 2010; Hong et al. 2012; Moreno
+et al. 2018), including instabilities with excitation conditions that de-
+pend on the mass ratio (Shalaby et al. 2021; Shalaby et al. 2022). This
+shows the need for a more efficient numerical method to complement
+the accurate results achieved by PIC simulations in order to enable
+simulations of realistic physics occurring on longer timescales.
+Fluid codes use a coarse-grained description of the plasma, which
+describes vast amounts of particles with just a few macroscopic pa-
+rameters. This results in a large speed-up in comparison to the PIC
+method, while sacrificing some accuracy by neglecting kinetic ef-
+fects. Hybrid-PIC codes (Lipatov 2002; Gargaté et al. 2007) treat
+electrons as a fluid and ions as particles. With the assumption of
+charge neutrality and the Darwin approximation (i.e. neglecting the
+transverse displacement current), these codes are able to overcome
+some computational barriers while omitting effects on the electron
+© 2022 The Authors
+arXiv:2301.04679v1  [astro-ph.HE]  11 Jan 2023
+
+2
+Lemmerz et al.
+time and length scale. Since this eliminates the need to resolve elec-
+tron scales, the increase in computational efficiency from pure-PIC
+to hybrid-PIC methods is roughly a factor of (𝑚i/𝑚e)1/2 in timescale
+and about the same factor in spatial scales.
+On the other hand, an even more efficient method exists, that com-
+bines a magneto-hydrodynamic (MHD) description of the thermal
+background plasma with PIC methods for the evolution of energetic
+particles such as cosmic rays (Bai et al. 2015; van Marle et al. 2018),
+called MHD-PIC. However, this method inherits the assumptions
+of MHD, in particular, the use of (simplified) Ohm’s law by fully
+neglecting the displacement current, which precludes physics asso-
+ciated with higher-order terms of Ohm’s law as well as the electron
+dynamics.
+To improve upon these shortcomings, we developed a fluid-PIC
+method, where a multi-fluid solver is coupled to the PIC method
+by summing their contributions to the charge and current densities
+used to solve Maxwell’s equations, and the resulting electromag-
+netic fields. Thus, the subsequent dynamics is dictated by fluid and
+PIC species. This enables treating any arbitrary number of species
+in thermal equilibrium by modelling them as separate fluids that
+interact electromagnetically with each other and with particles of
+arbitrary momentum distribution (modelled using the PIC method).
+In contrast to MHD-PIC and hybrid-PIC methods, we do not ex-
+plicitly assume Ohm’s law, and instead, solve Maxwell’s equations
+in a fully self-consistent manner in our fluid-PIC code. Therefore,
+displacement currents are included in our model and fast changes
+in the electric field and electron dynamics are captured. This, in
+turn, allows studying the interaction of high energy particles with
+the background plasma, e.g. to investigate cosmic ray streaming. An-
+other hybrid approach resolving electron timescales fully, but using
+pressure coupling, has been used for simulation of pick-up ions in
+the heliosphere by Burrows et al. (2014).
+Often implicit and semi-implicit methods are utilized for stabil-
+ity and resolution reasons to couple the multi-fluid equations to
+Maxwell’s equations (Hakim et al. 2006; Shumlak et al. 2011; Wang
+et al. 2020). However, this creates an interdependency between all
+fluids and has limited utility when coupled to explicit particles. We
+have developed an explicit multi-fluid solver in which each fluid
+and particle species is agnostic about each other and the coupling is
+achieved via an indirect current-coupling scheme. Because the PIC
+part of the code is the most computationally expensive part of the
+fluid-PIC, hybrid-PIC, and MHD-PIC methods, the computational
+efficiency is mostly determined by the number of particles required
+as well as the smallest time and length scales that need to be resolved.
+Hence, this fluid-PIC approach results in large speed-ups for cosmic
+ray propagation simulations in comparison to traditional hybrid-PIC
+codes, which treat every ion as a particle and need to initialise a
+large number of particles according to the density ratio, as well as in
+comparison to PIC-only simulations. Especially studying comic ray
+propagation in the interstellar medium (ISM), where the typical cos-
+mic ray density is of the order 10−9 times the ISM number density,
+is challenging. Since the fluid-PIC algorithm is faster by orders of
+magnitude in comparison to PIC in such a case, we can reach further
+into the realistic parameter regime without sacrificing some essential
+microphysics.
+One of the most important kinetic effects is arguably Landau
+damping. The fluid description can emulate this effect using Landau
+closures (Hammett & Perkins 1990; Umansky et al. 2015; Hunana
+et al. 2019), which necessitates the computation of the heat flux in
+Fourier space. While Fourier transforms in 1D are not easily par-
+allelizable, this bottleneck can partially be mitigated by performing
+global communications of the message-passing interface (MPI) in
+the background while processing the high computational load (e.g.
+resulting from evolving orbits of PIC particles) in the foreground.
+Simulations with periodic boundary conditions are currently han-
+dled by convolution with a finite-impulse-response (FIR) filter in our
+code, but other options are available in the literature (Dimits et al.
+2014; Wang et al. 2019). A number of simplifying local approxi-
+mations exist as well (Wang et al. 2015; Allmann-Rahn et al. 2018;
+Ng et al. 2020), which scale computationally well but become inac-
+curate for studying some multiscale plasma physics problems. Our
+code implements these different approaches so that an appropriate
+one can be chosen, dependent on the requirements of a simulation.
+Our implementation is massively parallelized and can be efficiently
+run on thousands of cores.
+Furthermore, the fluid-PIC method allows for any multi-fluid
+setup. As such, this framework allows for some straightforward ex-
+tensions. Potentially, this involves a setup with actively participating
+neutrals to incorporate ion-neutral damping into this method. To this
+end, the coupling between different fluids needs to be extended by a
+collision term, which is left as a future extension to the code.
+The outline of this paper is as follows. In Section 2, we introduce
+the pillars of this method and describe the PIC method, the fluid
+solver, how we couple both methods by means of electromagnetic
+fields, and describe various implementations of the Landau closure.
+In Section 3, we show validation tests of the fluid solver (shock tube
+tests), linear waves in an ion-electron plasma, and the damping rate
+of Langmuir waves in a single-electron fluid with Landau closures.
+We then investigate the non-linear effects of two interacting Alfvén
+waves as well as cosmic-ray-driven instabilities, where fluid-PIC and
+PIC results are compared. We conclude in Section 4. Throughout this
+work, we use the SI system of units.
+2 NUMERICAL METHOD
+After a review of the kinetic description of a plasma in Section 2.1,
+we briefly introduce our PIC method in Section 2.2. The fluid de-
+scription for plasmas and its assumptions are given in Section 2.3.
+The finite volume scheme we use to numerically solve the compress-
+ible Euler equations is described in Section 2.4, while the electro-
+magnetic interactions of the fluid are described in Section 2.5. In
+Section 2.6, we describe the Landau closure we adopt in order to
+mimic the Landau damping in kinetic thermal plasmas within the
+fluid description, and detail its implementation in our code. We close
+this section by describing the overall code structure of the fluid-PIC
+algorithm and finally discuss the interaction between the modules
+via the current-coupling scheme (Section 2.7).
+2.1 Kinetic description of a plasma
+The kinetic description of a collisionless relativistic plasma with
+particles of species s with elementary mass, 𝑚s, and elementary
+charge, 𝑞s, is given by the Vlasov equation,
+𝜕 𝑓s
+𝜕𝑡 + u
+𝛾 · ∇ 𝑓s + as · ∇𝑢 𝑓s = 0,
+(1)
+where 𝑓s = 𝑓s(x, 𝒗, 𝑡) is the distribution function, u = 𝛾𝒗 is the
+spatial component of the four-velocity with the Lorentz factor 𝛾 =
+[1 + (𝒗/𝑐)2]−1/2, and 𝑐 is the light speed. The acceleration due to
+the Lorentz force is given by
+as = 𝑞s
+𝑚s
+[E (x, 𝑡) + 𝒗 × B (x, 𝑡)] ,
+(2)
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+3
+where E (x, 𝑡) and B (x, 𝑡) are the electric and magnetic fields, re-
+spectively. The evolution of electric and magnetic fields is governed
+by Maxwell’s equations:
+𝜕B
+𝜕𝑡 = −∇ × E,
+∇ · B = 0,
+(3)
+𝜕E
+𝜕𝑡 = 𝑐2∇ × B − J
+𝜀0
+,
+∇ · E = 𝜌
+𝜀0
+,
+(4)
+where 𝑐 = 1/√𝜀0𝜇0 is the vacuum speed of light, and 𝜀0 and 𝜇0 are
+the permittivity and the permeability of free space, respectively. The
+evolution of the electro-magnetic fields is influenced by the charge
+density, 𝜌, and current density, J. They are given by the charge-
+weighted sum over all species of the number densities 𝑛s and bulk
+velocities 𝒘s respectively,
+𝜌 (x, 𝑡) =
+∑︁
+𝑠
+𝑞𝑠𝑛𝑠 (x, 𝑡)
+=
+∑︁
+𝑠
+𝑞𝑠
+∫
+𝑓𝑠 (x, 𝒗, 𝑡) d3𝑣,
+(5)
+J (x, 𝑡) =
+∑︁
+𝑠
+𝑞𝑠𝑛𝑠 (x, 𝑡) 𝒘𝑠 (x, 𝑡) =
+∑︁
+𝑠
+𝑞𝑠
+∫
+𝒗 𝑓𝑠 (x, 𝒗, 𝑡) d3𝑣.
+(6)
+2.2 The particle-in-cell method
+We use the PIC method to solve for the evolution of plasma species
+that are modelled with the kinetic description. The PIC method ini-
+tializes a number of computational macroparticles to approximate
+the distribution function in a Lagrangian fashion. Each macroparticle
+represents multiple physical particles and, as such, each macroparti-
+cle has a shape in position space which can be represented by a spline
+function. By depositing the particle motions and positions to the nu-
+merical grid (or computational cells), the electromagnetic fields can
+be computed. This step is followed by a back-interpolation of these
+fields to the particle positions so that the Lorentz forces on the par-
+ticles can be computed. In our implementation, these equations are
+solved using one spatial dimension and three velocity dimensions
+(1D3V), i.e. ∇ = (𝜕/𝜕𝑥, 0, 0)T.
+The code quantities are defined as multiples of the fiducial units
+given for time, fields (electric and magnetic), charge, current density
+and length
+𝑡0 =
+√︃
+𝑚0𝜖0/(𝑞2
+0𝑛0),
+𝐸0 =
+√︃
+𝑛0𝑚0𝑐2/𝜖0,
+𝜌0 = 𝑞0𝑛0,
+𝐽0 = 𝜌0𝑐,
+𝑥0 = 𝑐𝑡0.
+(7)
+This enables us to select a fixed time step of
+Δ𝑡 = 𝐶cfl𝑐Δ𝑥
+(8)
+where 𝐶cfl < 0.5 to satisfy the Courant-Friedrichs-Lewy (CFL) con-
+dition. The value of the reference density 𝑛0 is chosen such that the
+code timescale, 𝑡0, obeys 𝜔−2
+p
+= 𝑡2
+0. The total plasma frequency is
+𝜔p = (�
+𝑠 𝜔2𝑠)1/2, and related to the plasma frequencies of the in-
+dividual species, 𝜔2s = 𝑞2s 𝑛s/(𝑚𝑠𝜖0). We define the discretized time
+𝑡𝑘 = 𝑘Δ𝑡, position 𝑥𝑖 = 𝑖Δ𝑥 and quantities at discrete position and
+times as E𝑘
+𝑖 = E(𝑡𝑘, 𝑥𝑖). For details on the PIC code SHARP, the
+reader is referred to Shalaby et al. (2017a, 2021). Here, we focus
+on describing how SHARP is extended to include fluid treatment of
+some plasma species.
+2.3 Fluid description of plasma
+A straightforward way of coarse graining the Vlasov equation (1) is
+to reduce its dimensionality. By taking the 𝑗-th moment over velocity
+space, i.e.
+∫
+𝒗 𝑗 𝑓 𝑑3𝑣, we retrieve the fluid quantities and reduce the
+dimensionality of the 1D3V kinetic description to 1D. The number
+density 𝑛s and the bulk velocity 𝒘s are defined through the zeroth
+and first moment of the distribution function, respectively, while the
+total energy density per unit mass 𝜖𝑠 and the scalar pressure per unit
+mass 𝑝𝑠 are related to the second moment (Wang et al. 2015):
+𝑛s (x, 𝑡) =
+∫
+𝑓s (x, 𝒗, 𝑡) d3𝑣,
+(9)
+𝒘s (x, 𝑡) =
+∫
+1
+𝑛s (x, 𝑡) 𝒗 𝑓s (x, 𝒗, 𝑡) d3𝑣,
+(10)
+𝜖s (x, 𝑡) =
+∫
+1
+2𝒗2 𝑓s (x, 𝒗, 𝑡) d3𝑣,
+(11)
+𝑝s (x, 𝑡) =
+∫
+(𝑣𝑥 − 𝑤s,𝑥)2 𝑓s (x, 𝒗, 𝑡) d3𝑣
+= Γ − 1
+2
+∫
+(𝒗 − 𝒘s)2 𝑓s (x, 𝒗, 𝑡) d3𝑣.
+(12)
+Here, the pressure tensor is under the adiabatic assumption and the
+degrees of freedom are encoded in the adiabatic index Γ. The follow-
+ing relation is found from the definitions
+𝜖s =
+𝑝s
+Γ − 1 + 1
+2 𝑛s 𝒘s · 𝒘s.
+(13)
+The first three moments of the of the Vlasov equation are called
+the continuity, momentum, and energy conservation equations. A set
+of these equations is found for each fluid species, but the subscript s
+is neglected here for simplicity:
+𝜕𝑛
+𝜕𝑡 + ∇ · (𝑛𝒘) = 0,
+(14)
+𝜕𝑛𝒘
+𝜕𝑡
++ ∇ · [𝑝1 + 𝑛𝒘𝒘] = 𝑞
+𝑚 S𝑤 (𝑛, 𝒘, B, E) ,
+(15)
+𝜕𝜖
+𝜕𝑡 + ∇ · [(𝑝 + 𝜖)𝒘] +
+1
+Γ − 1∇ · Q = 𝑞
+𝑚 𝒘 · S𝑤 (𝑛, 𝒘, B, E) .
+(16)
+We assumed the non-relativistic limit and an isotropic pressure tensor
+with vanishing non-diagonal components, i.e. the inviscid limit. The
+notation 𝒘𝒘 indicates the dyadic product of the two vectors and 1
+is the unit matrix. Similar to the definition of the scalar pressure in
+equation (12) we use a definition of the heat flux vector, which is
+normalized to the degrees of freedom as well
+Q (x, 𝑡) = Γ − 1
+2
+∫
+(𝒗 − 𝒘)2 (𝒗 − 𝒘) 𝑓 (x, 𝒗, 𝑡) d3𝑣.
+(17)
+The electromagnetic source term is given by
+S𝑤 (𝑛, 𝒘, B, E) = 𝑛 (E + 𝒘 × B) .
+(18)
+The general form of the fluid equations can be written as
+𝜕 ˜U
+𝜕𝑡 + ∇ · F( ˜U) = S( ˜U),
+(19)
+where ˜U = ˜U(x, 𝑡) = (𝑛, 𝑛𝒘, 𝜖)T is the fluid state vector at position
+(x, 𝑡), F is the flux matrix, and S is the source vector.
+Numerically, the complexity of solving equation (19) can be re-
+duced by splitting the operator into less complex sub-operators using
+Strang operator splitting (Strang 1968; Hakim et al. 2006). This
+enables us to use the most appropriate solver for each subsystem
+sequentially. We split the fluid update into three parts; the flux F
+excluding the heat flux (see Section 2.4), the electromagnetic source
+Sem = S𝑤𝑞/𝑚 (see Section 2.5.1), and the heat flux Q (see Sec-
+tion 2.6). For commuting operators exp(Δ𝑡Q) and exp(Δ𝑡Sem) a
+second order accurate Strang splitting is obtained as
+U𝑛+ 1
+2 = e
+Δ𝑡
+2 FeΔ𝑡QeΔ𝑡Seme
+Δ𝑡
+2 FU𝑛− 1
+2 + 𝑂(Δ𝑡3).
+(20)
+MNRAS 000, 1–17 (2022)
+
+4
+Lemmerz et al.
+Since Q and S act independently1 on the entries 𝑝 and 𝒘 respectively,
+the order of applying them can be varied and they need to be evaluated
+only once.
+2.4 Finite volume scheme
+The 1D3V fluid equations are solved using a finite volume method,
+where the fluid equations are averaged over the cell volume, which
+is an interval of length Δ𝑥 in 1D,
+U𝑖 (𝑡) = 1
+Δ𝑥
+∫ 𝑥𝑖+ 1
+2
+𝑥𝑖− 1
+2
+˜U (𝑥, 𝑡) d𝑥.
+(21)
+This enables us to correctly conserve the overall fluid mass, fluid
+momentum and fluid energy, even in the presence of large gradients,
+by utilizing Gauss’ theorem:
+1
+Δ𝑥
+∫ 𝑥𝑖+ 1
+2
+𝑥𝑖− 1
+2
+𝜕F( ˜U)
+𝜕𝑥
+d𝑥 = 1
+Δ𝑥
+�
+F𝑖+ 1
+2 − F𝑖− 1
+2
+�
+(22)
+where the flux through an interface at 𝑥𝑖 is F𝑖 (𝑡) = F[ ˜U(𝑥𝑖, 𝑡)],
+leading to the update equation
+𝜕U𝑖(𝑡)
+𝜕𝑡
+= 1
+Δ𝑥
+�
+−F𝑖+ 1
+2 + F𝑖− 1
+2 +
+∫
+S� ˜U(𝑥, 𝑡)�d𝑥
+�
+.
+(23)
+Integrating equation (23) in time is achieved by using second, third, or
+fourth-order Runge-Kutte methods (Butcher 2016). In contrast to the
+finite difference scheme used for electromagnetic fields and particles,
+where electromagnetic quantities are point values, fluid quantities
+discretized with the finite volume method are cell averages. This is
+useful, because the finite difference method does not guarantee the
+conservation of the conservation equations (14) through (16), which
+are governing the fluid; while on the other hand using the finite
+volume method for the electromagnetic fields needs additional steps
+to satisfy the constraint ∇ · B = 0. Hybridization of both schemes
+to combine the advantages of each has been used before in other
+contexts, i.e. Soares Frazao & Zech (2002).
+The maximum time step in the 1D3V Euler equations, which al-
+lows for stable simulations, is Δ𝑡 < 𝐶cflΔ𝑥×(|𝑤|+𝑐s), with the speed
+of sound 𝑐s = (Γ𝑝/𝑛)1/2. For all realistic setups these velocities are
+limited naturally by the speed of light, |𝑤| < 𝑐 and 𝑐s < 𝑐, and
+this condition is automatically fulfilled by the time step criterion in
+equation (8). In practice, only equation (8) together with a suitable
+Courant number of 𝐶cfl ⩽ 0.5 is used to determine the time step of
+the simulation.
+2.4.1 Reconstruction
+To approximate the flux at interfaces, we need to reconstruct the
+fluid state at cell interfaces. The accuracy of the reconstruction has a
+crucial influence on the diffusivity. A lower-order reconstruction can
+lead to excessive damping of waves, which might suppress relevant
+physical effects on longer timescales.
+For reconstructing the point value ˜U(𝑥𝑖+1/2, 𝑡), which is needed
+to compute F𝑖+1/2, we employ a central weighted essentially non-
+oscillatory reconstruction (C-WENO) scheme of spatial order five.
+The reconstruction computes two point values at each interface
+1 In practice the formulation of Q might partially depend on 𝒘. In this case,
+Strang splitting is performed on this part of the operator Q as well, see
+equation (43).
+𝑥𝑖+1/2, an interpolation from the left- and right-hand side. We re-
+construct the primitive variables 𝑛, 𝒘, and 𝑝 individually.
+Our implementation of the C-WENO method is based on the 5th
+order scheme presented in Capdeville (2008). An introduction to
+the topic can be found in Cravero et al. (2018b). The C-WENO
+reconstruction uses a convex combination of multiple low-order re-
+construction polynomials to achieve high-order interpolations of the
+interface values while it employs a non-linear limiter to degrade this
+high-order interpolation to a lower order if the reconstructed quantity
+contains discontinuities. The fifth-order C-WENO uses three third-
+order polynomials 𝑃L(𝑥), 𝑃C(𝑥), 𝑃R(𝑥) for each cell 𝑖 to interpolate
+the four adjacent cells in the following way:
+𝑃L(𝑥)
+interpolates values at
+𝑖 − 2
+𝑖 − 1
+𝑖
+𝑃C(𝑥)
+interpolates values at
+𝑖 − 1
+𝑖
+𝑖 + 1
+𝑃R(𝑥)
+interpolates values at
+𝑖
+𝑖 + 1
+𝑖 + 2
+while the optimal fifth-order polynomial interpolates all of them:
+𝑃opt(𝑥)
+interpolates values at
+𝑖 − 2
+𝑖 − 1
+𝑖
+𝑖 + 1
+𝑖 + 2.
+We define an additional polynomial
+𝑃0(𝑥) = 1
+𝑑0
+������
+𝑃opt(𝑥) −
+∑︁
+𝑞∈[L,C,R]
+𝑑𝑞𝑃𝑞(𝑥)
+������
+,
+(24)
+where 𝑑0 + 𝑑L + 𝑑C + 𝑑R = 1. The polynomials 𝑃0, 𝑃L, 𝑃C, and 𝑃R
+are a convex representation of the 𝑃opt polynomial. We use 𝑑0 = 3/4,
+𝑑C = 2/16, and 𝑑L = 𝑑R = 1/16.
+In general, we would like to use the reconstruction provided by
+the 𝑃opt polynomial as frequently as possible because of its high-
+order nature. But this high-order reconstruction can cause oscillations
+similar to the Gibbs phenomenon at discontinuities. Therefore, we
+need to employ a limiting strategy to avoid such behaviour. In order
+to accomplish this, we re-weight all of our 𝑑-coefficients by taking
+the smoothness of the associated polynomial into account (Jiang &
+Shu 1996). We define
+𝛼𝑞 = 𝑑𝑞
+������
+1 +
+�
+𝜏
+IS[𝑃𝑞] + 10−9Δ𝑥
+�2������
+for 𝑞 ∈ [0, L, C, R],
+(25)
+where 𝜏 is a measure for the overall smoothness of the reconstructed
+variables, and IS[𝑃𝑞] defines a smoothness indicator of the low-order
+polynomials. Because the formulae for these smoothness indicators
+are quite cumbersome, we list them in Appendix A. These coefficients
+define a new set of normalized weights given by
+𝑤𝑞 =
+𝛼𝑞
+𝛼0 + 𝛼L + 𝛼C + 𝛼R
+for 𝑞 ∈ [0, L, C, R].
+(26)
+The final reconstructed polynomial is then given by the convex com-
+bination of the low-order polynomials using this set of normalized
+weights:
+𝑃rec(𝑥) = 𝑤0𝑃0(𝑥) + 𝑤L𝑃L(𝑥) + 𝑤C𝑃C(𝑥) + 𝑤R𝑃R(𝑥),
+(27)
+which we evaluate at the cell interfaces to calculate the required left-
+and right-handed interface values for the Riemann solver. We detail
+how these polynomials are evaluated in Appendix A.
+The smoothness indicators IS[𝑃𝑞] vanish if the underlying poly-
+nomials are smooth. In this case, the re-weighted coefficients reduce
+to their original value 𝛼𝑞 → 𝑑𝑞 and the reconstructed polynomial
+reduces to the optimal polynomial 𝑃rec(𝑥) → 𝑃opt(𝑥).
+2.4.2 Riemann solver
+The previous reconstruction step determines two, potentially differ-
+ent, values ˜UL and ˜UR for each quantity to the left and right of every
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+5
+interface, thereby providing the initial conditions for the Riemann
+problem:
+𝜕U
+𝜕𝑡 = −∇ · F( ˜U)
+(28)
+˜U(𝑥, 0) =
+� ˜UL,
+𝑥 < 0
+˜UR,
+𝑥 > 0
+(29)
+An (approximate) Riemann solver is employed to compute the nu-
+merical flux F( ˜U). While a number of different families of Riemann
+solvers have been developed with individual strengths and weak-
+nesses, we have decided to implement multiple solvers which can be
+changed on demand. Implemented solvers in fluid-SHARP include a
+Roe solver with entropy fix (Roe 1981; Harten & Hyman 1983) and
+an HLLC solver (Toro et al. 1994). While the Roe solver yields more
+accurate solutions and fewer overshoots in our tests in comparison
+to the HLLC solver, it becomes unstable in near vacuum flows and
+strong expansion shock waves. Even though differences between the
+solvers are easily visible in some shock setups and artificially ex-
+treme conditions, they are typically negligible in most applications
+common for thermal plasmas. We opt to employ the HLLC solver as
+our standard for stability purposes and use the Roe solver in cases
+where stronger shocks with overshoots are expected.
+2.5 Electromagnetic interaction with charged fluids
+In this section, we first introduce the Lorentz force as a source term
+in equation (15). Furthermore, we describe how the fluid influences
+the electromagnetic fields. With these two additional parts, the de-
+scription from an uncharged gas in Section 2.4 is expanded here to
+include plasmas.
+2.5.1 Treatment of electromagnetic source term
+Instead of integrating the energy equation (16), which would re-
+quire evaluating the source term on the right-hand side, we compute
+the time evolution of the primitive pressure variable, for which the
+electromagnetic source term conveniently vanishes:
+𝜕𝑝
+𝜕𝑡 + Γ𝑝∇ · 𝒘 + 𝒘 · ∇𝑝 + ∇ · Q = 0.
+(30)
+Then only the computation of the source term for the momentum
+equation (15) is left, which uses the Boris integrator (Boris et al.
+1970) to account for the Lorentz force on the fluid momentum vec-
+tors. Up until now we have only applied the C-WENO method for
+conservation laws, however, by adding the source term, we are left
+with a balance law. In C-WENO formulations for balance laws it
+is customary to approximate the integral of the source term (equa-
+tion 23) numerically to higher orders as well (Cravero et al. 2018a).
+We use Simpson’s Formula for approximating equation (23)
+∫ 𝑥𝑖+1/2
+𝑥𝑖−1/2
+S � ˜U� d𝑥 = 1
+6
+�
+S( ˜U𝑖− 1
+2 ) + 4S( ˜U𝑖) + S( ˜U𝑖+ 1
+2 )
+�
++ O(Δ𝑥5),
+(31)
+where the intra-cell values ˜U𝑖±1/2 are interpolated by the same C-
+WENO scheme as used for solving the hydrodynamical equations,
+and the centre-value is computed self-consistently with the numerical
+integration formula, i.e. ˜U𝑖 = (6U𝑖 − ˜U𝑖+1/2 − ˜U𝑖−1/2)/4. We also
+need to interpolate the electromagnetic field values to a comparable
+spatial order. This is achieved by performing finite-difference inter-
+polations for each component from the Yee mesh discretized fields,
+that is
+𝐸𝑖+ 1
+2 = 150(𝐸𝑖 + 𝐸𝑖+1) − 25(𝐸𝑖−1 + 𝐸𝑖+2) + 3(𝐸𝑖−2 + 𝐸𝑖+3)
+256
++ O(Δ𝑥6),
+(32)
+and temporal order, 𝐵𝑛 = (𝐵𝑛+1/2 + 𝐵𝑛−1/2)/2, again, for each
+component necessary. Lower order approximations produce, in our
+tests, similar results, but converge to slightly lower wave frequencies
+when compared with the analytical solution of the dispersion relation.
+2.5.2 Deposition of charges
+Equations (4) govern the electric field evolution, where Faraday’s or
+Gauss’ law might be used to compute E. In this section we focus on
+the one-dimensional setup without particle contributions, which are
+explained in Section 2.7. The perpendicular components’ update, 𝐸𝑦
+and 𝐸𝑧, is received straightforwardly by discretizing Faraday’s Law
+�𝐸𝑦
+�𝑛+1
+𝑖+ 1
+2 = �𝐸𝑦
+�𝑛
+𝑖+ 1
+2 −
+∑︁
+𝑠
+Δ𝑡
+𝜖0
+𝑞𝑠
+�𝑛𝑤𝑦
+�𝑛+ 1
+2
+𝑖+ 1
+2 ,𝑠
+− 𝑐2Δ𝑡
+Δ𝑥
+�
+(𝐵𝑧)𝑛+ 1
+2
+𝑖+1 − (𝐵𝑧)𝑛+ 1
+2
+𝑖
+�
+(33)
+(𝐸𝑧)𝑛+1
+𝑖+ 1
+2
+= (𝐸𝑧)𝑛
+𝑖+ 1
+2
+−
+∑︁
+𝑠
+Δ𝑡
+𝜖0
+𝑞𝑠 (𝑛𝑤𝑧)𝑛+ 1
+2
+𝑖+ 1
+2 ,𝑠
++ 𝑐2Δ𝑡
+Δ𝑥
+��𝐵𝑦
+�𝑛+ 1
+2
+𝑖+1 − �𝐵𝑦
+�𝑛+ 1
+2
+𝑖
+�
+,
+(34)
+where the sum is taken over all fluid species s and 𝑛𝒘 are components
+of the fluid vector U.
+For the 𝐸𝑥 component in spatial direction however, in order to
+enforce charge-conservation, Gauss’ law in discretized form needs
+to be enforced for all 𝑖 ⩾ 1 as well
+(𝐸𝑥)𝑛
+𝑖 = (𝐸𝑥)𝑛
+0 +
+∑︁
+𝑠
+𝑞𝑠
+𝜖0
+𝑖−1
+∑︁
+𝑗=0
+𝑛𝑛
+𝑗+ 1
+2 ,𝑠Δ𝑥
+= (𝐸𝑥)𝑛
+0 +
+∑︁
+𝑠
+𝑞𝑠
+𝜖0
+∫ 𝑥𝑖
+𝑥0
+˜𝑛𝑛
+𝑠 d𝑥,
+(35)
+where the second equality uses the definition of cell averages in the
+finite volume scheme (see equation 21) and shows, that this numeri-
+cal formula is exact. Another formula for updating (𝐸𝑥)0 to the time
+step 𝑛 is still needed. In the analytical case Gauss’ law in combina-
+tion with the density conservation equation (14) for the analytical
+flux (or cell values) 𝐽𝑥 ∝ 𝑞𝑛𝑤𝑥 can be shown to be equivalent to
+Faraday’s law; in the numerical case this equivalency is shown using
+the discretized conservation equation and corresponding numerical
+flux 𝐽𝑥 ∝ 𝑞𝐹𝑛( ˜U) ≃ 𝑞𝑛𝑤𝑥 for the current density 𝐽𝑥. Taking the
+time derivative of equation (35) in conjunction with the discretized
+density update equation (23) leads to the expression
+(𝐸𝑥)𝑛+1
+𝑖
+− (𝐸𝑥)𝑛
+𝑖
+Δ𝑡
++
+(𝐸𝑥)𝑛+1
+0
+− (𝐸𝑥)𝑛
+0
+Δ𝑡
+=
+∑︁
+𝑠
+𝑞𝑠
+𝜖0Δ𝑡
+∫ 𝑡𝑛+1
+𝑡𝑛
+�
+−(𝐹𝑛,𝑠)𝑖 + (𝐹𝑛,𝑠)0
+�
+d𝑡.
+(36)
+The integration in time using Runge-Kutta methods is the same as
+used to solve equation (23). Faraday’s law using fluxes in one spatial
+dimension is then given by
+(𝐸𝑥)𝑛+1
+𝑖
+= (𝐸𝑥)𝑛
+𝑖 −
+∑︁
+𝑠
+𝑞𝑠
+𝜖0
+∫ 𝑡𝑛+1
+𝑡𝑛
+�
+𝐹𝑛
+� ˜U��
+𝑖,𝑠 d𝑡,
+(37)
+MNRAS 000, 1–17 (2022)
+
+6
+Lemmerz et al.
+and enables us to identify 𝐽𝑥 by comparison to the charge conserva-
+tion equation (equation 14 multiplied by 𝑞s)
+(𝐽𝑥)𝑛+1/2
+𝑖
+=
+∑︁
+𝑠
+𝑞𝑠
+Δ𝑡
+∫ 𝑡𝑛+1
+𝑡𝑛
+�
+𝐹𝑛
+� ˜U��
+𝑖,𝑠 d𝑡.
+(38)
+Note, that the numerical flux also includes numerical diffusion and is
+directly related to changes in 𝜌. Due to this, other formulations for 𝐽𝑥
+violate the charge conservation equation and can lead to numerical
+instabilities.
+2.5.3 Magnetic field evolution
+Because the fluid evolution influences the magnetic field only in-
+directly, the finite-difference time-domain (FDTD) update for the
+magnetic field is unchanged from the previous SHARP code. For
+completeness we reproduce the formulae here (Shalaby et al. 2021)
+(𝐵𝑦)𝑛+ 1
+2
+𝑖
+= (𝐵𝑦)𝑛− 1
+2
+𝑖
++ Δ𝑡
+Δ𝑥
+�
+(𝐸𝑧)𝑛
+𝑖+ 1
+2
+− (𝐸𝑧)𝑛
+𝑖− 1
+2
+�
+,
+(39)
+(𝐵𝑧)𝑛+ 1
+2
+𝑖
+= (𝐵𝑧)𝑛− 1
+2
+𝑖
+− Δ𝑡
+Δ𝑥
+�
+(𝐸𝑧)𝑛
+𝑖+ 1
+2
+− (𝐸𝑦)𝑛
+𝑖− 1
+2
+�
+.
+(40)
+𝐵𝑥 is constant in the 1D3V model because of the requirement ∇·B =
+0.
+2.6 Landau closure for fluid species
+The highest retained fluid moment, which is in our case the specific
+heat flux Q, is not evolved in our set of equations. Instead, we need
+to estimate its value dynamically using an appropriate closure. The
+simple ideal gas closure sets Q = 0, which, however, prevents the
+energy dissipation of plasma waves. One important mechanism of
+such a dissipation is the collisionless damping of electrostatic waves
+achieved through Landau damping. Landau damping is a microphys-
+ical kinetic wave-particle interaction, where particles resonate with
+the wave exchange energy as a function of time. In essence, the reso-
+nant particles accelerate or decelerate to approach the wave’s phase
+velocity, thereby picking up energy or releasing it, respectively. For
+Maxwellian phase space distributions, there are more particles at ve-
+locities smaller than the phase velocity, which yields a net damping,
+i.e., energy loss of the wave (Boyd & Sanderson 2003).
+Various attempts, e.g. by Hammett & Perkins (1990), were carried
+out to approximate the heat flux Q of an almost Maxwellian dis-
+tributed plasma, such that the kinetic phenomenon of Landau damp-
+ing is mimicked in the linearized fluid equations. Landau damping is
+a non-isotropic effect, which can be reflected in the fluid descriptions.
+Accounting for the gyrotropy of the system around the magnetic field,
+often the double-adiabatic law with two adiabatic coefficients parallel
+and perpendicular to the magnetic field is presupposed (Hunana et al.
+2019). For now, we restrict our algorithm to isotropic pressures with
+only one common adiabatic coefficient for parallel and perpendicular
+pressure and leave this possibility of modelling anisotropic double-
+adiabatic systems open for future extensions of our algorithm. In our
+simplified model, we denote an isotropized pressure tensor with the
+adiabatic coefficient Γ = 5/3, instantly isotropizing all heating oc-
+curring due to the heat flux closure, while Γ = 3 denotes a negligible
+pressure in the 𝑦 and 𝑧-direction. Hence, we define only the perturbed
+scalar heat flux parallel to the magnetic field line 𝑄 = 𝑄 ∥ and no
+perpendicular heat flux.
+Here, we will introduce two different formulae for heat flux clo-
+sures. The first and most popular collisionless electrostatic closure
+was proposed by Hammett & Perkins (1990). We refer to it as the
+𝑅32 closure2 throughout this paper, and it approximates the heat flux
+at a fixed Γ = 3, in Fourier space, by
+ˆ𝑄 = −i sign (𝑘) 2
+√π
+√︁
+2𝜃0𝑐𝑛0𝑘B
+ˆ𝑇
+𝑚 ≡ ˆ𝑄𝑇 .
+(41)
+Here, hats are used to denote quantities in Fourier space along
+the magnetic field line, i.e. ˆ𝑄 = F∥(𝑄), and the subscript 0 refers
+to simulation box averages, that is 𝑛0 = �𝑁c
+𝑖=0 𝑛𝑖/𝑁c is an average
+over all 𝑁c cells. Furthermore 𝑘B is the Boltzmann-constant, and
+𝑘B ˆ𝑇 = (𝑚 ˆ𝑝 − 𝑘B𝑇0 ˆ𝑛) /𝑛0. Since the plasma average or equilibrium
+temperature evolves slowly as a function of time, we adjust the back-
+ground temperature 𝑇0 after every time step to synchronize it with
+the mean pressure, 𝑘B𝑇0(𝑡)/𝑚 = 𝑝0(𝑡)/𝑛0, while the density con-
+servation ensures that 𝑛0 stays constant. Note also, that 𝑄0 = 0. The
+dimensionless mass-normalized temperature is 𝜃0 = 𝑘B𝑇0/(𝑚𝑐2).
+A more recent approximation was proposed by Hunana et al.
+(2018), who restricts this closure to Γ = 3 only, for reasons men-
+tioned already. We use an ad hoc formulation of their closure with a
+variable Γ, thereby allowing our simplified model to be used. We re-
+fer to this closure as 𝑅31 and it approximates the heat flux, in Fourier
+space, by
+ˆ𝑄 =
+�
+4
+4 − π − Γ
+�
+𝑝0 ˆ𝑤
+������������������������������������
+ˆ𝑄𝑤
++
+�
+−i sign (𝑘)
+√︁
+2π𝜃0
+4 − π 𝑐𝑛0
+𝑘B ˆ𝑇
+𝑚
+�
+����������������������������������������������������������������������
+ˆ𝑄𝑇
+.
+(42)
+In comparison to the 𝑅32 closure, this closure has an additional
+dependence on the perturbed bulk velocity ˆ𝑤. This effectively in-
+creases the speed of sound obtained from the non-electromagnetic
+fluid equations and allows retrieving the correct damping rate with
+our ad-hoc assumption of variable Γ, see Appendix C. For Γ = 3,
+we retrieve the coefficient for ˆ𝑤 from the aforementioned literature
+4
+4−π − 3 = 3π−8
+4−π .
+In only one spatial dimension, as assumed in our code, the global
+integration along a magnetic field line is approximated to be along
+the spatial direction, i.e. F∥ = F𝑥. An extension to multiple spatial
+dimensions with an anisotropic pressure tensor is not straightforward
+because in this case, this approach can lead to spurious instabilities
+(Passot et al. 2014) and the integration would need to be carried out
+along magnetic field lines.
+A kinetic code does not need global communication to accurately
+reproduce Landau damping, since each particle (or particle bin)
+tracks its own interaction with each wave mode as a function of time
+and accumulates this information in the particle velocity. However,
+after integrating out the individual particle velocities when build-
+ing the evolution equations for the phase-space distribution function,
+i.e. equations (14)-(16), information about the individual particle-
+wave interaction is no longer collected. Because some information
+about this interaction is also contained in the wave, such non-local
+information can be used to approximate the gradient of the physical
+heat flux, i.e., a closure of the fluid moments that incorporates such
+missing information. This non-local information is approximated in
+equations (41) and (42), and is manifested by the term i sign (𝑘) in
+Fourier space, which is also referred to as the Hilbert transform.
+Numerically, we do not include the heat flux in the Riemann solver
+used to compute the fluid fluxes. Instead, we compute the spatial
+derivative of the heat flux ∇∥ · Q separately. We use Strang splitting
+2 The name 𝑅𝑚𝑛 is used to denote that the kinetic plasma response function
+𝑅 is mimicked for this closure by a Padé approximant with polynomials
+𝑃𝑚/𝑄𝑛 of order 𝑚 and 𝑛.
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+7
+for the 𝒘 dependent part Q𝑤 and the temperature dependent part Q𝑇
+to expand equation (20) into
+U𝑛+ 1
+2 = e
+Δ𝑡
+2 Fe
+Δ𝑡
+2 Q𝑤eΔ𝑡Q𝑇 eΔ𝑡Seme
+Δ𝑡
+2 Q𝑤e
+Δ𝑡
+2 FU𝑛− 1
+2 + 𝑂(Δ𝑡3),
+(43)
+such that only one non-global evaluation of Q𝑇 is needed. Using
+Heun’s method together with the fast Fourier transform (FFT) the
+update formulae for the pressure w.r.t. operators Q𝑤 and Q𝑇 are
+respectively
+𝑝𝑛+1���𝑄𝑤
+= eΔ𝑡𝑄𝑤 𝑝𝑛 = 𝑝𝑛 + Δ𝑡𝑎𝑤𝑝0∇∥ · 𝒘,
+(44)
+𝑝𝑛+1���𝑄𝑇
+= eΔ𝑡𝑄𝑇 𝑝𝑛 = 𝑝𝑛 + Δ𝑡F −1
+∥
+�
+|𝑘|𝑎𝑇
+�
+1 + Δ𝑡
+2 |𝑘|𝑎𝑇
+�
+ˆ𝑇𝑛
+�
+,
+(45)
+where the derivative in Fourier space was obtained by multiply-
+ing with i𝑘 and the inverse FFT is denoted by F −1. For the
+𝑅31 closure the coefficients are given by 𝑎𝑤 = 4/(4 − π) and
+𝑎𝑇 = (4 − π)−1(2π𝜃0)1/2𝑐𝑛0𝑘B/𝑚, while for the 𝑅32 closure these
+are given by 𝑎𝑤 = 0 and 𝑎𝑇 = 2(2𝜃0/π)1/2𝑐𝑛0𝑘B/𝑚. Both closures
+compute a term proportional to ˆ𝑇 (cf. equation 45)
+i𝑘 ˆ𝑄 ∝ −i sign (𝑘) i𝑘𝑎𝑇 ˆ𝑇 = |𝑘|𝑎𝑇 ˆ𝑇.
+(46)
+Computing this term naively using the FFT is expensive. This is
+why, in the following, we present local, semi-local, and efficient
+global (Fourier transform-based) numerical approximations of the
+Landau closures, which we have implemented in the fluid-SHARP
+code.
+2.6.1 Local approximations of the Hilbert transform
+The phase shift between the wanted derivative i𝑘 ˆ𝑄 and the input of
+ˆ𝑇 in equation (46) is exactly 0, while the amplitude is proportional
+to |𝑘|. This is therefore a special case (𝑎 = 1) of the fractional Riesz
+derivative 𝜕𝑎/𝜕|𝑥|𝑎 with Fourier representation
+F
+� 𝜕𝑎 𝑓 (𝑥)
+𝜕|𝑥|𝑎
+�
+= −|𝑘|𝑎 ˆ𝑓 (𝑘) ,
+(47)
+where 𝑎 ∈ R. Note, that all approximations mentioned here only
+introduce errors in the amplitude of |𝑘|, but not in its phase. This
+makes them easier to integrate into simulations in comparison to
+approximations which are not designed to prevent phase errors, be-
+cause large phase errors (between π/2 and 3π/2) in any wave mode
+transform the damping term into an exponentially growing numer-
+ical instability. The local approximations make use of the fact, that
+the fractional Riesz derivative is local and cheap to evaluate for the
+special case 𝑎 = 2𝑚 with 𝑚 ∈ N0, where it reproduces the usual
+derivative 𝜕2𝑚/𝜕|𝑥|2𝑚 = (−1)𝑚+1 𝜕2𝑚/𝜕𝑥2𝑚. Wang et al. (2015)
+use 𝑎 = 0, while Allmann-Rahn et al. (2018) and Ng et al. (2020)
+approximate the non-isotropic pressure tensors with 𝑎 = 2. These ap-
+proximations are scaled to a characteristic wavenumber 𝑘0 at which
+the damping is expected to occur.
+The choice of 𝑎 = 0 means, that the approximation is a scalar
+i𝑘 ˆ𝑄 ∝ |𝑘0| ˆ𝑇,
+(48)
+while the gradient-driven closures with 𝑎 = 2 use
+i𝑘 ˆ𝑄 ∝ 𝑘2
+|𝑘0|
+ˆ𝑇.
+(49)
+The gradient-driven closures are equal to the FFT solution at two
+wavelengths, 0 and 𝑘0, while the scalar closure is only exact at 𝑘0,
+see Fig. 1. Since i𝑘 ˆ𝑄 is not computed alongside with the conservative
+0
+휋/4
+휋/2
+3휋/4
+휋
+ˆ푘 [rad/sample]
+0
+1
+2
+3
+4
+5
+spectral magnitude
+FFT-based
+FIR filter
+gradient driven
+scalar
+푘0
+Figure 1. The magnitude of the frequency response, which is a quantification
+of how much the amplitude at a specific frequency is amplified or suppressed,
+of different approximations of the derivative of the Hilbert transform. ˆ𝑘 is
+given in normalized frequencies (with regards to the Nyquist frequency),
+while the negative frequencies in the interval [−π, 0] are not shown here due
+to the symmetric dependence of all plotted values on |𝑘 |. The FFT-based
+approach reproduces the correct, linear response. The scalar and gradient
+driven closures are given by equations (48) and (49) respectively with the
+parameter 𝑘0 marked as a grey, vertical line. The FIR filter is described by
+equation (51).
+fluxes in the Riemann solver, energy conservation is only preserved if
+the mean energy does not increase. To achieve this, the approximation
+for the derivative of the heat flux needs to vanish at wavenumber 0,
+which the scalar approximation does not fulfil.
+Because fluid closures are only approximately mimicking kinetic
+Landau damping anyway, these local approximations to the fluid
+closures are useful to save computational cost. Furthermore they
+are easier to implement, especially when the full pressure tensor is
+computed. However, they may lead to misleading results in multi-
+scale simulations, where multiple characteristic damping lengths are
+present and depend on the estimate of 𝑘0. For example, Allmann-
+Rahn et al. (2022) show a case where ion and electron heating inten-
+sities are switched qualitatively.
+2.6.2 Semi-local approximations of the Hilbert transform
+While the less accurate local approximations use an arbitrary value
+of 𝑘0, the FFT is expensive and depends on periodic boundary con-
+ditions. Here, we aim to have a fallback algorithm as a compromise
+between both approaches.
+A digital finite impulse response (FIR) filter can be designed to
+approximate the non-local effects by convolving the simulation data
+with adjacent auxiliary data points, where the filter length determines
+the maximum distance. For example, an asymmetric filter with an
+even number of entries is applied on an input 𝑥 using filter coefficients
+𝑏 𝑗, producing the output 𝑦:
+𝑦𝑖+0.5 =
+𝑁 𝑓 /2−0.5
+∑︁
+𝑗=−(𝑁 𝑓 /2−0.5)
+𝑏 𝑗𝑥𝑖+ 𝑗+0.5.
+(50)
+A numerical derivative is then an asymmetrical filter with 𝑁 𝑓 = 2
+and coefficients 𝑏±0.5 = ±/Δ𝑥, such that 𝑦𝑖+0.5 = (𝑥𝑖+1 − 𝑥𝑖)/Δ𝑥.
+Figure 1 shows the magnitude of the frequency response. The gra-
+dient driven case shows a quadratic 𝑘2 dependence, which is sup-
+MNRAS 000, 1–17 (2022)
+
+8
+Lemmerz et al.
+pressed for larger 𝑘. This is due to the relatively small uneven filter
+length of 7 used here; the filter length is an important parameter,
+since it influences the accuracy of the approximation. With a fil-
+ter length corresponding to the simulation box size the results can
+converge to the FFT-based algorithm (i.e. the 𝑘2 dependence is not
+suppressed at higher 𝑘), if the filter is designed appropriately. As
+noted previously, the local closures do not converge to 𝜕/𝜕|𝑥|. A
+correct convergence for approximating 𝜕/𝜕|𝑥| is obtained through
+the high order formulation by Ding et al. (2015). However, this filter
+violates energy conservation for smaller filter length and is thus, not
+suitable for our case. Instead, we construct the filter by adopting a
+convolution of two sub-filters, each of which has an odd amount of
+asymmetric entries3 similar to the numerical derivative mentioned
+already. By design, their output has a vanishing mean, thereby guar-
+anteeing energy conservation. A symmetric splitting into the sub-
+filters 𝜕/𝜕|𝑥| = (𝜕1/2/𝜕|𝑥|1/2)2 is possible, however its frequency
+response is not monotonic (and has visible ripples) for small filter
+lengths. This leads to the unphysical case that some waves at a par-
+ticular wavenumber 𝑘 are damped less than their slightly larger scale
+waves at 𝑘 − 𝛿𝑘.
+Instead, we opt to use the intuitive splitting of 𝜕/𝜕|𝑥| = 𝜕/𝜕𝑥H
+where the Hilbert-transform filter H is equivalent to −i sign (𝑘) in
+Fourier space. The filter H has coefficients 𝑏 𝑗 = 1/(π𝑗). We derive
+anequivalent formulationtoequation(45), whichisfirst order in time,
+by applying the derivative and Hilbert-transform filters successively,
+i.e.
+𝑝𝑛+1 = 𝑝𝑛 + Δ𝑡𝑎𝑇
+𝜕
+𝜕𝑥
+𝑁 𝑓 /2−0.5
+∑︁
+𝑗=−(𝑁 𝑓 /2−0.5)
+1
+π𝑗 𝑇𝑛
+𝑖+𝑗+0.5.
+(51)
+Note, that the derivative is also computed by convolution and has a
+separate filter length corresponding to its spatial order. We opt to use
+the same spatial order as in the C-WENO reconstruction for the finite
+volume scheme.
+Even for small Hilbert-transform filter lengths in comparison to
+the number of cells, e.g. 𝑁 𝑓 /𝑁c = 0.04 as shown in Fig. 1, this
+formulation dramatically improves the accuracy of multiscale prob-
+lems in comparison to local approximations. Here, 𝑁 𝑓 is critical for
+the accuracy at small wavenumbers 𝑘, while the spatial order of the
+derivative is critical for the accuracy at large 𝑘. Most importantly,
+this semi-local approach does not require setting an arbitrary damp-
+ing scale 𝑘0 such as the local approximations mentioned before. The
+only parameter of this approach is the filter length, which should be
+chosen to be sufficiently large.
+2.6.3 Efficient FFT-based computation of the Hilbert transform
+Provided the plasma background is uniform and periodic, the most
+accurate while computationally most expensive results are achieved
+by computing the heat flux of the fluid in Fourier space. While the
+FFT is easy to compute on a single computer using standard nu-
+merical libraries, our code is parallelized using MPI and an efficient
+one-dimensional FFT is needed. The computation of the Fourier
+transform is expensive for two reasons:
+(i) globally, each Fourier component needs to be informed about
+data from every other computational cell (which may be stored on a
+different processor), and
+(ii) the Fourier transform is not easily parallelizable in one di-
+mension, which precludes an efficient scalable Fourier algorithm.
+3 This is also called a Type IV filter.
+This naturally limits the overall computational scalability of the fluid
+part of the code. Communication over multiple MPI processes is time
+consuming because of latency and finite bandwidth. For this rea-
+son, parallel FFT algorithms are prone to become a computational
+bottleneck. However, using non-blocking MPI routines to perform
+communication in the background can be used while the high com-
+putational load of the particles is carried out. Thus, in our case of
+a combined fluid and PIC algorithm, the communication required
+for an accurate FFT-based heat flux computation is comparatively
+computationally cheaper, even with relatively small numbers of PIC
+particles. Hence, in our case the FFT algorithm does not necessarily
+become a bottleneck for larger problems.
+In order to distribute the computational load of the FFT, we employ
+a four-step algorithm in the first step of the computation (Bailey
+1990; Takahashi & Kanada 2000), which extends the Cooley-Tukey
+algorithm (Cooley & Tukey 1965) for multiple processors. We shortly
+describe the algorithm for complex input data as found in the literature
+and afterwards adapt the parallel FFT for real input data in our
+implementation. The four-step algorithm interprets the complex data
+vector 𝑥 𝑗 of length 𝑁 as a two-dimensional vector 𝑥 𝑗 = 𝑥 𝑗1, 𝑗2 with
+lengths 𝑛1 and 𝑛2 respectively, and volume 𝑛1𝑛2 = 𝑁. The mapping
+𝑗 = 𝑗1 + 𝑗2𝑛1 and 𝑘 = 𝑘2 + 𝑘1𝑛2 is inserted into the definition of the
+discrete Fourier transform, where Ψ = exp{−2πi}
+ˆ𝑥𝑘 =
+𝑁 −1
+∑︁
+𝑗=0
+𝑥 𝑗Ψ 𝑗𝑘/𝑁 ,
+(52)
+ˆ𝑥𝑘2,𝑘1 =
+𝑛1−1
+∑︁
+𝑗1=0
+𝑛2−1
+∑︁
+𝑗2=0
+𝑥 𝑗1, 𝑗2Ψ 𝑗2𝑘2/𝑛2Ψ𝑗1𝑘2/𝑁 Ψ 𝑗1𝑘1/𝑛1.
+(53)
+This way, a complex-to-complex parallel FFT of length 𝑁 is dis-
+tributed to 𝑛1 local FFTs of length 𝑛2, a multiplication by the twiddle
+factors Ψ 𝑗1𝑘2/𝑁 and finally 𝑛2 FFTs of length 𝑛1, with a communica-
+tion intensive transpose in between. All-to-all communication takes
+place two times, in the first step – cyclically distributing 𝑗 to 𝑗1 and
+𝑗2 – and for the transpose. A third all-to-all communication would
+be needed to properly sort the values in Fourier space. However, a
+scrambled output suffices for computing the heat flux. Furthermore,
+since often two FFTs, i.e. electrons and ions, need to be computed si-
+multaneously, they can be computed on different nodes. This has the
+advantage, that the second all-to-all communication for the transpose
+is not completely global resulting in reduced communication times.
+Adapting this algorithm to a real-to-complex FFT, where due to
+Hermitian symmetry only values of 𝑘 ⩽ ⌊𝑁/2⌋ need to be computed,
+a large amount of computational and communicational savings can
+be realized. A real-to-complex parallel FFT of length 𝑁 is distributed
+to 𝑛1 local real-to-complex FFTs of length 𝑛2, a multiplication by
+the twiddle factors Ψ 𝑗1𝑘2/𝑁 and, now only, ⌊𝑛2/2⌋ + 1 complex-
+to-complex FFTs of length 𝑛1. Up to two of the latter FFTs can be
+replaced by real-to-complex FFTs, along the axes 𝑘2 = 0 and, if 𝑛2
+is even, 𝑘2 = 𝑛2/2. A scrambled output is received, which, due to
+Hermitian symmetry, needs to be partially complex conjugated.
+A key point in ensuring the efficiency of the parallel four-step
+algorithm consists in choosing large 𝑛1 and 𝑛2. 𝑛1 ≃ 𝑛2 ≃
+√
+𝑁 is the
+optimal choice for the distributed complex-to-complex FFT, the real-
+to-complex FFT should prefer 𝑛1 ≃ ⌊𝑛2/2⌋ + 1 ≃ (
+√
+2𝑁 + 1 + 1)/2.
+The computational scaling with 𝑃 processors and roughly optimally
+distributed 𝑛1 and 𝑛2 is akin to O (𝑁/𝑃 log 𝑁), but degrades if 𝑁
+is a prime number, or, more generally, if 𝑛1 or 𝑛2/2 is smaller than
+the number of processors. This easily avoidable because 𝑁 is a free
+parameter, and so are 𝑛1 and 𝑛2. While this does not scale favourably
+in comparison to the O (𝑁/𝑃) scaling that dominates the rest of
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+9
+the fluid code, still, the FFT is trivially independent of the numbers
+of particles per cell 𝑁pc. The PIC-module on the other hand scales
+as O �𝑁pc𝑁/𝑃� and typical applications have 𝑁pc ≳ 100. In many
+applications the cost of the Fourier transform is, even with worse
+scaling, subdominant in comparison to the cost of the PIC part.
+In the remaining cases, local approximations, discussed above, are
+favourable.
+2.7 Current-coupled fluid-PIC algorithm
+The coupling in our code between various fluid and kinetic (PIC)
+species is achieved through a current-coupling scheme. Namely, both
+fluid and kinetic species contribute to the charge and current densi-
+ties. The electromagnetic fields then evolve in response to the total
+contributions. The fields are staggered on a Yee-mesh and are up-
+dated with the FDTD scheme. Subsequently, both fluid and kinetic
+species evolve in repose to the new electromagnetic fields. That is
+our current-coupling scheme does not make any assumption on the
+velocity distribution of the species modelled using the kinetic de-
+scription (Park et al. 1992).
+The PIC species, using fifth-order spline interpolation, are de-
+posited to specific points on the Yee-grid for which the charge density
+is defined at full-time steps while the current density is defined at
+half-time steps as discussed by Shalaby et al. (2017a, 2021). For fluid
+species, the fluid density and velocity are defined at the same time
+step. Therefore, during the evolution of the fluid, we deposit the fluid
+contribution to the charge and current densities, 𝜌 and J𝑦,𝑧 respec-
+tively, at the cell centres. The deposition for J𝑦,𝑧 is trivial at half-time
+steps, where the fluid vector U is defined, while the contribution to 𝜌
+is computed at full-time steps, i.e. before the electromagnetic source
+update according to equation (20). Note, that 𝜌 stays constant when
+computing the Lorentz force and heat flux updates.
+Our algorithm does not apply any approximations to the electrical
+field components or to Ohm’s law, requiring electron timescales
+and motions to be fully resolved. Consequently, we apply the same
+algorithm to fluid electrons and protons. This is accomplished using
+the modular design of the fluid SHARP code where each fluid species
+is represented by initialising a fluid code class. Each instance of this
+code class is initialized using the values of the mass and the charges
+of their respective particle species. The algorithms which define the
+evolution of each particle species are implemented as functions of the
+fluid class. This allows us to setup simulations with multiple species,
+all of which are evolved with the same numerical algorithms, with
+little effort.
+In Fig. 2 the main loop of the fluid-PIC algorithm is presented.
+It can be seen that the usual PIC-algorithm loop of electromagnetic
+update, interpolation to particle position, particle push, and field de-
+position is retrieved when no fluid species is initialised. On the other
+hand, without PIC particles, we retrieve a multispecies fluid plasma
+code. While our fluid-PIC algorithm can simulate an arbitrary mix-
+ture of species, it is most efficient if fluids are used for background
+species and particles for non-thermal particle distributions. Possi-
+bilities for task parallelization are shown in Fig. 2 by dashed lines,
+which allows maximizing computation-communication overlap.
+Our fluid implementation is included within the SHARP code,
+which uses a fifth-order spline function for deposition and back-
+interpolation for PIC species (Shalaby et al. 2017a, 2021). The PIC
+part of the code does not make use of filtering grid quantities and
+results in comparatively small numerical heating per time step, which
+(if present) would affect the reliability of the simulation results on
+long timescales (see section 5 in Shalaby et al. (2017a)). This prop-
+erty is important because we are specifically interested in studying
+Update 
+Flux - half step
+Update 
+Lorentz force
+Flux - half step
+Heat flux
+Lorentz force
+Deposition
+Fluid Module
+Particle Module
+EM Module
+Back interpolation
+Figure 2. Schematic representation of the interaction of the different modules
+in the fluid-SHARP code. Red boxes belong to the particle class, violet boxes
+to the electromagnetic class and blue boxes to the fluid class. Dashed lines
+show branches which are task parallelizable, i.e. where non-blocking MPI
+communication can be used for overlapping communication and computation.
+Table 1. Parameters adopted for the shock tube tests described in Section 3.1.
+Test
+𝑥0
+𝜌l
+𝑤l
+𝑝l
+𝜌r
+𝑤r
+𝑝r
+1
+0.3
+1
+0.75
+1
+0.125
+0
+0.1
+2
+0.8
+1
+-19.59745
+1000
+1
+-19.59745
+0.01
+microphysical effects on long timescales with our fluid-PIC code.
+Due to the modularity of our code, each part can be tested individ-
+ually. These tests, ranging from the uncharged fluid solver to full
+fluid-PIC simulations, are shown in the next section.
+3 CODE VALIDATION TESTS
+In this section, we present the results of various code tests. We
+start with two shock-tube tests in Section 3.1 before we show that
+our code is able to accurately capture all six branches of the two-
+fluid dispersion relation (Section 3.2). We describe code tests of
+Langmuir wave damping (Section 3.3) and of two interacting Alfvén
+waves generating a new, longitudinal wave along the magnetic field
+(Section 3.4). In Section 3.5, we test the entire fluid-PIC code with a
+simulation of the gyrotropic cosmic ray streaming instability, where
+PIC cosmic rays are streaming in a stationary electron-proton fluid
+background. Finally, we demonstrate the successful parallelization
+strategy of our code by performing scaling tests in Section 3.6.
+3.1 Shock tube
+As the fluid approximation will be primarily used for background
+plasmas without excessive gradients, the accuracy of resolving sharp
+discontinuities is of secondary importance in practical applications.
+Still, we stress test our implementation of the fluid equations to ensure
+its numerical robustness and to compare the numerical dispersion for
+different Riemann solvers. For the shock tests a numerical grid of 100
+cells is used with a constant CFL number𝐶cfl = 0.2 with the adiabatic
+coefficient Γ = 1.4. The boundary conditions are transmissive and
+MNRAS 000, 1–17 (2022)
+
+10
+Lemmerz et al.
+0.25
+0.50
+0.75
+1.00
+푛 [푛0]
+HLLC
+Roe
+exact
+2
+4
+6
+푛 [푛0]
+HLLC
+Roe
+exact
+0.0
+0.5
+1.0
+푤 [푤0]
+−2
+−1
+0
+푤 [푤0]
+×101
+0.0
+0.2
+0.4
+0.6
+0.8
+푥 [푥0]
+0.25
+0.50
+0.75
+1.00
+푝 [푝0]
+0.0
+0.2
+0.4
+0.6
+0.8
+푥 [푥0]
+0.0
+0.5
+1.0
+푝 [푝0]
+×103
+(a) Shock tube test 1, a modified Sod shock tube, at time 0.2 (code units).
+0.25
+0.50
+0.75
+1.00
+푛 [푛0]
+HLLC
+Roe
+exact
+2
+4
+6
+푛 [푛0]
+HLLC
+Roe
+exact
+0.0
+0.5
+1.0
+푤 [푤0]
+−2
+−1
+0
+푤 [푤0]
+×101
+0.0
+0.2
+0.4
+0.6
+0.8
+푥 [푥0]
+0.25
+0.50
+0.75
+1.00
+푝 [푝0]
+0.0
+0.2
+0.4
+0.6
+0.8
+푥 [푥0]
+0.0
+0.5
+1.0
+푝 [푝0]
+×103
+(b) Shock tube test 2 at time 0.012 (code units).
+Figure 3. 1D1V hydrodynamical shock tube tests with initial conditions given in Table 1. The simulations carried out with the HLLC and Roe Riemann solvers
+are compared to the exact solutions. Density, bulk velocity in 𝑥-direction and pressure are plotted for each test.
+the initial conditions for the tests are given in Table 1, which are the
+same as in Toro (2009), where a CFL number of 0.2 × 0.95 is used
+only in the first five steps and 0.95 afterward. The units used for these
+non-electromagnetic tests are arbitrary units and do not coincide with
+the usual simulation units.
+Test 1, as shown in Fig. 3a, is a modified Sod shock tube test.
+The sonic rarefaction wave on the left-hand side as well as the shock
+front on the right are well resolved without noticeable oscillations.
+The contact discontinuity in the middle introduces small oscillations
+in the density and is smeared out more than the shock front. While
+the Roe and HLLC solvers yield almost the same results, the HLLC
+solver is slightly better at resolving the sonic point at the head (to
+the left) of the sonic rarefaction wave, which the Roe solver can only
+resolve because an entropy fix is applied.
+Figure 3b shows a test of a stationary contact discontinuity with
+a shock front of a high Mach number travelling to the right and a
+rarefaction wave to the left. It can be seen, that while the HLLC
+method introduces more oscillations, it is also better at resolving the
+contact discontinuity.
+In low-density flows the Roe solver is not suitable because it is not
+robust without further modifications (Einfeldt et al. 1991), making the
+HLLC method slightly more robust while the Roe method is slightly
+less dispersive. However, for most practical applications studied here,
+both methods produce similar results.
+3.2 Two-fluid dispersion relation
+For an ideal two-fluid plasma the dispersion relation can be solved
+for six different wave branches (Stix 1992). We show the solutions to
+the dispersion relation of a two-fluid plasma in Fig. 4 for a realistic
+mass ratio of 𝑚i = 1836𝑚e and 𝛽i = 𝑛𝑘B𝑇i/[𝐵2
+0/(2𝜇0)] = 0.2 in an
+10−3
+10−2
+10−1
+k [kD]
+10−4
+10−3
+10−2
+10−1
+ω [ωp], log-scale
+0.8
+1.0
+1.2
+1.4
+ω [ωp]
+upper RCP
+Langmuir
+upper LCP
+lower RCP
+ion-acoustic
+lower LCP
+Figure 4. The six branches of the two-fluid dispersion relation are shown, with
+two electrostatic wave branches (Langmuir and ion-acoustic) as well as four
+electromagnetic left and right-hand circularly polarized wave branches (LCP
+and RCP). Often, the lower RCP is referred to as whistler branch and the lower
+LCP as ion cyclotron branch; for parallel propagation their phase velocities
+approach the Alfvén speed at small 𝑘. The upper RCP and LCP are modified
+light waves. We mark the six local extrema of the Fourier-transformed fluid
+simulation outputs at each wavenumber with crosses. Theoretical predictions
+are shown as lines.
+isothermal plasma. 𝐵0 is oriented along the 𝑥-axis and the Alfvén
+velocity is 𝑣A = 𝐵0/(𝜇0𝑛i𝑚i)1/2 = 5.83 × 10−3𝑐. Multiple simu-
+lations at different wavenumbers have been initialized that have all
+six wave modes simultaneously present and were run for a total time
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+11
+1.0
+1.1
+1.2
+1.3
+1.4
+1.5
+Re(휔) [휔p]
+theo: ideal gas
+theo: Landau 푅32
+theo: Landau 푅31
+theo: kinetic
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+Im(−휔) [휔p]
+sim: ideal gas
+sim: Landau 푅32
+sim: Landau 푅31
+sim: PIC
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+푘 [푘D]
+0.000
+0.002
+rel. error [%]
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+푘 [푘D]
+0.00
+0.01
+rel. error [%]
+Figure 5. The linear dispersion relations of a Langmuir wave with immobile ions. Shown are, on the left-hand side, the real frequency components and,
+on the right-hand side, the negative imaginary frequency components (which are responsible for damping). The crosses present data points obtained from
+simulations with the respective closure while the theoretical result is shown with a solid line. The relative error between simulation and theoretical results
+(𝜔sim − 𝜔theor)/𝜔theor is shown in the lower panels. For reference, the red crosses display the data points as given in table 1 of Shalaby et al. (2017a).
+of 14/min (𝜔), where 𝜔 denotes the wave frequencies, which are
+always completely real for an ideal fluid. Consequently, the waves
+should be undamped and any possible damping introduced is be-
+cause of numerical dissipation. Initial conditions for all of our fluid
+simulations as well as theoretical predictions are computed using an
+extended algorithm based on the dispersion solver by Xie (2014),
+which can take into account the effects of both heat flux closures.
+A Fourier analysis in time has been performed and the six largest
+local extrema are shown as crosses in Fig. 4. It can be seen, that the
+simulation results are in good agreement with the analytical results.
+In the Fourier-analysis the largest relative errors of at most 7 per cent
+in 𝜔 occur in the large-scale part of the ion-acoustic branch as well
+as close to the cut-off frequency of the lower LCP branch. In com-
+parison to this, the largest relative errors in the upper three branches
+are more than one magnitude less.
+3.3 Langmuir wave damping
+The electrostatic wave modes are directly subject to linear Landau
+damping, and thus present a good test for the heat flux closures. To
+test this, we initialize standing Langmuir waves in an electron plasma
+with immobile ions. We use the same grid layouts as in table 1 of
+Shalaby et al. (2017a), supplemented with fluid simulations run at
+𝑘/𝑘D ∈ {0.1, 0.2, 0.3} with a resolution of 𝜆/Δ𝑥 = 68 cells per
+wavelength and a domain size of length 𝐿 = 10𝜆 wavelengths. The
+wavenumber associated with the Debye length is the ratio of plasma
+frequency to thermal velocity, i.e. 𝑘D = 𝜔p/𝜃1/2𝑐. The amplitude of
+the wave is chosen, such that the density fluctuation to background
+ratio is fixed to 𝛿𝑛/𝑛0 = 10−3.
+In order to find the numerical dispersion relation we perform curve
+fitting with the Powell algorithm on the time series for times up to
+80 𝜔−1
+p , while the simulations at 𝑘/𝑘D = 0.01 and 0.05 with small
+damping are analysed up to 240 𝜔−1
+p . The computation of the heat
+fluxes for the 𝑅31 and 𝑅32 closures is performed using the FFT-based
+method. The results are shown in Fig. 5, where the ideal gas closure
+and the kinetic results are also depicted for reference.
+Generally, it can be seen, that at small scales the closures show
+larger deviations from each other, which is also where the fluid de-
+scription starts breaking down naturally as the particle distribution
+is not in equilibrium. At larger scales, the various descriptions of
+Landau damping converge and approach zero. The numerical rela-
+tive error of the fluid code is small and stays below 0.003 for real
+frequencies and below 0.002 for decay rates in this setup. The sim-
+ulation at 𝑘/𝑘D = 0.05 performs worse than the one at 𝑘/𝑘D = 0.1
+due to the significantly lower resolution. The error in 𝜔 decreases
+at second-order with increasing spatial resolution, as shown in Ap-
+pendix B.
+3.4 Interacting Alfvén waves
+A single Alfvén wave is purely transversal and not directly affected by
+Landau damping. However, two or more Alfvén waves drive a longi-
+tudinal electrostatic wave, which is susceptible to Landau damping,
+see Fig. 6. This leads to particle heating as a result of the collision-
+less damping of the Alfvén wave, also known as non-linear Landau
+damping.
+Restricting ourselves to a setup of pairwise interacting waves, we
+can identify two distinct cases. In the first case counter-propagating
+waves are interacting. In consequence, both waves damp, lose energy
+to the longitudinal wave and subsequently heat the particles. In the
+second case the waves are co-propagating. Here the wave with the
+smaller wavelength will not only transfer energy to the particles,
+but also to the other Alfvén wave. Lee & Völk (1973) describe
+this mechanism in detail and formulate the following coupled set
+of differential equations while adopting a measure for the magnetic
+energy of a wave, 𝐼 𝑗 =
+��𝐵 𝑗
+��2, where 𝑗 ∈ {1, 2}:
+d
+dt 𝐼 𝑗 = 2Γ 𝑗 𝐼 𝑗.
+(54)
+The coupling between the differential equations is implicit because
+the damping coefficient has the dependency Γ1 ∝ 𝐼2. For the counter-
+propagating case with an isothermal ion-electron-plasma in the high
+beta limit 𝛽i = 2𝜇0𝑛i𝑘B𝑇i/𝐵2
+0 = 2 ≫ 1, where 𝐵0 is the background
+magnetic field strength, the damping rate Γ𝑗 is approximately equal
+for both wave polarizations with similar frequencies 𝜔 𝑗 and may be
+approximated by (Holcomb 2019)
+Γ1 = −
+√π
+16
+𝐼2
+𝐵2
+0
+√︁
+𝛽i𝜔1.
+(55)
+MNRAS 000, 1–17 (2022)
+
+12
+Lemmerz et al.
+Figure 6. Two different Alfvén waves, with magnetic and velocity vectors
+B1, B2 and 𝒘1, 𝒘2, propagate transversally along the 𝑥-axis, where the elec-
+tromagnetic vectors rotate (counter-)clockwise around it. Because of their
+phase difference Δ𝑘𝑥 the overall Lorentz force (𝒘1 + 𝒘2) × (B1 + B2) in
+𝑥-direction is non-zero, thereby generating the longitudinal wave shown in
+dark yellow.
+1.8
+1.9
+2.0
+δB2
+total [B2
+0]
+×10−2
+L&V
+Landau R32
+Landau R31
+2
+4
+6
+8
+10
+12
+t [Pω]
+0.85
+0.90
+0.95
+1.00
+δB2
+j [B2
+0]
+×10−2
+RCP
+LCP
+Figure 7. Time evolution of the magnetic energy of a linearly polarized Alfvén
+wave in our fluid simulations with Landau damping. Time is measured in units
+of the period of the mean wave frequencies 𝑃𝜔 = 4π(𝜔1+ 𝜔2)−1. Analytical
+predictions for the damping rate are taken from Lee & Völk (1973, labelled
+L&V). The fluid simulations are presented with the different heat flux closures
+𝑅31 and 𝑅32. We compare the time evolution of the total magnetic wave
+energy (top panel) and the magnetic wave energy of the different polarization
+states (bottom panel). The right-hand circularly polarized wave has a higher
+phase velocity and loses energy more quickly in comparison to the left-hand
+circularly polarized wave.
+Note that Γ2 is found by substituting the subscripts 1 → 2 and 2 → 1.
+In Fig. 7 we show simulations of a linearly polarized Alfvén wave,
+which consists of two counter-propagating waves of equal amplitude.
+The pure fluid simulations are shown with a box size of 𝐿 = 252 𝑐/𝜔i
+and wavelengths 𝜆 = 𝐿/3. Right and left polarized waves are initial-
+ized with phase velocities 𝜔RCP/𝑘 = 0.0342 and 𝜔LCP/𝑘 = 0.0318
+with a perpendicular magnetic field amplitude of 𝛿𝐵 = 0.1 𝐵0. A
+reduced mass-ratio of 𝑚i/𝑚e = 100 is adapted here.
+Our simulations are carried out with the different heat flux clo-
+sures 𝑅32 and 𝑅31, as shown in Fig. 7. Both closures reproduce the
+theoretical predictions quite well. A PIC simulation with similar pa-
+rameters has been shown in figure 6.4 by Holcomb (2019), which
+reproduces half of the predicted damping rate until 𝑡 ∼ 2𝑃𝜔 and
+shows a quenching of the damping rate afterwards. In comparison
+to kinetic simulations, there is no saturation of the Landau-damping
+effect in fluids. This is because the distribution of the fluid particles
+is always assumed to be roughly Maxwellian and resonant particles
+are not depleted as a function of time. Hence, Landau fluid is implic-
+itly assumed to have small thermalization timescale in comparison
+to the damping timescale. On the other hand, PIC simulations are
+plagued by Poisson noise and an insufficient resolution of velocity
+space might lead to a reduced Landau damping rate.
+3.5 Gyrotropic cosmic ray streaming instability
+To test the entire code, we run cosmic ray streaming instability sim-
+ulations, where electron and ion cosmic rays (CR) are modelled with
+the PIC method and the background electron and ion plasmas are
+modelled as fluids. The initial CR momentum distribution for ions
+(electrons) is assumed to be a gyrotropic distribution with a non-
+vanishing (zero) pitch angle, while both CR electrons and ions are
+assumed to drift at the same velocity 𝑣dr. Namely, the phase space
+distributions for the electron and ion cosmic ray species 𝑠 ∈ {e, i}
+are given by (Shalaby et al. 2021)
+𝑓cr,𝑠(x, u) = 𝑛cr,𝑠
+2π𝑢⊥
+𝛿(𝑢 ∥ − 𝛾𝑠𝑣dr)𝛿(𝑢⊥ − 𝛾𝑠𝑣⊥,𝑠),
+(56)
+where 𝛾𝑠 = (1 − 𝑣2
+dr/𝑐2 − 𝑣2
+⊥,𝑠/𝑐2)−1/2 is the Lorentz factor and
+𝑣⊥,𝑠 is the perpendicular component of the CR velocity. We choose
+𝑣⊥,e = 0 and 𝑣⊥,i = 13.1𝑣A, where the ion Alfvén velocity is
+given by 𝑣A = 𝐵0/(𝜇0𝑛i𝑚i)1/2 = 0.01𝑐 with the background mag-
+netic field pointing along the spatial direction, and 𝑣dr of 5𝑣A re-
+sulting in a pitch angle for the ions of tan−1(𝑣⊥,i/𝑣dr) = 69.1◦.
+The thermal background species are isothermal with the tempera-
+tures 𝑘B𝑇/(𝑚𝑐2) = 0.0001 and a mass ratio 𝑚i/𝑚e = 1836. We
+use a periodic box of length 𝐿𝑥 = 10971.5 𝑐/𝜔p and resolution
+Δ𝑥 = 0.1 𝑐/𝜔p. The cosmic ray to background ratio number density
+ratio 𝛼 = 𝑛cr,i/𝑛i = 0.01.
+We run two simulations where the background plasmas are mod-
+elled as fluids. The first one uses an ideal gas closure without ac-
+counting for Landau damping (FPIC ideal gas) while we include the
+heat flux source term in the second simulation to mimic the impact of
+linear Landau damping using the 𝑅31 closure of equation (42) (FPIC
+Landau 𝑅31). We compare these two fluid-PIC simulations against
+PIC simulations where both CRs and background plasmas are mod-
+elled as PIC species. The number of CR ions per cell is 𝑁pc = 25(75)
+and we call this simulation “PIC normal (high) 𝑁pc” (Shalaby et al.
+2021). Like the “PIC normal 𝑁pc” simulation, the fluid-PIC simula-
+tions also use 25 particles per cell for modelling cosmic rays.
+Growth rates of the instability in the linear regime can be com-
+puted from the linear cold background plasma dispersion relation
+(Holcomb & Spitkovsky 2019; Shalaby et al. 2022):
+0 =1 − 𝑘2𝑐2
+𝜔2
++
+𝜔2
+i
+𝜔 �−𝜔 ± Ωi,0
+� +
+𝜔2e
+𝜔 �−𝜔 ± Ωe,0
+�
++ 𝛼𝜔2e
+𝛾e𝜔2
+�
+𝜔 − 𝑘𝑣dr
+𝑘𝑣dr − 𝜔 ± Ωe,0
+�
++
+𝛼𝜔2
+i
+𝛾i𝜔2
+���
+�
+𝜔 − 𝑘𝑣dr
+𝑘𝑣dr − 𝜔 ± Ωi
+−
+𝑣2
+⊥/𝑐2 �
+𝑘2𝑐2 − 𝜔2�
+2 (𝑘𝑣dr − 𝜔 ± Ωi) 2
+���
+�
+.
+(57)
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+13
+0
+20
+40
+60
+80
+100
+푡
+�
+Ω−1
+i
+�
+10−2
+10−1
+|훿퐵| [퐵0]
+0
+1
+2
+3
+4
+5
+10−2
+10−1
+FPIC ideal gas
+FPIC Landau 푅31
+PIC normal 푁pc
+PIC high 푁pc
+intermediate scale growth rate
+Figure 8. Growth of the perpendicular magnetic field as a function of time for a gyrotropic cosmic ray streaming setup. The maximum growth rate expected
+from the linear dispersion relation at intermediate scales is Γinter = 2.299Ωi and shown in dashed grey. because of the different initial seed populations for the
+particle species, the onset of the instabilities is not expected to happen at the same simulation time.Hence, we choose an arbitrary 𝑡 = 0 so that the different
+simulated growth phases roughly coincide.
+10−5
+10−4
+10−3
+10−2
+|훿퐵푘| [퐵0]
+FPIC ideal gas
+FPIC Landau 푅31
+PIC normal 푁pc
+PIC high 푁pc
+10−4
+10−3
+10−2
+10−1
+intermediate scale (푘푐/휔i = 4.91)
+10−5
+10−4
+10−3
+10−2
+|훿퐵푘| [퐵0]
+10−4
+10−3
+10−2
+10−1
+cascading scale (1.5 < 푘푐/휔i < 2.5)
+0
+2
+4
+6
+8
+10
+푡 [Ω−1
+i ]
+10−5
+10−4
+10−3
+10−2
+|훿퐵푘| [퐵0]
+0
+20
+40
+60
+80
+100
+푡 [Ω−1
+i ]
+10−4
+10−3
+10−2
+10−1
+gyro scale (0.1 < 푘푐/휔i < 0.6)
+Figure 9. Growth of the perpendicular magnetic field as a function of time at different scales for a gyrotropic cosmic ray streaming setup. We show mean values
+of the fields that are averaged over a range of wave vectors 𝑘, as indicated in the legends. The maximum growth rates at the gyro scale and the intermediate scale
+are given by Γgyro = 0.498Ωi and Γinter = 2.299Ωi, and indicated by the grey dotted and dashed lines, respectively. At wavenumbers corresponding to cascading
+scales, there is no instability expected according to the linear dispersion relation, and wave growth solely arises as a result of cascading from other (unstable)
+scales.
+The non-relativistic and relativistic cyclotron frequencies of each
+species are given by Ωs,0 = 𝑞𝑠𝐵0/𝑚𝑠 and Ωs = Ωs,0/𝛾s respectively.
+The wavelength of the most unstable wave mode at the gyroscale is
+λg = 2𝜋(𝑣dr − 𝑣A)/Ωi, which is properly captured in our setup using
+a box size of 𝐿𝑥 ∼ 10.15λg.
+We show the amplification of the perpendicular magnetic field
+components as a function of time for this unstable setup in Fig. 8
+for various simulations. It shows that the noise level of the fluid-PIC
+simulations is orders of magnitude lower in comparison to the “PIC
+normal 𝑁pc” resolution, even though the number of CR particles per
+cell is the same. Especially up to the saturation point (𝑡Ωi ∼ 10) the
+MNRAS 000, 1–17 (2022)
+
+14
+Lemmerz et al.
+fluid-PIC simulation compares more favourably to the PIC results
+with lower noise than to the PIC simulation with fewer 𝑁pc.
+After saturation, i.e. when Alfvén waves at many scales have built
+up and their interaction has created an electrostatic field, these waves
+start to lose some energy to Landau damping of the electrostatic
+waves (see Section 3.4). At that point, the Landau closure becomes
+relevant. Qualitatively the ideal gas closure has no efficient mech-
+anism for dissipating such electrostatic waves, resulting in a pro-
+longed growth period leading to saturation at higher values at the
+cascading and intermediate scales. Utilization of a Landau closure
+leads to some damping, albeit it is quantitatively smaller than in
+the PIC simulations. While Fig. 5 indicates faster damping for the
+Landau closures in comparison to the kinetic results in the electron
+electrostatic branches, damping in the ion-acoustic branch might be
+underestimated in the Landau closures. We have compared the ex-
+pected damping between kinetic and Landau fluid in the ion-acoustic
+branch for multiple wavenumbers, which confirmed that this is a
+likely scenario. The accuracy of this approximation is not the same
+at all scales, which can be seen in Fig. 9, where the magnetic field
+amplifications at various ranges of scales are compared. Especially
+in the highly Landau-damped scales, differences between fluid-PIC
+and PIC emerge. At ion gyro scales, where most of the magnetic en-
+ergy is stored at saturation, there is a good agreement over the entire
+time period. Exponential growth at every scale is also in good agree-
+ment between PIC and fluid-PIC simulations at all scales. The initial
+exponential growth can also be compared to the expected growth
+rates from the linear dispersion relation. The growth rates of the two
+local maxima are plotted alongside the simulated data, one at the
+intermediate scales around 𝑐𝑘 = 4.91𝜔i and one at the gyro scale
+at 𝑐𝑘 = 0.38𝜔i. The intermediate scale starts an inverse cascade to
+larger scales almost immediately, which causes a reduced growth
+rate in comparison to the expectation from linear theory. By contrast,
+the gyro scale instability follows linear expectations to very good
+approximation.
+While our fluid-PIC and PIC results are promisingly similar, dif-
+ferences after the saturation level might be attributed to multiple
+reasons. First, the Landau closures do not exactly reproduce the cor-
+rect damping, and therefore will deviate quantitatively. Second, due
+to the high electron temperature chosen, relativistic effects might
+occur in PIC, but not in the non-relativistic fluid that we assumed for
+the background plasma. Third, the PIC method might exhibit more
+numerical dissipation at the given 𝑁pc in comparison to the fluid
+method. However, Fig. 9 seems to indicate numerical convergence at
+the intermediate and gyro scale.
+Even though our simulations were run at unrealistically high
+𝛼, the background particles did not deviate significantly from the
+Maxwellian distribution at the end of the simulation time. This indi-
+cates, that a fluid description for background species is indeed a valid
+approach for this setup, especially for smaller, more realistic values
+of 𝛼.
+3.6 Computational scaling
+We show the strong scaling properties of our fluid-PIC code in
+Fig. 10. The tests were run on Intel Cascade 9242 processors with 96
+processors per node at the HLRN Emmy cluster. Simulations with
+3000 processors or more typically cause severe bottlenecks due to
+the latency and/or the finite bandwidth of input/ouput operations. For
+this number of processors the Fourier-based closures are roughly 20
+per cent more costly in comparison to the ideal gas closures. This
+is in stark contrast to pure PIC simulations, which scale with the
+inverse ratio of cosmic ray-to-background density 𝛼−1, consequently
+1000
+200
+300
+500
+700
+2000
+3000
+processors
+100
+time [s]
+disabled fluid module
+FPIC ideal gas
+FPIC Landau FFT-based
+Figure 10. Strong scaling of the fluid-PIC code, with and without Fourier-
+based Landau closures. Shown is the wall-clock time needed to simulate 1250
+time integration steps with 180000 cells at 1000 particles per cell at a varying
+number of processors. We show the perfect strong scaling that is proportional
+to the inverse number of processors as the grey dashed line for reference.
+For the disabled fluid module no background plasma was initialized and only
+cosmic rays are initialized, showing that the bulk of the computational work
+is performed by the PIC routines.
+the fluid-PIC algorithm leads to a speed-up of a factor of 100 for the
+simulation performed in Section 3.5, which adopted unrealistically
+large 𝛼.
+The bottleneck in the communication procedure of our implemen-
+tation is currently the “Ialltoallv” MPI routine, which is not optimized
+for hierarchical architecture networks as of now. Further optimiza-
+tions to this might provide fruitful in increasing the code’s scalability
+further if necessary.
+The fluid-PIC simulations in Section 3.5 used only 𝑁pc = 25 and
+seem to be sufficiently resolved. For such a low particle number, the
+FFT is the bottleneck for scalability because the overlap of commu-
+nication and computation is small, i.e. we measure a 260 per cent
+increase in time with 2880 processors, while at 192 processors the
+increase is below 20 per cent. This indicates that scalability of fluid-
+only simulations is dominated quickly by the FFT, while the cost is
+almost negligible for fluid-PIC simulations. Still, simulations with
+only a few particles per cell are computationally inexpensive so that
+there is no reason for performing such a simulation on thousands of
+processors. Furthermore, the example of a mono-energetic cold cos-
+mic ray beam is not very demanding regarding the phase-space res-
+olution. More realistic scenarios include power law distributions for
+the CR population as well as larger spatial density inhomogeneities,
+both resulting in an increased requirement for the number of parti-
+cles per cell in order to accurately resolve the velocity phase-space
+distribution along the entire spatial domain.
+4 CONCLUSION
+In this paper, we introduce a new technique termed fluid-PIC, which
+uses Maxwell’s equations to self-consistently couple the PIC method
+to the fluid equations. This technique is particularly aimed at simu-
+lating energetic particles like cosmic rays interacting with a thermal
+plasma. This enables us to resolve effects on electron time and length
+scales and to emulate Landau damping in the fluid by incorporating
+appropriate closures for the divergence of the heat flux. The under-
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+15
+lying building blocks of our implementation are the SHARP 1D3V
+PIC-code extended by a newly developed fluid module and the over-
+all algorithm is second-order accurate in space and time. While an
+ideal fluid does not exhibit Landau damping, we have implemented
+two different Landau fluid closures and studied their performance.
+Here we summarize our main findings:
+• We developed a stable multi-species fluid code that is coupled
+to explicit PIC algorithm. In order to couple multi-fluid equations to
+Maxwell’s equations, very often implicit and semi-implicit methods
+have been used for stability reasons. However, the resulting interde-
+pendency between all fluids complicates their coupling to explicit
+PIC methods. To ensure numerical stability, Riemann solvers that
+provide some numerical diffusion are used. However, we demonstrate
+that the level of numerical diffusivity needs to be carefully controlled
+so that it does not numerically damp small-amplitude plasma waves
+or quench plasma instabilities. Most importantly, our new fluid-PIC
+code fully resolves the electron timescales, precluding the need to
+adopt any simplifying assumptions to the electrical field components
+or to Ohm’s law.
+• We compare various Landau fluid closures and demonstrate
+that local closures only produce reliable results close to a charac-
+teristic scale while they are prone to fail in multi-scale problems.
+By contrast, semi-local spatial filters or global (Fourier-based) meth-
+ods to estimate Landau fluid closures produce reliable results for
+a large range of scales. Most importantly, we demonstrate that the
+inclusion of communication intensive (Fourier-based) fluid closures
+only have a minimal impact on our code performance (through the
+usage of non-blocking background communication) because the ma-
+jority of the computational workload is taken up by the much more
+cost-intensive PIC module. This enables us to make use of the more
+accurate Fourier-based Landau closure for the fluid instead of relying
+on local approximations only.
+• In numerical tests, our implementation of the multi-species fluid
+module showed excellent agreement with theoretical frequencies and
+damping rates of Langmuir waves, oscillation frequencies of various
+two fluid wave modes, as well as the non-linear Landau damping of
+Alfvén waves.
+• First simulations of the cosmic ray streaming instability with
+our combined fluid-PIC code provide very good agreement with the
+results of pure PIC simulations, especially for the growth rates and
+saturation levels of the gyro-scale and intermediate-scale instabili-
+ties. This success is achieved at a substantially lower Poisson noise
+of the background plasma at the same number of computational cos-
+mic ray particles per cell. Most importantly, the numerical cost of
+the fluid-PIC simulation is reduced by the cosmic ray-to-background
+number density ratio. However, we find that the late-time behaviour
+of the cosmic ray streaming instability differs for our fluid-PIC and
+PIC simulations. More work is needed to understand the reason for
+this, which could be either resulting from (i) numerical damping
+due to Poisson noise resulting from the finite number of PIC parti-
+cles, (ii) missing relativistic (electron) effects in our non-relativistic
+fluid dynamics, or (iii) missing physics in our fluid closures that
+may be underestimating other relevant collisionless wave damping
+processes.
+Three possible future extensions of the algorithm are left open
+here. (i) Extending the fluid formulation with a full pressure tensor,
+(ii) extending the code to two or three spatial dimensions, and (iii) the
+inclusion of direct interaction terms between the various fluids to ex-
+plicitly incorporate scattering processes such as ion-neutral damping.
+The novel fluid-PIC framework greatly extends the computationally
+limited parameter space accessible to pure PIC methods whilst not
+compromising on some of the most important microphysical plasma
+effects. This opens up many possibilities for studying cosmic ray
+physics in physically relevant parameter regimes, such as the growth
+and saturation of the cosmic ray streaming instability in different en-
+vironments, and including the effect of partial ionization, ion-neutral
+damping and inhomogeneities of the background plasma.
+ACKNOWLEDGEMENTS
+The authors acknowledge support by the European Research Coun-
+cil under ERC-CoG grant CRAGSMAN-646955 and ERC-AdG
+grant PICOGAL-101019746. The work was supported by the North-
+German Supercomputing Alliance (HLRN), project bbp00046.
+DATA AVAILABILITY
+The data underlying this article will be shared on reasonable request
+to the corresponding author.
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+APPENDIX A: C-WENO COEFFICIENTS
+We list all coefficients needed to implement the C-WENO recon-
+struction in this section. Because our reconstruction procedure is
+applied component-wise to each of the primitive variables, we as-
+sume for this appendix that we are reconstructing a single quantity
+𝑢. The smoothness indicator for the low-order polynomials are given
+by (Jiang & Shu 1996):
+IS[𝑃L] = 13
+12 (𝑢𝑖−2 − 2𝑢𝑖−1 + 𝑢𝑖)2 + 1
+4 (𝑢𝑖−2 − 4𝑢𝑖−1 + 3𝑢𝑖)2 ,
+(A1)
+IS[𝑃C] = 13
+12 (𝑢𝑖−1 − 2𝑢𝑖 + 𝑢𝑖+1)2 + 1
+4 (𝑢𝑖+1 − 𝑢𝑖−1)2 ,
+(A2)
+IS[𝑃R] = 13
+12 (𝑢𝑖 − 2𝑢𝑖+1 + 𝑢𝑖+2)2 + 1
+4 (3𝑢𝑖 − 4𝑢𝑖+1 + 𝑢𝑖+2)2 ,
+(A3)
+while four auxiliary variables are defined
+𝐷1 = (6𝑤0 − 1) (𝑢𝑖−2 + 𝑢𝑖+2) − 2 (18𝑤0 − 1) (𝑢𝑖−1 − 𝑢𝑖+1)
+48𝑤0
+, (A4)
+𝐷2 =
+1
+16𝑤0
+[(2𝑤0 − 3) (𝑢𝑖−2 + 𝑢𝑖+2) − 2 (2𝑤0 + 9) 𝑢𝑖+
++ 12 (𝑢𝑖−1 + 𝑢𝑖+1)],
+(A5)
+𝐷3 = −𝑢𝑖−2 + 2 (𝑢𝑖−1 − 𝑢𝑖+1) + 𝑢𝑖+2
+12𝑤0
+,
+(A6)
+𝐷4 = 𝑢𝑖−2 − 4𝑢𝑖−1 + 6𝑢𝑖 − 4𝑢𝑖+1 + 𝑢𝑖+2
+24𝑤0
+,
+(A7)
+to define the smoothness indicator for the 𝑃0 polynomial:
+IS[𝑃0] = 𝐷2
+1 +
+13𝐷2
+2
+3
++
+3129𝐷2
+3
+80
++
+87617𝐷2
+4
+140
++ 𝐷3𝐷1
+2
++ 21𝐷2𝐷4
+5
+.
+(A8)
+The overall smoothness indicator is given by (Cravero et al. 2018b):
+𝜏 = |IS[𝑃L] − IS[𝑃R]| .
+(A9)
+The low-order polynomials are evaluated at the left-hand interface
+of a given cell via:
+𝑃L
+�
+𝑥𝑖− 1
+2
+�
+= 1
+6 (−𝑢𝑖−2 + 5𝑢𝑖−1 + 2𝑢𝑖),
+(A10)
+𝑃C
+�
+𝑥𝑖− 1
+2
+�
+= 1
+6 (2𝑢𝑖−1 + 5𝑢𝑖 − 𝑢𝑖+1),
+(A11)
+𝑃R
+�
+𝑥𝑖− 1
+2
+�
+= 1
+6 (11𝑢𝑖 − 7𝑢𝑖+1 + 2𝑢𝑖+2),
+(A12)
+while they evaluate to
+𝑃L
+�
+𝑥𝑖+ 1
+2
+�
+= 1
+6 (2𝑢𝑖−2 − 7𝑢𝑖−1 + 11𝑢𝑖),
+(A13)
+𝑃C
+�
+𝑥𝑖+ 1
+2
+�
+= 1
+6 (−𝑢𝑖−1 + 5𝑢𝑖 + 2𝑢𝑖+1),
+(A14)
+𝑃R
+�
+𝑥𝑖+ 1
+2
+�
+= 1
+6 (2𝑢𝑖 + 5𝑢𝑖+1 − 𝑢𝑖+2),
+(A15)
+at the right-hand interface. The optimal polynomial evaluates to
+𝑃opt
+�
+𝑥𝑖− 1
+2
+�
+= 1
+60 (−3𝑢𝑖−2 + 27𝑢𝑖−1 + 47𝑢𝑖 − 13𝑢𝑖+1 + 7𝑢𝑖+2)
+= 1
+10
+�
+3𝑃L
+�
+𝑥𝑖− 1
+2
+�
++ 6𝑃C
+�
+𝑥𝑖− 1
+2
+�
++ 𝑃R
+�
+𝑥𝑖− 1
+2
+��
+,
+(A16)
+𝑃opt
+�
+𝑥𝑖+ 1
+2
+�
+= 1
+10
+�
+𝑃L
+�
+𝑥𝑖+ 1
+2
+�
++ 6𝑃C
+�
+𝑥𝑖+ 1
+2
+�
++ 3𝑃R
+�
+𝑥𝑖+ 1
+2
+��
+, (A17)
+at both interfaces of the cell. The interface values of 𝑃0 can be derived
+from equation (24).
+APPENDIX B: CONVERGENCE ORDER
+In order to numerically prove a second order scaling of the plasma
+frequency for the different heat flux closures, the linear dispersion of
+MNRAS 000, 1–17 (2022)
+
+Fluid-particle-in-cell method with Landau closures
+17
+24
+25
+26
+27
+28
+29
+cells per wave length [resolution]
+10−5
+10−4
+10−3
+10−2
+10−1
+rel. error |휔| [%]
+ideal gas
+Landau 푅32
+Landau 푅31
+Figure B1. Relative error
+��(𝜔sim − 𝜔theor)/𝜔theor�� of the simulated fre-
+quency of a Langmuir wave at 𝑘 = 0.05𝑘D. The same simulation setup is
+used in Fig. 5, where we use a resolution of 68 cells per wavelength. The
+resolution here is varied between 68/4 = 17 to 68 × 10 cells per wavelength.
+The grey line is a reference line for the second-order scaling of the error.
+the Langmuir wave setup described in Section 3.3 is simulated at dif-
+ferent resolutions of 𝜆/Δ𝑥. We concentrate here on the convergence
+of a wave with wavenumber 𝑘/𝑘D = 0.05. The results are shown in
+Fig. B1 and demonstrate a very good match with the predicted errors
+assuming a second order convergence. At first sight, the Landau clo-
+sures do not seem to scale ideally for higher resolutions. However,
+this is the result of physical plasma heating due to wave damping
+in our setup leading to a non-linear increase in the expected plasma
+frequency.
+APPENDIX C: 𝑅31 CLOSURE AND ADIABATIC
+COEFFICIENTS
+While the 𝑅32 closure assumes a fixed adiabatic index Γ of 3, the 𝑅31
+closure introduces a term proportional to ˆ𝑤 which alters the pressure
+equation in such a way that it increases the effective adiabatic index.
+To show this, we simplify equation (42) by introducing the numerical
+coefficients 𝑎𝑤 and 𝑎𝑇 which are defined by comparing
+ˆ𝑄 = 𝑎𝑤𝑝0 ˆ𝑤 + i sign (𝑘) 𝑎𝑇 ˆ𝑇.
+(C1)
+to equation (42). Using this ansatz and perturbing the pressure equa-
+tion (30) with 𝑝 = 𝑝0 + 𝑝1, where 𝑝1 is the perturbation to the mean
+pressure 𝑝0, in the absence of direct Landau damping (𝑎𝑇 = 0), we
+have
+𝜕𝑝1
+𝜕𝑡
+= (−Γ𝑝 − 𝑎𝑤𝑝0) ∇ · 𝒘 − 𝒘 · ∇𝑝
+= (−Γeff 𝑝0 − Γ𝑝1) ∇ · 𝒘 − 𝒘 · ∇𝑝,
+(C2)
+where Γeff = 𝑎𝑤 + Γ = 4/(4 − π) ≃ 4.66 can be interpreted as the
+effective adiabatic index of the fluid. The evolution of sound waves
+of a non-electromagnetic fluid in the linear regime is governed by
+the linear term Γeff 𝑝0∇ · 𝒘 while the term Γ𝑝1∇ · 𝒘 adds non-
+linearity to this equation. In the linear approximation, the speed
+of sound becomes 𝑐s = (Γeff 𝑝0/𝑛0)1/2 which coincides with the
+typical expression for the sound speed 𝑐s = (Γ𝑝0/𝑛0)1/2 in the limit
+of 𝑎𝑤 = 0. This implies that the speed of sound is increased for the
+𝑅31 closure even if direct Landau damping is not present (𝑎𝑇 = 0).
+Interestingly, the effective adiabatic index and the speed of sound
+are independent of the choice of Γ. If direct Landau damping, as
+described by the 𝑅31 closure, is affecting the fluid (i.e., 𝑎𝑇 ≠ 0),
+then the effective adiabatic index attains somewhat smaller values in
+comparison to 𝑎𝑤 + Γ while the wave frequency becomes complex
+because of the associated damping. Both are still independent of the
+choice of Γ.
+This has consequences for simulations that model mildly relativis-
+tic fluids. If a simulation setup includes a fluid with an associated
+speed of sound near the speed of light 𝑐s ≲ 𝑐, then a simulation that
+uses this setup with the 𝑅31 closure can become unstable because
+𝑐s can now exceed the speed of light because of the aforementioned
+reason.
+This paper has been typeset from a TEX/LATEX file prepared by the author.
+MNRAS 000, 1–17 (2022)
+
diff --git a/G9E3T4oBgHgl3EQftwvH/content/tmp_files/load_file.txt b/G9E3T4oBgHgl3EQftwvH/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a86e9579eddf919e3af709f3f4eb6d9035b3e41e
--- /dev/null
+++ b/G9E3T4oBgHgl3EQftwvH/content/tmp_files/load_file.txt
@@ -0,0 +1,1197 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf,len=1196
+page_content='MNRAS 000, 1–17 (2022)  Preprint 13 January 2023  Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  Coupling multi-fluid dynamics equipped with Landau closures to the  particle-in-cell method  Rouven Lemmerz,1,2 ★ Mohamad Shalaby,1 † Timon Thomas,1 Christoph Pfrommer1  1 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany  2 University of Potsdam, Institute of Physics and Astronomy, Karl-Liebknecht-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 24-25, 14476 Potsdam, Germany  Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' in original form ZZZ  ABSTRACT  The particle-in-cell (PIC) method is successfully used to study magnetized plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, this requires large computational  costs and limits simulations to short physical run-times and often to setups in less than three spatial dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Tradition-  ally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC  methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Because both methods  preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-  conservative multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell’s  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This avoids simplifications typically adopted for Ohm’s Law and enables us to fully resolve the electron temporal  and spatial scales while retaining the versatility of initializing any number of ion, electron, or neutral species with arbitrary  velocity distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The fluid solver includes closures emulating Landau damping so that we can account for this important  kinetic process in our fluid species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Our fluid-PIC code is second-order accurate in space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The code is successfully  validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping  rates of waves in unmagnetized and magnetized plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' It also matches growth rates and saturation levels of the gyro-scale and  intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison  to linear theory and PIC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This new fluid-SHARP code is specially designed for studying high-energy cosmic rays  interacting with thermal plasmas over macroscopic timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Key words: plasmas – hydrodynamics – methods: numerical – cosmic rays  1 INTRODUCTION  The PIC method (Dawson 1962;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Langdon & Birdsall 1970;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hockney  1988;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Birdsall & Langdon 1991) has become one of the most used  methods for studying plasmas from laboratory to astrophysical scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Due to its ability to resolve kinetic processes, it became one of the  most successful research tools in computational plasma physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Ex-  amples of that include revolutionizing our understanding of the rich  physics found in collisionless shocks (Spitkovsky 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Marcowith  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2016), magnetic reconnection (Daughton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2006, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Sironi & Spitkovsky 2014), instabilities driven by highly relativis-  tic electron-positron beams (Bret et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2017b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2018, 2020), as well as the transport of non-thermal  particle populations like cosmic rays (Holcomb & Spitkovsky 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, the PIC method needs to advance nu-  merous particles per cell each time step, and thus it is quick to reach  its computational limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Even one-dimensional simulations usually  only capture dynamics on very short physical times and the extent  to which two or three-dimensional simulations can be performed is  very limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The time-gap between the inverse of the electron plasma frequency,  ★ E-mail: rlemmerz@aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='de (RL)  † E-mail: mshalaby@live.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='ca (MS)  𝜔−1  e , (which is necessary to ensure the stability of the PIC algorithm)  and that of the ion plasma frequency, 𝜔−1  i , depends on the ion-to-  electron mass ratio, since 𝜔−1  i /𝜔−1  e  = (𝑚i/𝑚e)1/2, assuming charge  neutrality, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' that the electron and ion densities are equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' There-  fore, one frequently used trick to increase the computational effi-  ciency in PIC simulations is to adopt a reduced ion-to-electron mass  ratio to bridge the gap between the smallest timescale in the simula-  tion and the larger timescale on which interesting physical processes  occur/evolve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, this might lead to artificial suppression of  physical effects (Bret & Dieckmann 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Moreno  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2018), including instabilities with excitation conditions that de-  pend on the mass ratio (Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This  shows the need for a more efficient numerical method to complement  the accurate results achieved by PIC simulations in order to enable  simulations of realistic physics occurring on longer timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Fluid codes use a coarse-grained description of the plasma, which  describes vast amounts of particles with just a few macroscopic pa-  rameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This results in a large speed-up in comparison to the PIC  method, while sacrificing some accuracy by neglecting kinetic ef-  fects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hybrid-PIC codes (Lipatov 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Gargaté et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2007) treat  electrons as a fluid and ions as particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' With the assumption of  charge neutrality and the Darwin approximation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' neglecting the  transverse displacement current), these codes are able to overcome  some computational barriers while omitting effects on the electron  © 2022 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='04679v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='HE]  11 Jan 2023  2  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  time and length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Since this eliminates the need to resolve elec-  tron scales, the increase in computational efficiency from pure-PIC  to hybrid-PIC methods is roughly a factor of (𝑚i/𝑚e)1/2 in timescale  and about the same factor in spatial scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  On the other hand, an even more efficient method exists, that com-  bines a magneto-hydrodynamic (MHD) description of the thermal  background plasma with PIC methods for the evolution of energetic  particles such as cosmic rays (Bai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' van Marle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2018),  called MHD-PIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, this method inherits the assumptions  of MHD, in particular, the use of (simplified) Ohm’s law by fully  neglecting the displacement current, which precludes physics asso-  ciated with higher-order terms of Ohm’s law as well as the electron  dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  To improve upon these shortcomings, we developed a fluid-PIC  method, where a multi-fluid solver is coupled to the PIC method  by summing their contributions to the charge and current densities  used to solve Maxwell’s equations, and the resulting electromag-  netic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Thus, the subsequent dynamics is dictated by fluid and  PIC species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This enables treating any arbitrary number of species  in thermal equilibrium by modelling them as separate fluids that  interact electromagnetically with each other and with particles of  arbitrary momentum distribution (modelled using the PIC method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In contrast to MHD-PIC and hybrid-PIC methods, we do not ex-  plicitly assume Ohm’s law, and instead, solve Maxwell’s equations  in a fully self-consistent manner in our fluid-PIC code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Therefore,  displacement currents are included in our model and fast changes  in the electric field and electron dynamics are captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This, in  turn, allows studying the interaction of high energy particles with  the background plasma, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' to investigate cosmic ray streaming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' An-  other hybrid approach resolving electron timescales fully, but using  pressure coupling, has been used for simulation of pick-up ions in  the heliosphere by Burrows et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Often implicit and semi-implicit methods are utilized for stabil-  ity and resolution reasons to couple the multi-fluid equations to  Maxwell’s equations (Hakim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Shumlak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Wang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, this creates an interdependency between all  fluids and has limited utility when coupled to explicit particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We  have developed an explicit multi-fluid solver in which each fluid  and particle species is agnostic about each other and the coupling is  achieved via an indirect current-coupling scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Because the PIC  part of the code is the most computationally expensive part of the  fluid-PIC, hybrid-PIC, and MHD-PIC methods, the computational  efficiency is mostly determined by the number of particles required  as well as the smallest time and length scales that need to be resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Hence, this fluid-PIC approach results in large speed-ups for cosmic  ray propagation simulations in comparison to traditional hybrid-PIC  codes, which treat every ion as a particle and need to initialise a  large number of particles according to the density ratio, as well as in  comparison to PIC-only simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Especially studying comic ray  propagation in the interstellar medium (ISM), where the typical cos-  mic ray density is of the order 10−9 times the ISM number density,  is challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Since the fluid-PIC algorithm is faster by orders of  magnitude in comparison to PIC in such a case, we can reach further  into the realistic parameter regime without sacrificing some essential  microphysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  One of the most important kinetic effects is arguably Landau  damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The fluid description can emulate this effect using Landau  closures (Hammett & Perkins 1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Umansky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hunana  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2019), which necessitates the computation of the heat flux in  Fourier space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While Fourier transforms in 1D are not easily par-  allelizable, this bottleneck can partially be mitigated by performing  global communications of the message-passing interface (MPI) in  the background while processing the high computational load (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  resulting from evolving orbits of PIC particles) in the foreground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Simulations with periodic boundary conditions are currently han-  dled by convolution with a finite-impulse-response (FIR) filter in our  code, but other options are available in the literature (Dimits et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A number of simplifying local approxi-  mations exist as well (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Allmann-Rahn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2020), which scale computationally well but become inac-  curate for studying some multiscale plasma physics problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Our  code implements these different approaches so that an appropriate  one can be chosen, dependent on the requirements of a simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Our implementation is massively parallelized and can be efficiently  run on thousands of cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Furthermore, the fluid-PIC method allows for any multi-fluid  setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' As such, this framework allows for some straightforward ex-  tensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Potentially, this involves a setup with actively participating  neutrals to incorporate ion-neutral damping into this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' To this  end, the coupling between different fluids needs to be extended by a  collision term, which is left as a future extension to the code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The outline of this paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In Section 2, we introduce  the pillars of this method and describe the PIC method, the fluid  solver, how we couple both methods by means of electromagnetic  fields, and describe various implementations of the Landau closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In Section 3, we show validation tests of the fluid solver (shock tube  tests), linear waves in an ion-electron plasma, and the damping rate  of Langmuir waves in a single-electron fluid with Landau closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  We then investigate the non-linear effects of two interacting Alfvén  waves as well as cosmic-ray-driven instabilities, where fluid-PIC and  PIC results are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We conclude in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Throughout this  work, we use the SI system of units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2 NUMERICAL METHOD  After a review of the kinetic description of a plasma in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1,  we briefly introduce our PIC method in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The fluid de-  scription for plasmas and its assumptions are given in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The finite volume scheme we use to numerically solve the compress-  ible Euler equations is described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4, while the electro-  magnetic interactions of the fluid are described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In  Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6, we describe the Landau closure we adopt in order to  mimic the Landau damping in kinetic thermal plasmas within the  fluid description, and detail its implementation in our code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We close  this section by describing the overall code structure of the fluid-PIC  algorithm and finally discuss the interaction between the modules  via the current-coupling scheme (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 Kinetic description of a plasma  The kinetic description of a collisionless relativistic plasma with  particles of species s with elementary mass, 𝑚s, and elementary  charge, 𝑞s, is given by the Vlasov equation,  𝜕 𝑓s  𝜕𝑡 + u  𝛾 · ∇ 𝑓s + as · ∇𝑢 𝑓s = 0,  (1)  where 𝑓s = 𝑓s(x, 𝒗, 𝑡) is the distribution function, u = 𝛾𝒗 is the  spatial component of the four-velocity with the Lorentz factor 𝛾 =  [1 + (𝒗/𝑐)2]−1/2, and 𝑐 is the light speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The acceleration due to  the Lorentz force is given by  as = 𝑞s  𝑚s  [E (x, 𝑡) + 𝒗 × B (x, 𝑡)] ,  (2)  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  3  where E (x, 𝑡) and B (x, 𝑡) are the electric and magnetic fields, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The evolution of electric and magnetic fields is governed  by Maxwell’s equations:  𝜕B  𝜕𝑡 = −∇ × E,  ∇ · B = 0,  (3)  𝜕E  𝜕𝑡 = 𝑐2∇ × B − J  𝜀0  ,  ∇ · E = 𝜌  𝜀0  ,  (4)  where 𝑐 = 1/√𝜀0𝜇0 is the vacuum speed of light, and 𝜀0 and 𝜇0 are  the permittivity and the permeability of free space, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  evolution of the electro-magnetic fields is influenced by the charge  density, 𝜌, and current density, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' They are given by the charge-  weighted sum over all species of the number densities 𝑛s and bulk  velocities 𝒘s respectively,  𝜌 (x, 𝑡) =  ∑︁  𝑠  𝑞𝑠𝑛𝑠 (x, 𝑡)  =  ∑︁  𝑠  𝑞𝑠  ∫  𝑓𝑠 (x, 𝒗, 𝑡) d3𝑣,  (5)  J (x, 𝑡) =  ∑︁  𝑠  𝑞𝑠𝑛𝑠 (x, 𝑡) 𝒘𝑠 (x, 𝑡) =  ∑︁  𝑠  𝑞𝑠  ∫  𝒗 𝑓𝑠 (x, 𝒗, 𝑡) d3𝑣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (6)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 The particle-in-cell method  We use the PIC method to solve for the evolution of plasma species  that are modelled with the kinetic description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The PIC method ini-  tializes a number of computational macroparticles to approximate  the distribution function in a Lagrangian fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Each macroparticle  represents multiple physical particles and, as such, each macroparti-  cle has a shape in position space which can be represented by a spline  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' By depositing the particle motions and positions to the nu-  merical grid (or computational cells), the electromagnetic fields can  be computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This step is followed by a back-interpolation of these  fields to the particle positions so that the Lorentz forces on the par-  ticles can be computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In our implementation, these equations are  solved using one spatial dimension and three velocity dimensions  (1D3V), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' ∇ = (𝜕/𝜕𝑥, 0, 0)T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The code quantities are defined as multiples of the fiducial units  given for time, fields (electric and magnetic), charge, current density  and length  𝑡0 =  √︃  𝑚0𝜖0/(𝑞2  0𝑛0),  𝐸0 =  √︃  𝑛0𝑚0𝑐2/𝜖0,  𝜌0 = 𝑞0𝑛0,  𝐽0 = 𝜌0𝑐,  𝑥0 = 𝑐𝑡0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (7)  This enables us to select a fixed time step of  Δ𝑡 = 𝐶cfl𝑐Δ𝑥  (8)  where 𝐶cfl < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 to satisfy the Courant-Friedrichs-Lewy (CFL) con-  dition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The value of the reference density 𝑛0 is chosen such that the  code timescale, 𝑡0, obeys 𝜔−2  p  = 𝑡2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The total plasma frequency is  𝜔p = (�  𝑠 𝜔2𝑠)1/2, and related to the plasma frequencies of the in-  dividual species, 𝜔2s = 𝑞2s 𝑛s/(𝑚𝑠𝜖0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We define the discretized time  𝑡𝑘 = 𝑘Δ𝑡, position 𝑥𝑖 = 𝑖Δ𝑥 and quantities at discrete position and  times as E𝑘  𝑖 = E(𝑡𝑘, 𝑥𝑖).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For details on the PIC code SHARP, the  reader is referred to Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2017a, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Here, we focus  on describing how SHARP is extended to include fluid treatment of  some plasma species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3 Fluid description of plasma  A straightforward way of coarse graining the Vlasov equation (1) is  to reduce its dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' By taking the 𝑗-th moment over velocity  space, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  ∫  𝒗 𝑗 𝑓 𝑑3𝑣, we retrieve the fluid quantities and reduce the  dimensionality of the 1D3V kinetic description to 1D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The number  density 𝑛s and the bulk velocity 𝒘s are defined through the zeroth  and first moment of the distribution function, respectively, while the  total energy density per unit mass 𝜖𝑠 and the scalar pressure per unit  mass 𝑝𝑠 are related to the second moment (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2015):  𝑛s (x, 𝑡) =  ∫  𝑓s (x, 𝒗, 𝑡) d3𝑣,  (9)  𝒘s (x, 𝑡) =  ∫  1  𝑛s (x, 𝑡) 𝒗 𝑓s (x, 𝒗, 𝑡) d3𝑣,  (10)  𝜖s (x, 𝑡) =  ∫  1  2𝒗2 𝑓s (x, 𝒗, 𝑡) d3𝑣,  (11)  𝑝s (x, 𝑡) =  ∫  (𝑣𝑥 − 𝑤s,𝑥)2 𝑓s (x, 𝒗, 𝑡) d3𝑣  = Γ − 1  2  ∫  (𝒗 − 𝒘s)2 𝑓s (x, 𝒗, 𝑡) d3𝑣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (12)  Here, the pressure tensor is under the adiabatic assumption and the  degrees of freedom are encoded in the adiabatic index Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The follow-  ing relation is found from the definitions  𝜖s =  𝑝s  Γ − 1 + 1  2 𝑛s 𝒘s · 𝒘s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (13)  The first three moments of the of the Vlasov equation are called  the continuity, momentum, and energy conservation equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A set  of these equations is found for each fluid species, but the subscript s  is neglected here for simplicity:  𝜕𝑛  𝜕𝑡 + ∇ · (𝑛𝒘) = 0,  (14)  𝜕𝑛𝒘  𝜕𝑡  + ∇ · [𝑝1 + 𝑛𝒘𝒘] = 𝑞  𝑚 S𝑤 (𝑛, 𝒘, B, E) ,  (15)  𝜕𝜖  𝜕𝑡 + ∇ · [(𝑝 + 𝜖)𝒘] +  1  Γ − 1∇ · Q = 𝑞  𝑚 𝒘 · S𝑤 (𝑛, 𝒘, B, E) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (16)  We assumed the non-relativistic limit and an isotropic pressure tensor  with vanishing non-diagonal components, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' the inviscid limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  notation 𝒘𝒘 indicates the dyadic product of the two vectors and 1  is the unit matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Similar to the definition of the scalar pressure in  equation (12) we use a definition of the heat flux vector, which is  normalized to the degrees of freedom as well  Q (x, 𝑡) = Γ − 1  2  ∫  (𝒗 − 𝒘)2 (𝒗 − 𝒘) 𝑓 (x, 𝒗, 𝑡) d3𝑣.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (17)  The electromagnetic source term is given by  S𝑤 (𝑛, 𝒘, B, E) = 𝑛 (E + 𝒘 × B) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (18)  The general form of the fluid equations can be written as  𝜕 ˜U  𝜕𝑡 + ∇ · F( ˜U) = S( ˜U),  (19)  where ˜U = ˜U(x, 𝑡) = (𝑛, 𝑛𝒘, 𝜖)T is the fluid state vector at position  (x, 𝑡), F is the flux matrix, and S is the source vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Numerically, the complexity of solving equation (19) can be re-  duced by splitting the operator into less complex sub-operators using  Strang operator splitting (Strang 1968;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hakim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This  enables us to use the most appropriate solver for each subsystem  sequentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We split the fluid update into three parts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' the flux F  excluding the heat flux (see Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4), the electromagnetic source  Sem = S𝑤𝑞/𝑚 (see Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1), and the heat flux Q (see Sec-  tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For commuting operators exp(Δ𝑡Q) and exp(Δ𝑡Sem) a  second order accurate Strang splitting is obtained as  U𝑛+ 1  2 = e  Δ𝑡  2 FeΔ𝑡QeΔ𝑡Seme  Δ𝑡  2 FU𝑛− 1  2 + 𝑂(Δ𝑡3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (20)  MNRAS 000, 1–17 (2022)  4  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Since Q and S act independently1 on the entries 𝑝 and 𝒘 respectively,  the order of applying them can be varied and they need to be evaluated  only once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4 Finite volume scheme  The 1D3V fluid equations are solved using a finite volume method,  where the fluid equations are averaged over the cell volume, which  is an interval of length Δ𝑥 in 1D,  U𝑖 (𝑡) = 1  Δ𝑥  ∫ 𝑥𝑖+ 1  2  𝑥𝑖− 1  2  ˜U (𝑥, 𝑡) d𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (21)  This enables us to correctly conserve the overall fluid mass, fluid  momentum and fluid energy, even in the presence of large gradients,  by utilizing Gauss’ theorem:  1  Δ𝑥  ∫ 𝑥𝑖+ 1  2  𝑥𝑖− 1  2  𝜕F( ˜U)  𝜕𝑥  d𝑥 = 1  Δ𝑥  �  F𝑖+ 1  2 − F𝑖− 1  2  �  (22)  where the flux through an interface at 𝑥𝑖 is F𝑖 (𝑡) = F[ ˜U(𝑥𝑖, 𝑡)],  leading to the update equation  𝜕U𝑖(𝑡)  𝜕𝑡  = 1  Δ𝑥  �  −F𝑖+ 1  2 + F𝑖− 1  2 +  ∫  S� ˜U(𝑥, 𝑡)�d𝑥  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (23)  Integrating equation (23) in time is achieved by using second, third, or  fourth-order Runge-Kutte methods (Butcher 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In contrast to the  finite difference scheme used for electromagnetic fields and particles,  where electromagnetic quantities are point values, fluid quantities  discretized with the finite volume method are cell averages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is  useful, because the finite difference method does not guarantee the  conservation of the conservation equations (14) through (16), which  are governing the fluid;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' while on the other hand using the finite  volume method for the electromagnetic fields needs additional steps  to satisfy the constraint ∇ · B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hybridization of both schemes  to combine the advantages of each has been used before in other  contexts, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Soares Frazao & Zech (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The maximum time step in the 1D3V Euler equations, which al-  lows for stable simulations, is Δ𝑡 < 𝐶cflΔ𝑥×(|𝑤|+𝑐s), with the speed  of sound 𝑐s = (Γ𝑝/𝑛)1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For all realistic setups these velocities are  limited naturally by the speed of light, |𝑤| < 𝑐 and 𝑐s < 𝑐, and  this condition is automatically fulfilled by the time step criterion in  equation (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In practice, only equation (8) together with a suitable  Courant number of 𝐶cfl ⩽ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 is used to determine the time step of  the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 Reconstruction  To approximate the flux at interfaces, we need to reconstruct the  fluid state at cell interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The accuracy of the reconstruction has a  crucial influence on the diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A lower-order reconstruction can  lead to excessive damping of waves, which might suppress relevant  physical effects on longer timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  For reconstructing the point value ˜U(𝑥𝑖+1/2, 𝑡), which is needed  to compute F𝑖+1/2, we employ a central weighted essentially non-  oscillatory reconstruction (C-WENO) scheme of spatial order five.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The reconstruction computes two point values at each interface  1 In practice the formulation of Q might partially depend on 𝒘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In this case,  Strang splitting is performed on this part of the operator Q as well, see  equation (43).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  𝑥𝑖+1/2, an interpolation from the left- and right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We re-  construct the primitive variables 𝑛, 𝒘, and 𝑝 individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Our implementation of the C-WENO method is based on the 5th  order scheme presented in Capdeville (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' An introduction to  the topic can be found in Cravero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The C-WENO  reconstruction uses a convex combination of multiple low-order re-  construction polynomials to achieve high-order interpolations of the  interface values while it employs a non-linear limiter to degrade this  high-order interpolation to a lower order if the reconstructed quantity  contains discontinuities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The fifth-order C-WENO uses three third-  order polynomials 𝑃L(𝑥), 𝑃C(𝑥), 𝑃R(𝑥) for each cell 𝑖 to interpolate  the four adjacent cells in the following way:  𝑃L(𝑥)  interpolates values at  𝑖 − 2  𝑖 − 1  𝑖  𝑃C(𝑥)  interpolates values at  𝑖 − 1  𝑖  𝑖 + 1  𝑃R(𝑥)  interpolates values at  𝑖  𝑖 + 1  𝑖 + 2  while the optimal fifth-order polynomial interpolates all of them:  𝑃opt(𝑥)  interpolates values at  𝑖 − 2  𝑖 − 1  𝑖  𝑖 + 1  𝑖 + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  We define an additional polynomial  𝑃0(𝑥) = 1  𝑑0  ������  𝑃opt(𝑥) −  ∑︁  𝑞∈[L,C,R]  𝑑𝑞𝑃𝑞(𝑥)  ������  ,  (24)  where 𝑑0 + 𝑑L + 𝑑C + 𝑑R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The polynomials 𝑃0, 𝑃L, 𝑃C, and 𝑃R  are a convex representation of the 𝑃opt polynomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We use 𝑑0 = 3/4,  𝑑C = 2/16, and 𝑑L = 𝑑R = 1/16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In general, we would like to use the reconstruction provided by  the 𝑃opt polynomial as frequently as possible because of its high-  order nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' But this high-order reconstruction can cause oscillations  similar to the Gibbs phenomenon at discontinuities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Therefore, we  need to employ a limiting strategy to avoid such behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In order  to accomplish this, we re-weight all of our 𝑑-coefficients by taking  the smoothness of the associated polynomial into account (Jiang &  Shu 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We define  𝛼𝑞 = 𝑑𝑞  ������  1 +  �  𝜏  IS[𝑃𝑞] + 10−9Δ𝑥  �2������  for 𝑞 ∈ [0, L, C, R],  (25)  where 𝜏 is a measure for the overall smoothness of the reconstructed  variables, and IS[𝑃𝑞] defines a smoothness indicator of the low-order  polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Because the formulae for these smoothness indicators  are quite cumbersome, we list them in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' These coefficients  define a new set of normalized weights given by  𝑤𝑞 =  𝛼𝑞  𝛼0 + 𝛼L + 𝛼C + 𝛼R  for 𝑞 ∈ [0, L, C, R].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (26)  The final reconstructed polynomial is then given by the convex com-  bination of the low-order polynomials using this set of normalized  weights:  𝑃rec(𝑥) = 𝑤0𝑃0(𝑥) + 𝑤L𝑃L(𝑥) + 𝑤C𝑃C(𝑥) + 𝑤R𝑃R(𝑥),  (27)  which we evaluate at the cell interfaces to calculate the required left-  and right-handed interface values for the Riemann solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We detail  how these polynomials are evaluated in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The smoothness indicators IS[𝑃𝑞] vanish if the underlying poly-  nomials are smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In this case, the re-weighted coefficients reduce  to their original value 𝛼𝑞 → 𝑑𝑞 and the reconstructed polynomial  reduces to the optimal polynomial 𝑃rec(𝑥) → 𝑃opt(𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 Riemann solver  The previous reconstruction step determines two, potentially differ-  ent, values ˜UL and ˜UR for each quantity to the left and right of every  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  5  interface, thereby providing the initial conditions for the Riemann  problem:  𝜕U  𝜕𝑡 = −∇ · F( ˜U)  (28)  ˜U(𝑥, 0) =  � ˜UL,  𝑥 < 0  ˜UR,  𝑥 > 0  (29)  An (approximate) Riemann solver is employed to compute the nu-  merical flux F( ˜U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While a number of different families of Riemann  solvers have been developed with individual strengths and weak-  nesses, we have decided to implement multiple solvers which can be  changed on demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Implemented solvers in fluid-SHARP include a  Roe solver with entropy fix (Roe 1981;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Harten & Hyman 1983) and  an HLLC solver (Toro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While the Roe solver yields more  accurate solutions and fewer overshoots in our tests in comparison  to the HLLC solver, it becomes unstable in near vacuum flows and  strong expansion shock waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Even though differences between the  solvers are easily visible in some shock setups and artificially ex-  treme conditions, they are typically negligible in most applications  common for thermal plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We opt to employ the HLLC solver as  our standard for stability purposes and use the Roe solver in cases  where stronger shocks with overshoots are expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 Electromagnetic interaction with charged fluids  In this section, we first introduce the Lorentz force as a source term  in equation (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Furthermore, we describe how the fluid influences  the electromagnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' With these two additional parts, the de-  scription from an uncharged gas in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4 is expanded here to  include plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 Treatment of electromagnetic source term  Instead of integrating the energy equation (16), which would re-  quire evaluating the source term on the right-hand side, we compute  the time evolution of the primitive pressure variable, for which the  electromagnetic source term conveniently vanishes:  𝜕𝑝  𝜕𝑡 + Γ𝑝∇ · 𝒘 + 𝒘 · ∇𝑝 + ∇ · Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (30)  Then only the computation of the source term for the momentum  equation (15) is left, which uses the Boris integrator (Boris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  1970) to account for the Lorentz force on the fluid momentum vec-  tors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Up until now we have only applied the C-WENO method for  conservation laws, however, by adding the source term, we are left  with a balance law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In C-WENO formulations for balance laws it  is customary to approximate the integral of the source term (equa-  tion 23) numerically to higher orders as well (Cravero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  We use Simpson’s Formula for approximating equation (23)  ∫ 𝑥𝑖+1/2  𝑥𝑖−1/2  S � ˜U� d𝑥 = 1  6  �  S( ˜U𝑖− 1  2 ) + 4S( ˜U𝑖) + S( ˜U𝑖+ 1  2 )  �  + O(Δ𝑥5),  (31)  where the intra-cell values ˜U𝑖±1/2 are interpolated by the same C-  WENO scheme as used for solving the hydrodynamical equations,  and the centre-value is computed self-consistently with the numerical  integration formula, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' ˜U𝑖 = (6U𝑖 − ˜U𝑖+1/2 − ˜U𝑖−1/2)/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We also  need to interpolate the electromagnetic field values to a comparable  spatial order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is achieved by performing finite-difference inter-  polations for each component from the Yee mesh discretized fields,  that is  𝐸𝑖+ 1  2 = 150(𝐸𝑖 + 𝐸𝑖+1) − 25(𝐸𝑖−1 + 𝐸𝑖+2) + 3(𝐸𝑖−2 + 𝐸𝑖+3)  256  + O(Δ𝑥6),  (32)  and temporal order, 𝐵𝑛 = (𝐵𝑛+1/2 + 𝐵𝑛−1/2)/2, again, for each  component necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Lower order approximations produce, in our  tests, similar results, but converge to slightly lower wave frequencies  when compared with the analytical solution of the dispersion relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 Deposition of charges  Equations (4) govern the electric field evolution, where Faraday’s or  Gauss’ law might be used to compute E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In this section we focus on  the one-dimensional setup without particle contributions, which are  explained in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The perpendicular components’ update, 𝐸𝑦  and 𝐸𝑧, is received straightforwardly by discretizing Faraday’s Law  �𝐸𝑦  �𝑛+1  𝑖+ 1  2 = �𝐸𝑦  �𝑛  𝑖+ 1  2 −  ∑︁  𝑠  Δ𝑡  𝜖0  𝑞𝑠  �𝑛𝑤𝑦  �𝑛+ 1  2  𝑖+ 1  2 ,𝑠  − 𝑐2Δ𝑡  Δ𝑥  �  (𝐵𝑧)𝑛+ 1  2  𝑖+1 − (𝐵𝑧)𝑛+ 1  2  𝑖  �  (33)  (𝐸𝑧)𝑛+1  𝑖+ 1  2  = (𝐸𝑧)𝑛  𝑖+ 1  2  −  ∑︁  𝑠  Δ𝑡  𝜖0  𝑞𝑠 (𝑛𝑤𝑧)𝑛+ 1  2  𝑖+ 1  2 ,𝑠  + 𝑐2Δ𝑡  Δ𝑥  ��𝐵𝑦  �𝑛+ 1  2  𝑖+1 − �𝐵𝑦  �𝑛+ 1  2  𝑖  �  ,  (34)  where the sum is taken over all fluid species s and 𝑛𝒘 are components  of the fluid vector U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  For the 𝐸𝑥 component in spatial direction however, in order to  enforce charge-conservation, Gauss’ law in discretized form needs  to be enforced for all 𝑖 ⩾ 1 as well  (𝐸𝑥)𝑛  𝑖 = (𝐸𝑥)𝑛  0 +  ∑︁  𝑠  𝑞𝑠  𝜖0  𝑖−1  ∑︁  𝑗=0  𝑛𝑛  𝑗+ 1  2 ,𝑠Δ𝑥  = (𝐸𝑥)𝑛  0 +  ∑︁  𝑠  𝑞𝑠  𝜖0  ∫ 𝑥𝑖  𝑥0  ˜𝑛𝑛  𝑠 d𝑥,  (35)  where the second equality uses the definition of cell averages in the  finite volume scheme (see equation 21) and shows, that this numeri-  cal formula is exact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Another formula for updating (𝐸𝑥)0 to the time  step 𝑛 is still needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In the analytical case Gauss’ law in combina-  tion with the density conservation equation (14) for the analytical  flux (or cell values) 𝐽𝑥 ∝ 𝑞𝑛𝑤𝑥 can be shown to be equivalent to  Faraday’s law;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' in the numerical case this equivalency is shown using  the discretized conservation equation and corresponding numerical  flux 𝐽𝑥 ∝ 𝑞𝐹𝑛( ˜U) ≃ 𝑞𝑛𝑤𝑥 for the current density 𝐽𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Taking the  time derivative of equation (35) in conjunction with the discretized  density update equation (23) leads to the expression  (𝐸𝑥)𝑛+1  𝑖  − (𝐸𝑥)𝑛  𝑖  Δ𝑡  +  (𝐸𝑥)𝑛+1  0  − (𝐸𝑥)𝑛  0  Δ𝑡  =  ∑︁  𝑠  𝑞𝑠  𝜖0Δ𝑡  ∫ 𝑡𝑛+1  𝑡𝑛  �  −(𝐹𝑛,𝑠)𝑖 + (𝐹𝑛,𝑠)0  �  d𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (36)  The integration in time using Runge-Kutta methods is the same as  used to solve equation (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Faraday’s law using fluxes in one spatial  dimension is then given by  (𝐸𝑥)𝑛+1  𝑖  = (𝐸𝑥)𝑛  𝑖 −  ∑︁  𝑠  𝑞𝑠  𝜖0  ∫ 𝑡𝑛+1  𝑡𝑛  �  𝐹𝑛  � ˜U��  𝑖,𝑠 d𝑡,  (37)  MNRAS 000, 1–17 (2022)  6  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  and enables us to identify 𝐽𝑥 by comparison to the charge conserva-  tion equation (equation 14 multiplied by 𝑞s)  (𝐽𝑥)𝑛+1/2  𝑖  =  ∑︁  𝑠  𝑞𝑠  Δ𝑡  ∫ 𝑡𝑛+1  𝑡𝑛  �  𝐹𝑛  � ˜U��  𝑖,𝑠 d𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (38)  Note, that the numerical flux also includes numerical diffusion and is  directly related to changes in 𝜌.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Due to this, other formulations for 𝐽𝑥  violate the charge conservation equation and can lead to numerical  instabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3 Magnetic field evolution  Because the fluid evolution influences the magnetic field only in-  directly, the finite-difference time-domain (FDTD) update for the  magnetic field is unchanged from the previous SHARP code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For  completeness we reproduce the formulae here (Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2021)  (𝐵𝑦)𝑛+ 1  2  𝑖  = (𝐵𝑦)𝑛− 1  2  𝑖  + Δ𝑡  Δ𝑥  �  (𝐸𝑧)𝑛  𝑖+ 1  2  − (𝐸𝑧)𝑛  𝑖− 1  2  �  ,  (39)  (𝐵𝑧)𝑛+ 1  2  𝑖  = (𝐵𝑧)𝑛− 1  2  𝑖  − Δ𝑡  Δ𝑥  �  (𝐸𝑧)𝑛  𝑖+ 1  2  − (𝐸𝑦)𝑛  𝑖− 1  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (40)  𝐵𝑥 is constant in the 1D3V model because of the requirement ∇·B =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6 Landau closure for fluid species  The highest retained fluid moment, which is in our case the specific  heat flux Q, is not evolved in our set of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Instead, we need  to estimate its value dynamically using an appropriate closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  simple ideal gas closure sets Q = 0, which, however, prevents the  energy dissipation of plasma waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' One important mechanism of  such a dissipation is the collisionless damping of electrostatic waves  achieved through Landau damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Landau damping is a microphys-  ical kinetic wave-particle interaction, where particles resonate with  the wave exchange energy as a function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In essence, the reso-  nant particles accelerate or decelerate to approach the wave’s phase  velocity, thereby picking up energy or releasing it, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For  Maxwellian phase space distributions, there are more particles at ve-  locities smaller than the phase velocity, which yields a net damping,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', energy loss of the wave (Boyd & Sanderson 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Various attempts, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' by Hammett & Perkins (1990), were carried  out to approximate the heat flux Q of an almost Maxwellian dis-  tributed plasma, such that the kinetic phenomenon of Landau damp-  ing is mimicked in the linearized fluid equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Landau damping is  a non-isotropic effect, which can be reflected in the fluid descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Accounting for the gyrotropy of the system around the magnetic field,  often the double-adiabatic law with two adiabatic coefficients parallel  and perpendicular to the magnetic field is presupposed (Hunana et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For now, we restrict our algorithm to isotropic pressures with  only one common adiabatic coefficient for parallel and perpendicular  pressure and leave this possibility of modelling anisotropic double-  adiabatic systems open for future extensions of our algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In our  simplified model, we denote an isotropized pressure tensor with the  adiabatic coefficient Γ = 5/3, instantly isotropizing all heating oc-  curring due to the heat flux closure, while Γ = 3 denotes a negligible  pressure in the 𝑦 and 𝑧-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hence, we define only the perturbed  scalar heat flux parallel to the magnetic field line 𝑄 = 𝑄 ∥ and no  perpendicular heat flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Here, we will introduce two different formulae for heat flux clo-  sures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The first and most popular collisionless electrostatic closure  was proposed by Hammett & Perkins (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We refer to it as the  𝑅32 closure2 throughout this paper, and it approximates the heat flux  at a fixed Γ = 3, in Fourier space, by  ˆ𝑄 = −i sign (𝑘) 2  √π  √︁  2𝜃0𝑐𝑛0𝑘B  ˆ𝑇  𝑚 ≡ ˆ𝑄𝑇 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (41)  Here, hats are used to denote quantities in Fourier space along  the magnetic field line, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' ˆ𝑄 = F∥(𝑄), and the subscript 0 refers  to simulation box averages, that is 𝑛0 = �𝑁c  𝑖=0 𝑛𝑖/𝑁c is an average  over all 𝑁c cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Furthermore 𝑘B is the Boltzmann-constant, and  𝑘B ˆ𝑇 = (𝑚 ˆ𝑝 − 𝑘B𝑇0 ˆ𝑛) /𝑛0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Since the plasma average or equilibrium  temperature evolves slowly as a function of time, we adjust the back-  ground temperature 𝑇0 after every time step to synchronize it with  the mean pressure, 𝑘B𝑇0(𝑡)/𝑚 = 𝑝0(𝑡)/𝑛0, while the density con-  servation ensures that 𝑛0 stays constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Note also, that 𝑄0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  dimensionless mass-normalized temperature is 𝜃0 = 𝑘B𝑇0/(𝑚𝑐2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  A more recent approximation was proposed by Hunana et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (2018), who restricts this closure to Γ = 3 only, for reasons men-  tioned already.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We use an ad hoc formulation of their closure with a  variable Γ, thereby allowing our simplified model to be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We re-  fer to this closure as 𝑅31 and it approximates the heat flux, in Fourier  space, by  ˆ𝑄 =  �  4  4 − π − Γ  �  𝑝0 ˆ𝑤  ������������������������������������  ˆ𝑄𝑤  +  �  −i sign (𝑘)  √︁  2π𝜃0  4 − π 𝑐𝑛0  𝑘B ˆ𝑇  𝑚  �  ����������������������������������������������������������������������  ˆ𝑄𝑇  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (42)  In comparison to the 𝑅32 closure, this closure has an additional  dependence on the perturbed bulk velocity ˆ𝑤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This effectively in-  creases the speed of sound obtained from the non-electromagnetic  fluid equations and allows retrieving the correct damping rate with  our ad-hoc assumption of variable Γ, see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For Γ = 3,  we retrieve the coefficient for ˆ𝑤 from the aforementioned literature  4  4−π − 3 = 3π−8  4−π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In only one spatial dimension, as assumed in our code, the global  integration along a magnetic field line is approximated to be along  the spatial direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' F∥ = F𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' An extension to multiple spatial  dimensions with an anisotropic pressure tensor is not straightforward  because in this case, this approach can lead to spurious instabilities  (Passot et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2014) and the integration would need to be carried out  along magnetic field lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  A kinetic code does not need global communication to accurately  reproduce Landau damping, since each particle (or particle bin)  tracks its own interaction with each wave mode as a function of time  and accumulates this information in the particle velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However,  after integrating out the individual particle velocities when build-  ing the evolution equations for the phase-space distribution function,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' equations (14)-(16), information about the individual particle-  wave interaction is no longer collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Because some information  about this interaction is also contained in the wave, such non-local  information can be used to approximate the gradient of the physical  heat flux, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', a closure of the fluid moments that incorporates such  missing information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This non-local information is approximated in  equations (41) and (42), and is manifested by the term i sign (𝑘) in  Fourier space, which is also referred to as the Hilbert transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Numerically, we do not include the heat flux in the Riemann solver  used to compute the fluid fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Instead, we compute the spatial  derivative of the heat flux ∇∥ · Q separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We use Strang splitting  2 The name 𝑅𝑚𝑛 is used to denote that the kinetic plasma response function  𝑅 is mimicked for this closure by a Padé approximant with polynomials  𝑃𝑚/𝑄𝑛 of order 𝑚 and 𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  7  for the 𝒘 dependent part Q𝑤 and the temperature dependent part Q𝑇  to expand equation (20) into  U𝑛+ 1  2 = e  Δ𝑡  2 Fe  Δ𝑡  2 Q𝑤eΔ𝑡Q𝑇 eΔ𝑡Seme  Δ𝑡  2 Q𝑤e  Δ𝑡  2 FU𝑛− 1  2 + 𝑂(Δ𝑡3),  (43)  such that only one non-global evaluation of Q𝑇 is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Using  Heun’s method together with the fast Fourier transform (FFT) the  update formulae for the pressure w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' operators Q𝑤 and Q𝑇 are  respectively  𝑝𝑛+1���𝑄𝑤  = eΔ𝑡𝑄𝑤 𝑝𝑛 = 𝑝𝑛 + Δ𝑡𝑎𝑤𝑝0∇∥ · 𝒘,  (44)  𝑝𝑛+1���𝑄𝑇  = eΔ𝑡𝑄𝑇 𝑝𝑛 = 𝑝𝑛 + Δ𝑡F −1  ∥  �  |𝑘|𝑎𝑇  �  1 + Δ𝑡  2 |𝑘|𝑎𝑇  �  ˆ𝑇𝑛  �  ,  (45)  where the derivative in Fourier space was obtained by multiply-  ing with i𝑘 and the inverse FFT is denoted by F −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For the  𝑅31 closure the coefficients are given by 𝑎𝑤 = 4/(4 − π) and  𝑎𝑇 = (4 − π)−1(2π𝜃0)1/2𝑐𝑛0𝑘B/𝑚, while for the 𝑅32 closure these  are given by 𝑎𝑤 = 0 and 𝑎𝑇 = 2(2𝜃0/π)1/2𝑐𝑛0𝑘B/𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Both closures  compute a term proportional to ˆ𝑇 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' equation 45)  i𝑘 ˆ𝑄 ∝ −i sign (𝑘) i𝑘𝑎𝑇 ˆ𝑇 = |𝑘|𝑎𝑇 ˆ𝑇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (46)  Computing this term naively using the FFT is expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is  why, in the following, we present local, semi-local, and efficient  global (Fourier transform-based) numerical approximations of the  Landau closures, which we have implemented in the fluid-SHARP  code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 Local approximations of the Hilbert transform  The phase shift between the wanted derivative i𝑘 ˆ𝑄 and the input of  ˆ𝑇 in equation (46) is exactly 0, while the amplitude is proportional  to |𝑘|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is therefore a special case (𝑎 = 1) of the fractional Riesz  derivative 𝜕𝑎/𝜕|𝑥|𝑎 with Fourier representation  F  � 𝜕𝑎 𝑓 (𝑥)  𝜕|𝑥|𝑎  �  = −|𝑘|𝑎 ˆ𝑓 (𝑘) ,  (47)  where 𝑎 ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Note, that all approximations mentioned here only  introduce errors in the amplitude of |𝑘|, but not in its phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This  makes them easier to integrate into simulations in comparison to  approximations which are not designed to prevent phase errors, be-  cause large phase errors (between π/2 and 3π/2) in any wave mode  transform the damping term into an exponentially growing numer-  ical instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The local approximations make use of the fact, that  the fractional Riesz derivative is local and cheap to evaluate for the  special case 𝑎 = 2𝑚 with 𝑚 ∈ N0, where it reproduces the usual  derivative 𝜕2𝑚/𝜕|𝑥|2𝑚 = (−1)𝑚+1 𝜕2𝑚/𝜕𝑥2𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2015)  use 𝑎 = 0, while Allmann-Rahn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2018) and Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2020)  approximate the non-isotropic pressure tensors with 𝑎 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' These ap-  proximations are scaled to a characteristic wavenumber 𝑘0 at which  the damping is expected to occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The choice of 𝑎 = 0 means, that the approximation is a scalar  i𝑘 ˆ𝑄 ∝ |𝑘0| ˆ𝑇,  (48)  while the gradient-driven closures with 𝑎 = 2 use  i𝑘 ˆ𝑄 ∝ 𝑘2  |𝑘0|  ˆ𝑇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (49)  The gradient-driven closures are equal to the FFT solution at two  wavelengths, 0 and 𝑘0, while the scalar closure is only exact at 𝑘0,  see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Since i𝑘 ˆ𝑄 is not computed alongside with the conservative  0  휋/4  휋/2  3휋/4  휋  ˆ푘 [rad/sample]  0  1  2  3  4  5  spectral magnitude  FFT-based  FIR filter  gradient driven  scalar  푘0  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The magnitude of the frequency response, which is a quantification  of how much the amplitude at a specific frequency is amplified or suppressed,  of different approximations of the derivative of the Hilbert transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' ˆ𝑘 is  given in normalized frequencies (with regards to the Nyquist frequency),  while the negative frequencies in the interval [−π, 0] are not shown here due  to the symmetric dependence of all plotted values on |𝑘 |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The FFT-based  approach reproduces the correct, linear response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The scalar and gradient  driven closures are given by equations (48) and (49) respectively with the  parameter 𝑘0 marked as a grey, vertical line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The FIR filter is described by  equation (51).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  fluxes in the Riemann solver, energy conservation is only preserved if  the mean energy does not increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' To achieve this, the approximation  for the derivative of the heat flux needs to vanish at wavenumber 0,  which the scalar approximation does not fulfil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Because fluid closures are only approximately mimicking kinetic  Landau damping anyway, these local approximations to the fluid  closures are useful to save computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Furthermore they  are easier to implement, especially when the full pressure tensor is  computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, they may lead to misleading results in multi-  scale simulations, where multiple characteristic damping lengths are  present and depend on the estimate of 𝑘0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For example, Allmann-  Rahn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2022) show a case where ion and electron heating inten-  sities are switched qualitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 Semi-local approximations of the Hilbert transform  While the less accurate local approximations use an arbitrary value  of 𝑘0, the FFT is expensive and depends on periodic boundary con-  ditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Here, we aim to have a fallback algorithm as a compromise  between both approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  A digital finite impulse response (FIR) filter can be designed to  approximate the non-local effects by convolving the simulation data  with adjacent auxiliary data points, where the filter length determines  the maximum distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For example, an asymmetric filter with an  even number of entries is applied on an input 𝑥 using filter coefficients  𝑏 𝑗, producing the output 𝑦:  𝑦𝑖+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 =  𝑁 𝑓 /2−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  ∑︁  𝑗=−(𝑁 𝑓 /2−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5)  𝑏 𝑗𝑥𝑖+ 𝑗+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (50)  A numerical derivative is then an asymmetrical filter with 𝑁 𝑓 = 2  and coefficients 𝑏±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 = ±/Δ𝑥, such that 𝑦𝑖+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 = (𝑥𝑖+1 − 𝑥𝑖)/Δ𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Figure 1 shows the magnitude of the frequency response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The gra-  dient driven case shows a quadratic 𝑘2 dependence, which is sup-  MNRAS 000, 1–17 (2022)  8  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  pressed for larger 𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is due to the relatively small uneven filter  length of 7 used here;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' the filter length is an important parameter,  since it influences the accuracy of the approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' With a fil-  ter length corresponding to the simulation box size the results can  converge to the FFT-based algorithm (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' the 𝑘2 dependence is not  suppressed at higher 𝑘), if the filter is designed appropriately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' As  noted previously, the local closures do not converge to 𝜕/𝜕|𝑥|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A  correct convergence for approximating 𝜕/𝜕|𝑥| is obtained through  the high order formulation by Ding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, this filter  violates energy conservation for smaller filter length and is thus, not  suitable for our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Instead, we construct the filter by adopting a  convolution of two sub-filters, each of which has an odd amount of  asymmetric entries3 similar to the numerical derivative mentioned  already.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' By design, their output has a vanishing mean, thereby guar-  anteeing energy conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A symmetric splitting into the sub-  filters 𝜕/𝜕|𝑥| = (𝜕1/2/𝜕|𝑥|1/2)2 is possible, however its frequency  response is not monotonic (and has visible ripples) for small filter  lengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This leads to the unphysical case that some waves at a par-  ticular wavenumber 𝑘 are damped less than their slightly larger scale  waves at 𝑘 − 𝛿𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Instead, we opt to use the intuitive splitting of 𝜕/𝜕|𝑥| = 𝜕/𝜕𝑥H  where the Hilbert-transform filter H is equivalent to −i sign (𝑘) in  Fourier space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The filter H has coefficients 𝑏 𝑗 = 1/(π𝑗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We derive  anequivalent formulationtoequation(45), whichisfirst order in time,  by applying the derivative and Hilbert-transform filters successively,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  𝑝𝑛+1 = 𝑝𝑛 + Δ𝑡𝑎𝑇  𝜕  𝜕𝑥  𝑁 𝑓 /2−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  ∑︁  𝑗=−(𝑁 𝑓 /2−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5)  1  π𝑗 𝑇𝑛  𝑖+𝑗+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (51)  Note, that the derivative is also computed by convolution and has a  separate filter length corresponding to its spatial order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We opt to use  the same spatial order as in the C-WENO reconstruction for the finite  volume scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Even for small Hilbert-transform filter lengths in comparison to  the number of cells, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 𝑁 𝑓 /𝑁c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='04 as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 1, this  formulation dramatically improves the accuracy of multiscale prob-  lems in comparison to local approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Here, 𝑁 𝑓 is critical for  the accuracy at small wavenumbers 𝑘, while the spatial order of the  derivative is critical for the accuracy at large 𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Most importantly,  this semi-local approach does not require setting an arbitrary damp-  ing scale 𝑘0 such as the local approximations mentioned before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  only parameter of this approach is the filter length, which should be  chosen to be sufficiently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3 Efficient FFT-based computation of the Hilbert transform  Provided the plasma background is uniform and periodic, the most  accurate while computationally most expensive results are achieved  by computing the heat flux of the fluid in Fourier space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While the  FFT is easy to compute on a single computer using standard nu-  merical libraries, our code is parallelized using MPI and an efficient  one-dimensional FFT is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The computation of the Fourier  transform is expensive for two reasons:  (i) globally, each Fourier component needs to be informed about  data from every other computational cell (which may be stored on a  different processor), and  (ii) the Fourier transform is not easily parallelizable in one di-  mension, which precludes an efficient scalable Fourier algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3 This is also called a Type IV filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  This naturally limits the overall computational scalability of the fluid  part of the code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Communication over multiple MPI processes is time  consuming because of latency and finite bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For this rea-  son, parallel FFT algorithms are prone to become a computational  bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, using non-blocking MPI routines to perform  communication in the background can be used while the high com-  putational load of the particles is carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Thus, in our case of  a combined fluid and PIC algorithm, the communication required  for an accurate FFT-based heat flux computation is comparatively  computationally cheaper, even with relatively small numbers of PIC  particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hence, in our case the FFT algorithm does not necessarily  become a bottleneck for larger problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In order to distribute the computational load of the FFT, we employ  a four-step algorithm in the first step of the computation (Bailey  1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Takahashi & Kanada 2000), which extends the Cooley-Tukey  algorithm (Cooley & Tukey 1965) for multiple processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We shortly  describe the algorithm for complex input data as found in the literature  and afterwards adapt the parallel FFT for real input data in our  implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The four-step algorithm interprets the complex data  vector 𝑥 𝑗 of length 𝑁 as a two-dimensional vector 𝑥 𝑗 = 𝑥 𝑗1, 𝑗2 with  lengths 𝑛1 and 𝑛2 respectively, and volume 𝑛1𝑛2 = 𝑁.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The mapping  𝑗 = 𝑗1 + 𝑗2𝑛1 and 𝑘 = 𝑘2 + 𝑘1𝑛2 is inserted into the definition of the  discrete Fourier transform, where Ψ = exp{−2πi}  ˆ𝑥𝑘 =  𝑁 −1  ∑︁  𝑗=0  𝑥 𝑗Ψ 𝑗𝑘/𝑁 ,  (52)  ˆ𝑥𝑘2,𝑘1 =  𝑛1−1  ∑︁  𝑗1=0  𝑛2−1  ∑︁  𝑗2=0  𝑥 𝑗1, 𝑗2Ψ 𝑗2𝑘2/𝑛2Ψ𝑗1𝑘2/𝑁 Ψ 𝑗1𝑘1/𝑛1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (53)  This way, a complex-to-complex parallel FFT of length 𝑁 is dis-  tributed to 𝑛1 local FFTs of length 𝑛2, a multiplication by the twiddle  factors Ψ 𝑗1𝑘2/𝑁 and finally 𝑛2 FFTs of length 𝑛1, with a communica-  tion intensive transpose in between.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' All-to-all communication takes  place two times, in the first step – cyclically distributing 𝑗 to 𝑗1 and  𝑗2 – and for the transpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A third all-to-all communication would  be needed to properly sort the values in Fourier space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, a  scrambled output suffices for computing the heat flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Furthermore,  since often two FFTs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' electrons and ions, need to be computed si-  multaneously, they can be computed on different nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This has the  advantage, that the second all-to-all communication for the transpose  is not completely global resulting in reduced communication times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Adapting this algorithm to a real-to-complex FFT, where due to  Hermitian symmetry only values of 𝑘 ⩽ ⌊𝑁/2⌋ need to be computed,  a large amount of computational and communicational savings can  be realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A real-to-complex parallel FFT of length 𝑁 is distributed  to 𝑛1 local real-to-complex FFTs of length 𝑛2, a multiplication by  the twiddle factors Ψ 𝑗1𝑘2/𝑁 and, now only, ⌊𝑛2/2⌋ + 1 complex-  to-complex FFTs of length 𝑛1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Up to two of the latter FFTs can be  replaced by real-to-complex FFTs, along the axes 𝑘2 = 0 and, if 𝑛2  is even, 𝑘2 = 𝑛2/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A scrambled output is received, which, due to  Hermitian symmetry, needs to be partially complex conjugated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  A key point in ensuring the efficiency of the parallel four-step  algorithm consists in choosing large 𝑛1 and 𝑛2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 𝑛1 ≃ 𝑛2 ≃  √  𝑁 is the  optimal choice for the distributed complex-to-complex FFT, the real-  to-complex FFT should prefer 𝑛1 ≃ ⌊𝑛2/2⌋ + 1 ≃ (  √  2𝑁 + 1 + 1)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The computational scaling with 𝑃 processors and roughly optimally  distributed 𝑛1 and 𝑛2 is akin to O (𝑁/𝑃 log 𝑁), but degrades if 𝑁  is a prime number, or, more generally, if 𝑛1 or 𝑛2/2 is smaller than  the number of processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This easily avoidable because 𝑁 is a free  parameter, and so are 𝑛1 and 𝑛2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While this does not scale favourably  in comparison to the O (𝑁/𝑃) scaling that dominates the rest of  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  9  the fluid code, still, the FFT is trivially independent of the numbers  of particles per cell 𝑁pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The PIC-module on the other hand scales  as O �𝑁pc𝑁/𝑃� and typical applications have 𝑁pc ≳ 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In many  applications the cost of the Fourier transform is, even with worse  scaling, subdominant in comparison to the cost of the PIC part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In the remaining cases, local approximations, discussed above, are  favourable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='7 Current-coupled fluid-PIC algorithm  The coupling in our code between various fluid and kinetic (PIC)  species is achieved through a current-coupling scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Namely, both  fluid and kinetic species contribute to the charge and current densi-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The electromagnetic fields then evolve in response to the total  contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The fields are staggered on a Yee-mesh and are up-  dated with the FDTD scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Subsequently, both fluid and kinetic  species evolve in repose to the new electromagnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' That is  our current-coupling scheme does not make any assumption on the  velocity distribution of the species modelled using the kinetic de-  scription (Park et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The PIC species, using fifth-order spline interpolation, are de-  posited to specific points on the Yee-grid for which the charge density  is defined at full-time steps while the current density is defined at  half-time steps as discussed by Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2017a, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For fluid  species, the fluid density and velocity are defined at the same time  step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Therefore, during the evolution of the fluid, we deposit the fluid  contribution to the charge and current densities, 𝜌 and J𝑦,𝑧 respec-  tively, at the cell centres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The deposition for J𝑦,𝑧 is trivial at half-time  steps, where the fluid vector U is defined, while the contribution to 𝜌  is computed at full-time steps, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' before the electromagnetic source  update according to equation (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Note, that 𝜌 stays constant when  computing the Lorentz force and heat flux updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Our algorithm does not apply any approximations to the electrical  field components or to Ohm’s law, requiring electron timescales  and motions to be fully resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Consequently, we apply the same  algorithm to fluid electrons and protons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is accomplished using  the modular design of the fluid SHARP code where each fluid species  is represented by initialising a fluid code class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Each instance of this  code class is initialized using the values of the mass and the charges  of their respective particle species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The algorithms which define the  evolution of each particle species are implemented as functions of the  fluid class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This allows us to setup simulations with multiple species,  all of which are evolved with the same numerical algorithms, with  little effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2 the main loop of the fluid-PIC algorithm is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  It can be seen that the usual PIC-algorithm loop of electromagnetic  update, interpolation to particle position, particle push, and field de-  position is retrieved when no fluid species is initialised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' On the other  hand, without PIC particles, we retrieve a multispecies fluid plasma  code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While our fluid-PIC algorithm can simulate an arbitrary mix-  ture of species, it is most efficient if fluids are used for background  species and particles for non-thermal particle distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Possi-  bilities for task parallelization are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2 by dashed lines,  which allows maximizing computation-communication overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Our fluid implementation is included within the SHARP code,  which uses a fifth-order spline function for deposition and back-  interpolation for PIC species (Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2017a, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The PIC  part of the code does not make use of filtering grid quantities and  results in comparatively small numerical heating per time step, which  (if present) would affect the reliability of the simulation results on  long timescales (see section 5 in Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2017a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This prop-  erty is important because we are specifically interested in studying  Update  Flux - half step  Update  Lorentz force  Flux - half step  Heat flux  Lorentz force  Deposition  Fluid Module  Particle Module  EM Module  Back interpolation  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Schematic representation of the interaction of the different modules  in the fluid-SHARP code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Red boxes belong to the particle class, violet boxes  to the electromagnetic class and blue boxes to the fluid class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Dashed lines  show branches which are task parallelizable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' where non-blocking MPI  communication can be used for overlapping communication and computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Parameters adopted for the shock tube tests described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Test  𝑥0  𝜌l  𝑤l  𝑝l  𝜌r  𝑤r  𝑝r  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='75  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='125  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  1  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='59745  1000  1  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='59745  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='01  microphysical effects on long timescales with our fluid-PIC code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Due to the modularity of our code, each part can be tested individ-  ually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' These tests, ranging from the uncharged fluid solver to full  fluid-PIC simulations, are shown in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3 CODE VALIDATION TESTS  In this section, we present the results of various code tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We  start with two shock-tube tests in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 before we show that  our code is able to accurately capture all six branches of the two-  fluid dispersion relation (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We describe code tests of  Langmuir wave damping (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3) and of two interacting Alfvén  waves generating a new, longitudinal wave along the magnetic field  (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5, we test the entire fluid-PIC code with a  simulation of the gyrotropic cosmic ray streaming instability, where  PIC cosmic rays are streaming in a stationary electron-proton fluid  background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Finally, we demonstrate the successful parallelization  strategy of our code by performing scaling tests in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 Shock tube  As the fluid approximation will be primarily used for background  plasmas without excessive gradients, the accuracy of resolving sharp  discontinuities is of secondary importance in practical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Still, we stress test our implementation of the fluid equations to ensure  its numerical robustness and to compare the numerical dispersion for  different Riemann solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For the shock tests a numerical grid of 100  cells is used with a constant CFL number𝐶cfl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 with the adiabatic  coefficient Γ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The boundary conditions are transmissive and  MNRAS 000, 1–17 (2022)  10  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  푛 [푛0]  HLLC  Roe  exact  2  4  6  푛 [푛0]  HLLC  Roe  exact  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  푤 [푤0]  −2  −1  0  푤 [푤0]  ×101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  푥 [푥0]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  푝 [푝0]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  푥 [푥0]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  푝 [푝0]  ×103  (a) Shock tube test 1, a modified Sod shock tube, at time 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 (code units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  푛 [푛0]  HLLC  Roe  exact  2  4  6  푛 [푛0]  HLLC  Roe  exact  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  푤 [푤0]  −2  −1  0  푤 [푤0]  ×101  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  푥 [푥0]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  푝 [푝0]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  푥 [푥0]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  푝 [푝0]  ×103  (b) Shock tube test 2 at time 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='012 (code units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 1D1V hydrodynamical shock tube tests with initial conditions given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The simulations carried out with the HLLC and Roe Riemann solvers  are compared to the exact solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Density, bulk velocity in 𝑥-direction and pressure are plotted for each test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  the initial conditions for the tests are given in Table 1, which are the  same as in Toro (2009), where a CFL number of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='95 is used  only in the first five steps and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='95 afterward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The units used for these  non-electromagnetic tests are arbitrary units and do not coincide with  the usual simulation units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Test 1, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 3a, is a modified Sod shock tube test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The sonic rarefaction wave on the left-hand side as well as the shock  front on the right are well resolved without noticeable oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The contact discontinuity in the middle introduces small oscillations  in the density and is smeared out more than the shock front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While  the Roe and HLLC solvers yield almost the same results, the HLLC  solver is slightly better at resolving the sonic point at the head (to  the left) of the sonic rarefaction wave, which the Roe solver can only  resolve because an entropy fix is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Figure 3b shows a test of a stationary contact discontinuity with  a shock front of a high Mach number travelling to the right and a  rarefaction wave to the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' It can be seen, that while the HLLC  method introduces more oscillations, it is also better at resolving the  contact discontinuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In low-density flows the Roe solver is not suitable because it is not  robust without further modifications (Einfeldt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 1991), making the  HLLC method slightly more robust while the Roe method is slightly  less dispersive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, for most practical applications studied here,  both methods produce similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 Two-fluid dispersion relation  For an ideal two-fluid plasma the dispersion relation can be solved  for six different wave branches (Stix 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We show the solutions to  the dispersion relation of a two-fluid plasma in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 4 for a realistic  mass ratio of 𝑚i = 1836𝑚e and 𝛽i = 𝑛𝑘B𝑇i/[𝐵2  0/(2𝜇0)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2 in an  10−3  10−2  10−1  k [kD]  10−4  10−3  10−2  10−1  ω [ωp], log-scale  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  ω [ωp]  upper RCP  Langmuir  upper LCP  lower RCP  ion-acoustic  lower LCP  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The six branches of the two-fluid dispersion relation are shown, with  two electrostatic wave branches (Langmuir and ion-acoustic) as well as four  electromagnetic left and right-hand circularly polarized wave branches (LCP  and RCP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Often, the lower RCP is referred to as whistler branch and the lower  LCP as ion cyclotron branch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' for parallel propagation their phase velocities  approach the Alfvén speed at small 𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The upper RCP and LCP are modified  light waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We mark the six local extrema of the Fourier-transformed fluid  simulation outputs at each wavenumber with crosses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Theoretical predictions  are shown as lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  isothermal plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 𝐵0 is oriented along the 𝑥-axis and the Alfvén  velocity is 𝑣A = 𝐵0/(𝜇0𝑛i𝑚i)1/2 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='83 × 10−3𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Multiple simu-  lations at different wavenumbers have been initialized that have all  six wave modes simultaneously present and were run for a total time  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  Re(휔) [휔p]  theo: ideal gas  theo: Landau 푅32  theo: Landau 푅31  theo: kinetic  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='25  Im(−휔) [휔p]  sim: ideal gas  sim: Landau 푅32  sim: Landau 푅31  sim: PIC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6  푘 [푘D]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='002  rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' error [%]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6  푘 [푘D]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='01  rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' error [%]  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The linear dispersion relations of a Langmuir wave with immobile ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Shown are, on the left-hand side, the real frequency components and,  on the right-hand side, the negative imaginary frequency components (which are responsible for damping).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The crosses present data points obtained from  simulations with the respective closure while the theoretical result is shown with a solid line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The relative error between simulation and theoretical results  (𝜔sim − 𝜔theor)/𝜔theor is shown in the lower panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For reference, the red crosses display the data points as given in table 1 of Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2017a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  of 14/min (𝜔), where 𝜔 denotes the wave frequencies, which are  always completely real for an ideal fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Consequently, the waves  should be undamped and any possible damping introduced is be-  cause of numerical dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Initial conditions for all of our fluid  simulations as well as theoretical predictions are computed using an  extended algorithm based on the dispersion solver by Xie (2014),  which can take into account the effects of both heat flux closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  A Fourier analysis in time has been performed and the six largest  local extrema are shown as crosses in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' It can be seen, that the  simulation results are in good agreement with the analytical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In the Fourier-analysis the largest relative errors of at most 7 per cent  in 𝜔 occur in the large-scale part of the ion-acoustic branch as well  as close to the cut-off frequency of the lower LCP branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In com-  parison to this, the largest relative errors in the upper three branches  are more than one magnitude less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3 Langmuir wave damping  The electrostatic wave modes are directly subject to linear Landau  damping, and thus present a good test for the heat flux closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' To  test this, we initialize standing Langmuir waves in an electron plasma  with immobile ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We use the same grid layouts as in table 1 of  Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (2017a), supplemented with fluid simulations run at  𝑘/𝑘D ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3} with a resolution of 𝜆/Δ𝑥 = 68 cells per  wavelength and a domain size of length 𝐿 = 10𝜆 wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  wavenumber associated with the Debye length is the ratio of plasma  frequency to thermal velocity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 𝑘D = 𝜔p/𝜃1/2𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The amplitude of  the wave is chosen, such that the density fluctuation to background  ratio is fixed to 𝛿𝑛/𝑛0 = 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In order to find the numerical dispersion relation we perform curve  fitting with the Powell algorithm on the time series for times up to  80 𝜔−1  p , while the simulations at 𝑘/𝑘D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='01 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='05 with small  damping are analysed up to 240 𝜔−1  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The computation of the heat  fluxes for the 𝑅31 and 𝑅32 closures is performed using the FFT-based  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 5, where the ideal gas closure  and the kinetic results are also depicted for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Generally, it can be seen, that at small scales the closures show  larger deviations from each other, which is also where the fluid de-  scription starts breaking down naturally as the particle distribution  is not in equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' At larger scales, the various descriptions of  Landau damping converge and approach zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The numerical rela-  tive error of the fluid code is small and stays below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='003 for real  frequencies and below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='002 for decay rates in this setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The sim-  ulation at 𝑘/𝑘D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='05 performs worse than the one at 𝑘/𝑘D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1  due to the significantly lower resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The error in 𝜔 decreases  at second-order with increasing spatial resolution, as shown in Ap-  pendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4 Interacting Alfvén waves  A single Alfvén wave is purely transversal and not directly affected by  Landau damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, two or more Alfvén waves drive a longi-  tudinal electrostatic wave, which is susceptible to Landau damping,  see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This leads to particle heating as a result of the collision-  less damping of the Alfvén wave, also known as non-linear Landau  damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Restricting ourselves to a setup of pairwise interacting waves, we  can identify two distinct cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In the first case counter-propagating  waves are interacting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In consequence, both waves damp, lose energy  to the longitudinal wave and subsequently heat the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In the  second case the waves are co-propagating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Here the wave with the  smaller wavelength will not only transfer energy to the particles,  but also to the other Alfvén wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Lee & Völk (1973) describe  this mechanism in detail and formulate the following coupled set  of differential equations while adopting a measure for the magnetic  energy of a wave, 𝐼 𝑗 =  ��𝐵 𝑗  ��2, where 𝑗 ∈ {1, 2}:  d  dt 𝐼 𝑗 = 2Γ 𝑗 𝐼 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (54)  The coupling between the differential equations is implicit because  the damping coefficient has the dependency Γ1 ∝ 𝐼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For the counter-  propagating case with an isothermal ion-electron-plasma in the high  beta limit 𝛽i = 2𝜇0𝑛i𝑘B𝑇i/𝐵2  0 = 2 ≫ 1, where 𝐵0 is the background  magnetic field strength, the damping rate Γ𝑗 is approximately equal  for both wave polarizations with similar frequencies 𝜔 𝑗 and may be  approximated by (Holcomb 2019)  Γ1 = −  √π  16  𝐼2  𝐵2  0  √︁  𝛽i𝜔1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (55)  MNRAS 000, 1–17 (2022)  12  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Two different Alfvén waves, with magnetic and velocity vectors  B1, B2 and 𝒘1, 𝒘2, propagate transversally along the 𝑥-axis, where the elec-  tromagnetic vectors rotate (counter-)clockwise around it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Because of their  phase difference Δ𝑘𝑥 the overall Lorentz force (𝒘1 + 𝒘2) × (B1 + B2) in  𝑥-direction is non-zero, thereby generating the longitudinal wave shown in  dark yellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0  δB2  total [B2  0]  ×10−2  L&V  Landau R32  Landau R31  2  4  6  8  10  12  t [Pω]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='00  δB2  j [B2  0]  ×10−2  RCP  LCP  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Time evolution of the magnetic energy of a linearly polarized Alfvén  wave in our fluid simulations with Landau damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Time is measured in units  of the period of the mean wave frequencies 𝑃𝜔 = 4π(𝜔1+ 𝜔2)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Analytical  predictions for the damping rate are taken from Lee & Völk (1973, labelled  L&V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The fluid simulations are presented with the different heat flux closures  𝑅31 and 𝑅32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We compare the time evolution of the total magnetic wave  energy (top panel) and the magnetic wave energy of the different polarization  states (bottom panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The right-hand circularly polarized wave has a higher  phase velocity and loses energy more quickly in comparison to the left-hand  circularly polarized wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Note that Γ2 is found by substituting the subscripts 1 → 2 and 2 → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 7 we show simulations of a linearly polarized Alfvén wave,  which consists of two counter-propagating waves of equal amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The pure fluid simulations are shown with a box size of 𝐿 = 252 𝑐/𝜔i  and wavelengths 𝜆 = 𝐿/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Right and left polarized waves are initial-  ized with phase velocities 𝜔RCP/𝑘 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0342 and 𝜔LCP/𝑘 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0318  with a perpendicular magnetic field amplitude of 𝛿𝐵 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 𝐵0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A  reduced mass-ratio of 𝑚i/𝑚e = 100 is adapted here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Our simulations are carried out with the different heat flux clo-  sures 𝑅32 and 𝑅31, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Both closures reproduce the  theoretical predictions quite well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' A PIC simulation with similar pa-  rameters has been shown in figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4 by Holcomb (2019), which  reproduces half of the predicted damping rate until 𝑡 ∼ 2𝑃𝜔 and  shows a quenching of the damping rate afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In comparison  to kinetic simulations, there is no saturation of the Landau-damping  effect in fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This is because the distribution of the fluid particles  is always assumed to be roughly Maxwellian and resonant particles  are not depleted as a function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Hence, Landau fluid is implic-  itly assumed to have small thermalization timescale in comparison  to the damping timescale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' On the other hand, PIC simulations are  plagued by Poisson noise and an insufficient resolution of velocity  space might lead to a reduced Landau damping rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 Gyrotropic cosmic ray streaming instability  To test the entire code, we run cosmic ray streaming instability sim-  ulations, where electron and ion cosmic rays (CR) are modelled with  the PIC method and the background electron and ion plasmas are  modelled as fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The initial CR momentum distribution for ions  (electrons) is assumed to be a gyrotropic distribution with a non-  vanishing (zero) pitch angle, while both CR electrons and ions are  assumed to drift at the same velocity 𝑣dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Namely, the phase space  distributions for the electron and ion cosmic ray species 𝑠 ∈ {e, i}  are given by (Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2021)  𝑓cr,𝑠(x, u) = 𝑛cr,𝑠  2π𝑢⊥  𝛿(𝑢 ∥ − 𝛾𝑠𝑣dr)𝛿(𝑢⊥ − 𝛾𝑠𝑣⊥,𝑠),  (56)  where 𝛾𝑠 = (1 − 𝑣2  dr/𝑐2 − 𝑣2  ⊥,𝑠/𝑐2)−1/2 is the Lorentz factor and  𝑣⊥,𝑠 is the perpendicular component of the CR velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We choose  𝑣⊥,e = 0 and 𝑣⊥,i = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1𝑣A, where the ion Alfvén velocity is  given by 𝑣A = 𝐵0/(𝜇0𝑛i𝑚i)1/2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='01𝑐 with the background mag-  netic field pointing along the spatial direction, and 𝑣dr of 5𝑣A re-  sulting in a pitch angle for the ions of tan−1(𝑣⊥,i/𝑣dr) = 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The thermal background species are isothermal with the tempera-  tures 𝑘B𝑇/(𝑚𝑐2) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='0001 and a mass ratio 𝑚i/𝑚e = 1836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We  use a periodic box of length 𝐿𝑥 = 10971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 𝑐/𝜔p and resolution  Δ𝑥 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 𝑐/𝜔p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The cosmic ray to background ratio number density  ratio 𝛼 = 𝑛cr,i/𝑛i = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  We run two simulations where the background plasmas are mod-  elled as fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The first one uses an ideal gas closure without ac-  counting for Landau damping (FPIC ideal gas) while we include the  heat flux source term in the second simulation to mimic the impact of  linear Landau damping using the 𝑅31 closure of equation (42) (FPIC  Landau 𝑅31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We compare these two fluid-PIC simulations against  PIC simulations where both CRs and background plasmas are mod-  elled as PIC species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The number of CR ions per cell is 𝑁pc = 25(75)  and we call this simulation “PIC normal (high) 𝑁pc” (Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Like the “PIC normal 𝑁pc” simulation, the fluid-PIC simula-  tions also use 25 particles per cell for modelling cosmic rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Growth rates of the instability in the linear regime can be com-  puted from the linear cold background plasma dispersion relation  (Holcomb & Spitkovsky 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Shalaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2022):  0 =1 − 𝑘2𝑐2  𝜔2  +  𝜔2  i  𝜔 �−𝜔 ± Ωi,0  � +  𝜔2e  𝜔 �−𝜔 ± Ωe,0  �  + 𝛼𝜔2e  𝛾e𝜔2  �  𝜔 − 𝑘𝑣dr  𝑘𝑣dr − 𝜔 ± Ωe,0  �  +  𝛼𝜔2  i  𝛾i𝜔2  ���  �  𝜔 − 𝑘𝑣dr  𝑘𝑣dr − 𝜔 ± Ωi  −  𝑣2  ⊥/𝑐2 �  𝑘2𝑐2 − 𝜔2�  2 (𝑘𝑣dr − 𝜔 ± Ωi) 2  ���  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (57)  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  13  0  20  40  60  80  100  푡  �  Ω−1  i  �  10−2  10−1  |훿퐵| [퐵0]  0  1  2  3  4  5  10−2  10−1  FPIC ideal gas  FPIC Landau 푅31  PIC normal 푁pc  PIC high 푁pc  intermediate scale growth rate  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Growth of the perpendicular magnetic field as a function of time for a gyrotropic cosmic ray streaming setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The maximum growth rate expected  from the linear dispersion relation at intermediate scales is Γinter = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='299Ωi and shown in dashed grey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' because of the different initial seed populations for the  particle species, the onset of the instabilities is not expected to happen at the same simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='Hence, we choose an arbitrary 𝑡 = 0 so that the different  simulated growth phases roughly coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  10−5  10−4  10−3  10−2  |훿퐵푘| [퐵0]  FPIC ideal gas  FPIC Landau 푅31  PIC normal 푁pc  PIC high 푁pc  10−4  10−3  10−2  10−1  intermediate scale (푘푐/휔i = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='91)  10−5  10−4  10−3  10−2  |훿퐵푘| [퐵0]  10−4  10−3  10−2  10−1  cascading scale (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 < 푘푐/휔i < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5)  0  2  4  6  8  10  푡 [Ω−1  i ]  10−5  10−4  10−3  10−2  |훿퐵푘| [퐵0]  0  20  40  60  80  100  푡 [Ω−1  i ]  10−4  10−3  10−2  10−1  gyro scale (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='1 < 푘푐/휔i < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6)  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Growth of the perpendicular magnetic field as a function of time at different scales for a gyrotropic cosmic ray streaming setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We show mean values  of the fields that are averaged over a range of wave vectors 𝑘, as indicated in the legends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The maximum growth rates at the gyro scale and the intermediate scale  are given by Γgyro = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='498Ωi and Γinter = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='299Ωi, and indicated by the grey dotted and dashed lines, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' At wavenumbers corresponding to cascading  scales, there is no instability expected according to the linear dispersion relation, and wave growth solely arises as a result of cascading from other (unstable)  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The non-relativistic and relativistic cyclotron frequencies of each  species are given by Ωs,0 = 𝑞𝑠𝐵0/𝑚𝑠 and Ωs = Ωs,0/𝛾s respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The wavelength of the most unstable wave mode at the gyroscale is  λg = 2𝜋(𝑣dr − 𝑣A)/Ωi, which is properly captured in our setup using  a box size of 𝐿𝑥 ∼ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='15λg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  We show the amplification of the perpendicular magnetic field  components as a function of time for this unstable setup in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 8  for various simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' It shows that the noise level of the fluid-PIC  simulations is orders of magnitude lower in comparison to the “PIC  normal 𝑁pc” resolution, even though the number of CR particles per  cell is the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Especially up to the saturation point (𝑡Ωi ∼ 10) the  MNRAS 000, 1–17 (2022)  14  Lemmerz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  fluid-PIC simulation compares more favourably to the PIC results  with lower noise than to the PIC simulation with fewer 𝑁pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  After saturation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' when Alfvén waves at many scales have built  up and their interaction has created an electrostatic field, these waves  start to lose some energy to Landau damping of the electrostatic  waves (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' At that point, the Landau closure becomes  relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Qualitatively the ideal gas closure has no efficient mech-  anism for dissipating such electrostatic waves, resulting in a pro-  longed growth period leading to saturation at higher values at the  cascading and intermediate scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Utilization of a Landau closure  leads to some damping, albeit it is quantitatively smaller than in  the PIC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 5 indicates faster damping for the  Landau closures in comparison to the kinetic results in the electron  electrostatic branches, damping in the ion-acoustic branch might be  underestimated in the Landau closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We have compared the ex-  pected damping between kinetic and Landau fluid in the ion-acoustic  branch for multiple wavenumbers, which confirmed that this is a  likely scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The accuracy of this approximation is not the same  at all scales, which can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 9, where the magnetic field  amplifications at various ranges of scales are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Especially  in the highly Landau-damped scales, differences between fluid-PIC  and PIC emerge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' At ion gyro scales, where most of the magnetic en-  ergy is stored at saturation, there is a good agreement over the entire  time period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Exponential growth at every scale is also in good agree-  ment between PIC and fluid-PIC simulations at all scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The initial  exponential growth can also be compared to the expected growth  rates from the linear dispersion relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The growth rates of the two  local maxima are plotted alongside the simulated data, one at the  intermediate scales around 𝑐𝑘 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='91𝜔i and one at the gyro scale  at 𝑐𝑘 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='38𝜔i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The intermediate scale starts an inverse cascade to  larger scales almost immediately, which causes a reduced growth  rate in comparison to the expectation from linear theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' By contrast,  the gyro scale instability follows linear expectations to very good  approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  While our fluid-PIC and PIC results are promisingly similar, dif-  ferences after the saturation level might be attributed to multiple  reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' First, the Landau closures do not exactly reproduce the cor-  rect damping, and therefore will deviate quantitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Second, due  to the high electron temperature chosen, relativistic effects might  occur in PIC, but not in the non-relativistic fluid that we assumed for  the background plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Third, the PIC method might exhibit more  numerical dissipation at the given 𝑁pc in comparison to the fluid  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 9 seems to indicate numerical convergence at  the intermediate and gyro scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Even though our simulations were run at unrealistically high  𝛼, the background particles did not deviate significantly from the  Maxwellian distribution at the end of the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This indi-  cates, that a fluid description for background species is indeed a valid  approach for this setup, especially for smaller, more realistic values  of 𝛼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='6 Computational scaling  We show the strong scaling properties of our fluid-PIC code in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The tests were run on Intel Cascade 9242 processors with 96  processors per node at the HLRN Emmy cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Simulations with  3000 processors or more typically cause severe bottlenecks due to  the latency and/or the finite bandwidth of input/ouput operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For  this number of processors the Fourier-based closures are roughly 20  per cent more costly in comparison to the ideal gas closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This  is in stark contrast to pure PIC simulations, which scale with the  inverse ratio of cosmic ray-to-background density 𝛼−1, consequently  1000  200  300  500  700  2000  3000  processors  100  time [s]  disabled fluid module  FPIC ideal gas  FPIC Landau FFT-based  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Strong scaling of the fluid-PIC code, with and without Fourier-  based Landau closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Shown is the wall-clock time needed to simulate 1250  time integration steps with 180000 cells at 1000 particles per cell at a varying  number of processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We show the perfect strong scaling that is proportional  to the inverse number of processors as the grey dashed line for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  For the disabled fluid module no background plasma was initialized and only  cosmic rays are initialized, showing that the bulk of the computational work  is performed by the PIC routines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  the fluid-PIC algorithm leads to a speed-up of a factor of 100 for the  simulation performed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5, which adopted unrealistically  large 𝛼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The bottleneck in the communication procedure of our implemen-  tation is currently the “Ialltoallv” MPI routine, which is not optimized  for hierarchical architecture networks as of now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Further optimiza-  tions to this might provide fruitful in increasing the code’s scalability  further if necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The fluid-PIC simulations in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='5 used only 𝑁pc = 25 and  seem to be sufficiently resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' For such a low particle number, the  FFT is the bottleneck for scalability because the overlap of commu-  nication and computation is small, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' we measure a 260 per cent  increase in time with 2880 processors, while at 192 processors the  increase is below 20 per cent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This indicates that scalability of fluid-  only simulations is dominated quickly by the FFT, while the cost is  almost negligible for fluid-PIC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Still, simulations with  only a few particles per cell are computationally inexpensive so that  there is no reason for performing such a simulation on thousands of  processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Furthermore, the example of a mono-energetic cold cos-  mic ray beam is not very demanding regarding the phase-space res-  olution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' More realistic scenarios include power law distributions for  the CR population as well as larger spatial density inhomogeneities,  both resulting in an increased requirement for the number of parti-  cles per cell in order to accurately resolve the velocity phase-space  distribution along the entire spatial domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  4 CONCLUSION  In this paper, we introduce a new technique termed fluid-PIC, which  uses Maxwell’s equations to self-consistently couple the PIC method  to the fluid equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This technique is particularly aimed at simu-  lating energetic particles like cosmic rays interacting with a thermal  plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This enables us to resolve effects on electron time and length  scales and to emulate Landau damping in the fluid by incorporating  appropriate closures for the divergence of the heat flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The under-  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  15  lying building blocks of our implementation are the SHARP 1D3V  PIC-code extended by a newly developed fluid module and the over-  all algorithm is second-order accurate in space and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' While an  ideal fluid does not exhibit Landau damping, we have implemented  two different Landau fluid closures and studied their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Here we summarize our main findings:  We developed a stable multi-species fluid code that is coupled  to explicit PIC algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In order to couple multi-fluid equations to  Maxwell’s equations, very often implicit and semi-implicit methods  have been used for stability reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, the resulting interde-  pendency between all fluids complicates their coupling to explicit  PIC methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' To ensure numerical stability, Riemann solvers that  provide some numerical diffusion are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, we demonstrate  that the level of numerical diffusivity needs to be carefully controlled  so that it does not numerically damp small-amplitude plasma waves  or quench plasma instabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Most importantly, our new fluid-PIC  code fully resolves the electron timescales, precluding the need to  adopt any simplifying assumptions to the electrical field components  or to Ohm’s law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  We compare various Landau fluid closures and demonstrate  that local closures only produce reliable results close to a charac-  teristic scale while they are prone to fail in multi-scale problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  By contrast, semi-local spatial filters or global (Fourier-based) meth-  ods to estimate Landau fluid closures produce reliable results for  a large range of scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Most importantly, we demonstrate that the  inclusion of communication intensive (Fourier-based) fluid closures  only have a minimal impact on our code performance (through the  usage of non-blocking background communication) because the ma-  jority of the computational workload is taken up by the much more  cost-intensive PIC module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This enables us to make use of the more  accurate Fourier-based Landau closure for the fluid instead of relying  on local approximations only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  In numerical tests, our implementation of the multi-species fluid  module showed excellent agreement with theoretical frequencies and  damping rates of Langmuir waves, oscillation frequencies of various  two fluid wave modes, as well as the non-linear Landau damping of  Alfvén waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  First simulations of the cosmic ray streaming instability with  our combined fluid-PIC code provide very good agreement with the  results of pure PIC simulations, especially for the growth rates and  saturation levels of the gyro-scale and intermediate-scale instabili-  ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This success is achieved at a substantially lower Poisson noise  of the background plasma at the same number of computational cos-  mic ray particles per cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Most importantly, the numerical cost of  the fluid-PIC simulation is reduced by the cosmic ray-to-background  number density ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However, we find that the late-time behaviour  of the cosmic ray streaming instability differs for our fluid-PIC and  PIC simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' More work is needed to understand the reason for  this, which could be either resulting from (i) numerical damping  due to Poisson noise resulting from the finite number of PIC parti-  cles, (ii) missing relativistic (electron) effects in our non-relativistic  fluid dynamics, or (iii) missing physics in our fluid closures that  may be underestimating other relevant collisionless wave damping  processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Three possible future extensions of the algorithm are left open  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (i) Extending the fluid formulation with a full pressure tensor,  (ii) extending the code to two or three spatial dimensions, and (iii) the  inclusion of direct interaction terms between the various fluids to ex-  plicitly incorporate scattering processes such as ion-neutral damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The novel fluid-PIC framework greatly extends the computationally  limited parameter space accessible to pure PIC methods whilst not  compromising on some of the most important microphysical plasma  effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This opens up many possibilities for studying cosmic ray  physics in physically relevant parameter regimes, such as the growth  and saturation of the cosmic ray streaming instability in different en-  vironments, and including the effect of partial ionization, ion-neutral  damping and inhomogeneities of the background plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  The authors acknowledge support by the European Research Coun-  cil under ERC-CoG grant CRAGSMAN-646955 and ERC-AdG  grant PICOGAL-101019746.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The work was supported by the North-  German Supercomputing Alliance (HLRN), project bbp00046.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  DATA AVAILABILITY  The data underlying this article will be shared on reasonable request  to the corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
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+page_content=', 1994, Shock Waves, 4, 25  Umansky M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
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+page_content=', 2015,  Journal of Nuclear Materials, 463, 506  Wang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Hakim A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Bhattacharjee A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Germaschewski K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', 2015, Physics  of Plasmas, 22, 012108  Wang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Zhu B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Xu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='-q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Li B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', 2019, AIP Advances, 9, 015217  Wang L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Hakim A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Ng J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Dong C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Germaschewski K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', 2020, Journal of  Computational Physics, 415, 109510  Xie H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='-s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', 2014, Computer Physics Communications, 185, 670  van Marle A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Casse F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', Marcowith A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', 2018, MNRAS, 473, 3394  APPENDIX A: C-WENO COEFFICIENTS  We list all coefficients needed to implement the C-WENO recon-  struction in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Because our reconstruction procedure is  applied component-wise to each of the primitive variables, we as-  sume for this appendix that we are reconstructing a single quantity  𝑢.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The smoothness indicator for the low-order polynomials are given  by (Jiang & Shu 1996):  IS[𝑃L] = 13  12 (𝑢𝑖−2 − 2𝑢𝑖−1 + 𝑢𝑖)2 + 1  4 (𝑢𝑖−2 − 4𝑢𝑖−1 + 3𝑢𝑖)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A1)  IS[𝑃C] = 13  12 (𝑢𝑖−1 − 2𝑢𝑖 + 𝑢𝑖+1)2 + 1  4 (𝑢𝑖+1 − 𝑢𝑖−1)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A2)  IS[𝑃R] = 13  12 (𝑢𝑖 − 2𝑢𝑖+1 + 𝑢𝑖+2)2 + 1  4 (3𝑢𝑖 − 4𝑢𝑖+1 + 𝑢𝑖+2)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A3)  while four auxiliary variables are defined  𝐷1 = (6𝑤0 − 1) (𝑢𝑖−2 + 𝑢𝑖+2) − 2 (18𝑤0 − 1) (𝑢𝑖−1 − 𝑢𝑖+1)  48𝑤0  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' (A4)  𝐷2 =  1  16𝑤0  [(2𝑤0 − 3) (𝑢𝑖−2 + 𝑢𝑖+2) − 2 (2𝑤0 + 9) 𝑢𝑖+  + 12 (𝑢𝑖−1 + 𝑢𝑖+1)],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A5)  𝐷3 = −𝑢𝑖−2 + 2 (𝑢𝑖−1 − 𝑢𝑖+1) + 𝑢𝑖+2  12𝑤0  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A6)  𝐷4 = 𝑢𝑖−2 − 4𝑢𝑖−1 + 6𝑢𝑖 − 4𝑢𝑖+1 + 𝑢𝑖+2  24𝑤0  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A7)  to define the smoothness indicator for the 𝑃0 polynomial:  IS[𝑃0] = 𝐷2  1 +  13𝐷2  2  3  +  3129𝐷2  3  80  +  87617𝐷2  4  140  + 𝐷3𝐷1  2  + 21𝐷2𝐷4  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A8)  The overall smoothness indicator is given by (Cravero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 2018b):  𝜏 = |IS[𝑃L] − IS[𝑃R]| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (A9)  The low-order polynomials are evaluated at the left-hand interface  of a given cell via:  𝑃L  �  𝑥𝑖− 1  2  �  = 1  6 (−𝑢𝑖−2 + 5𝑢𝑖−1 + 2𝑢𝑖),  (A10)  𝑃C  �  𝑥𝑖− 1  2  �  = 1  6 (2𝑢𝑖−1 + 5𝑢𝑖 − 𝑢𝑖+1),  (A11)  𝑃R  �  𝑥𝑖− 1  2  �  = 1  6 (11𝑢𝑖 − 7𝑢𝑖+1 + 2𝑢𝑖+2),  (A12)  while they evaluate to  𝑃L  �  𝑥𝑖+ 1  2  �  = 1  6 (2𝑢𝑖−2 − 7𝑢𝑖−1 + 11𝑢𝑖),  (A13)  𝑃C  �  𝑥𝑖+ 1  2  �  = 1  6 (−𝑢𝑖−1 + 5𝑢𝑖 + 2𝑢𝑖+1),  (A14)  𝑃R  �  𝑥𝑖+ 1  2  �  = 1  6 (2𝑢𝑖 + 5𝑢𝑖+1 − 𝑢𝑖+2),  (A15)  at the right-hand interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The optimal polynomial evaluates to  𝑃opt  �  𝑥𝑖− 1  2  �  = 1  60 (−3𝑢𝑖−2 + 27𝑢𝑖−1 + 47𝑢𝑖 − 13𝑢𝑖+1 + 7𝑢𝑖+2)  = 1  10  �  3𝑃L  �  𝑥𝑖− 1  2  �  + 6𝑃C  �  𝑥𝑖− 1  2  �  + 𝑃R  �  𝑥𝑖− 1  2  ��  ,  (A16)  𝑃opt  �  𝑥𝑖+ 1  2  �  = 1  10  �  𝑃L  �  𝑥𝑖+ 1  2  �  + 6𝑃C  �  𝑥𝑖+ 1  2  �  + 3𝑃R  �  𝑥𝑖+ 1  2  ��  , (A17)  at both interfaces of the cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The interface values of 𝑃0 can be derived  from equation (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  APPENDIX B: CONVERGENCE ORDER  In order to numerically prove a second order scaling of the plasma  frequency for the different heat flux closures, the linear dispersion of  MNRAS 000, 1–17 (2022)  Fluid-particle-in-cell method with Landau closures  17  24  25  26  27  28  29  cells per wave length [resolution]  10−5  10−4  10−3  10−2  10−1  rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' error |휔| [%]  ideal gas  Landau 푅32  Landau 푅31  Figure B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Relative error  ��(𝜔sim − 𝜔theor)/𝜔theor�� of the simulated fre-  quency of a Langmuir wave at 𝑘 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='05𝑘D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The same simulation setup is  used in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' 5, where we use a resolution of 68 cells per wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The  resolution here is varied between 68/4 = 17 to 68 × 10 cells per wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  The grey line is a reference line for the second-order scaling of the error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  the Langmuir wave setup described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='3 is simulated at dif-  ferent resolutions of 𝜆/Δ𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' We concentrate here on the convergence  of a wave with wavenumber 𝑘/𝑘D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The results are shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' B1 and demonstrate a very good match with the predicted errors  assuming a second order convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' At first sight, the Landau clo-  sures do not seem to scale ideally for higher resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' However,  this is the result of physical plasma heating due to wave damping  in our setup leading to a non-linear increase in the expected plasma  frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  APPENDIX C: 𝑅31 CLOSURE AND ADIABATIC  COEFFICIENTS  While the 𝑅32 closure assumes a fixed adiabatic index Γ of 3, the 𝑅31  closure introduces a term proportional to ˆ𝑤 which alters the pressure  equation in such a way that it increases the effective adiabatic index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  To show this, we simplify equation (42) by introducing the numerical  coefficients 𝑎𝑤 and 𝑎𝑇 which are defined by comparing  ˆ𝑄 = 𝑎𝑤𝑝0 ˆ𝑤 + i sign (𝑘) 𝑎𝑇 ˆ𝑇.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  (C1)  to equation (42).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Using this ansatz and perturbing the pressure equa-  tion (30) with 𝑝 = 𝑝0 + 𝑝1, where 𝑝1 is the perturbation to the mean  pressure 𝑝0, in the absence of direct Landau damping (𝑎𝑇 = 0), we  have  𝜕𝑝1  𝜕𝑡  = (−Γ𝑝 − 𝑎𝑤𝑝0) ∇ · 𝒘 − 𝒘 · ∇𝑝  = (−Γeff 𝑝0 − Γ𝑝1) ∇ · 𝒘 − 𝒘 · ∇𝑝,  (C2)  where Γeff = 𝑎𝑤 + Γ = 4/(4 − π) ≃ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='66 can be interpreted as the  effective adiabatic index of the fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' The evolution of sound waves  of a non-electromagnetic fluid in the linear regime is governed by  the linear term Γeff 𝑝0∇ · 𝒘 while the term Γ𝑝1∇ · 𝒘 adds non-  linearity to this equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' In the linear approximation, the speed  of sound becomes 𝑐s = (Γeff 𝑝0/𝑛0)1/2 which coincides with the  typical expression for the sound speed 𝑐s = (Γ𝑝0/𝑛0)1/2 in the limit  of 𝑎𝑤 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' This implies that the speed of sound is increased for the  𝑅31 closure even if direct Landau damping is not present (𝑎𝑇 = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  Interestingly, the effective adiabatic index and the speed of sound  are independent of the choice of Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' If direct Landau damping, as  described by the 𝑅31 closure, is affecting the fluid (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=', 𝑎𝑇 ≠ 0),  then the effective adiabatic index attains somewhat smaller values in  comparison to 𝑎𝑤 + Γ while the wave frequency becomes complex  because of the associated damping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' Both are still independent of the  choice of Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  This has consequences for simulations that model mildly relativis-  tic fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content=' If a simulation setup includes a fluid with an associated  speed of sound near the speed of light 𝑐s ≲ 𝑐, then a simulation that  uses this setup with the 𝑅31 closure can become unstable because  𝑐s can now exceed the speed of light because of the aforementioned  reason.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  This paper has been typeset from a TEX/LATEX file prepared by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
+page_content='  MNRAS 000, 1–17 (2022)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9E3T4oBgHgl3EQftwvH/content/2301.04679v1.pdf'}
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+A stochastic approach to the quantum noise of a single-emitter nanolaser
+Matias Bundgaard-Nielsen,1, 2 Emil Vosmar Denning,1, 2, 3 Marco Saldutti,1, 2 and Jesper Mørk1, 2
+1Department of Electrical and Photonics Engineering,
+Technical University of Denmark, Building 343, 2800 Kongens Lyngby, Denmark
+2NanoPhoton-Center for Nanophotonics, Technical University of Denmark, Building 343, 2800 Kongens Lyngby, Denmark
+3Nichtlineare Optik und Quantenelektronik, Institut f¨ur Theoretische Physik, Technische Universit¨at Berlin, Berlin, Germany
+(Dated: January 30, 2023)
+It is shown that the intensity quantum noise of a single-emitter nanolaser can be accurately
+computed by adopting a stochastic interpretation of the standard rate equation model under the
+only assumption that the emitter excitation and photon number are stochastic variables with integer
+values. This extends the validity of rate equations beyond the mean-field limit and avoids using
+the standard Langevin approach, which is shown to fail for few emitters. The model is validated
+by comparison to full quantum simulations of the relative intensity noise and second-order intensity
+correlation function, g(2)(τ).
+Surprisingly, even when the full quantum model displays vacuum
+Rabi oscillations, which are not accounted for by rate equations, the intensity quantum noise is
+correctly predicted by the stochastic approach. Adopting a simple discretization of the emitter and
+photon populations, thus, goes a long way in describing quantum noise in lasers. Besides providing
+a versatile and easy-to-use tool for modeling a new generation of nanolasers with many possible
+applications, these results provide insight into the fundamental nature of quantum noise in lasers.
+The ability of a laser to generate a coherent optical
+signal with ultra-low noise is key to a wide range of
+applications, including the internet [1], sensors [2], as
+well as fundamental tests of physics, including the de-
+tection of gravitational waves [3]. Recent advancements
+in nanotechnology have enabled the realization of a new
+generation of microscopic lasers, for instance, based on
+semiconductor quantum dots in photonic crystals [4–6],
+opening new possibilities in, e.g., on-chip communica-
+tions [7–10] and quantum technology [11]. However, as
+the laser shrinks into the microscopic regime, the power
+diminishes, and the intrinsic quantum noise of the laser
+may well be the limiting factor. The noise of lasers is
+a rich and complex field which is still developing [12–
+22]. For few emitters, it is, in principle, possible to per-
+form full-scale quantum simulations of the noise proper-
+ties [23–27]. However, such simulations are numerically
+demanding, add little insight into the physics, and it is
+difficult to design laser structures with optimal proper-
+ties directly based on this approach. Rather, the use of
+rate equations has proven extremely successful in realiz-
+ing the advanced modern semiconductor laser of today
+[28]. However, rate equations are derived in the mean-
+field limit, which we show is not valid for few emitters,
+even if stochastic Langevin noise terms are included [29].
+In this paper, we consider the ultimate limit of a
+nanolaser, where the gain medium is a single-emitter,
+e.g., a quantum dot in a photonic crystal cavity as stud-
+ied in [30, 31], and shown in Fig. 1.
+We show that
+the quantum noise of such nanolasers can be quantita-
+tively described by classical rate equations by adopting
+a simple stochastic interpretation with discrete popula-
+tion changes [14, 15, 32, 33]. This is surprising since rate
+equations are derived in a mean-field limit and neglect
+coherent emitter-photon interactions. We find excellent
+agreement with full quantum mechanical master eqs. re-
+garding the intensity noise, even in the regime where vac-
+uum Rabi oscillations manifest. The appearance of sub-
+Poissonian statistics below threshold is also predicted by
+our approach, while standard Langevin approaches fail
+in this regime.
+Our finding enables a new approach towards the quan-
+tum noise of nanolasers.
+Not only does it provide an
+intuitive and simple simulation tool, but it also offers
+new insights into the origin of quantum noise in lasers.
+In second quantization, the single-emitter laser is de-
+scribed by a master equation of the form [23, 24]:
+∂ρ
+∂t = − i
+ℏ[H, ρ]+κDa[ρ]+γDDσ†σ[ρ]+γADσ[ρ]+PDσ†[ρ]
+(1)
+where H = −ℏ∆a†a + ℏg(σ†a + a†σ) is the Jaynes-
+Cummings Hamiltonian with g =
+�
+d2ωeg/ (2ℏϵ0ϵV ) be-
+ing the light-matter coupling [34]. Here d is the emitter
+dipole moment, ϵ is the dielectric constant of the back-
+ground material, V is the cavity mode volume, σ = |g⟩ ⟨e|
+is the atomic transition operator, a is the cavity mode an-
+nihilation operator, ∆ = ωeg−ωc is the detuning between
+the electronic transition ωeg and the cavity frequency ωc,
+and DA[·] = 1
+2(2A(·)A†−(·)A†A−A†A(·)) is the Lindblad
+operator. The various Lindblad terms describe dissipa-
+tive processes relevant to single-emitter lasers; κ is the
+cavity decay rate, γD is the pure dephasing rate, aris-
+ing from, e.g., phonons in quantum dot emitters [31], γA
+is the non-radiative decay and/or decay into non-lasing
+modes, and P is the pump rate of the emitter, modeled
+as incoherent pumping [23, 35]. The master equation is
+numerically implemented by using QuTIP [36, 37].
+Under the assumption of a large dephasing rate, such
+that the polarization can be eliminated [31, 35, 38], a rate
+arXiv:2301.11815v1  [quant-ph]  27 Jan 2023
+
+2
+FIG. 1. Schematic of a photonic crystal cavity laser with a
+single quantum dot.
+Examples of photon distributions in-
+side and outside the cavity, calculated with the stochastic ap-
+proach, are shown above threshold for the same parameters
+as in Fig. 3 and 4.
+equation can be derived from the master equation in eq.
+(1). With na =
+�
+a†a
+�
+and ne =
+�
+σ†σ
+�
+and making a
+mean-field approximation we get:
+dna
+dt = γr(2ne − 1)na + γrne − κna
+(2)
+dne
+dt = Png − γr(2ne − 1)na − γrne − γAne
+(3)
+where an emitter-cavity coupling rate given by γr =
+4g2/(P + κ + γD + γA). Since the polarization was adi-
+abatically eliminated, this model does not display Rabi
+oscillations. Furthermore, the equations only govern the
+average emitter excitation and number of cavity photons
+and do not include quantum noise. Conventionally, quan-
+tum noise is accounted for by adding random Langevin
+forces to the RHS. of eqs. (2) and (3) [28]. As we shall
+see, however, this leads to incorrect results for the in-
+tensity correlation, g(2)(0), which has been recognized as
+essential in identifying the regime of lasing [12, 16].
+Another approach to include noise in the rate equa-
+tions is to interpret Eqs. (2) and (3) as a stochastic pro-
+cess for integer-valued variables, ne and na [14, 33]. The
+stochastic approach was introduced for many emitters
+but is here applied to the case of a single-emitter.
+In
+essence, it replaces the rates in eqs. (2)-(3) by Poisson
+processes, thus attributing all the quantum noise of the
+laser to the discrete nature of photons and emitter ex-
+citation.
+Notably, this approach does not require the
+calculation of diffusion coefficients for Langevin forces,
+nor does it assume small perturbations around a steady
+state.
+Here, to numerically solve the stochastic equation, we
+use Gillespies first-reaction method, which is numerically
+exact [15].
+We choose parameters compatible with a
+single quantum dot in a photonic crystal cavity with a
+light-matter coupling of g = 0.1 ps−1 [30] and a cav-
+ity decay rate κ = 0.02 ps−1 [19]. Furthermore, we use
+γA = 0.012 ps−1 and study three different pure dephasing
+rates γD = 0, 1, 10 ps−1. Ignoring pump broadening, this
+gives β-factors of β = γr/(γr + γA) = 0.999, 0.764, 0.249,
+thus placing the laser in the high-β or ”thresholdless”
+regime. It is worth noting that recent advances in di-
+electric nanocavities with deep subwavelength confine-
+ment [39–42] enable even larger values of g. Fig. 2 shows
+the results obtained from the master equation and the
+stochastic approach. The mean photon number na, the
+intensity correlation function g(2)(0), RIN, emission spec-
+trum, and linewidth are depicted. See supplementary for
+details on calculations.
+Fig. 2 (a,b,c) demonstrate excellent agreement between
+the stochastic approach and the master equation for the
+mean photon number, intensity correlation, and RIN.
+This is the case for all dephasing values and pump rates.
+The results of adding Langevin noise terms to eqs. (2)
+and (3) is also shown and we refer to [14] for details. It
+is clear that the Langevin approach captures the mean
+photon number and RIN relatively well, while there is a
+large deviation in the intensity correlation. This shows a
+fundamental problem of the Langevin approach for few
+emitters, since g(2)(0) is a key measure of the statistics
+of the light [12, 13, 35]. Below threshold, the light is an-
+tibunched in the single-emitter case, which is correctly
+identified by g(2)(0) < 1 for the master equation and
+stochastic approach, while the Langevin approach pre-
+dicts super-Poissonian statistics, g(2)(0) > 1. Further-
+more, surprisingly, the results produced by the stochas-
+tic approach are also correct in the ”bad cavity limit”
+where κ > γD, γA (red curves) and the adiabatic ap-
+proximation, which is at the heart of the rate equation
+approximation, breaks down.
+Fig. 2(d) shows the emission spectrum for the case of
+γD = 0.
+Note that the stochastic approach, which in
+its present form does not contain information about the
+phase, cannot calculate the emission spectrum. In the
+emission spectrum, we observe two peaks for low pump
+values that reflect Rabi oscillations and correspondingly
+have a splitting of 2g = 0.2 ps−1.
+As the pump rate
+is increased, we see the transition to lasing as the Rabi
+peaks coalesce into a single peak at the cavity frequency,
+whose linewidth narrows significantly. This is seen from
+Fig. 2(e) which shows the corresponding linewidth ∆ν
+(FWHM) calculated from the Liouville gap (the smallest
+real eigenvalue in the system) [16].
+In contrast to macroscopic lasers, characterized by
+β << 1, the transition to lasing in nanolasers with β
+of order unity, does not show a clear phase transition
+[43], giving rise to vivid discussion of the proper defini-
+tion of threshold [18, 44–46]. This highlights the ambi-
+guity in defining the threshold for nanolasers, in contrast
+to the case of macroscopic lasers. In Fig. 2(d,e) vertical
+lines show the prediction of two threshold definitions, Ppr
+and Pcl, to be further discussed below. In both expres-
+sions, the number of carriers at lasing threshold, ne,th,
+
+3
+is defined by the balance between gain and cavity loss
+γr(2ne,th − 1) = γc. From here, the classical approach
+[28] is to compute the corresponding pump rate by as-
+suming that the photon population below threshold is
+zero. This procedure leads to the following expression,
+where we have ignored pump broadening [47]
+Pcl =
+�
+2
+1 − 1/(2ξ)
+� 1
+2
+γc
+β (1 + 2ξ)
+(4)
+with ξ = γr/(2γc).
+However, in the presence of a
+near-unity β-factor, the number of photons below trans-
+parency may be non-negligible [48]. At the same time, if
+γr is sufficiently larger than κ, a generated photon has a
+significant chance of being re-absorbed rather than escap-
+ing the cavity. This cycle of spontaneous emission into
+the lasing mode and stimulated re-absorption, i.e. pho-
+ton recycling [47, 48], may effectively increase the carrier
+lifetime and lower the pump rate required to reach the
+lasing threshold. By including the effect of photon recy-
+cling, one arrives at the following expression [47]:
+Ppr =
+�
+2
+1 − 1/(2ξ)
+� 1
+2
+γc
+βeff
+,
+βeff =
+β
+1 + 2ξ(1 − β) (5)
+It is seen that Ppr marks the pump value at which the
+Rabi peaks coalesce, g(2)(0) approaches 1 from below,
+and also the linewidth starts narrowing. At the pump
+value of Pcl, the linewidth has reduced significantly and
+one enters a regime with g(2)(0) ≈ 1, independently
+of the pump value. At a critical pump value, denoted
+as the quenching threshold and indicated by Pqn, the
+linewidth starts to rebroaden, and g(2)(0) quickly ap-
+proaches the thermal value of 2. This quenching behavior
+at high pump values is in agreement with previous work
+[23, 24, 35] and occurs because pump-induced dephasing
+dominates the emitter broadening.
+See supplementary
+for details on Pqn and also analytical expressions for the
+linewidth, which are compared to the simulations of the
+master equation in Fig. 2(e).
+Reaching the classical threshold requires a larger pump
+rate compared to the photon recycling threshold. There-
+fore, the photon number is larger, and the linewidth
+has narrowed significantly. The photon recycling thresh-
+old, however, reliably marks the pump rate at which
+the linewidth starts to narrow, and the photon statis-
+tics change from anti-bunched to the thermal regime with
+super-Poissonian statistics preceding lasing. This feature
+becomes particularly clear when various light-matter cou-
+pling rates (not shown here) are considered. Conversely,
+the classical threshold would not mark a consistent stage
+in the evolution toward coherent laser light.
+10
+2
+100
+Mean photonnumber, 
+ np
+Pure dephasing rates:
+(a)
+Stochastic
+Master equation
+Langevin
+Stochastic
+Master equation
+Langevin
+Stochastic
+Master equation
+Langevin
+γD = 0
+γD = 1 ps−1
+γD = 10 ps−1
+1.0
+1.5
+2.0
+Intensity correlation,
+ g(2)(0)
+(b)
+100
+102
+RIN
+(c)
+0.2
+0.1
+0.0
+0.1
+0.2
+Frequency,
+ ω − ωeg[ps−1]
+γD = 0
+Ppr
+Pcl
+Pqn
+(d)
+10
+4
+10
+3
+10
+2
+10
+1
+100
+101
+Pump rate [ps−1]
+100
+101
+102
+Linewidth [GHz]
+γD = 0
+(e)
+Master equation
+Modified Schawlow-Townes
+Supplementary eq. (7) and (9)
+0.00
+0.15
+0.30
+0.45
+0.60
+0.75
+0.90
+1.05
+FIG. 2. (a) Cavity population, (b) second-order correlation
+function g(2)(0), (c) RIN, (d) emission spectrum, and (e)
+linewidth vs.
+pump-rate, for three different pure dephas-
+ing rates:
+γD = 0(red), γD = 1 ps−1(blue), and γD =
+10 ps−1(green).
+The spectrum is only shown for γD = 0,
+normalized to 1 for each pump rate, and is calculated using
+the master equation. The characteristic pump rates, Pre, Pcl,
+and Pqu separate the laser into four qualitatively different
+regimes I-IV.
+To further characterize the quantum noise, we con-
+sider the frequency dependence of the RIN spectrum.
+The spectrum of the outcoupled signal is the experimen-
+tally relevant observable and differs qualitatively from
+the intra-cavity spectrum due to the non-trivial action of
+
+4
+0.0
+10.0
+20.0
+30.0
+40.0
+50.0
+Frequency [GHz]
+120
+110
+100
+90
+RIN [dB/Hz]
+out-coupled
+intra-cavity
+Pure dephasing rates:
+Below threshold
+Stochastic
+Master equation
+Langevin
+Stochastic
+Master equation
+Langevin
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+17.5
+20.0
+Frequency [GHz]
+120
+115
+110
+105
+RIN [dB/Hz]
+out-coupled
+intra-cavity
+Pure dephasing rates:
+Pure dephasing rates:
+Above threshold
+FIG. 3.
+RIN spectra for intra-cavity and outcoupled pho-
+tons, below and above threshold.
+The RIN is calculated
+by the master equation, stochastic approach, and the ana-
+lytic Langevin approach.
+The parameters are the same as
+in Fig. 2 with P = 0.0012 ps−1 and P = 0.3023 ps−1 in
+respectively below and above threshold. The detector inte-
+gration times are T = γ−1
+r
+= 0.83 ps−1 and 8.36 ps−1 re-
+spectively, the vertical dashed line shows the Rabi frequency
+at f = 2g/2π = 31.8GHz, and the horizontal dots mark the
+standard quantum limit.
+the outcoupling mirror [49]. This is illustrated in Fig. 1,
+where the photon distribution changes drastically outside
+the cavity. We calculate the outcoupled noise spectrum
+by simulating the detection of photons outside the cav-
+ity with an integration time T. In the master equation,
+this is done using normally ordered photodetection the-
+ory [23, 50–52], and for the stochastic approach, we track
+all outcoupling events [32]; see supplementary material
+for details. In the calculations, we choose a detector in-
+tegration time small enough to capture all features in the
+outcoupled spectrum. Empirically, the inverse emission
+rate γ−1
+r
+is a good choice.
+Fig. 3 shows RIN spectra for the intra-cavity and out-
+coupled photons for two pump values: one below thresh-
+old and one above. We also show results based on the
+analytic Langevin approach introduced in ref. [28] and
+adopted to the nanolaser rate eqs. in ref.
+[32].
+Be-
+low threshold, Rabi oscillations manifest themselves in
+the intra-cavity RIN spectrum calculated by the mas-
+ter equation as a peak around 2πf = 2g.
+These os-
+cillations arise due to the dynamics of the atomic po-
+larization, which neither the Langevin approach nor the
+stochastic rate equation approach can capture, due to
+the adiabatic elimination carried out in the rate equa-
+tions [15, 32]. Considering the outcoupled RIN instead,
+we see that the noise is dominated heavily by the parti-
+tion noise at the cavity mirrors [28] and it is accurately
+given by the standard quantum limit: SN = 2/(naκ),
+without any features of Rabi oscillations.
+Above threshold, Rabi oscillations do not manifest
+themselves in the RIN spectrum, and all three approaches
+agree. We again see that the shot noise stemming from
+the cavity mirrors dominates the outcoupled RIN spec-
+trum. Note, however, that the outcoupled RIN spectrum
+is not simply given by the intra-cavity RIN spectrum with
+the added shot noise. Below 5 GHz, the outcoupled RIN
+is thus smaller than the intra-cavity RIN [28, 32]. While
+outcoupling at the laser mirror introduces quantization
+(shot) noise of the outcoupled photons, the noise is re-
+duced at low frequencies due to anti-correlation effects
+[28, 32]. The partition noise at the cavity mirrors can
+thus lower the noise for low frequencies.
+We now consider the time-dependency of the intra-
+cavity intensity correlation function, g2(τ) (see supple-
+mentary). The results can be seen in Fig. 4, where we
+see deviations between the stochastic approach and the
+master equation below and above threshold. The devia-
+tion below threshold clearly arises from Rabi oscillations,
+which, as mentioned, cannot be captured by the stochas-
+tic approach.
+Above threshold, the absolute deviation
+is quite small (within 1-2%), but the qualitative behav-
+ior is significantly different. Although not visible in the
+spectrum, transitions in the Jaynes-Cummings Ladder
+still affect the two-time correlation function.
+We thus
+find that the master eq. results can be well fitted by the
+following expression derived in [26]:
+g(2)(τ) = 1 + d1 exp(−τ/τc) +
+m=3
+�
+m=1
+cm cos(ωmt)e−τ/τm
+(6)
+Here, τ −1
+c
+= κ − P/4g2 is the coherence time for the
+non-oscillating term, and d1, cm, ωm, and τm are fit-
+ted. ωm is fitted to values of ω1 ≈ g, ω2 ≈ 2g
+√
+2, and
+ω3 ≈ 2g
+√
+4 which corresponds to the following transi-
+tions in the Jaynes-Cummings ladder: |1, +⟩ → |g, 0⟩,
+|1, +⟩ → |1, −⟩, and |3, +⟩ → |3, −⟩ respectively, where
+we here defined |n, ±⟩ = (|g⟩ |n + 1⟩ ± |e⟩ |n⟩)/
+√
+2 [53].
+The oscillating terms, thus, stem from Rabi oscillations
+and play the same role as the correction δg(2)(τ) to
+the Siegert relation found in ref. [54], where they write:
+g(2)(τ) = 1+|g(1)(τ)|2+δg(2)(τ). They show that the cor-
+rection δg(2)(τ) is necessary when either strong emitter-
+emitter or emitter-photon correlations are present. We
+find a similar result. Only including the non-oscillating
+term with coherence time τc, i.e. g(2)(τ) = 1 + (g2(0) −
+1)e−τ/τc, is sufficient to describe g2(τ) as obtained from
+the stochastic approach. The stochastic approach, how-
+
+5
+0
+50
+100
+150
+200
+250
+300
+0.6
+0.8
+1.0
+g(2)(τ)
+Below Threshold
+0
+50
+100
+150
+200
+250
+300
+τ [ps]
+1.00
+1.02
+1.04
+g(2)(τ)
+Above Threshold
+Stochastic
+Master equation
+Rabi Fit (eq. 8)
+1 + (g2(0) − 1)e−τ/τc
+Stochastic
+Master equation
+Rabi Fit (eq. 8)
+1 + (g2(0) − 1)e−τ/τc
+FIG. 4.
+Computed correlation function g(2)(τ) below and
+above the laser threshold for the same parameters as in Fig. 2
+and 3. A fit to the master equation with the expression (6) is
+also shown, as well as a monotonically decaying exponential
+with coherence lifetime τ −1
+c
+= κ − P/4g2.
+ever, cannot capture the shorter-lived Rabi oscillations
+with τm ≈ 1/(5κ), leading to the master equation ini-
+tially decaying much faster and thus explaining the de-
+viation.
+In conclusion, we have shown that a simple stochastic
+interpretation [15] of standard rate equations accurately
+accounts for the intensity quantum noise of a single-
+emitter laser.
+In contrast, the conventional Langevin
+approach [28] breaks down, implying that the intensity
+quantum noise of a laser originates solely from the dis-
+crete nature of photon and emitter excitations. We also
+analyze the single-emitter lasing transition in detail and
+compare two definitions of the lasing threshold.
+The
+stochastic simulations can easily be extended to multi-
+ple emitters [14, 47], where quantum master equations
+become too numerically demanding. Our findings may,
+therefore, facilitate the analysis and design of a new gen-
+eration of nanolasers while also allowing for a fundamen-
+tal understanding of quantum noise.
+ACKNOWLEDGEMENTS
+This work was supported by the Danish National Re-
+search Foundation through NanoPhoton - Center for
+Nanophotonics, Grant No.
+DNRF147.
+EVD acknowl-
+edges support from Independent Research Fund Den-
+mark through an International Postdoc fellowship, grant
+no. 0164-00014B.
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diff --git a/G9FKT4oBgHgl3EQfcS40/content/tmp_files/load_file.txt b/G9FKT4oBgHgl3EQfcS40/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf,len=555
+page_content='A stochastic approach to the quantum noise of a single-emitter nanolaser  Matias Bundgaard-Nielsen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2 Emil Vosmar Denning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 3 Marco Saldutti,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2 and Jesper Mørk1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2  1Department of Electrical and Photonics Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Technical University of Denmark,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Building 343,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2800 Kongens Lyngby,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Denmark  2NanoPhoton-Center for Nanophotonics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Technical University of Denmark,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Building 343,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2800 Kongens Lyngby,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Denmark  3Nichtlineare Optik und Quantenelektronik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Institut f¨ur Theoretische Physik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Technische Universit¨at Berlin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Berlin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Germany  (Dated: January 30,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2023)  It is shown that the intensity quantum noise of a single-emitter nanolaser can be accurately  computed by adopting a stochastic interpretation of the standard rate equation model under the  only assumption that the emitter excitation and photon number are stochastic variables with integer  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This extends the validity of rate equations beyond the mean-field limit and avoids using  the standard Langevin approach, which is shown to fail for few emitters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The model is validated  by comparison to full quantum simulations of the relative intensity noise and second-order intensity  correlation function, g(2)(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Surprisingly, even when the full quantum model displays vacuum  Rabi oscillations, which are not accounted for by rate equations, the intensity quantum noise is  correctly predicted by the stochastic approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Adopting a simple discretization of the emitter and  photon populations, thus, goes a long way in describing quantum noise in lasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Besides providing  a versatile and easy-to-use tool for modeling a new generation of nanolasers with many possible  applications, these results provide insight into the fundamental nature of quantum noise in lasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The ability of a laser to generate a coherent optical  signal with ultra-low noise is key to a wide range of  applications, including the internet [1], sensors [2], as  well as fundamental tests of physics, including the de-  tection of gravitational waves [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Recent advancements  in nanotechnology have enabled the realization of a new  generation of microscopic lasers, for instance, based on  semiconductor quantum dots in photonic crystals [4–6],  opening new possibilities in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=', on-chip communica-  tions [7–10] and quantum technology [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' However, as  the laser shrinks into the microscopic regime, the power  diminishes, and the intrinsic quantum noise of the laser  may well be the limiting factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The noise of lasers is  a rich and complex field which is still developing [12–  22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' For few emitters, it is, in principle, possible to per-  form full-scale quantum simulations of the noise proper-  ties [23–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' However, such simulations are numerically  demanding, add little insight into the physics, and it is  difficult to design laser structures with optimal proper-  ties directly based on this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Rather, the use of  rate equations has proven extremely successful in realiz-  ing the advanced modern semiconductor laser of today  [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' However, rate equations are derived in the mean-  field limit, which we show is not valid for few emitters,  even if stochastic Langevin noise terms are included [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  In this paper, we consider the ultimate limit of a  nanolaser, where the gain medium is a single-emitter,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=', a quantum dot in a photonic crystal cavity as stud-  ied in [30, 31], and shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  We show that  the quantum noise of such nanolasers can be quantita-  tively described by classical rate equations by adopting  a simple stochastic interpretation with discrete popula-  tion changes [14, 15, 32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This is surprising since rate  equations are derived in a mean-field limit and neglect  coherent emitter-photon interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' We find excellent  agreement with full quantum mechanical master eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' re-  garding the intensity noise, even in the regime where vac-  uum Rabi oscillations manifest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The appearance of sub-  Poissonian statistics below threshold is also predicted by  our approach, while standard Langevin approaches fail  in this regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Our finding enables a new approach towards the quan-  tum noise of nanolasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Not only does it provide an  intuitive and simple simulation tool, but it also offers  new insights into the origin of quantum noise in lasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  In second quantization, the single-emitter laser is de-  scribed by a master equation of the form [23, 24]:  ∂ρ  ∂t = − i  ℏ[H, ρ]+κDa[ρ]+γDDσ†σ[ρ]+γADσ[ρ]+PDσ†[ρ]  (1)  where H = −ℏ∆a†a + ℏg(σ†a + a†σ) is the Jaynes-  Cummings Hamiltonian with g =  �  d2ωeg/ (2ℏϵ0ϵV ) be-  ing the light-matter coupling [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Here d is the emitter  dipole moment, ϵ is the dielectric constant of the back-  ground material, V is the cavity mode volume, σ = |g⟩ ⟨e|  is the atomic transition operator, a is the cavity mode an-  nihilation operator, ∆ = ωeg−ωc is the detuning between  the electronic transition ωeg and the cavity frequency ωc,  and DA[·] = 1  2(2A(·)A†−(·)A†A−A†A(·)) is the Lindblad  operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The various Lindblad terms describe dissipa-  tive processes relevant to single-emitter lasers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' κ is the  cavity decay rate, γD is the pure dephasing rate, aris-  ing from, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=', phonons in quantum dot emitters [31], γA  is the non-radiative decay and/or decay into non-lasing  modes, and P is the pump rate of the emitter, modeled  as incoherent pumping [23, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The master equation is  numerically implemented by using QuTIP [36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Under the assumption of a large dephasing rate, such  that the polarization can be eliminated [31, 35, 38], a rate  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='11815v1  [quant-ph]  27 Jan 2023  2  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Schematic of a photonic crystal cavity laser with a  single quantum dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Examples of photon distributions in-  side and outside the cavity, calculated with the stochastic ap-  proach, are shown above threshold for the same parameters  as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  equation can be derived from the master equation in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' With na =  �  a†a  �  and ne =  �  σ†σ  �  and making a  mean-field approximation we get:  dna  dt = γr(2ne − 1)na + γrne − κna  (2)  dne  dt = Png − γr(2ne − 1)na − γrne − γAne  (3)  where an emitter-cavity coupling rate given by γr =  4g2/(P + κ + γD + γA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Since the polarization was adi-  abatically eliminated, this model does not display Rabi  oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Furthermore, the equations only govern the  average emitter excitation and number of cavity photons  and do not include quantum noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Conventionally, quan-  tum noise is accounted for by adding random Langevin  forces to the RHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' of eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' (2) and (3) [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' As we shall  see, however, this leads to incorrect results for the in-  tensity correlation, g(2)(0), which has been recognized as  essential in identifying the regime of lasing [12, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Another approach to include noise in the rate equa-  tions is to interpret Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' (2) and (3) as a stochastic pro-  cess for integer-valued variables, ne and na [14, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The  stochastic approach was introduced for many emitters  but is here applied to the case of a single-emitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  In  essence, it replaces the rates in eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' (2)-(3) by Poisson  processes, thus attributing all the quantum noise of the  laser to the discrete nature of photons and emitter ex-  citation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Notably, this approach does not require the  calculation of diffusion coefficients for Langevin forces,  nor does it assume small perturbations around a steady  state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Here, to numerically solve the stochastic equation, we  use Gillespies first-reaction method, which is numerically  exact [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  We choose parameters compatible with a  single quantum dot in a photonic crystal cavity with a  light-matter coupling of g = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='1 ps−1 [30] and a cav-  ity decay rate κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='02 ps−1 [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Furthermore, we use  γA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='012 ps−1 and study three different pure dephasing  rates γD = 0, 1, 10 ps−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Ignoring pump broadening, this  gives β-factors of β = γr/(γr + γA) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='999, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='764, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='249,  thus placing the laser in the high-β or ”thresholdless”  regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' It is worth noting that recent advances in di-  electric nanocavities with deep subwavelength confine-  ment [39–42] enable even larger values of g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2 shows  the results obtained from the master equation and the  stochastic approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The mean photon number na, the  intensity correlation function g(2)(0), RIN, emission spec-  trum, and linewidth are depicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' See supplementary for  details on calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2 (a,b,c) demonstrate excellent agreement between  the stochastic approach and the master equation for the  mean photon number, intensity correlation, and RIN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  This is the case for all dephasing values and pump rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The results of adding Langevin noise terms to eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' (2)  and (3) is also shown and we refer to [14] for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' It  is clear that the Langevin approach captures the mean  photon number and RIN relatively well, while there is a  large deviation in the intensity correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This shows a  fundamental problem of the Langevin approach for few  emitters, since g(2)(0) is a key measure of the statistics  of the light [12, 13, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Below threshold, the light is an-  tibunched in the single-emitter case, which is correctly  identified by g(2)(0) < 1 for the master equation and  stochastic approach, while the Langevin approach pre-  dicts super-Poissonian statistics, g(2)(0) > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Further-  more, surprisingly, the results produced by the stochas-  tic approach are also correct in the ”bad cavity limit”  where κ > γD, γA (red curves) and the adiabatic ap-  proximation, which is at the heart of the rate equation  approximation, breaks down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2(d) shows the emission spectrum for the case of  γD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Note that the stochastic approach, which in  its present form does not contain information about the  phase, cannot calculate the emission spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' In the  emission spectrum, we observe two peaks for low pump  values that reflect Rabi oscillations and correspondingly  have a splitting of 2g = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='2 ps−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  As the pump rate  is increased, we see the transition to lasing as the Rabi  peaks coalesce into a single peak at the cavity frequency,  whose linewidth narrows significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This is seen from  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2(e) which shows the corresponding linewidth ∆ν  (FWHM) calculated from the Liouville gap (the smallest  real eigenvalue in the system) [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  In contrast to macroscopic lasers, characterized by  β << 1, the transition to lasing in nanolasers with β  of order unity, does not show a clear phase transition  [43], giving rise to vivid discussion of the proper defini-  tion of threshold [18, 44–46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This highlights the ambi-  guity in defining the threshold for nanolasers, in contrast  to the case of macroscopic lasers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2(d,e) vertical  lines show the prediction of two threshold definitions, Ppr  and Pcl, to be further discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' In both expres-  sions, the number of carriers at lasing threshold, ne,th,  3  is defined by the balance between gain and cavity loss  γr(2ne,th − 1) = γc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' From here, the classical approach  [28] is to compute the corresponding pump rate by as-  suming that the photon population below threshold is  zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This procedure leads to the following expression,  where we have ignored pump broadening [47]  Pcl =  �  2  1 − 1/(2ξ)  � 1  2  γc  β (1 + 2ξ)  (4)  with ξ = γr/(2γc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  However, in the presence of a  near-unity β-factor, the number of photons below trans-  parency may be non-negligible [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' At the same time, if  γr is sufficiently larger than κ, a generated photon has a  significant chance of being re-absorbed rather than escap-  ing the cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This cycle of spontaneous emission into  the lasing mode and stimulated re-absorption, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' pho-  ton recycling [47, 48], may effectively increase the carrier  lifetime and lower the pump rate required to reach the  lasing threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' By including the effect of photon recy-  cling, one arrives at the following expression [47]:  Ppr =  �  2  1 − 1/(2ξ)  � 1  2  γc  βeff  ,  βeff =  β  1 + 2ξ(1 − β) (5)  It is seen that Ppr marks the pump value at which the  Rabi peaks coalesce, g(2)(0) approaches 1 from below,  and also the linewidth starts narrowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' At the pump  value of Pcl, the linewidth has reduced significantly and  one enters a regime with g(2)(0) ≈ 1, independently  of the pump value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' At a critical pump value, denoted  as the quenching threshold and indicated by Pqn, the  linewidth starts to rebroaden, and g(2)(0) quickly ap-  proaches the thermal value of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This quenching behavior  at high pump values is in agreement with previous work  [23, 24, 35] and occurs because pump-induced dephasing  dominates the emitter broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  See supplementary  for details on Pqn and also analytical expressions for the  linewidth, which are compared to the simulations of the  master equation in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Reaching the classical threshold requires a larger pump  rate compared to the photon recycling threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' There-  fore, the photon number is larger, and the linewidth  has narrowed significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The photon recycling thresh-  old, however, reliably marks the pump rate at which  the linewidth starts to narrow, and the photon statis-  tics change from anti-bunched to the thermal regime with  super-Poissonian statistics preceding lasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This feature  becomes particularly clear when various light-matter cou-  pling rates (not shown here) are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Conversely,  the classical threshold would not mark a consistent stage  in the evolution toward coherent laser light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  10  2  100  Mean photonnumber,  np  Pure dephasing rates:  (a)  Stochastic  Master equation  Langevin  Stochastic  Master equation  Langevin  Stochastic  Master equation  Langevin  γD = 0  γD = 1 ps−1  γD = 10 ps−1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  Intensity correlation,  g(2)(0)  (b)  100  102  RIN  (c)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='2  Frequency,  ω − ωeg[ps−1]  γD = 0  Ppr  Pcl  Pqn  (d)  10  4  10  3  10  2  10  1  100  101  Pump rate [ps−1]  100  101  102  Linewidth [GHz]  γD = 0  (e)  Master equation  Modified Schawlow-Townes  Supplementary eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' (7) and (9)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='90  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='05  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' (a) Cavity population, (b) second-order correlation  function g(2)(0), (c) RIN, (d) emission spectrum, and (e)  linewidth vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  pump-rate, for three different pure dephas-  ing rates:  γD = 0(red), γD = 1 ps−1(blue), and γD =  10 ps−1(green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The spectrum is only shown for γD = 0,  normalized to 1 for each pump rate, and is calculated using  the master equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The characteristic pump rates, Pre, Pcl,  and Pqu separate the laser into four qualitatively different  regimes I-IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  To further characterize the quantum noise, we con-  sider the frequency dependence of the RIN spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The spectrum of the outcoupled signal is the experimen-  tally relevant observable and differs qualitatively from  the intra-cavity spectrum due to the non-trivial action of  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  Frequency [GHz]  120  110  100  90  RIN [dB/Hz]  out-coupled  intra-cavity  Pure dephasing rates:  Below threshold  Stochastic  Master equation  Langevin  Stochastic  Master equation  Langevin  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  Frequency [GHz]  120  115  110  105  RIN [dB/Hz]  out-coupled  intra-cavity  Pure dephasing rates:  Pure dephasing rates:  Above threshold  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  RIN spectra for intra-cavity and outcoupled pho-  tons, below and above threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The RIN is calculated  by the master equation, stochastic approach, and the ana-  lytic Langevin approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The parameters are the same as  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2 with P = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0012 ps−1 and P = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='3023 ps−1 in  respectively below and above threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The detector inte-  gration times are T = γ−1  r  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='83 ps−1 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='36 ps−1 re-  spectively, the vertical dashed line shows the Rabi frequency  at f = 2g/2π = 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='8GHz, and the horizontal dots mark the  standard quantum limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  the outcoupling mirror [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' This is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 1,  where the photon distribution changes drastically outside  the cavity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' We calculate the outcoupled noise spectrum  by simulating the detection of photons outside the cav-  ity with an integration time T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' In the master equation,  this is done using normally ordered photodetection the-  ory [23, 50–52], and for the stochastic approach, we track  all outcoupling events [32];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' see supplementary material  for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' In the calculations, we choose a detector in-  tegration time small enough to capture all features in the  outcoupled spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Empirically, the inverse emission  rate γ−1  r  is a good choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 3 shows RIN spectra for the intra-cavity and out-  coupled photons for two pump values: one below thresh-  old and one above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' We also show results based on the  analytic Langevin approach introduced in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' [28] and  adopted to the nanolaser rate eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Be-  low threshold, Rabi oscillations manifest themselves in  the intra-cavity RIN spectrum calculated by the mas-  ter equation as a peak around 2πf = 2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  These os-  cillations arise due to the dynamics of the atomic po-  larization, which neither the Langevin approach nor the  stochastic rate equation approach can capture, due to  the adiabatic elimination carried out in the rate equa-  tions [15, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Considering the outcoupled RIN instead,  we see that the noise is dominated heavily by the parti-  tion noise at the cavity mirrors [28] and it is accurately  given by the standard quantum limit: SN = 2/(naκ),  without any features of Rabi oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Above threshold, Rabi oscillations do not manifest  themselves in the RIN spectrum, and all three approaches  agree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' We again see that the shot noise stemming from  the cavity mirrors dominates the outcoupled RIN spec-  trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Note, however, that the outcoupled RIN spectrum  is not simply given by the intra-cavity RIN spectrum with  the added shot noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Below 5 GHz, the outcoupled RIN  is thus smaller than the intra-cavity RIN [28, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' While  outcoupling at the laser mirror introduces quantization  (shot) noise of the outcoupled photons, the noise is re-  duced at low frequencies due to anti-correlation effects  [28, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The partition noise at the cavity mirrors can  thus lower the noise for low frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  We now consider the time-dependency of the intra-  cavity intensity correlation function, g2(τ) (see supple-  mentary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The results can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 4, where we  see deviations between the stochastic approach and the  master equation below and above threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The devia-  tion below threshold clearly arises from Rabi oscillations,  which, as mentioned, cannot be captured by the stochas-  tic approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Above threshold, the absolute deviation  is quite small (within 1-2%), but the qualitative behav-  ior is significantly different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Although not visible in the  spectrum, transitions in the Jaynes-Cummings Ladder  still affect the two-time correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  We thus  find that the master eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' results can be well fitted by the  following expression derived in [26]:  g(2)(τ) = 1 + d1 exp(−τ/τc) +  m=3  �  m=1  cm cos(ωmt)e−τ/τm  (6)  Here, τ −1  c  = κ − P/4g2 is the coherence time for the  non-oscillating term, and d1, cm, ωm, and τm are fit-  ted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' ωm is fitted to values of ω1 ≈ g, ω2 ≈ 2g  √  2, and  ω3 ≈ 2g  √  4 which corresponds to the following transi-  tions in the Jaynes-Cummings ladder: |1, +⟩ → |g, 0⟩,  |1, +⟩ → |1, −⟩, and |3, +⟩ → |3, −⟩ respectively, where  we here defined |n, ±⟩ = (|g⟩ |n + 1⟩ ± |e⟩ |n⟩)/  √  2 [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The oscillating terms, thus, stem from Rabi oscillations  and play the same role as the correction δg(2)(τ) to  the Siegert relation found in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' [54], where they write:  g(2)(τ) = 1+|g(1)(τ)|2+δg(2)(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' They show that the cor-  rection δg(2)(τ) is necessary when either strong emitter-  emitter or emitter-photon correlations are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' We  find a similar result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Only including the non-oscillating  term with coherence time τc, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' g(2)(τ) = 1 + (g2(0) −  1)e−τ/τc, is sufficient to describe g2(τ) as obtained from  the stochastic approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' The stochastic approach, how-  5  0  50  100  150  200  250  300  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='0  g(2)(τ)  Below Threshold  0  50  100  150  200  250  300  τ [ps]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='04  g(2)(τ)  Above Threshold  Stochastic  Master equation  Rabi Fit (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 8)  1 + (g2(0) − 1)e−τ/τc  Stochastic  Master equation  Rabi Fit (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 8)  1 + (g2(0) − 1)e−τ/τc  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  Computed correlation function g(2)(τ) below and  above the laser threshold for the same parameters as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 2  and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' A fit to the master equation with the expression (6) is  also shown, as well as a monotonically decaying exponential  with coherence lifetime τ −1  c  = κ − P/4g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  ever, cannot capture the shorter-lived Rabi oscillations  with τm ≈ 1/(5κ), leading to the master equation ini-  tially decaying much faster and thus explaining the de-  viation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  In conclusion, we have shown that a simple stochastic  interpretation [15] of standard rate equations accurately  accounts for the intensity quantum noise of a single-  emitter laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  In contrast, the conventional Langevin  approach [28] breaks down, implying that the intensity  quantum noise of a laser originates solely from the dis-  crete nature of photon and emitter excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' We also  analyze the single-emitter lasing transition in detail and  compare two definitions of the lasing threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  The  stochastic simulations can easily be extended to multi-  ple emitters [14, 47], where quantum master equations  become too numerically demanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' Our findings may,  therefore, facilitate the analysis and design of a new gen-  eration of nanolasers while also allowing for a fundamen-  tal understanding of quantum noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  This work was supported by the Danish National Re-  search Foundation through NanoPhoton - Center for  Nanophotonics, Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  DNRF147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content='  EVD acknowl-  edges support from Independent Research Fund Den-  mark through an International Postdoc fellowship, grant  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
+page_content=' 0164-00014B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
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+page_content=' Yu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
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+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
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+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/G9FKT4oBgHgl3EQfcS40/content/2301.11815v1.pdf'}
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diff --git a/IdFKT4oBgHgl3EQfdi7q/content/tmp_files/2301.11821v1.pdf.txt b/IdFKT4oBgHgl3EQfdi7q/content/tmp_files/2301.11821v1.pdf.txt
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index 0000000000000000000000000000000000000000..a4bd12e8af63f8e3cd5d089f39a894f9576b7857
--- /dev/null
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+arXiv:2301.11821v1  [gr-qc]  27 Jan 2023
+Dynamical gravastars may evade no-go results for exotic compact objects
+Stephen L. Adler∗
+Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA.
+Using graphs plotted from the Mathematica notebooks posted with our paper “Dynamical
+Gravastars”, we show that a dynamical gravastar has no hard surface, and that a second
+light sphere resides in the deep interior where there is maximum time dilation. These facts
+may permit dynamical gravastars to evade no-go results for exotic compact objects relating
+to light leakage inside the shadow, and nonlinear instabilities arising from an interior light
+sphere. Testing either of these surmises will require further detailed modeling calculations.
+I.
+INTRODUCTION
+The EHT observations [1] of Sg A* and M87 confirm the presence of the basic exterior spacetime
+geometry expected for a black hole, but leave open the question of what lies inside the light sphere.
+Is it a true mathematical black hole, or a novel type of relativistic star or “exotic compact object”
+[2]? In a recent paper [3] we have presented a theory of “dynamical gravastars”, based on using
+as input only the Tolman-Oppenheimer-Volkoff equations and an assumed equation of state, with
+continuous pressure p ≥ 0 and a jump in the interior density ρ from a relativistic matter state
+ρ = 3p to a state with p + ρ = β, where 0 < β << 1. We presented results in [3] and in online
+supplementary material in the form of Mathematica notebooks [4] for the cases B = .1, .01, .001,
+respectively labeled TOV.1, TOV.01, TOV.001. Our purpose here is to present additional plots
+obtained from the notebooks TOV.01 and TOV.001 to address objections that have been raised to
+interpreting the EHT observations as indicating anything other than a true black hole. The analyses
+in the following sections show that these objections may be evaded by the internal structure of
+dynamical gravastars. Further confirmation will require detailed simulations and computations
+beyond what can be inferred from the Mathematica notebooks [4] alone.
+∗Electronic address: adler@ias.edu
+
+2
+II.
+LIGHT LEAKAGE INSIDE THE SHADOW
+The first objection that has been raised against an exotic compact object mimicking the galactic
+center black hole Sg A*, or the extragalactic hole M87, concerns the dark space within the imaged
+ring, i.e., the lack of observed emission inside the shadow. If a postulated exotic object has a
+surface, then as suggested in [5], reviewed in [6], and simulated in detail in the EHT analysis paper
+VI [7], the energy of a hot accretion inward flow striking the surface will be thermalized, giving
+a surface luminosity as viewed from large distances that would violate bounds set by the EHT
+observations.
+However, this argument does not directly apply to the dynamical gravastar analyzed in [3]. In
+Fig. 1 we plot the density ρ(r) from the TOV.01 notebook versus radius r, and in Fig. 2 we give
+the similar plot from the TOV.001 notebook. In both cases we see that there is no sharply defined
+surface at which the density jumps to its maximum value. Instead, the density increases smoothly
+as r decreases from the vicinity of the nominal boundary, approaching its maximum value in both
+cases at a radius of about 0.82 times the nominal boundary radius. Thus, energy from an accretion
+flow will be dissipated over a range of radii, and the thermalization and resulting external luminosity
+may be significantly less than when calcuated assuming a sharp surface. Detailed simulations based
+on the dynamical gravastar density profile will be needed to assess whether the objections raised
+in the case of a sharp surface still apply.
+III.
+COLLAPSE RESULTING FROM AN INTERIOR SECOND LIGHT SPHERE
+The second objection that has been raised against an exotic compact object mimicking Sg A*
+or M87 concerns the existence of a second, interior light sphere and possible associated nonlinear
+instabilities. The argument, developed in the papers [8]-[10] and [11], shows that on topological
+grounds one in general expects an even number of light spheres around a spherically symmetric
+exotic compact object. The outer one is the usual one, which is unstable in the sense that light near
+this sphere moves away from it, either inwards or outwards. But the general topological argument
+shows that there is also an inner light sphere which is stable in the sense that light moves towards
+it, from inside and outside. This leads to possible nonlinear instabilities of the exotic compact
+object, associated with the nonlinear growth of null geodesic modes. If the relevant time scale for
+instability growth is not cosmological in magnitude, this can lead to collapse or explosion of the
+object on observable time scales.
+
+3
+Writing the metric as
+ds2 = B(r)dt2 − A(r)dr2 − r2(dθ2 + sin2 θdφ2)
+,
+(1)
+the photon sphere radius is determined [12] by solution(s) of the equation
+d
+dr
+� r2
+B(r)
+�
+= 0
+,
+(2)
+which can be expanded as
+Q(r) ≡ 2 −
+r
+B(r)
+dB(r)
+dr
+= 0
+.
+(3)
+Writing B(r) = eν(r) as in [3], this becomes
+Q(r) ≡ 2 − rdν(r)
+dr
+= 0
+.
+(4)
+This can be rewritten by substituting the TOV equations [3]1
+dm(r)
+dr
+=4πr2ρ(r)
+,
+A(r)−1 ≡ e−λ(r) =1 − 2m(r)
+r
+,
+dν(r)
+dr
+=
+Nν
+1 − 2m(r)/r
+,
+Nν(r) =(2/r2)
+�
+m(r) + 4πr3p(r)
+�
+,
+dp(r)
+dr
+= − ρ(r) + p(r)
+2
+dν(r)
+dr
+,
+(5)
+which after some algebraic rearrangement gives
+Q(r) = 3 − 1 + 8πr2p(r)
+1 − 2m(r)/r
+.
+(6)
+Since r2p(r) and m(r)/r both vanish at r = 0 and at r = ∞, one has Q(0) = Q(∞) = 2. This
+implies that Q(r) must have an even number of zeros (this is the radial version of the more general
+topological argument of [8], [9]) and so in addition to the usual light sphere at r ≃ 3M there must
+be a second light sphere. In Fig. 3 we plot Q(r) as calculated in the TOV.01 notebook, and we
+see that in addition to the external light sphere at r ≃ 49.5 there is a second zero crossing of Q(r),
+indicating another light sphere, at the interior point r ≃ 3.5. A similar plot of Q(r) from the
+1 We are ignoring a possible very small cosmological constant contribution, so dispense with the caret notation used
+in the TOV equations in [3].
+
+4
+TOV.001 notebook is given in Fig. 7, in which the exterior light sphere is far off scale to the right,
+and the second zero crossing can be seen at r ≃ 11.5.
+To assess the stability of the interior light sphere, we follow the analysis of [11], who show
+that stability (instability) corresponds to a negative (positive) value of the second derivative of the
+potential V ′′, which (omitting a positive factor L2/
+�
+A(r)r4�
+, with L the angular momentum) is
+given by
+V ′′(r) = 2 − r2B′′(r)/B(r)
+,
+(7)
+which can be rewritten in terms of quantities appearing in the TOV equations as
+V ′′(r) =2 − r2(ν′′(r) + ν′(r)2)
+,
+ν′(r) =
+Nν(r)
+(1 − 2m(r)/r)
+,
+dNν(r)/dr = − (4/r3)
+�
+m(r) + 4πr3p(r)
+�
++ (2/r2)
+�
+dm(r)/dr + 12πr2p(r) + 4πr3dp(r)/dr
+�
+,
+ν′′(r) = dNν(r)/dr
+1 − 2m(r)/r + 2Nν(r)
+�
+r−1dm(r)/dr − m(r)/r2�
+(1 − 2m(r)/r)2
+.
+(8)
+In Fig. 4 we plot V ′′(r) for the TOV.01 notebook, showing that it is positive at at the outer light
+sphere radius of r ≃ 49.5, indicating instability, and may be negative at the inner light sphere
+radius of r ≃ 3.5. In Fig. 5 we repeat this plot with a much finer vertical scale, showing that V ′′(r)
+is negative, indicating stability, at the inner light sphere radius of r ≃ 3.5. In Fig. 8, we plot V ′′(r)
+for the TOV.001 notebook, showing that it is negative, again indicating stability, at the inner light
+sphere radius r ≃ 11.5.
+Stability of the inner light ring raises the possibility of a pileup of null geodesics at that radius,
+leading to a possible dynamical instability that, on a sufficiently long time scale, could blow up or
+collapse an exotic compact object [13]–[15], [10]. Simulations for two models of bosonic compact
+objects in [10] suggests that for these models this instability occurs on physically accessible time
+scales, ruling out these compact objects as candidates for black hole mimickers.
+However, for
+gravastars the situation may be very different, and this objection may be evaded.
+In Fig.
+6
+we plot ν(r) = log B(r) = log g00(r) for the TOV.01 notebook, which shows that the inner light
+sphere radius corresponds to an exponentially small ν(r), and therefore an exponentially large time
+dilation. In Fig. 9 we give a similar plot for the TOV.001 notebook, showing that the smallness
+of ν(r) at the inner light sphere radius is even more extreme, and the trend shows that as β
+approaches zero, the trend of ν(r) at the inner light sphere radius is to even smaller values than
+
+5
+shown in Figs. 6 and 9. This means that for parameters giving physically realistic gravastars, the
+time scale for instability development at the inner light sphere may be very large on a cosmological
+time scale. Again, detailed gravastar simulations will be needed to assess whether the objections
+raised in [10] are relevant.
+IV.
+DISCUSSION
+We remark that neither of the features emerging from the plots, that a dynamical gravastar has
+no hard surface, and that a second light sphere resides in the deep interior where there is maximum
+time dilation, could have been anticipated in advance without a numerical solution of the TOV
+equations with a density jump.
+[1] The Event Horizon Telescope Collaboration, Phys. Rev. Lett. 125, 141104 (2020), arXiv:2010.01055.
+[2] V. Cardoso and P. Pani, Living Rev. Relativ. 22, 4 (2019), arXiv:1904.05363.
+[3] S. L. Adler, Phys. Rev. D 106, 104061 (2022), arXiv:2209.02537.
+[4] The Mathematica noteboooks URL is: https://gitlab.com/stephenadler/Gravastar . Click the “down-
+load” downarrow on the right to get a working Mathematica notebook. (Using “save as” downloads
+as html.) These notebooks were written in Mathematica version 12.2. They use the functions Exp,
+Log, Print, Plot, and Show, which were introduced in version 1.0; NDSolve and Evaluate, which were
+introduced in version 2.0; and LogPlot, which was introduced in version 6.0.
+[5] F. Yuan and R. Narayan, Ann. Rev. Astonomy and Astrophysics 52, 529 (2014), arXiv:1401.0586.
+[6] R. Narayan and I. Yi, Astrophysical Journal 452, 710 (1995), arXiv:astro-ph/9411059.
+[7] The Event Horizon Telescope Collaboration, Astrophysical Journal Letters 930, L17 (2022), open
+access.
+[8] P. V. P. Cunha, E. Berti, and C. A. R. Herdeiro, Phys. Rev. Lett. 119, 251102 (2017), arXiv:1708.04211.
+[9] P. V. P. Cunha and C. A. R. Herdeiro, Phys. Rev. Lett. 124, 181101 (2020), arXiv:2003.06445.
+[10] P. V. P. Cunha, C. Herdeiro, E. Radu, and N. Sanchis-Gual, Phys. Rev. Lett. (in press),
+arXiv:2207.13713.
+[11] V. Cardoso, A.S. Miranda, E. Berti, H. Witek, and V. T. Zanchin, Phys. Rev. D 79, 064016 (2009),
+arXiv:0812.1806.
+[12] S. L. Adler and K. S. Virbhadra, General Relativity and Gravitation 54, 93 (2022), arXiv:2205.04628.
+[13] J. Keir, Class. Quant. Grav. 33, 135009 (2016), arXiv:1404.7036.
+[14] V. Cardoso, L. C. B. Crispino, C. F. B. Macedo, H. Okawa, and P. Pani, Phys. Rev. D 90, 044069
+(2014), arXiv:1406.5510.
+
+6
+[15] G. Benomio, Anal. Part. Diff. Eq. 14, 2427 (2021), arXiv:1809.07795.
+
+7
+10
+20
+30
+40
+50
+60
+r
+-1.0
+-0.5
+0.5
+1.0
+1.5
+2.0
+2.5
+rho
+FIG. 1: Plot of the density ρ(r) for the TOV.01 notebook. The nominal boundary is M ≃ 33.
+20000
+40000
+60000
+80000
+r
+-1.0
+-0.5
+0.5
+1.0
+1.5
+2.0
+2.5
+rho
+FIG. 2:
+Plot of the density ρ(r) for the TOV.001 notebook. The nominal boundary is M ≃ 55, 200.
+
+8
+10
+20
+30
+40
+50
+60
+r
+-0.04
+-0.02
+0.02
+0.04
+Q[r]
+FIG. 3: Plot of Q(r) for the TOV.01 notebook. The exterior light sphere is the zero at r = 3M ≃ 49.5;
+there is an interior second light sphere at r ≃ 3.5.
+10
+20
+30
+40
+50
+60
+r
+-10
+-5
+5
+10
+V ��
+FIG. 4: The quantity V ′′ of Eq. (36) of Cardoso et. al [14] for the TOV.01 notebook, with the positive
+factors L2/r4 scaled out. One sees that V ′′ is positive at r ≃ 49.5, and may be negative at r ≃ 3.5.
+
+9
+10
+20
+30
+40
+50
+60
+r
+-0.10
+-0.05
+0.05
+0.10
+� ��
+FIG. 5: The quantity V ′′ of Eq. (36) of Cardoso et. al [14] for the TOV.01 notebook, with the positive
+factors L2/r4 factored out, plotted with a much finer vertical scale than used in Fig. 4. One sees that V ′′
+is negative at r ≃ 3.5.
+10
+20
+30
+40
+50
+60
+r
+-20
+-15
+-10
+-5
+n �
+FIG. 6: Plot of ν(r) for the TOV.01 notebook. The large negative value at r ≃ 3.5 corresponds to a large
+time dilation.
+
+10
+5
+10
+15
+20
+r
+-0.04
+-0.02
+0.02
+0.04
+�[r]
+FIG. 7: Plot of Q(r) for the TOV.001 notebook. The exterior light sphere is a zero at r = 3M ≃ 82, 800,
+far off scale to the right; there is an interior second light sphere at r ≃ 11.5.
+5
+10
+15
+20
+r
+-0.010
+-0.005
+0.005
+0.010
+� ��
+FIG. 8: The quantity V ′′ of Eq. (36) of Cardoso et. al [14] for the TOV.001 notebook, with the positive
+factors L2/r4 factored out. One sees that V ′′ is negative at r ≃ 11.5.
+
+11
+20000
+40000
+60000
+80000
+r
+-50
+-40
+-3
+
+-20
+-10
+nu
+FIG. 9: Plot of ν(r) for the TOV.001 notebook. The large negative value at r ≃ 11.5 corresponds to a large
+time dilation.
+
diff --git a/IdFKT4oBgHgl3EQfdi7q/content/tmp_files/load_file.txt b/IdFKT4oBgHgl3EQfdi7q/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,297 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf,len=296
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='11821v1  [gr-qc]  27 Jan 2023  Dynamical gravastars may evade no-go results for exotic compact objects  Stephen L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Adler∗  Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  Using graphs plotted from the Mathematica notebooks posted with our paper “Dynamical  Gravastars”, we show that a dynamical gravastar has no hard surface, and that a second  light sphere resides in the deep interior where there is maximum time dilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' These facts  may permit dynamical gravastars to evade no-go results for exotic compact objects relating  to light leakage inside the shadow, and nonlinear instabilities arising from an interior light  sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Testing either of these surmises will require further detailed modeling calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  INTRODUCTION  The EHT observations [1] of Sg A* and M87 confirm the presence of the basic exterior spacetime  geometry expected for a black hole, but leave open the question of what lies inside the light sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  Is it a true mathematical black hole, or a novel type of relativistic star or “exotic compact object”  [2]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In a recent paper [3] we have presented a theory of “dynamical gravastars”, based on using  as input only the Tolman-Oppenheimer-Volkoff equations and an assumed equation of state, with  continuous pressure p ≥ 0 and a jump in the interior density ρ from a relativistic matter state  ρ = 3p to a state with p + ρ = β, where 0 < β << 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' We presented results in [3] and in online  supplementary material in the form of Mathematica notebooks [4] for the cases B = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001,  respectively labeled TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='1, TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01, TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Our purpose here is to present additional plots  obtained from the notebooks TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 and TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 to address objections that have been raised to  interpreting the EHT observations as indicating anything other than a true black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The analyses  in the following sections show that these objections may be evaded by the internal structure of  dynamical gravastars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Further confirmation will require detailed simulations and computations  beyond what can be inferred from the Mathematica notebooks [4] alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  ∗Electronic address: adler@ias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='edu  2  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  LIGHT LEAKAGE INSIDE THE SHADOW  The first objection that has been raised against an exotic compact object mimicking the galactic  center black hole Sg A*, or the extragalactic hole M87, concerns the dark space within the imaged  ring, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=', the lack of observed emission inside the shadow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' If a postulated exotic object has a  surface, then as suggested in [5], reviewed in [6], and simulated in detail in the EHT analysis paper  VI [7], the energy of a hot accretion inward flow striking the surface will be thermalized, giving  a surface luminosity as viewed from large distances that would violate bounds set by the EHT  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  However, this argument does not directly apply to the dynamical gravastar analyzed in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 1 we plot the density ρ(r) from the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook versus radius r, and in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 2 we give  the similar plot from the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In both cases we see that there is no sharply defined  surface at which the density jumps to its maximum value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Instead, the density increases smoothly  as r decreases from the vicinity of the nominal boundary, approaching its maximum value in both  cases at a radius of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='82 times the nominal boundary radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Thus, energy from an accretion  flow will be dissipated over a range of radii, and the thermalization and resulting external luminosity  may be significantly less than when calcuated assuming a sharp surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Detailed simulations based  on the dynamical gravastar density profile will be needed to assess whether the objections raised  in the case of a sharp surface still apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  COLLAPSE RESULTING FROM AN INTERIOR SECOND LIGHT SPHERE  The second objection that has been raised against an exotic compact object mimicking Sg A*  or M87 concerns the existence of a second, interior light sphere and possible associated nonlinear  instabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The argument, developed in the papers [8]-[10] and [11], shows that on topological  grounds one in general expects an even number of light spheres around a spherically symmetric  exotic compact object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The outer one is the usual one, which is unstable in the sense that light near  this sphere moves away from it, either inwards or outwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' But the general topological argument  shows that there is also an inner light sphere which is stable in the sense that light moves towards  it, from inside and outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' This leads to possible nonlinear instabilities of the exotic compact  object, associated with the nonlinear growth of null geodesic modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' If the relevant time scale for  instability growth is not cosmological in magnitude, this can lead to collapse or explosion of the  object on observable time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  3  Writing the metric as  ds2 = B(r)dt2 − A(r)dr2 − r2(dθ2 + sin2 θdφ2)  ,  (1)  the photon sphere radius is determined [12] by solution(s) of the equation  d  dr  � r2  B(r)  �  = 0  ,  (2)  which can be expanded as  Q(r) ≡ 2 −  r  B(r)  dB(r)  dr  = 0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  (3)  Writing B(r) = eν(r) as in [3], this becomes  Q(r) ≡ 2 − rdν(r)  dr  = 0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  (4)  This can be rewritten by substituting the TOV equations [3]1  dm(r)  dr  =4πr2ρ(r)  ,  A(r)−1 ≡ e−λ(r) =1 − 2m(r)  r  ,  dν(r)  dr  =  Nν  1 − 2m(r)/r  ,  Nν(r) =(2/r2)  �  m(r) + 4πr3p(r)  �  ,  dp(r)  dr  = − ρ(r) + p(r)  2  dν(r)  dr  ,  (5)  which after some algebraic rearrangement gives  Q(r) = 3 − 1 + 8πr2p(r)  1 − 2m(r)/r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  (6)  Since r2p(r) and m(r)/r both vanish at r = 0 and at r = ∞, one has Q(0) = Q(∞) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' This  implies that Q(r) must have an even number of zeros (this is the radial version of the more general  topological argument of [8], [9]) and so in addition to the usual light sphere at r ≃ 3M there must  be a second light sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 3 we plot Q(r) as calculated in the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook, and we  see that in addition to the external light sphere at r ≃ 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5 there is a second zero crossing of Q(r),  indicating another light sphere, at the interior point r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' A similar plot of Q(r) from the  1 We are ignoring a possible very small cosmological constant contribution, so dispense with the caret notation used  in the TOV equations in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  4  TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 7, in which the exterior light sphere is far off scale to the right,  and the second zero crossing can be seen at r ≃ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  To assess the stability of the interior light sphere,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' we follow the analysis of [11],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' who show  that stability (instability) corresponds to a negative (positive) value of the second derivative of the  potential V ′′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' which (omitting a positive factor L2/  �  A(r)r4�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' with L the angular momentum) is  given by  V ′′(r) = 2 − r2B′′(r)/B(r)  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  (7)  which can be rewritten in terms of quantities appearing in the TOV equations as  V ′′(r) =2 − r2(ν′′(r) + ν′(r)2)  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  ν′(r) =  Nν(r)  (1 − 2m(r)/r)  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  dNν(r)/dr = − (4/r3)  �  m(r) + 4πr3p(r)  �  + (2/r2)  �  dm(r)/dr + 12πr2p(r) + 4πr3dp(r)/dr  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  ν′′(r) = dNν(r)/dr  1 − 2m(r)/r + 2Nν(r)  �  r−1dm(r)/dr − m(r)/r2�  (1 − 2m(r)/r)2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  (8)  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 4 we plot V ′′(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook, showing that it is positive at at the outer light  sphere radius of r ≃ 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5, indicating instability, and may be negative at the inner light sphere  radius of r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 5 we repeat this plot with a much finer vertical scale, showing that V ′′(r)  is negative, indicating stability, at the inner light sphere radius of r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 8, we plot V ′′(r)  for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook, showing that it is negative, again indicating stability, at the inner light  sphere radius r ≃ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  Stability of the inner light ring raises the possibility of a pileup of null geodesics at that radius,  leading to a possible dynamical instability that, on a sufficiently long time scale, could blow up or  collapse an exotic compact object [13]–[15], [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Simulations for two models of bosonic compact  objects in [10] suggests that for these models this instability occurs on physically accessible time  scales, ruling out these compact objects as candidates for black hole mimickers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  However, for  gravastars the situation may be very different, and this objection may be evaded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  6  we plot ν(r) = log B(r) = log g00(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook, which shows that the inner light  sphere radius corresponds to an exponentially small ν(r), and therefore an exponentially large time  dilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 9 we give a similar plot for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook, showing that the smallness  of ν(r) at the inner light sphere radius is even more extreme, and the trend shows that as β  approaches zero, the trend of ν(r) at the inner light sphere radius is to even smaller values than  5  shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 6 and 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' This means that for parameters giving physically realistic gravastars, the  time scale for instability development at the inner light sphere may be very large on a cosmological  time scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Again, detailed gravastar simulations will be needed to assess whether the objections  raised in [10] are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  DISCUSSION  We remark that neither of the features emerging from the plots, that a dynamical gravastar has  no hard surface, and that a second light sphere resides in the deep interior where there is maximum  time dilation, could have been anticipated in advance without a numerical solution of the TOV  equations with a density jump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  [1] The Event Horizon Telescope Collaboration, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 125, 141104 (2020), arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01055.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  [2] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Cardoso and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Pani, Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Relativ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 22, 4 (2019), arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='05363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Adler, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' D 106, 104061 (2022), arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='02537.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  [4] The Mathematica noteboooks URL is: https://gitlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content=' Click the “down-  load” downarrow on the right to get a working Mathematica notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' (Using “save as” downloads  as html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content='  [5] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Yuan and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Narayan, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Astonomy and Astrophysics 52, 529 (2014), arXiv:1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='0586.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  [6] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content=' Yi, Astrophysical Journal 452, 710 (1995), arXiv:astro-ph/9411059.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  [7] The Event Horizon Telescope Collaboration, Astrophysical Journal Letters 930, L17 (2022), open  access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Cunha, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Berti, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 14, 2427 (2021), arXiv:1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+page_content='5  rho  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 1: Plot of the density ρ(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The nominal boundary is M ≃ 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  20000  40000  60000  80000  r  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5  rho  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 2:  Plot of the density ρ(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The nominal boundary is M ≃ 55, 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  8  10  20  30  40  50  60  r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='04  Q[r]  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 3: Plot of Q(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The exterior light sphere is the zero at r = 3M ≃ 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  there is an interior second light sphere at r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  10  20  30  40  50  60  r  10  5  5  10  V ��  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 4: The quantity V ′′ of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' (36) of Cardoso et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' al [14] for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook, with the positive  factors L2/r4 scaled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' One sees that V ′′ is positive at r ≃ 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5, and may be negative at r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  9  10  20  30  40  50  60  r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='10  � ��  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 5: The quantity V ′′ of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' (36) of Cardoso et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' al [14] for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook, with the positive  factors L2/r4 factored out, plotted with a much finer vertical scale than used in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' One sees that V ′′  is negative at r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  10  20  30  40  50  60  r  20  15  10  5  n �  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 6: Plot of ν(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='01 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The large negative value at r ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5 corresponds to a large  time dilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  10  5  10  15  20  r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='04  �[r]  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 7: Plot of Q(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The exterior light sphere is a zero at r = 3M ≃ 82, 800,  far off scale to the right;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' there is an interior second light sphere at r ≃ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  5  10  15  20  r  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='010  � ��  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 8: The quantity V ′′ of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' (36) of Cardoso et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' al [14] for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook, with the positive  factors L2/r4 factored out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' One sees that V ′′ is negative at r ≃ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='  11  20000  40000  60000  80000  r  50  40  3  20  10  nu  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' 9: Plot of ν(r) for the TOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='001 notebook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content=' The large negative value at r ≃ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
+page_content='5 corresponds to a large  time dilation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFKT4oBgHgl3EQfdi7q/content/2301.11821v1.pdf'}
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+arXiv:2301.03813v1  [math.AG]  10 Jan 2023
+CONNECTIONS AND GENUINELY RAMIFIED MAPS OF CURVES
+INDRANIL BISWAS, FRANCOIS-XAVIER MACHU, AND A. J. PARAMESWARAN
+Abstract. Given a singular connection D on a vector bundle E over an irreducible
+smooth projective curve X, defined over an algebraically closed field, we show that there
+is a unique maximal subsheaf of E on which D induces a nonsingular connection. Given
+a generically smooth map φ : Y −→ X between irreducible smooth projective curves,
+and a singular connection (V, D) on Y , the direct image φ∗V has a singular connection.
+Let R(φ∗OY ) be the unique maximal subsheaf on which the singular connection on φ∗OY
+— corresponding to the trivial connection on OY — induces a nonsingular connection.
+We prove that the homomorphism of ´etale fundamental groups φ∗ : πet
+1 (Y, y0) −→
+πet
+1 (X, φ(y0)) induced by φ is surjective if and only if OX ⊂ R(φ∗OY ) is the unique
+maximal semistable subsheaf.
+When the characteristic of the base field is zero, this homomorphism φ∗ is surjective
+if and only if OX = R(φ∗OY ). For any nonsingular connection D on a vector bundle
+V over X, there is a natural map V ֒→ R(φ∗φ∗V ). When the characteristic of the base
+field is zero, we prove that the map φ is genuinely ramified if and only if V = R(φ∗φ∗V ).
+1. Introduction
+Let X and Y be irreducible smooth projective curves, defined over an algebraically
+closed field k, and let φ : Y
+−→ X be a morphism which is generically smooth (in
+other words, φ is surjective and separable). Fix a base point y0 ∈ Y , and consider the
+homomorphism of ´etale fundamental groups φ∗ : πet
+1 (Y, y0) −→ πet
+1 (X, φ(y0)) induced
+by φ. The map φ is called genuinely ramified if φ∗ is surjective [BP]. There are many
+equivalent formulations of the property of being genuinely ramified, which we recall below.
+A map φ as above is genuinely ramified if and only if one (hence all) of the following
+equivalent conditions holds (see [BP]):
+(1) The map φ does not factor through some nontrivial ´etale cover of X (in particular,
+φ is not nontrivial ´etale).
+(2) The fiber product Y ×X Y is connected.
+(3) dim H0(Y, φ∗φ∗OY ) = 1.
+(4) The maximal semistable subbundle of the direct image φ∗OY is OX.
+(5) For every stable vector bundle E on X, the pulled back vector bundle φ∗E on Y
+is also stable.
+The main theorem of [BP] says that the third statement in the above list holds for φ if
+and only if the fifth statement in the above list holds.
+2010 Mathematics Subject Classification. 14H30, 14H60, 53B15.
+Key words and phrases. Genuinely ramified map, connection, singularity.
+1
+
+2
+I. BISWAS, F.-X. MACHU, AND A. J. PARAMESWARAN
+Our aim is to understand the direct image of connections and to interpret the genuinely
+ramified maps using the direct image of a particular connection.
+Let E be a vector bundle on X equipped with a singular connection D. We prove that
+there is a unique maximal subsheaf
+R(E) ⊂ E
+on which D induces a nonsingular connection (see Lemma 2.1 and Definition 2.3).
+If V is a vector bundle on Y equipped with a singular connection D, then the direct
+image φ∗V on X is equipped with a natural singular connection (see Lemma 2.5). Now set
+(V, D) to be OY equipped with the trivial connection given by the de Rham differential
+d. Let dφ denote the singular connection on φ∗OY given by the trivial connection on OY .
+We prove the following (see Proposition 2.7):
+The map φ is ´etale if and only if the connection dφ is nonsingular.
+Let
+R(φ∗OY ) ⊂ φ∗OY
+be the unique maximal subsheaf on which dφ induces a nonsingular connection. Then we
+have
+OX ⊂ R(φ∗OY ) ⊂ φ∗OY .
+(1.1)
+We prove the following (see Corollary 3.4):
+The map φ is genuinely ramified if and only if the subsheaf OX ֒→ R(φ∗OY ) in (1.1)
+is the (unique) maximal semistable subsheaf.
+We next prove the following (see Theorem 3.5):
+Assume that the characteristic of the base field k is zero. The morphism φ is genuinely
+ramified if and only if the inclusion map
+OX ֒→ R(φ∗OY )
+in (1.1) is actually an isomorphism.
+We note that Theorem 3.5 actually fails when the characteristic of the base field k is
+positive (see Remark 3.6).
+Take a vector bundle V on X equipped with a nonsingular connection D. Then φ∗V
+has the pulled back nonsingular connection φ∗D. Denote by �D the singular connection on
+φ∗φ∗V induced by φ∗D. Let
+R(φ∗φ∗V ) ⊂ φ∗φ∗V
+be the unique maximal subsheaf on which �D induces a nonsingular connection.
+We prove the following (see Proposition 4.1 and Proposition 4.2):
+Assume that the characteristic of the base field k is zero. There is a natural map V ֒→
+R(φ∗φ∗V ). The map φ is genuinely ramified if and only if V = R(φ∗φ∗V ).
+Proposition 4.2 was kindly pointed out by the referee.
+
+CONNECTIONS AND GENUINELY RAMIFIED MAPS
+3
+2. Singular connection on direct image
+The base field k is assumed to be algebraically closed. Let X be an irreducible smooth
+projective curve defined over k. Fix a finite subset
+S := {x1, · · · , xn} ⊂ X .
+The reduced effective divisor �n
+i=1 xi on X will also be denoted by S. The cotangent
+bundle of X will be denoted by KX.
+Let E be a vector bundle on X. A connection on E is a differential operator of order
+one
+D : E −→ E ⊗ KX
+such that
+D(fs) = fD(s) + s ⊗ df
+(2.1)
+for every locally defined function f on X and every locally defined section s of E. A
+singular connection on E with poles of order m on points of S is a differential operator of
+order one
+D : E −→ E ⊗ KX ⊗ OX(mS)
+such that (2.1) holds. A logarithmic connection on E singular over S is a singular con-
+nection on E with poles of order one on S. A singular connection on E with poles over S
+is a singular connection on E with poles of order m on S for some m.
+We now give some examples of connections. When the characteristic of k is zero, a vector
+bundle E on X admits a (nonsingular) connection if and only if every direct summand
+of E (this includes E) is of degree zero [We], [At] (in [At] and [We] this is proved under
+the assumption that the base field is complex numbers; see [BS, p. 145, Proposition 3.1]
+for the general case). If the characteristic of k is p > 0, and E is a vector bundle on X
+admitting a connection, then the degree of every direct summand of E is a multiple of p
+[BS, p. 145, Proposition 3.1]. If the characteristic of k is positive, and FX : X −→ X
+is the absolute Frobenius morphism of X, then for any vector bundle E on X, the pulled
+back vector bundle F ∗
+XE has a natural connection (see [Ka], [Gi]). Moreover, a subsheaf
+V ⊂ F ∗
+XE is the pullback of a subsheaf of E if and only if V is preserved by this natural
+connection on F ∗
+XE.
+Lemma 2.1. Let E be a vector bundle on X and D a singular connection on E with poles
+of order m on S. Then there is a unique maximal subsheaf F of E on which D induces a
+(nonsingular) connection.
+Proof. Take coherent subsheaves F1, F2 ⊂ E such that
+D(Fi) ⊂ Fi ⊗ KX ⊂ E ⊗ KX ⊗ OX(mS)
+for i = 1, 2. Then the coherent subsheaf F1 + F2 ⊂ E, generated by F1 and F2, clearly
+satisfies the condition that
+D(F1 + F2) ⊂ (F1 + F2) ⊗ KX ⊂ E ⊗ KX ⊗ OX(mS) .
+The lemma follows immediately from this observation.
+□
+
+4
+I. BISWAS, F.-X. MACHU, AND A. J. PARAMESWARAN
+Remark 2.2. The maximal subsheaf F ⊂ E in Lemma 2.1 on which D induces a (nonsin-
+gular) connection need not be a subbundle, or in other words, E/F need not be torsionfree.
+To give an example, consider OX(S) equipped with the logarithmic connection given by
+the de Rham differential d. Then OX ⊂ OX(S) is the maximal subsheaf on which the
+logarithmic connection induces a (nonsingular) connection. The quotient OX(S)/OX is a
+nonzero torsion sheaf.
+Definition 2.3. Let E be a vector bundle on X and D a singular connection on E with
+poles of order m on S. The subsheaf
+R(E) := F ⊂ E
+in Lemma 2.1 will be called the maximal regular subsheaf.
+Remark 2.4. Let E be a vector bundle on X and D a singular connection on E with
+poles of order m on S. It may happen that there is no nonzero subsheaf F of E satisfying
+the condition that
+D(F) ⊂ F ⊗ KX.
+See the proof of Proposition 4.1 for such an example. If there is no nonzero subsheaf F of
+E such that D(F) ⊂ F ⊗ KX, then R(E) in Definition 2.3 is the zero subsheaf of E.
+Let X and Y be irreducible smooth projective curves defined over k, and let
+φ : Y −→ X
+(2.2)
+be a generically smooth morphism. Let S ⊂ X be the smallest subset such that φ is ´etale
+over the complement X \ S. The reduced inverse image φ−1(S)red will be denoted by SY .
+Lemma 2.5. Let E be a vector bundle on Y , and let D be a singular connection on E
+with poles of order m on SY . Then D produces a singular connection on the direct image
+φ∗E with poles over S.
+Proof. Denote the complements X \ S and Y \ SY by X′ and Y ′ respectively. The re-
+striction of φ to Y ′ will be denoted by �φ. Note that �φ∗KX′ = KY ′. The restriction of D
+(respectively, E) to Y ′ ⊂ Y will be denoted by D′ (respectively, E′). Taking the direct
+image of the operator
+D′ : E′ −→ E′ ⊗ KY ′
+we get
+�φ∗D′ : �φ∗E′ −→ �φ∗(E′ ⊗ KY ′) = �φ∗(E′ ⊗ �φ∗KX′) .
+The projection formula (see [Ha, p. 124, Ex. 5.1(d)]) gives that �φ∗(E′⊗ �φ∗KX′) = (�φ∗E′)⊗
+KX′, and hence we have
+�φ∗D′ : �φ∗E′ −→ (�φ∗E′) ⊗ KX′ .
+It is straightforward to check that �φ∗D′ is a connection on �φ∗E′. This connection �φ∗D′
+on �φ∗E′ extends to a singular connection on φ∗E with poles over S. Indeed, this follows
+immediately from the fact that the differential operator �φ∗D′ is algebraic.
+An upper
+bound of the order of pole of this connection at any x ∈ S is d′(r′ + 1), where d′ is the
+
+CONNECTIONS AND GENUINELY RAMIFIED MAPS
+5
+maximum of the orders of poles of D′ over the points of φ−1(x) and r′ is the maximum of
+the ramification orders of φ at the points of φ−1(x).
+□
+Corollary 2.6. The direct image φ∗OY has a natural singular connection with poles over
+S.
+Proof. Consider the trivial connection f �−→ df on OY given by the de Rham differential.
+In view of Lemma 2.5, this connection produces a singular connection on φ∗OY with poles
+over S.
+□
+Proposition 2.7. The map φ in (2.2) is ´etale if and only if the (possibly singular) con-
+nection on φ∗OY obtained in Corollary 2.6 is actually nonsingular.
+Proof. Let dφ denote the singular connection on φ∗OY obtained in Corollary 2.6.
+If the map φ is ´etale, then S in Corollary 2.6 is the zero divisor. So in that case dφ is
+actually nonsingular.
+To prove the converse, assume that φ is not ´etale. Take a point y ∈ Y where the
+differential of φ vanishes. Fix a Zariski open neighborhood U ⊊ X of φ(y). Let f be a
+function defined on φ−1(U) such that df(y) ̸= 0. If ω is a 1-form on U, then
+φ∗ω ∈ H0(φ−1(U), Kφ−1(U))
+vanishes at y, because the differential of φ vanishes at y. Consequently, df does not lie in
+the image of the homomorphism
+H0(U, KU) −→ H0(φ−1(U), Kφ−1(U)),
+ω �−→ φ∗ω .
+(2.3)
+Let
+�f ∈ H0 �
+U, φ∗OY
+��
+U
+�
+be the section corresponding to f. Since df does not lie in the image of the homomorphism
+in (2.3), we conclude that
+dφ( �f) /∈ H0 �
+U, (φ∗OY )
+��
+U ⊗ KU
+�
+.
+Consequently, the connection dφ is definitively singular at the point φ(y).
+□
+3. Characterization of the genuinely ramified maps
+Take X, Y and φ as in (2.2). For the singular connection on φ∗OY in Corollary 2.6, let
+R(φ∗OY ) ⊂ φ∗OY
+(3.1)
+be the maximal regular subsheaf (see Definition 2.3).
+Since
+H0(Y, Hom(OY , OY )) = H0(Y, Hom(φ∗OX, OY )) = H0(X, Hom(OX, φ∗OY ))
+(see [Ha, p. 110]), the identity map of OY produces a nonzero homomorphism
+ι : OX ֒→ φ∗OY .
+(3.2)
+
+6
+I. BISWAS, F.-X. MACHU, AND A. J. PARAMESWARAN
+Remark 3.1.
+(1) The coherent subsheaf OX ⊂ φ∗OY in (3.2) is actually a subbundle.
+Indeed,
+this follows immediately from the fact that for any Zariski open neighborhood
+U ⊂ X of any x ∈ X, and any f ∈ H0(U, OU) with f(x) ̸= 0, the section
+f ◦ φ ∈ H0(φ−1(U), Oφ−1(U)) does not vanish on any point of φ−1(x).
+(2) When the characteristic of the base field k is zero, then φ∗OY actually splits as
+OX ⊕ T ∗
+φ, where Tφ is known as the Tschirnhausen bundle (see [CLV]). We note
+that φ∗OY does not split in general when the characteristic of k is positive. For
+example, take k to be of characteristic two, and take φ to be a nontrivial ´etale
+covering of degree two. Then φ∗OY is a nontrivial extension of a degree zero line
+bundle by OX. Indeed, this follows immediately from the fact that the group ring
+k[Z/2Z] is not completely reducible as a Z/2Z module; the submodule
+{λ · 1 + λ · g | λ ∈ k} ⊂ k[Z/2Z],
+where Z/2Z = {1, g}, does not have a complement.
+Proposition 3.2. The subsheaf OX in (3.2) is contained in the subsheaf R(φ∗OY ) in
+(3.1).
+Proof. Let dX (respectively, dY ) denote the connection on OX (respectively, OY ) given by
+the de Rham differential on X (respectively, Y ). The natural isomorphism φ∗OX
+∼
+−→ OY
+takes the pulled back connection φ∗dX on φ∗OX to the connection dY on OY . Using this
+it follows that the following diagram is commutative:
+OX
+ι
+−→
+φ∗OY
+�dX
+��dY
+KX
+ι⊗ξ
+−→
+(φ∗OY ) ⊗ KX ⊗ OX(∆)
+(3.3)
+where
+• ι is the homomorphism in (3.2),
+• �dY is the (singular) connection on φ∗OY obtained in Corollary 2.6 from the non-
+singular connection dY on OY ,
+• ∆ is the polar divisor for �dY , and
+• ξ : KX −→ KX ⊗ OX(∆) is the natural homomorphism.
+In view of the commutativity of (3.3), from the definition of the maximal regular subsheaf
+R(φ∗OY ) it follows immediately that OX ⊂ R(φ∗OY ).
+□
+Let
+0 ⊊ H1 ⊂ · · · ⊂ Hb−1 ⊂ Hb = φ∗OY
+(3.4)
+be the Harder–Narasimhan filtration of φ∗OY (see [HL, § 1.3]). We note that H1 is the
+unique maximal semistable (also called the maximal destabilizing) subbundle of φ∗OY .
+Let
+0 ⊊ G1 ⊂ · · · ⊂ Gc−1 ⊂ Gc = R(φ∗OY )
+(3.5)
+
+CONNECTIONS AND GENUINELY RAMIFIED MAPS
+7
+be the Harder–Narasimhan filtration of R(φ∗OY ). As before, G1 is the unique maximal
+semistable subbundle of R(φ∗OY ).
+Proposition 3.3. The subsheaf G1 ⊂ R(φ∗OY ) ⊂ φ∗OY in (3.5) coincides with the
+subsheaf H1 in (3.4).
+Proof. We know that
+degree(H1) = 0
+(3.6)
+(see [BP, p. 12825, (2.7)]). So degree(G1) ≤ 0, because R(φ∗OY ) ⊂ φ∗OY . On the other
+hand, degree(G1) ≥ 0, because OX ⊂ R(φ∗OY ) (see Proposition 3.2). These together
+imply that
+degree(G1) = 0.
+(3.7)
+In view of (3.6) and (3.7), from the properties of the Harder–Narasimhan filtration we
+conclude that
+G1 ⊂ H1.
+(3.8)
+We will now show that
+H1 ⊂ G1.
+(3.9)
+Recall that OX ⊂ H1 ⊂ φ∗OY . First assume that H1 = OX. But we have OX ⊂ G1,
+because OX ⊂ R(φ∗OY ) (see Proposition 3.2) and (3.7) holds. Therefore, in this case
+(3.9) holds.
+Next assume that OX ⊊ H1. Then there is a nontrivial ´etale covering
+g : �
+X −→ X
+and a morphism h : Y −→ �
+X such that
+(1) g ◦ h = φ, and
+(2) the subsheaf
+ι : g∗O �
+X ֒→ φ∗OY ,
+(3.10)
+given by the factoring of φ in (1), coincides with H1.
+(See the proof of (2) =⇒ (1) in the proof of [BP, Proposition 2.6].) Since g is ´etale, from
+Proposition 2.7 it follows that the connection on g∗O �
+X obtained in Corollary 2.6 is non-
+singular. On the other hand, homomorphism ι in (3.10) is clearly connection preserving.
+In other words, the following diagram is commutative:
+g∗O �
+X
+ι
+−→
+φ∗OY
+�
+�dφ
+(g∗O �
+X) ⊗ KX
+ι⊗ξ
+−→
+(φ∗OY ) ⊗ KX ⊗ OX(∆)
+where ∆ is the polar divisor for the singular connection �dY (see (3.3)) and ξ is the homo-
+morphism in (3.3). Therefore, we conclude that
+g∗O �
+X ⊂ R(φ∗OY ).
+This again implies (3.9).
+□
+
+8
+I. BISWAS, F.-X. MACHU, AND A. J. PARAMESWARAN
+Fix a base point y0 ∈ Y . The morphism φ in (2.2) is called a genuinely ramified map
+if the corresponding homomorphism of ´etale fundamental groups
+φ∗ : πet
+1 (Y, y0) −→ πet
+1 (X, φ(y0))
+is surjective [BP].
+From (3.7) and Proposition 3.2 it follows that
+OX ֒→ G1.
+(3.11)
+Corollary 3.4. The map φ is genuinely ramified if and only if the inclusion map OX ֒→
+G1 in (3.11) is an isomorphism.
+Proof. From [BP, p. 12828, Proposition 2.6] we know that φ is genuinely ramified if and
+only if H1 = OX, where H1 is the subsheaf in (3.4). So the result follows immediately
+from Proposition 3.3.
+□
+Theorem 3.5. Assume that the characteristic of the base field k is zero. The morphism
+φ in (2.2) is genuinely ramified if and only if the inclusion map
+OX ֒→ R(φ∗OY )
+in Proposition 3.2 is an isomorphism.
+Proof. First assume that φ is not a genuinely ramified map. This implies that there is a
+nontrivial ´etale covering
+γ : Z −→ X
+and a morphism β : Y −→ Z such that φ = γ ◦β [BP, Proposition 2.6]. Since φ = γ ◦β,
+we have
+ι : γ∗OZ ֒→ φ∗OY .
+(3.12)
+The possibly singular connection on γ∗OZ (respectively, φ∗OY ) given by Corollary 2.6
+will be denoted by dγ (respectively, dφ). Since γ is ´etale from Proposition 2.7 we know
+that dγ is nonsingular. On the other hand, the homomorphism ι in (3.12) intertwines dγ
+and dφ, meaning the following diagram is commutative:
+γ∗OZ
+ι
+−→
+φ∗OY
+�dγ
+�dφ
+KX
+ι⊗ξ
+−→
+(φ∗OY ) ⊗ KX ⊗ OX(∆)
+where ∆ is the polar divisor for dφ and ξ : KX −→ KX ⊗ OX(∆) is the natural homo-
+morphism. Hence we have
+ι(γ∗OZ) ⊂ R(φ∗OY ) .
+Since rank(ι(γ∗OZ)) = degree(γ) > 1 (recall that γ is a nontrivial ´etale covering), it
+follows that rank(OX) < rank(R(φ∗OY )).
+We will now prove that OX = R(φ∗OY ) if φ is a genuinely ramified map.
+
+CONNECTIONS AND GENUINELY RAMIFIED MAPS
+9
+As before, let dφ denote the possibly singular connection on φ∗OY given by Corollary
+2.6. Since dφ induces a nonsingular connection on R(φ∗OY ), and the characteristic of k is
+zero, we conclude that
+degree(R(φ∗OY )) = 0
+(3.13)
+(see [BS, p. 145, Proposition 3.1]). As in (3.4), let
+H1 ⊂ φ∗OY
+be the maximal semistable subbundle. Since µ(H1) = 0 [BP, p. 12825, (2.7)], from (3.13)
+it follows immediately that
+R(φ∗OY ) ⊂ H1 .
+(3.14)
+But H1 = OX if φ is a genuinely ramified map [BP, p. 12828, Definition 2.5]. So (3.14)
+implies that R(φ∗OY ) ⊂ OX is φ is a genuinely ramified map. Using this and Proposition
+3.2 it follows that OX = R(φ∗OY ) if φ is a genuinely ramified map.
+□
+Remark 3.6. Theorem 3.5 is not valid if the assumption that the characteristic of k is
+zero is removed. To explain this, assume that the characteristic of k is positive, and let
+FY : Y −→ Y
+be the absolute Frobenius morphism of Y . Consider the subsheaf
+F −1
+Y OY ֒→ OY ;
+note that it is not a coherent subsheaf. This inclusion map produces an inclusion map
+φ∗F −1
+Y OY ֒→ φ∗OY .
+Let W ⊂ φ∗OY denote the coherent subsheaf generated by φ∗F −1
+Y OY . Then it is straight-
+forward to check that the (singular) connection dφ on φ∗OY preserves W and, furthermore,
+the resulting connection on W is nonsingular. This implies that
+W ⊂ R(φ∗OY ) .
+But clearly,
+OX ⊊ W.
+To complete the example, if we take X = P1
+k, then φ is genuinely ramified.
+4. Pullback of irreducible connections
+Take X, Y and φ as in (2.2). Let E be a vector bundle on X equipped with a nonsingular
+connection D. The connection D induces a connection on φ∗E; this induced connection
+will be denoted by φ∗D. The singular connection on φ∗φ∗E, obtained in Lemma 2.5 from
+φ∗D, will be denoted by
+�D.
+(4.1)
+Let
+R(φ∗φ∗E) ֒→ φ∗φ∗E
+(4.2)
+be the maximal regular subsheaf for this singular connection �D.
+
+10
+I. BISWAS, F.-X. MACHU, AND A. J. PARAMESWARAN
+Using the projection formula, [Ha, p. 124, Ex. 5.1(d)], we have
+φ∗φ∗E = E ⊗ φ∗OY .
+(4.3)
+The inclusion map ι : OX ֒→ φ∗OY in (3.2) produces an injective homomorphism
+H := IdE ⊗ ι : E = E ⊗ OX −→ E ⊗ φ∗OY = φ∗φ∗E .
+(4.4)
+From Remark 3.1(1) we know that H(E) is a subbundle of φ∗φ∗E.
+Proposition 4.1. Assume that the characteristic of the base field k is zero. Assume that
+the map φ in (2.2) is genuinely ramified. Then
+R(φ∗φ∗E) = H(E)
+as subsheaves of φ∗φ∗E (see (4.2) and (4.4)).
+Proof. As before, let dφ denote the singular connection on φ∗OY obtained in Corollary
+2.6. The connection D on E and this singular connection dφ together produce a singular
+connection on E⊗φ∗OY ; this singular connection on E⊗φ∗OY will be denoted by �Dφ. The
+identification E ⊗ φ∗OY = φ∗φ∗E in (4.3) takes �Dφ to �D (see (4.1)). Indeed, this follows
+from the construction of �D (see Lemma 2.5). The subsheaf ι(OX) ⊂ φ∗OY (see (4.4)) is
+preserved by the singular connection dφ (see Proposition 3.2 and its proof). This, and the
+fact that the identification E ⊗ φ∗OY = φ∗φ∗E in (4.3) takes the singular connection on
+E ⊗ φ∗OY induced by D and dφ to the singular connection �D on φ∗φ∗E, together imply
+that the homomorphism H in (4.4) takes the connection D (on E) to �D in (4.1). In other
+words, the following diagram is commutative:
+E
+H
+−→
+φ∗φ∗E
+�D
+� �D
+E ⊗ KX
+H⊗ξ
+−→
+E ⊗ KX ⊗ OX(∆)
+(4.5)
+where ∆ is the polar divisor for �D and ξ : KX −→ KX ⊗OX(∆) is the natural homomor-
+phism; recall that D is a nonsingular connection. Now the commutativity of (4.5) implies
+that
+• the subsheaf
+H(E) ⊂ φ∗φ∗E
+is preserved by the singular connection �D on φ∗φ∗E, and
+• �D induces a nonsingular connection on H(E).
+Consequently, we have
+H(E) ⊂ R(φ∗φ∗E) .
+(4.6)
+Note that
+(φ∗φ∗E)/H(E) = (E ⊗ φ∗OY )/E = E ⊗ (φ∗OY /ι(OX)) .
+
+CONNECTIONS AND GENUINELY RAMIFIED MAPS
+11
+Since φ∗OY /ι(OX) is locally free (see Remark 3.1(1)), the subsheaf H(E) ⊂ φ∗φ∗E is a
+subbundle. Consider the quotient map
+q : R(φ∗φ∗E) −→ (φ∗φ∗E)/H(E) = E ⊗ (φ∗OY /ι(OX)) .
+(4.7)
+In view of (4.6), to prove the proposition it suffices to show that q = 0.
+Since both H(E) and R(φ∗φ∗E) are preserved by the singular connection �D on φ∗φ∗E,
+(1) �D induces a singular connection on (φ∗φ∗E)/H(E) (recall that (φ∗φ∗E)/H(E) is
+locally free), and
+(2) the homomorphism q in (4.7) takes the nonsingular connection on R(φ∗φ∗E) (given
+by �D) to the singular connection on
+(φ∗φ∗E)/H(E) = E ⊗ ((φ∗OY )/ι(OX))
+induced by �D.
+Let
+q′ : E∗ ⊗ R(φ∗φ∗E) −→ (φ∗OY )/ι(OX)
+(4.8)
+be the homomorphism obtained by composing
+IdE∗ ⊗ q : E∗ ⊗ R(φ∗φ∗E) −→ E∗ ⊗ E ⊗ ((φ∗OY )/ι(OX))
+(see (4.7)) with the homomorphism E∗ ⊗ E ⊗ ((φ∗OY )/ι(OX)) −→ (φ∗OY )/ι(OX) con-
+structed using the natural pairing E∗ ⊗ E −→ OX.
+Let D∗ denote the nonsingular connection on E∗ given by the nonsingular connection D
+on E. The connection D∗, and the connection on R(φ∗φ∗E) given by �D, together produce a
+connection on E∗⊗R(φ∗φ∗E); this connection on E∗⊗R(φ∗φ∗E) will be denoted by D1. As
+noted before, The subbundle ι(OX) ⊂ φ∗OY (see (4.4) and Remark 3.1(1)) is preserved by
+the singular connection dφ. Consequently, dφ induces a singular connection on the quotient
+bundle (φ∗OY )/ι(OX); this singular connection on (φ∗OY )/ι(OX) will be denoted by D2.
+Since q in (4.7) takes the nonsingular connection on R(φ∗φ∗E) (given by �D) to the singular
+connection on (φ∗φ∗E)/H(E) = E ⊗ ((φ∗OY )/ι(OX)), it follows immediately that q′ in
+(4.8) takes the above defined singular connection D1 on E∗ ⊗ R(φ∗φ∗E) to the singular
+connection D2 on (φ∗OY )/ι(OX).
+Now note that D1 is a nonsingular connection, because both D∗, and the connection on
+R(φ∗φ∗E) given by �D, are nonsingular. On the other hand, since φ is genuinely ramified,
+it can be shown that (φ∗OY )/ι(OX) does not contain any nonzero subsheaf on which
+D2 induces a nonsingular connection.
+Indeed, if D2 induces a nonsingular connection
+connection on V ⊂ (φ∗OY )/ι(OX), then consider the inverse image �V ⊂ φ∗OY of V for
+the quotient map φ∗OY −→ (φ∗OY )/ι(OX). The singular connection dφ on φ∗OY induces
+a nonsingular connection on �V, because D2 induces a nonsingular connection connection
+on V. From Theorem 3.5 it follows that �V = ι(OX), and hence V = 0. So (φ∗OY )/ι(OX)
+does not contain any nonzero subsheaf on which D2 induces a nonsingular connection.
+Since q′ in (4.8) takes D1 to D2, and D1 is a nonsingular connection, while (φ∗OY )/ι(OX)
+does not contain any nonzero subsheaf on which D2 induces a nonsingular connection,
+
+12
+I. BISWAS, F.-X. MACHU, AND A. J. PARAMESWARAN
+considering the image of q′ it follows that
+q′ = 0 .
+This implies that q in (4.7) vanishes identically, and hence H(E) = R(φ∗φ∗E).
+□
+The following converse of Proposition 4.1 was pointed out by the referee.
+Proposition 4.2. Assume that the characteristic of the base field k is zero. Assume that
+R(φ∗φ∗E) = H(E)
+as subsheaves of φ∗φ∗E (see (4.2) and (4.4)).
+Then the map φ in (2.2) is genuinely
+ramified.
+Proof. To prove the proposition by contradiction, assume that the map φ is not genuinely
+ramified. Then, as noted in the proof of Proposition 3.3, there is a nontrivial ´etale covering
+g : �
+X −→ X
+and a morphism h : Y −→ �
+X such that
+g ◦ h = φ.
+(4.9)
+From (4.9) it follows immediately that
+ι : g∗g∗E ֒→ φ∗φ∗E.
+(4.10)
+Consider the nonsingular connection g∗D on g∗E given by D. Let �D denote the connec-
+tion on g∗g∗E obtained in Lemma 2.5 from g∗D. We note that this connection �D on g∗g∗E
+is nonsingular. Indeed, this follows from the observation that g∗KX = K �
+X, because the
+map g is ´etale, and hence
+g∗((g∗E) ⊗ K �
+X) = (g∗g∗E) ⊗ KX
+(projection formula).
+The map in (4.10) intertwines the connections �D (see (4.1)) and �D (see above) on φ∗φ∗E
+and g∗g∗E respectively, meaning the following diagram is commutative:
+g∗g∗E
+ι
+−→
+φ∗φ∗E
+� �D
+� �D
+(g∗g∗E) ⊗ KX
+ι⊗ξ
+−→
+(φ∗φ∗E) ⊗ KX ⊗ OX(∆)
+where ∆ is the polar divisor for �D and ξ : KX −→ KX ⊗ OX(∆) is the natural homo-
+morphism. Consequently, we have
+g∗g∗E ⊂ R(φ∗φ∗E).
+This implies that
+rank(R(φ∗φ∗E)) ≥ rank(g∗g∗E) = rank(E) · degree(g) > rank(E) = rank(H(E))
+because g is a nontrivial ´etale covering. In particular, we have
+R(φ∗φ∗E) ̸= H(E).
+
+CONNECTIONS AND GENUINELY RAMIFIED MAPS
+13
+This completes the proof.
+□
+Acknowledgements
+We are very grateful to the referee for Proposition 4.2 and also for helpful comments to
+improve the manuscript.
+References
+[At]
+M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957),
+181–207.
+[BS]
+I. Biswas and S. Subramanian, Vector bundles on curves admitting a connection, Q. J. Math.
+57 (2006), 143–150.
+[BP]
+I. Biswas and A. J. Parameswaran, Ramified covering maps and stability of pulled back bundles,
+Int. Math. Res. Not. (to appear), arXiv:2102.08744.
+[CLV]
+I. Coskun, E. Larson and I. Vogt, Stability of Tschirnhausen bundles, arXiv:2207.07257.
+[Gi]
+D. Gieseker, Flat vector bundles and the fundamental group in non-zero characteristics, Ann.
+Scuola Norm. Sup. Pisa 2 (1975), 1–31.
+[Ha]
+R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag,
+New York-Heidelberg, 1977.
+[HL]
+D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics,
+E31, Friedr. Vieweg & Sohn, Braunschweig, 1997.
+[Ka]
+N. M. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of
+Turrittin, Inst. Hautes ´Etudes Sci. Publ. Math. 39 (1970), 175–232.
+[Se]
+J.-P. Serre, G´eom´etrie alg´ebrique et g´eom´etrie analytique, Ann. Inst. Fourier 6 (1956), 1–42.
+[We]
+A. Weil, G´en´eralisation des fonctions ab´eliennes, Jour. Math. Pures Appl. 17 (1938), 47–87.
+School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road,
+Mumbai 400005, India
+Email address: indranil@math.tifr.res.in
+ESIEA, 74 bis Av. Maurice Thorez, 94200 Ivry-sur-Seine, France
+Email address: fx.machu@gmail.com
+School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road,
+Mumbai 400005, India
+Email address: param@math.tifr.res.in
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf,len=538
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='03813v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='AG]  10 Jan 2023  CONNECTIONS AND GENUINELY RAMIFIED MAPS OF CURVES  INDRANIL BISWAS, FRANCOIS-XAVIER MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Given a singular connection D on a vector bundle E over an irreducible  smooth projective curve X, defined over an algebraically closed field, we show that there  is a unique maximal subsheaf of E on which D induces a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Given  a generically smooth map φ : Y −→ X between irreducible smooth projective curves,  and a singular connection (V, D) on Y , the direct image φ∗V has a singular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let R(φ∗OY ) be the unique maximal subsheaf on which the singular connection on φ∗OY  — corresponding to the trivial connection on OY — induces a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We prove that the homomorphism of ´etale fundamental groups φ∗ : πet  1 (Y, y0) −→  πet  1 (X, φ(y0)) induced by φ is surjective if and only if OX ⊂ R(φ∗OY ) is the unique  maximal semistable subsheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  When the characteristic of the base field is zero, this homomorphism φ∗ is surjective  if and only if OX = R(φ∗OY ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' For any nonsingular connection D on a vector bundle  V over X, there is a natural map V ֒→ R(φ∗φ∗V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' When the characteristic of the base  field is zero, we prove that the map φ is genuinely ramified if and only if V = R(φ∗φ∗V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Introduction  Let X and Y be irreducible smooth projective curves, defined over an algebraically  closed field k, and let φ : Y  −→ X be a morphism which is generically smooth (in  other words, φ is surjective and separable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Fix a base point y0 ∈ Y , and consider the  homomorphism of ´etale fundamental groups φ∗ : πet  1 (Y, y0) −→ πet  1 (X, φ(y0)) induced  by φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The map φ is called genuinely ramified if φ∗ is surjective [BP].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' There are many  equivalent formulations of the property of being genuinely ramified, which we recall below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  A map φ as above is genuinely ramified if and only if one (hence all) of the following  equivalent conditions holds (see [BP]):  (1) The map φ does not factor through some nontrivial ´etale cover of X (in particular,  φ is not nontrivial ´etale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (2) The fiber product Y ×X Y is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3) dim H0(Y, φ∗φ∗OY ) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4) The maximal semistable subbundle of the direct image φ∗OY is OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (5) For every stable vector bundle E on X, the pulled back vector bundle φ∗E on Y  is also stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  The main theorem of [BP] says that the third statement in the above list holds for φ if  and only if the fifth statement in the above list holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 14H30, 14H60, 53B15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Genuinely ramified map, connection, singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  1  2  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' BISWAS, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  Our aim is to understand the direct image of connections and to interpret the genuinely  ramified maps using the direct image of a particular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let E be a vector bundle on X equipped with a singular connection D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' We prove that  there is a unique maximal subsheaf  R(E) ⊂ E  on which D induces a nonsingular connection (see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1 and Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  If V is a vector bundle on Y equipped with a singular connection D, then the direct  image φ∗V on X is equipped with a natural singular connection (see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Now set  (V, D) to be OY equipped with the trivial connection given by the de Rham differential  d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let dφ denote the singular connection on φ∗OY given by the trivial connection on OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We prove the following (see Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7):  The map φ is ´etale if and only if the connection dφ is nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let  R(φ∗OY ) ⊂ φ∗OY  be the unique maximal subsheaf on which dφ induces a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then we  have  OX ⊂ R(φ∗OY ) ⊂ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)  We prove the following (see Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4):  The map φ is genuinely ramified if and only if the subsheaf OX ֒→ R(φ∗OY ) in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)  is the (unique) maximal semistable subsheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We next prove the following (see Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5):  Assume that the characteristic of the base field k is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The morphism φ is genuinely  ramified if and only if the inclusion map  OX ֒→ R(φ∗OY )  in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1) is actually an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We note that Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5 actually fails when the characteristic of the base field k is  positive (see Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Take a vector bundle V on X equipped with a nonsingular connection D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then φ∗V  has the pulled back nonsingular connection φ∗D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Denote by �D the singular connection on  φ∗φ∗V induced by φ∗D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let  R(φ∗φ∗V ) ⊂ φ∗φ∗V  be the unique maximal subsheaf on which �D induces a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We prove the following (see Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1 and Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2):  Assume that the characteristic of the base field k is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' There is a natural map V ֒→  R(φ∗φ∗V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The map φ is genuinely ramified if and only if V = R(φ∗φ∗V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2 was kindly pointed out by the referee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  CONNECTIONS AND GENUINELY RAMIFIED MAPS  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Singular connection on direct image  The base field k is assumed to be algebraically closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let X be an irreducible smooth  projective curve defined over k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Fix a finite subset  S := {x1, · · · , xn} ⊂ X .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  The reduced effective divisor �n  i=1 xi on X will also be denoted by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The cotangent  bundle of X will be denoted by KX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let E be a vector bundle on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' A connection on E is a differential operator of order  one  D : E −→ E ⊗ KX  such that  D(fs) = fD(s) + s ⊗ df  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)  for every locally defined function f on X and every locally defined section s of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' A  singular connection on E with poles of order m on points of S is a differential operator of  order one  D : E −→ E ⊗ KX ⊗ OX(mS)  such that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' A logarithmic connection on E singular over S is a singular con-  nection on E with poles of order one on S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' A singular connection on E with poles over S  is a singular connection on E with poles of order m on S for some m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We now give some examples of connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' When the characteristic of k is zero, a vector  bundle E on X admits a (nonsingular) connection if and only if every direct summand  of E (this includes E) is of degree zero [We], [At] (in [At] and [We] this is proved under  the assumption that the base field is complex numbers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' see [BS, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 145, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1]  for the general case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' If the characteristic of k is p > 0, and E is a vector bundle on X  admitting a connection, then the degree of every direct summand of E is a multiple of p  [BS, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 145, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' If the characteristic of k is positive, and FX : X −→ X  is the absolute Frobenius morphism of X, then for any vector bundle E on X, the pulled  back vector bundle F ∗  XE has a natural connection (see [Ka], [Gi]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Moreover, a subsheaf  V ⊂ F ∗  XE is the pullback of a subsheaf of E if and only if V is preserved by this natural  connection on F ∗  XE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let E be a vector bundle on X and D a singular connection on E with poles  of order m on S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then there is a unique maximal subsheaf F of E on which D induces a  (nonsingular) connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Take coherent subsheaves F1, F2 ⊂ E such that  D(Fi) ⊂ Fi ⊗ KX ⊂ E ⊗ KX ⊗ OX(mS)  for i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then the coherent subsheaf F1 + F2 ⊂ E, generated by F1 and F2, clearly  satisfies the condition that  D(F1 + F2) ⊂ (F1 + F2) ⊗ KX ⊂ E ⊗ KX ⊗ OX(mS) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  The lemma follows immediately from this observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  4  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' BISWAS, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The maximal subsheaf F ⊂ E in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1 on which D induces a (nonsin-  gular) connection need not be a subbundle, or in other words, E/F need not be torsionfree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  To give an example, consider OX(S) equipped with the logarithmic connection given by  the de Rham differential d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then OX ⊂ OX(S) is the maximal subsheaf on which the  logarithmic connection induces a (nonsingular) connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The quotient OX(S)/OX is a  nonzero torsion sheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let E be a vector bundle on X and D a singular connection on E with  poles of order m on S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The subsheaf  R(E) := F ⊂ E  in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1 will be called the maximal regular subsheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let E be a vector bundle on X and D a singular connection on E with  poles of order m on S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' It may happen that there is no nonzero subsheaf F of E satisfying  the condition that  D(F) ⊂ F ⊗ KX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  See the proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1 for such an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' If there is no nonzero subsheaf F of  E such that D(F) ⊂ F ⊗ KX, then R(E) in Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3 is the zero subsheaf of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let X and Y be irreducible smooth projective curves defined over k, and let  φ : Y −→ X  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2)  be a generically smooth morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let S ⊂ X be the smallest subset such that φ is ´etale  over the complement X \\ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The reduced inverse image φ−1(S)red will be denoted by SY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let E be a vector bundle on Y , and let D be a singular connection on E  with poles of order m on SY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then D produces a singular connection on the direct image  φ∗E with poles over S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Denote the complements X \\ S and Y \\ SY by X′ and Y ′ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The re-  striction of φ to Y ′ will be denoted by �φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Note that �φ∗KX′ = KY ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The restriction of D  (respectively, E) to Y ′ ⊂ Y will be denoted by D′ (respectively, E′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Taking the direct  image of the operator  D′ : E′ −→ E′ ⊗ KY ′  we get  �φ∗D′ : �φ∗E′ −→ �φ∗(E′ ⊗ KY ′) = �φ∗(E′ ⊗ �φ∗KX′) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  The projection formula (see [Ha, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 124, Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1(d)]) gives that �φ∗(E′⊗ �φ∗KX′) = (�φ∗E′)⊗  KX′, and hence we have  �φ∗D′ : �φ∗E′ −→ (�φ∗E′) ⊗ KX′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  It is straightforward to check that �φ∗D′ is a connection on �φ∗E′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' This connection �φ∗D′  on �φ∗E′ extends to a singular connection on φ∗E with poles over S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Indeed, this follows  immediately from the fact that the differential operator �φ∗D′ is algebraic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  An upper  bound of the order of pole of this connection at any x ∈ S is d′(r′ + 1), where d′ is the  CONNECTIONS AND GENUINELY RAMIFIED MAPS  5  maximum of the orders of poles of D′ over the points of φ−1(x) and r′ is the maximum of  the ramification orders of φ at the points of φ−1(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The direct image φ∗OY has a natural singular connection with poles over  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Consider the trivial connection f �−→ df on OY given by the de Rham differential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  In view of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5, this connection produces a singular connection on φ∗OY with poles  over S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The map φ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is ´etale if and only if the (possibly singular) con-  nection on φ∗OY obtained in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6 is actually nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let dφ denote the singular connection on φ∗OY obtained in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  If the map φ is ´etale, then S in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6 is the zero divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' So in that case dφ is  actually nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  To prove the converse, assume that φ is not ´etale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Take a point y ∈ Y where the  differential of φ vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Fix a Zariski open neighborhood U ⊊ X of φ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let f be a  function defined on φ−1(U) such that df(y) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' If ω is a 1-form on U, then  φ∗ω ∈ H0(φ−1(U), Kφ−1(U))  vanishes at y, because the differential of φ vanishes at y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Consequently, df does not lie in  the image of the homomorphism  H0(U, KU) −→ H0(φ−1(U), Kφ−1(U)),  ω �−→ φ∗ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3)  Let  �f ∈ H0 �  U, φ∗OY  ��  U  �  be the section corresponding to f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Since df does not lie in the image of the homomorphism  in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3), we conclude that  dφ( �f) /∈ H0 �  U, (φ∗OY )  ��  U ⊗ KU  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Consequently, the connection dφ is definitively singular at the point φ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Characterization of the genuinely ramified maps  Take X, Y and φ as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' For the singular connection on φ∗OY in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6, let  R(φ∗OY ) ⊂ φ∗OY  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)  be the maximal regular subsheaf (see Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Since  H0(Y, Hom(OY , OY )) = H0(Y, Hom(φ∗OX, OY )) = H0(X, Hom(OX, φ∗OY ))  (see [Ha, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 110]), the identity map of OY produces a nonzero homomorphism  ι : OX ֒→ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2)  6  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' BISWAS, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (1) The coherent subsheaf OX ⊂ φ∗OY in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is actually a subbundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Indeed,  this follows immediately from the fact that for any Zariski open neighborhood  U ⊂ X of any x ∈ X, and any f ∈ H0(U, OU) with f(x) ̸= 0, the section  f ◦ φ ∈ H0(φ−1(U), Oφ−1(U)) does not vanish on any point of φ−1(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (2) When the characteristic of the base field k is zero, then φ∗OY actually splits as  OX ⊕ T ∗  φ, where Tφ is known as the Tschirnhausen bundle (see [CLV]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' We note  that φ∗OY does not split in general when the characteristic of k is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' For  example, take k to be of characteristic two, and take φ to be a nontrivial ´etale  covering of degree two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then φ∗OY is a nontrivial extension of a degree zero line  bundle by OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Indeed, this follows immediately from the fact that the group ring  k[Z/2Z] is not completely reducible as a Z/2Z module;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' the submodule  {λ · 1 + λ · g | λ ∈ k} ⊂ k[Z/2Z],  where Z/2Z = {1, g}, does not have a complement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The subsheaf OX in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is contained in the subsheaf R(φ∗OY ) in  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let dX (respectively, dY ) denote the connection on OX (respectively, OY ) given by  the de Rham differential on X (respectively, Y ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The natural isomorphism φ∗OX  ∼  −→ OY  takes the pulled back connection φ∗dX on φ∗OX to the connection dY on OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Using this  it follows that the following diagram is commutative:  OX  ι  −→  φ∗OY  \uf8e6\uf8e6�dX  \uf8e6\uf8e6��dY  KX  ι⊗ξ  −→  (φ∗OY ) ⊗ KX ⊗ OX(∆)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3)  where  ι is the homomorphism in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2),  �dY is the (singular) connection on φ∗OY obtained in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6 from the non-  singular connection dY on OY ,  ∆ is the polar divisor for �dY , and  ξ : KX −→ KX ⊗ OX(∆) is the natural homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  In view of the commutativity of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3), from the definition of the maximal regular subsheaf  R(φ∗OY ) it follows immediately that OX ⊂ R(φ∗OY ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  Let  0 ⊊ H1 ⊂ · · · ⊂ Hb−1 ⊂ Hb = φ∗OY  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4)  be the Harder–Narasimhan filtration of φ∗OY (see [HL, § 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' We note that H1 is the  unique maximal semistable (also called the maximal destabilizing) subbundle of φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let  0 ⊊ G1 ⊂ · · · ⊂ Gc−1 ⊂ Gc = R(φ∗OY )  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5)  CONNECTIONS AND GENUINELY RAMIFIED MAPS  7  be the Harder–Narasimhan filtration of R(φ∗OY ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' As before, G1 is the unique maximal  semistable subbundle of R(φ∗OY ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The subsheaf G1 ⊂ R(φ∗OY ) ⊂ φ∗OY in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5) coincides with the  subsheaf H1 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' We know that  degree(H1) = 0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6)  (see [BP, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 12825, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' So degree(G1) ≤ 0, because R(φ∗OY ) ⊂ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' On the other  hand, degree(G1) ≥ 0, because OX ⊂ R(φ∗OY ) (see Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' These together  imply that  degree(G1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7)  In view of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7), from the properties of the Harder–Narasimhan filtration we  conclude that  G1 ⊂ H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='8)  We will now show that  H1 ⊂ G1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='9)  Recall that OX ⊂ H1 ⊂ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' First assume that H1 = OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' But we have OX ⊂ G1,  because OX ⊂ R(φ∗OY ) (see Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Therefore, in this case  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='9) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Next assume that OX ⊊ H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then there is a nontrivial ´etale covering  g : �  X −→ X  and a morphism h : Y −→ �  X such that  (1) g ◦ h = φ, and  (2) the subsheaf  ι : g∗O �  X ֒→ φ∗OY ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='10)  given by the factoring of φ in (1), coincides with H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (See the proof of (2) =⇒ (1) in the proof of [BP, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=') Since g is ´etale, from  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7 it follows that the connection on g∗O �  X obtained in Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6 is non-  singular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' On the other hand, homomorphism ι in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='10) is clearly connection preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  In other words, the following diagram is commutative:  g∗O �  X  ι  −→  φ∗OY  \uf8e6\uf8e6�  \uf8e6\uf8e6�dφ  (g∗O �  X) ⊗ KX  ι⊗ξ  −→  (φ∗OY ) ⊗ KX ⊗ OX(∆)  where ∆ is the polar divisor for the singular connection �dY (see (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3)) and ξ is the homo-  morphism in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Therefore, we conclude that  g∗O �  X ⊂ R(φ∗OY ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  This again implies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  8  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' BISWAS, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  Fix a base point y0 ∈ Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The morphism φ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is called a genuinely ramified map  if the corresponding homomorphism of ´etale fundamental groups  φ∗ : πet  1 (Y, y0) −→ πet  1 (X, φ(y0))  is surjective [BP].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  From (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7) and Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2 it follows that  OX ֒→ G1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='11)  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The map φ is genuinely ramified if and only if the inclusion map OX ֒→  G1 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='11) is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' From [BP, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 12828, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6] we know that φ is genuinely ramified if and  only if H1 = OX, where H1 is the subsheaf in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' So the result follows immediately  from Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Assume that the characteristic of the base field k is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The morphism  φ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is genuinely ramified if and only if the inclusion map  OX ֒→ R(φ∗OY )  in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2 is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' First assume that φ is not a genuinely ramified map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' This implies that there is a  nontrivial ´etale covering  γ : Z −→ X  and a morphism β : Y −→ Z such that φ = γ ◦β [BP, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Since φ = γ ◦β,  we have  ι : γ∗OZ ֒→ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='12)  The possibly singular connection on γ∗OZ (respectively, φ∗OY ) given by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6  will be denoted by dγ (respectively, dφ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Since γ is ´etale from Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7 we know  that dγ is nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' On the other hand, the homomorphism ι in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='12) intertwines dγ  and dφ, meaning the following diagram is commutative:  γ∗OZ  ι  −→  φ∗OY  \uf8e6\uf8e6�dγ  \uf8e6\uf8e6�dφ  KX  ι⊗ξ  −→  (φ∗OY ) ⊗ KX ⊗ OX(∆)  where ∆ is the polar divisor for dφ and ξ : KX −→ KX ⊗ OX(∆) is the natural homo-  morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Hence we have  ι(γ∗OZ) ⊂ R(φ∗OY ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Since rank(ι(γ∗OZ)) = degree(γ) > 1 (recall that γ is a nontrivial ´etale covering), it  follows that rank(OX) < rank(R(φ∗OY )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  We will now prove that OX = R(φ∗OY ) if φ is a genuinely ramified map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  CONNECTIONS AND GENUINELY RAMIFIED MAPS  9  As before, let dφ denote the possibly singular connection on φ∗OY given by Corollary  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Since dφ induces a nonsingular connection on R(φ∗OY ), and the characteristic of k is  zero, we conclude that  degree(R(φ∗OY )) = 0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='13)  (see [BS, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 145, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' As in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4), let  H1 ⊂ φ∗OY  be the maximal semistable subbundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Since µ(H1) = 0 [BP, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 12825, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7)], from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='13)  it follows immediately that  R(φ∗OY ) ⊂ H1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='14)  But H1 = OX if φ is a genuinely ramified map [BP, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 12828, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' So (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='14)  implies that R(φ∗OY ) ⊂ OX is φ is a genuinely ramified map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Using this and Proposition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2 it follows that OX = R(φ∗OY ) if φ is a genuinely ramified map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5 is not valid if the assumption that the characteristic of k is  zero is removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' To explain this, assume that the characteristic of k is positive, and let  FY : Y −→ Y  be the absolute Frobenius morphism of Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Consider the subsheaf  F −1  Y OY ֒→ OY ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  note that it is not a coherent subsheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' This inclusion map produces an inclusion map  φ∗F −1  Y OY ֒→ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let W ⊂ φ∗OY denote the coherent subsheaf generated by φ∗F −1  Y OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then it is straight-  forward to check that the (singular) connection dφ on φ∗OY preserves W and, furthermore,  the resulting connection on W is nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' This implies that  W ⊂ R(φ∗OY ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  But clearly,  OX ⊊ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  To complete the example, if we take X = P1  k, then φ is genuinely ramified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Pullback of irreducible connections  Take X, Y and φ as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let E be a vector bundle on X equipped with a nonsingular  connection D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The connection D induces a connection on φ∗E;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' this induced connection  will be denoted by φ∗D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The singular connection on φ∗φ∗E, obtained in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5 from  φ∗D, will be denoted by  �D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)  Let  R(φ∗φ∗E) ֒→ φ∗φ∗E  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2)  be the maximal regular subsheaf for this singular connection �D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  10  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' BISWAS, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  Using the projection formula, [Ha, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 124, Ex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1(d)], we have  φ∗φ∗E = E ⊗ φ∗OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3)  The inclusion map ι : OX ֒→ φ∗OY in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) produces an injective homomorphism  H := IdE ⊗ ι : E = E ⊗ OX −→ E ⊗ φ∗OY = φ∗φ∗E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4)  From Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1(1) we know that H(E) is a subbundle of φ∗φ∗E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Assume that the characteristic of the base field k is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Assume that  the map φ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is genuinely ramified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then  R(φ∗φ∗E) = H(E)  as subsheaves of φ∗φ∗E (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' As before, let dφ denote the singular connection on φ∗OY obtained in Corollary  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The connection D on E and this singular connection dφ together produce a singular  connection on E⊗φ∗OY ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' this singular connection on E⊗φ∗OY will be denoted by �Dφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The  identification E ⊗ φ∗OY = φ∗φ∗E in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3) takes �Dφ to �D (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Indeed, this follows  from the construction of �D (see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The subsheaf ι(OX) ⊂ φ∗OY (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4)) is  preserved by the singular connection dφ (see Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2 and its proof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' This, and the  fact that the identification E ⊗ φ∗OY = φ∗φ∗E in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3) takes the singular connection on  E ⊗ φ∗OY induced by D and dφ to the singular connection �D on φ∗φ∗E, together imply  that the homomorphism H in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4) takes the connection D (on E) to �D in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' In other  words, the following diagram is commutative:  E  H  −→  φ∗φ∗E  \uf8e6\uf8e6�D  \uf8e6\uf8e6� �D  E ⊗ KX  H⊗ξ  −→  E ⊗ KX ⊗ OX(∆)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5)  where ∆ is the polar divisor for �D and ξ : KX −→ KX ⊗OX(∆) is the natural homomor-  phism;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' recall that D is a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Now the commutativity of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5) implies  that  the subsheaf  H(E) ⊂ φ∗φ∗E  is preserved by the singular connection �D on φ∗φ∗E, and  �D induces a nonsingular connection on H(E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Consequently, we have  H(E) ⊂ R(φ∗φ∗E) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6)  Note that  (φ∗φ∗E)/H(E) = (E ⊗ φ∗OY )/E = E ⊗ (φ∗OY /ι(OX)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  CONNECTIONS AND GENUINELY RAMIFIED MAPS  11  Since φ∗OY /ι(OX) is locally free (see Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1(1)), the subsheaf H(E) ⊂ φ∗φ∗E is a  subbundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Consider the quotient map  q : R(φ∗φ∗E) −→ (φ∗φ∗E)/H(E) = E ⊗ (φ∗OY /ι(OX)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7)  In view of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='6), to prove the proposition it suffices to show that q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Since both H(E) and R(φ∗φ∗E) are preserved by the singular connection �D on φ∗φ∗E,  (1) �D induces a singular connection on (φ∗φ∗E)/H(E) (recall that (φ∗φ∗E)/H(E) is  locally free), and  (2) the homomorphism q in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7) takes the nonsingular connection on R(φ∗φ∗E) (given  by �D) to the singular connection on  (φ∗φ∗E)/H(E) = E ⊗ ((φ∗OY )/ι(OX))  induced by �D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let  q′ : E∗ ⊗ R(φ∗φ∗E) −→ (φ∗OY )/ι(OX)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='8)  be the homomorphism obtained by composing  IdE∗ ⊗ q : E∗ ⊗ R(φ∗φ∗E) −→ E∗ ⊗ E ⊗ ((φ∗OY )/ι(OX))  (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7)) with the homomorphism E∗ ⊗ E ⊗ ((φ∗OY )/ι(OX)) −→ (φ∗OY )/ι(OX) con-  structed using the natural pairing E∗ ⊗ E −→ OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Let D∗ denote the nonsingular connection on E∗ given by the nonsingular connection D  on E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The connection D∗, and the connection on R(φ∗φ∗E) given by �D, together produce a  connection on E∗⊗R(φ∗φ∗E);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' this connection on E∗⊗R(φ∗φ∗E) will be denoted by D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' As  noted before, The subbundle ι(OX) ⊂ φ∗OY (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4) and Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1(1)) is preserved by  the singular connection dφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Consequently, dφ induces a singular connection on the quotient  bundle (φ∗OY )/ι(OX);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' this singular connection on (φ∗OY )/ι(OX) will be denoted by D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Since q in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7) takes the nonsingular connection on R(φ∗φ∗E) (given by �D) to the singular  connection on (φ∗φ∗E)/H(E) = E ⊗ ((φ∗OY )/ι(OX)), it follows immediately that q′ in  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='8) takes the above defined singular connection D1 on E∗ ⊗ R(φ∗φ∗E) to the singular  connection D2 on (φ∗OY )/ι(OX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Now note that D1 is a nonsingular connection, because both D∗, and the connection on  R(φ∗φ∗E) given by �D, are nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' On the other hand, since φ is genuinely ramified,  it can be shown that (φ∗OY )/ι(OX) does not contain any nonzero subsheaf on which  D2 induces a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Indeed, if D2 induces a nonsingular connection  connection on V ⊂ (φ∗OY )/ι(OX), then consider the inverse image �V ⊂ φ∗OY of V for  the quotient map φ∗OY −→ (φ∗OY )/ι(OX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' The singular connection dφ on φ∗OY induces  a nonsingular connection on �V, because D2 induces a nonsingular connection connection  on V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' From Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5 it follows that �V = ι(OX), and hence V = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' So (φ∗OY )/ι(OX)  does not contain any nonzero subsheaf on which D2 induces a nonsingular connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Since q′ in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='8) takes D1 to D2, and D1 is a nonsingular connection, while (φ∗OY )/ι(OX)  does not contain any nonzero subsheaf on which D2 induces a nonsingular connection,  12  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' BISWAS, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' MACHU, AND A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' PARAMESWARAN  considering the image of q′ it follows that  q′ = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  This implies that q in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='7) vanishes identically, and hence H(E) = R(φ∗φ∗E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  The following converse of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1 was pointed out by the referee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Assume that the characteristic of the base field k is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Assume that  R(φ∗φ∗E) = H(E)  as subsheaves of φ∗φ∗E (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='4)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Then the map φ in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2) is genuinely  ramified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' To prove the proposition by contradiction, assume that the map φ is not genuinely  ramified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Then, as noted in the proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='3, there is a nontrivial ´etale covering  g : �  X −→ X  and a morphism h : Y −→ �  X such that  g ◦ h = φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='9)  From (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='9) it follows immediately that  ι : g∗g∗E ֒→ φ∗φ∗E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='10)  Consider the nonsingular connection g∗D on g∗E given by D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Let �D denote the connec-  tion on g∗g∗E obtained in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='5 from g∗D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' We note that this connection �D on g∗g∗E  is nonsingular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Indeed, this follows from the observation that g∗KX = K �  X, because the  map g is ´etale, and hence  g∗((g∗E) ⊗ K �  X) = (g∗g∗E) ⊗ KX  (projection formula).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  The map in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='10) intertwines the connections �D (see (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='1)) and �D (see above) on φ∗φ∗E  and g∗g∗E respectively, meaning the following diagram is commutative:  g∗g∗E  ι  −→  φ∗φ∗E  \uf8e6\uf8e6� �D  \uf8e6\uf8e6� �D  (g∗g∗E) ⊗ KX  ι⊗ξ  −→  (φ∗φ∗E) ⊗ KX ⊗ OX(∆)  where ∆ is the polar divisor for �D and ξ : KX −→ KX ⊗ OX(∆) is the natural homo-  morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' Consequently, we have  g∗g∗E ⊂ R(φ∗φ∗E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  This implies that  rank(R(φ∗φ∗E)) ≥ rank(g∗g∗E) = rank(E) · degree(g) > rank(E) = rank(H(E))  because g is a nontrivial ´etale covering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content=' In particular, we have  R(φ∗φ∗E) ̸= H(E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  CONNECTIONS AND GENUINELY RAMIFIED MAPS  13  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='  □  Acknowledgements  We are very grateful to the referee for Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='2 and also for helpful comments to  improve the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
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+page_content='machu@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='com  School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road,  Mumbai 400005, India  Email address: param@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='tifr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
+page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE2T4oBgHgl3EQfUgdI/content/2301.03813v1.pdf'}
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+Identification of Magnetic Field Errors in Synchrotrons
+based on Deep Lie Map Networks
+Conrad Caliari1, Adrian Oeftiger2, and Oliver Boine-Frankenheim1,2
+1TEMF, TU-Darmstadt, Schlossgartenstr. 8, 64289 Darmstadt, Germany
+and
+2GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany
+(Dated: January 13, 2023)
+Magnetic field errors pose a limitation in the performance of synchrotrons, as they excite non-
+systematic resonances, reduce dynamic aperture and may result in beam loss. Their effect can be
+compensated assuming knowledge of their location and strength. Established identification proce-
+dures are based on orbit response matrices or resonance driving terms. While they sequentially build
+a field error model for subsequent accelerator sections, a method detecting field errors in parallel
+could save valuable beam time. We introduce deep Lie map networks, which enable construction
+of an accelerator model including multipole components for the magnetic field errors by linking
+charged particle dynamics with machine learning methodology in a data-driven approach. Based on
+simulated beam-position-monitor readings for the example case of SIS18 at GSI, we demonstrate
+inference of location and strengths of gradient and sextupole errors for all accelerator sections in par-
+allel. The obtained refined accelerator model may support setup of corrector magnets in operation
+to allow more precise control over tunes, chromaticities and resonance compensation.
+I.
+INTRODUCTION
+Synchrotron performance requirements necessitate de-
+tailed knowledge of magnetic fields errors present in the
+accelerator in order to minimize losses and maintain
+beam quality. Magnetic field errors cause beam loss by
+resonance excitation and demand compensation schemes
+if the working point cannot be freely changed.
+While
+particle tracking simulations are suited to predict and
+optimize corrector magnet settings with respect to beam
+loss, they depend on detailed knowledge of the magnetic
+field errors distributed along the beam line.
+Magnetic
+imperfections due to misalignments and fabrication er-
+rors are often present and their location and magnitude
+is essential for conclusive simulations. This work empha-
+sizes that an accurate field error model can be obtained
+from a systematic comparison of simulation results to
+measurements. The magnetic field errors are recovered
+by minimizing discrepancies between predicted and mea-
+sured motion of bunch centroids.
+Existing approaches are based on measurements which
+assert the effect of steerer magnets or closed orbit bumps
+in a systematic scheme. Ref. [1] establishes the LOCO
+(linear optics form closed orbits) algorithm to model lin-
+ear field errors. The orbit response matrix Aij, i.e. the
+change in position at the i-th beam position monitor
+caused by a modification to the j-th corrector magnets
+deflection angle, is measured and compared to predic-
+tions of a computer model. Fitting the predicted to the
+measured orbit response matrix by variation of magnetic
+multipole components yields dipole, as well as normal
+and skew quadrupole field errors. Several methods have
+been proposed to obtain a non-linear magnetic field error
+model of a synchrotron by measurements. In [2] the beam
+is excited by an ac dipole or a transversal kick in order
+to retrieve resonance driving terms. In [3] the authors
+propose to observe tune shifts induced by field errors in
+case the orbit is distorted globally. The effect of steerer
+magnets distributed along the synchrotron on measured
+tunes yields a response matrix, comparable to the orbit
+response matrix, and access to non-linear field errors. Or-
+der and resolution of the searched multipole components
+are limited by the resolution of the tune measurement,
+which relies on excitation of betatron oscillations by a
+kicker . These methods assume good knowledge of the
+linear field components.
+Machine learning techniques yield the potential to
+model physical systems in a data-efficient way.
+This
+promises the identifcation of magnetic field errors with-
+out the time-consuming measurement of an orbit re-
+sponse matrix or installation of orbit bumps around the
+accelerator, but from few trajectories observed after ex-
+citation by a transversal kick.
+Physics-informed neu-
+ral networks (PINN) have recently gained track in data-
+driven modelling of physical systems [4, 5]. They consist
+of an universal function approximator, the neural net-
+work, which is trained to reproduce measurements while
+obeying the physical laws governing the dynamics of the
+modelled system. This is achieved by minimizing a loss
+function L = Ldata + Lreg, where Ldata quantifies the
+discrepancy between prediction and measurement. The
+second term Lreg as a regularization term restricts the
+neural network to the space of possible solutions to the
+differential equations which express the considered laws
+of physics. A physics-informed neural network based on
+Taylor map layers has been successfully applied to orbit
+correction in [6], where the symplecticity of Hamiltonian
+systems is enforced as a soft constraint by Lsymp
+reg
+. The
+approach yields an effective model in form of transfor-
+mations of particle coordinates between beam-position
+monitors.
+This model works well for correction of closed orbit
+distortion due to dipole errors, also for application in
+simulations to the heavy-ion synchrotron SIS18 at GSI
+[7]. The Taylor map based PINN is capable of describ-
+ing the phase advance between beam-position monitors,
+arXiv:2301.04914v1  [physics.acc-ph]  12 Jan 2023
+
+2
+but after training predicted tunes show deviations of sev-
+eral percent. We observe a systematic failure to predict
+non-linear dynamics arising from sextupole errors. Since
+symplecticity is not strictly maintained during training
+by Lsymp
+reg
+, the training results remain poor. This is pos-
+sibly linked to failure modes related to the regularization
+term described in [8].
+As an alternative approach, we propose to replace
+the neural network by an accelerator model based on
+Lie algebra techniques and the thin-lens approximation
+[9]and embed it into the framework of machine learning.
+This model will be referred to as deep Lie map network
+(DLMN) in this work. In contrast to a PINN, this model
+choice does not involve a search for suited network struc-
+tures, which is a non-trivial problem frequently tackled
+by a trial-and-error approach.
+By design, the DLMN
+represents a symplectic solution to the equations of mo-
+tion, its degrees of freedom are given by magnetic mul-
+tipole components. Hence, the DLMN approach enables
+a physical interpretation of the model and its degrees of
+freedom during any stage of the training process.
+The large number of magnets constituting a syn-
+chrotron together with non-linear beam dynamics form
+a complex and high-dimensional optimization problem.
+We demonstrate the potential of the DLMN model
+trained by means of the ADAM [10] algorithm to iden-
+tify magnetic field errors in synchrotrons in simulations.
+Randomly distributed gradient and sextupole errors can
+be identified in the SIS18 synchrotron [11] in simulations,
+and tunes and chromaticities as well as resonance dia-
+grams are reproduced in good agreement with the accel-
+erator simulation providing training data.
+The contribution is structured as follows: Section II
+introduces the DLMN model, its training procedure is
+described in Section III and simulation results for the
+SIS18 synchrotron are reported in Section IV. A conclu-
+sion is given in Section V.
+II.
+DLMN MODEL
+Crucial to the objective of creating an accurate repre-
+sentation of the accelerator is the chosen modelling ap-
+proach. In this work, the modelling approach considers
+only drift spaces and transverse magnetic fields.
+The
+particle beam is reduced to a single particle representing
+its centroid. The equation of motion for single particle
+dynamics can be solved approximately in the framework
+of Hamiltonian dynamics [12].
+The thin-lens approxi-
+mation consists of consecutive updates to position and
+momentum, known as drifts and kicks. The quality of
+the approximation depends on the order of the symplec-
+tic integrator, the arrangement of drifts and kicks, and
+symplectic integrators up to arbitrary order are known
+[13].
+The particle tracking algorithms in MAD-X [14]
+and SixTrackLib [15] for instance, are based on this ap-
+proach.
+Similar to layers of neurons forming neural networks,
+the accelerator model consists of a concatenation of sim-
+ple building blocks, the drifts and kicks. The transfer
+map of a single lattice element Ml arises from drifts D
+and kicks K
+Ml = Dl
+1 ◦ Kl
+1 ◦ ... ◦ Dl
+i ◦ Kl
+i
+,
+(1)
+and the transfer map between two locations in the lat-
+tice Ml→m like beam-position monitors is given by their
+concatenation
+Ml→m = Ml ◦ Ml+1 ◦ ... ◦ Mm
+.
+(2)
+This enables its implementation in the framework of
+PINNs and allows to leverage existing tooling.
+The model is capable of representing lattice magnets
+including linear fringe fields, but lacks rf cavities. Drift
+spaces are modelled without truncation and, thus, in-
+clude non-linear effects like natural amplitude detuning.
+Chromatic detuning due to finite momentum spread of
+the beam and non-linear effects like amplitude detun-
+ing, cause motion of the beam centroid to deviate from
+motion of a single particle. The resolution of magnetic
+field errors correspondingly depends on transversal emit-
+tances as well as momentum spread of the beam. Fur-
+thermore, this limits the meaningful simulation time to
+less than a synchrotron period and thus, we negelect rf-
+cavities in the model. Collective effects like space charge,
+wakefields or electron clouds are neglected. An advanced
+implementation of the DLMN model could account for
+these collective effects, as they can be included in terms
+of automatic differentiation as well.
+III.
+TRAINING PROCEDURE
+Training describes the process of fitting the accelerator
+model to measurement data acquired by beam-position
+monitors.
+The optimal fit parameters reveal insights
+into the distribution of field errors since they rep-
+resent magnetic multipole components.
+Besides the
+model, central to training are the training data itself,
+a metric quantifying the discrepancy between model
+predictions and training data, referred to as loss L,
+and an optimization algorithm suited to minimize L.
+In case of successful training, the model is capable of
+reproducing the measurements forming the training set
+and generalization beyond. Throughout the article we
+refer to the accelerator model being subject to training
+as the model, whereas the source of training data, which
+is either a simulated or real machine, is referred to
+as accelerator.
+The capability of the model to predict
+correct trajectories from initial conditions not included
+into the training set is confirmed by additional data in a
+validation set.
+
+3
+A.
+Training Data
+The training set consists of measured centroid trajec-
+tories, which shall be reproduced by the model. In or-
+der to predict the motion of the beam centroid an initial
+condition must be given as input to the model. In ma-
+chine experiments, an initial condition can be created by
+means of a kicker deflecting the beam from its equilib-
+rium state. The kicker affects the beam in both planes
+and the transversal momentum of the beam centroid is
+inferred from the kicker voltage. Additionally, the beam
+energy may be offset by slightly mismatching the rf fre-
+quency with respect to the revolution time at the current
+magnetic rigidity. A set of training data T is obtained
+by varying the kick strength and / or the rf frequency,
+while the beam position monitors are used to observe the
+beam centroid motion.
+Convergence speed is found to increase if training is
+performed in two stages. In the first stage, initial condi-
+tions used for training
+T1 = {−∆px, ∆px} × {−∆py, ∆py}
+(3)
+comprise horizontal ∆px resp. vertical ∆py excitation
+amplitude via the kicker.
+This allows a first estimate
+of gradient errors. In the second stage, off-momentum
+initial conditions are used for training,
+T2 = {−∆px, ∆px} × {−∆py, ∆py} × {−δ, δ}
+(4)
+enabling identification of sextupole errors and chro-
+maticities with high fidelity.
+Since deviations between centroid motion and single par-
+ticle motion due to chromatic and amplitude detuning
+grow over time, the number of turns M shall be small.
+In addition, the computational complexity of tracking
+grows with M. Observation for more than one turn is es-
+sential to include the periodicity of a synchrotron, which
+enables a magnetic field error to influence the centroid
+motion globally regardless of its location. In case a single
+turn is used for training, we find the algorithm underes-
+timates the relevance of field errors located close to the
+end of the turn, as they affect only few BPM readings
+downstream.
+In case of SIS18, we find M = 3 to be a good setting
+for the considered accelerator, which is short compared
+to the observation time necessary for a tune measurement
+required by alternative approaches.
+B.
+Loss
+In order to judge the quality of model predictions
+they need to be compared to observations.
+A metric
+L(q(⃗z0), ˆq(⃗z0)) called loss is introduced to quantify the
+discrepancy between model output ˆq(⃗z0) and measure-
+ment q(⃗z0).
+In this work, a modified version of the mean-squared er-
+ror (MSE), common to machine learning and regression,
+is used. The loss
+L({q, ˆq}r∈R) = 1
+M
+R
+�
+r=1
+M
+�
+m=1
+N
+�
+n=1
+�
+⃗qr,m,n − ˆ⃗qr,m,n
+�2
+σr
+(5)
+compares predicted and measured centroid positions
+⃗q =
+�x, y�T at discrete locations of N beam position
+monitors over M turns for R initial conditions. The nor-
+malization factor
+σr
+�
+⃗z(r)
+0
+�
+= max{Aq
+�
+⃗z(r)
+0
+�
+}q∈{x,y}
+(6)
+is given by the single-particle amplitude
+Aq =
+�
+2βqJq + D2qδ2
+,
+(7)
+which depends on the initial condition ⃗z(r)
+0
+≡ [px, py, δ].
+Beta-functions βq, dispersions Dq and linearized actions
+Jq are computed from the initial accelerator model.
+Since the loss L compares model predictions to
+measurements, it depends on the magnetic multipole
+strengths of the model ⃗k.
+The optimal multipole
+strengths ⃗k∗ : L(⃗k) ≥ L(⃗k∗)∀⃗k ∈ D over some set of field
+strengths D entail that the model reproduces measured
+trajectories. Thus, a comparison of the converged mul-
+tipole strengths to those of the untrained initial model
+reveals magnetic field errors present in the accelerator.
+For a single FODO cell in thin-lens approximation, the
+eigenvalues of the Hessian of the loss L with respect to
+quadrupole strengths can be calculated analytically. For
+not too large gradient errors, the Hessian is positive-
+definite and thus optimization of L poses a convex op-
+timization problem, e.g. a unique extremum exists on D.
+In case of non-linear beam dynamics, e.g. non-linearities
+originating from truncation free drifts and lattice sex-
+tupoles powered to correct chromaticity, this finding is
+not altered. A scan of the loss L as a function of model
+quadrupole strengths show a unique minimum in case the
+model matches the quadrupole strengths of the acceler-
+ator, cf. Fig. 1. This emphasizes that minimization of
+L is a well-posed problem in presence of non-linearities:
+the proposed method can, hence, be applied to non-linear
+beam dynamics.
+C.
+Optimization
+The DLMN model is trained by minimizing the loss
+over the training data set. Since the model is differen-
+tiable, gradient-based optimization algorithms, which are
+established in various high-dimensional fit problems of
+machine learning, can be employed. In simulations, the
+
+4
+50
+0
+50
+1st quad. k1/k1 / %
+100
+50
+0
+50
+100
+2nd quad. k1/k1 / %
+10
+3
+10
+2
+10
+1
+100
+101
+loss
+FIG. 1. Loss of SIS18 cell vs. gradient errors of first and sec-
+ond quadrupole. The training set consists of a single condition
+{px, py, δ} = {10−3, 10−3, 0}
+ADAM [10] algorithm outperformed options like plain
+gradient descent, Adagrad [16] or Adadelta [17].
+The
+ADAM optimizer is capable of dealing with sparse gra-
+dients and parameters whose gradients differ in size by
+orders of magnitude.
+The derivatives of the loss with
+respect to model parameters are obtained by automatic
+differentiation.
+Automatic differentiation [18] leverages that the model
+consists of a concatenation of simple maps, the drift and
+kicks, which can be differentiated analytically in closed
+form. The derivatives of the whole model are then cal-
+culated by exploitation of the chain rule, which allows
+to break down their calculation to a concatenation of
+the analytic derivatives of drift and kicks, similar to the
+concatenation of drifts and kicks yielding the particle
+tracking simulation in the first place. Since the scalar
+loss function is differentiated w.r.t.
+many multipole
+strengths characterizing each kick, we employ reverse-
+mode automatic differentiation, which is more efficient
+than forward-mode automatic differentiation in this case.
+In contrast to numerical differentiation based on finite
+differences, automatic differentiation is not prone to
+rounding errors and thus, noisy gradients. The deriva-
+tion of an analytic expression for loss derivatives is in-
+feasible because of expression swelling, which causes the
+number of terms to grow exponentially with the number
+of drifts and kicks.
+The DLMN model as well as the training procedure
+are implemented in the Julia programming language [19].
+Automatic differentiation is used via the library [20], an
+implementation of the ADAM algorithm is taken from
+[21]. Additionally, the learning rate of the optimizer is
+decreased exponentially as a function of iterations over
+the training set.
+Both learning rate, also known as step size, and its de-
+cay rate form two hyperparameters of the training pro-
+TABLE I. Properties of SIS18 and key beam parameters.
+Parameter
+Value
+Circumference
+216 m
+Momentum compaction αC
+3.4 × 10−2
+Transition energy
+5.5
+Synchrotron tune Qs
+> 100 turns
+Betatron tunes Qx, Qy
+4.2, 3.4
+Natural (absolute) chromaticity ξ(nat)
+x
+, ξ(nat)
+y
+-6.43 / -4.89
+Magnetic Rigidity (Bρ)max
+18.5 T m
+Ion
+proton
+Energy E
+5 GeV
+Energy Spred σE/E
+3.6 × 10−4
+Transverse Emittances ϵ4-rms
+norm
+0.9 µm
+cedure. A tree-structured Parzen estimator [22] imple-
+mented in [23] is employed for their optimization. We
+find that the hyperparameters need rather limited tun-
+ing and optimal values are identified within few iterations
+of the Parzen estimator.
+IV.
+APPLICATION TO SIS18 IN SIMULATIONS
+The DLMN model is applied to the SIS18 at GSI in
+simulations. The SIS18 is a 216 m long synchrotron de-
+signed to accelerate ions ranging from protons to ura-
+nium. It features twelve identical cells, where each cell
+hosts two bending magnets, two quadrupoles as well as
+two sextupole magnets, c.f. Figure 3. Key properties are
+listed in Table I, and a more detailed description is given
+in [24].
+The simulated synchrotron features various combina-
+tions of gradient and sextupole errors, and provides
+beam-position monitor readings of the beam centroid po-
+sition as outputs. The recovery of field errors hidden in
+the accelerator simulation is limited by the models ap-
+proximation of the beam by a single particle. Thus, the
+resolution of gradient and sextupole errors is evaluated
+in dependence of transverse emittance and energy spread
+of the beam.
+Training is performed on a detailed simulation of SIS18
+based on the MAD-X / SixTrackLib codes, where the
+former is used for matching of tunes and chromaticities
+and the latter for 6D particle tracking. The simulation
+model consists of lattice magnets including linear fringe
+fields. Furthermore, the simulation includes an rf cavity
+enabling a bunched beam necessary for usage of the beam
+position monitors. The beam consists of protons injected
+by the UNILAC [25]. Key beam parameters can be found
+in Table I. Comparable emittances can be achieved with
+ion beams by employing the existing electron cooler [26,
+27].
+In Subsection IV A the possible resolution of gradient
+and sextupole errors in dependence of beam parameters
+is discussed. Subsection IV B covers the case in which
+the model lacks a degree of freedom at the location of
+a field error. The simultaneous identification of a set of
+
+5
+0.3
+0.6
+1.0
+1.8
+energy spread (E)/E / 10
+4
+0.0
+0.1
+1.0
+10.0
+1rms
+norm / m (both planes)
+0.3
+0.6
+1.0
+1.8
+energy spread (E)/E / 10
+4
+0.0
+0.1
+1.0
+10.0
+1rms
+norm / m (both planes)
+0.01
+0.1
+k1 / k1 / %
+0.1
+1
+10
+k2 / k2 / %
+FIG. 2. Resolution of gradient and sextupole errors in dependence of beam transverse emittance and energy spread. A gradient
+k1l =5.2 × 10−3 m−1 and a sextupole k2l =1.6 × 10−2 /m2 field error are introduced to the lattice. The dashed line marks the
+normalized 1-rms emittance of the UNILAC proton beam.
+0
+5
+10
+15
+[m]
+0
+10
+20
+30
+[m]
+x
+y
+Dx
+FIG. 3. A 18 m long cell of SIS18 drawn to scale. Bending
+magnets are shown in blue, quadrupoles in yellow and sex-
+tupoles in red.
+distributed field errors is presented in Subsection IV C.
+Physical plausibility of the model predictions is under-
+pinned by correct prediction of tunes and chromaticities.
+A.
+Resolution
+The resolution of magnetic multipole components is
+limited by the approximation of the beam centroid by
+a single particle. Due to adiabatic damping, the trans-
+verse beam size is smallest at high energy. Thus, non-
+linear effects such as amplitude detuning become less
+influential.
+To benefit from this effect, training data
+is collected at flat-top energy.
+A single gradient er-
+ror k1l=5.2 × 10−3 m−1 together with a single sextupole
+error k2l=1.6 × 10−2 m−2 are introduced to the accel-
+erator, causing a shift in tune ∆Qx/Qx ≈1.2 × 10−3
+and chromaticity ∆ξx/ξx ≈1.7 × 10−2. Training is per-
+formed for different transverse emittances as well as en-
+ergy spreads and the achieved resolution of field errors is
+quantified by the discrepancy
+Di =
+����
+kacc
+i
+− kmodel
+i
+kacc
+i
+����
+(8)
+between the models multipole strength and its ac-
+tual counterpart in the accelerator, which is displayed
+in Figure 2. The discrepancy in both gradient and sex-
+tupole strengths is determined primarily by the beam en-
+ergy spread. Additionally, the discrepancy in sextupole
+strengths grows beyond 10 % in case the normalized 1-
+rms emittance exceeds 10 µm. The beam size of the pro-
+ton beam is suited for resolving sextupole components in
+the order of magnitude k2l ≈10−2 m−2 with a discrep-
+ancy of D2 < 10 %. Therefore, it is suited to identify un-
+documented sextupole contributions related to the main
+dipoles in SIS18, but resolution is reduced significantly
+in case of heavy-ion beams featuring larger transverse
+emittances.
+B.
+Orbit Distortion
+In addition to field errors, another source of deviations
+between accelerator and model is distortion of the closed
+orbit. Besides moving the center of betatron oscillations,
+a displacement d of the closed orbit with respect to the
+geometric centre of a magnet induces multipole compo-
+nents of lower orders. In case the magnet is a 2(n+1)-pole
+
+6
+the dominant feed-down contribution acts like a (2n)-
+pole, i.e. an orbit distortion inside a sextupole field k2
+induces a gradient component ksext
+1
+,
+∆px = k2L
+2 (x + d)2
+= k2L
+2 x2 + k2Ld
+� �� �
+ksext
+1
+·x + k2L
+2 d2
+(9)
+This effective ksext
+1
+yields a corresponding tune shift.
+Therefore, training in presence of feed-down yields an
+effective model, whose multipole components may differ
+from those given a series expansion around a magnets
+geometric center.
+In order to train the model in presence of orbit dis-
+tortions, BPM readings are aligned to zero mean. The
+remaining deviations originate from feed-down. We in-
+vestigate the effect of a closed orbit bump inside a single
+sextupole, for the scenario that sextupoles are used to
+correct chromaticity to zero in both transverse planes in
+SIS18. The degrees of freedom of the model comprise the
+focusing strengths of the quadrupoles, which will be ad-
+justed during the training process. The orbit bump leads
+to an effective gradient error at the location of the sex-
+tupole, which cannot be resolved by training because the
+model lacks a gradient degree of freedom at the sextupole
+location.
+Instead, training is capable to predict global proper-
+ties, e.g. the tunes in both planes, by adjusting the clos-
+est quadrupole degree of freedom. The tune shift induced
+by the orbit excursion is resolved accurately, cf. Fig. 4. In
+contrast to all other quadrupole strengths, the strength
+of the neighboring quadrupole does incorporate the gra-
+dient error induced by the orbit bump in the sextupole.
+Training adjusts the degree of freedom closest to the er-
+ror and thus, localization of the cell hosting the error is
+possible. A large orbit bump induces an additional dipole
+error due to feed-down. Since the focusing strengths as
+degrees of freedom cannot reproduce the closed orbit,
+resolution worsens for large bump excursions.
+C.
+Random Field Errors
+Besides systematic field errors, also random contribu-
+tions due to fabrication errors and misalignments are
+likely to be distributed across the accelerator. During op-
+eration of SIS18, measurements of global properties like
+tunes and chromaticities differ from predictions by the
+existing accelerator model. This discrepancy is large es-
+pecially in the case of chromaticities and depends on the
+excitation current of the dipole magnets. Therefore, it is
+of interest to investigate the applicability of the DLMN
+model to quantify sextupole components present in the
+accelerator ring.
+Random gradient and sextupole errors are added to the
+24 main quadrupoles and 24 bending magnets of SIS18 in
+2
+0
+2
+feeddown ksext
+1
+ / 10
+3 m
+1
+2
+0
+2
+k1 neigh. quad. / 10
+3 m
+1
+3.434
+3.435
+3.436
+3.437
+ver. tune Qy
+FIG. 4.
+Training results for a closed orbit distortion sce-
+nario. The final quadrupole deviation of the closest neighbor-
+ing quadrupole is compared to the gradient feed-down induced
+by the orbit bump. The vertical tune predicted by the model
+is compared to the actual accelerator tune (dotted).
+the simulation model. The error multipole strengths are
+sampled from a normal distribution with standard devi-
+ation σquad and σsext for gradient and sextupole errors,
+respectively. The magnitude is chosen such that each er-
+ror perturbs betatron tune Q and (absolute) chromaticity
+ξ by
+∆Qx
+Qx
+(σquad) = 10−3,
+∆ξx
+ξx,nat
+(σsext) = 8 · 10−2 ,
+likewise for the vertical plane.
+The DLMN model is tasked to identify normal dis-
+tributed gradient and sextupole errors.
+Its degrees of
+freedom comprise sextupole strengths of the main dipoles
+and gradient strengths of the lattice quadrupoles. Train-
+ing is capable of successfully minimizing the loss over
+the training set. Simultaneously, the discrepancy in mul-
+tipole strength is significantly decreased for quadrupole
+as well as sextupole strengths.
+The switch of training
+sets causes a peak in multipole deviations as the ADAM
+algorithm needs to adapt its step size. Training on off-
+momentum trajectories enables improved resolution of
+sextupoles eventually, cf. Figure 5. Observation of off-
+momentum trajectories is therefore essential to model
+sextupole components.
+The evolution of tunes and chromaticities predicted by
+the DLMN model converge in both planes against their
+counterparts present in the accelerator simulation that
+generated the training data in the first place. The reso-
+lution of tunes exceeds typical measurement uncertainties
+of these quantities.
+The DLMN model is found to be capable of predicting
+the magnitude of distributed gradient and sextupole er-
+rors present in SIS18 in simulations. The field errors are
+
+7
+0
+1000
+2000
+# epoch
+10
+10
+10
+8
+10
+6
+10
+4
+10
+2
+k1L / m
+1
+0
+1000
+2000
+# epoch
+10
+6
+10
+4
+10
+2
+k2L / m
+2
+0
+1000
+2000
+# epoch
+4.26
+4.28
+4.30
+4.32
+Qx
+0
+1000
+2000
+# epoch
+0.65
+0.60
+0.55
+0.50
+0.45
+0.40
+x        
+3.41
+3.42
+3.43
+3.44
+3.45
+        Qy
+0.40
+0.45
+0.50
+y
+FIG. 5. Training results in case of normal distributed gradient and sextupole errors. The maximum deviation between gradient
+and sextupole strengths between model and accelerator during training is shown in blue, gray lines represent individual multipole
+strengths. Tunes Q and chromaticities ξ in both planes converge against those present in the accelerator, denoted by dashed
+lines.
+correctly identified for an accelerator setup both at nat-
+ural chromaticity as well as for corrected chromaticity,
+ξx,y → 0, where strong systematic sextupole fields are
+present in the lattice sextupoles. The field errors identi-
+fied during training can potentially explain observed dis-
+crepancies in tune and chromaticity in real accelerators.
+The training works just as well for other betatron tunes
+than the indicated SIS18 working point. In general, these
+random field errors drive non-systematic betatron reso-
+nances. In a dedicated study, the betatron tune has been
+varied scanning through such a regular sextupole reso-
+nance.
+As a result of the study, the resolution of the
+identified gradient and sextupole errors was found to be
+rather independent of the nearby resonance.
+Therefore, the trained DLMN model can be applied
+to support operations for precise control of tunes and
+chromaticities, as well as resonance compensation.
+V.
+CONCLUSION
+In order to identify magnetic field errors, this work
+combines conventional modelling approaches in beam dy-
+namics with training techniques designed for artificial
+neural networks. The proposed Deep Lie Map Network
+(DLMN) model enables identification of field errors based
+on observations of beam centroid motion by means of
+beam position monitors. This data-driven modelling ap-
+proach yields an effective model of the accelerator, which
+encapsulates location and magnitude of magnetic field er-
+rors. It can therefore be used to compute resonance dia-
+grams and driving terms. In contrast to methods like the
+LOCO algorithm [1], the non-linear tune response matrix
+[3] or measurement of the resonance driving terms [2], the
+proposed method does not require the time-consuming
+systematic installation of closed-orbit bumps around the
+synchrotron. The trained DLMN model predicts tunes
+and chromaticities in good agreement with the accelera-
+
+8
+tor being subject to training. In the simulated example
+case of SIS18, the training procedure has been demon-
+strated to quantify gradient and sextupole errors.
+In
+principle, the developed training procedure can be ap-
+plied to higher-order field errors like octupoles.
+In contrast to a physics-informed neural network [6],
+the DLMN approach inherently incorporates the sym-
+plectic structure of beam dynamics and is guaranteed
+to be a valid solution to the equations of motion. The
+DLMN model parameters are physically meaningful mag-
+netic multipole components and can, therefore, be inter-
+preted at any stage of the training procedure. This war-
+rants further use of the trained effective model in estab-
+lished tools and (tracking) codes of accelerator physics
+such as, for instance, MAD-X and SixTrackLib. When
+modelling large accelerator rings, the present approach in
+thin-lens approximation may require a larger amount of
+concatenated drifts and kicks to obtain highly resolved
+field errors. In order to reduce the computing time in
+the context of automatic differentiation as required for
+the gradient-descent training algorithm, further research
+could refine the developed Lie map network by modelling
+thick elements based on the Truncated Power Series Al-
+gebra technique.
+DLMN model training yields the potential to reduce
+the need for beam time dedicated to identify unknown
+magnetic field errors and establish an effective machine
+model, which may increase availability and performance
+of synchrotrons. The small size of the required training
+data set facilitates short time windows of data collection
+and, thus, monitoring of field errors throughout the year.
+The trained effective machine model may serve to sup-
+port precise control of betatron tunes, chromaticities and
+resonance compensation.
+
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diff --git a/JNE4T4oBgHgl3EQfIgz1/content/tmp_files/load_file.txt b/JNE4T4oBgHgl3EQfIgz1/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,486 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf,len=485
+page_content='Identification of Magnetic Field Errors in Synchrotrons  based on Deep Lie Map Networks  Conrad Caliari1, Adrian Oeftiger2, and Oliver Boine-Frankenheim1,2  1TEMF, TU-Darmstadt, Schlossgartenstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 8, 64289 Darmstadt, Germany  and  2GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany  (Dated: January 13, 2023)  Magnetic field errors pose a limitation in the performance of synchrotrons, as they excite non-  systematic resonances, reduce dynamic aperture and may result in beam loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Their effect can be  compensated assuming knowledge of their location and strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Established identification proce-  dures are based on orbit response matrices or resonance driving terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' While they sequentially build  a field error model for subsequent accelerator sections, a method detecting field errors in parallel  could save valuable beam time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' We introduce deep Lie map networks, which enable construction  of an accelerator model including multipole components for the magnetic field errors by linking  charged particle dynamics with machine learning methodology in a data-driven approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Based on  simulated beam-position-monitor readings for the example case of SIS18 at GSI, we demonstrate  inference of location and strengths of gradient and sextupole errors for all accelerator sections in par-  allel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The obtained refined accelerator model may support setup of corrector magnets in operation  to allow more precise control over tunes, chromaticities and resonance compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  INTRODUCTION  Synchrotron performance requirements necessitate de-  tailed knowledge of magnetic fields errors present in the  accelerator in order to minimize losses and maintain  beam quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Magnetic field errors cause beam loss by  resonance excitation and demand compensation schemes  if the working point cannot be freely changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  While  particle tracking simulations are suited to predict and  optimize corrector magnet settings with respect to beam  loss, they depend on detailed knowledge of the magnetic  field errors distributed along the beam line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Magnetic  imperfections due to misalignments and fabrication er-  rors are often present and their location and magnitude  is essential for conclusive simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This work empha-  sizes that an accurate field error model can be obtained  from a systematic comparison of simulation results to  measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The magnetic field errors are recovered  by minimizing discrepancies between predicted and mea-  sured motion of bunch centroids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Existing approaches are based on measurements which  assert the effect of steerer magnets or closed orbit bumps  in a systematic scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' [1] establishes the LOCO  (linear optics form closed orbits) algorithm to model lin-  ear field errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The orbit response matrix Aij, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' the  change in position at the i-th beam position monitor  caused by a modification to the j-th corrector magnets  deflection angle, is measured and compared to predic-  tions of a computer model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Fitting the predicted to the  measured orbit response matrix by variation of magnetic  multipole components yields dipole, as well as normal  and skew quadrupole field errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Several methods have  been proposed to obtain a non-linear magnetic field error  model of a synchrotron by measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In [2] the beam  is excited by an ac dipole or a transversal kick in order  to retrieve resonance driving terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In [3] the authors  propose to observe tune shifts induced by field errors in  case the orbit is distorted globally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The effect of steerer  magnets distributed along the synchrotron on measured  tunes yields a response matrix, comparable to the orbit  response matrix, and access to non-linear field errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Or-  der and resolution of the searched multipole components  are limited by the resolution of the tune measurement,  which relies on excitation of betatron oscillations by a  kicker .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' These methods assume good knowledge of the  linear field components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Machine learning techniques yield the potential to  model physical systems in a data-efficient way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  This  promises the identifcation of magnetic field errors with-  out the time-consuming measurement of an orbit re-  sponse matrix or installation of orbit bumps around the  accelerator, but from few trajectories observed after ex-  citation by a transversal kick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Physics-informed neu-  ral networks (PINN) have recently gained track in data-  driven modelling of physical systems [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' They consist  of an universal function approximator, the neural net-  work, which is trained to reproduce measurements while  obeying the physical laws governing the dynamics of the  modelled system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This is achieved by minimizing a loss  function L = Ldata + Lreg, where Ldata quantifies the  discrepancy between prediction and measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The  second term Lreg as a regularization term restricts the  neural network to the space of possible solutions to the  differential equations which express the considered laws  of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A physics-informed neural network based on  Taylor map layers has been successfully applied to orbit  correction in [6], where the symplecticity of Hamiltonian  systems is enforced as a soft constraint by Lsymp  reg  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The  approach yields an effective model in form of transfor-  mations of particle coordinates between beam-position  monitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  This model works well for correction of closed orbit  distortion due to dipole errors, also for application in  simulations to the heavy-ion synchrotron SIS18 at GSI  [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The Taylor map based PINN is capable of describ-  ing the phase advance between beam-position monitors,  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='04914v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='acc-ph]  12 Jan 2023  2  but after training predicted tunes show deviations of sev-  eral percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' We observe a systematic failure to predict  non-linear dynamics arising from sextupole errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Since  symplecticity is not strictly maintained during training  by Lsymp  reg  , the training results remain poor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This is pos-  sibly linked to failure modes related to the regularization  term described in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  As an alternative approach, we propose to replace  the neural network by an accelerator model based on  Lie algebra techniques and the thin-lens approximation  [9]and embed it into the framework of machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  This model will be referred to as deep Lie map network  (DLMN) in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In contrast to a PINN, this model  choice does not involve a search for suited network struc-  tures, which is a non-trivial problem frequently tackled  by a trial-and-error approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  By design, the DLMN  represents a symplectic solution to the equations of mo-  tion, its degrees of freedom are given by magnetic mul-  tipole components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Hence, the DLMN approach enables  a physical interpretation of the model and its degrees of  freedom during any stage of the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The large number of magnets constituting a syn-  chrotron together with non-linear beam dynamics form  a complex and high-dimensional optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  We demonstrate the potential of the DLMN model  trained by means of the ADAM [10] algorithm to iden-  tify magnetic field errors in synchrotrons in simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Randomly distributed gradient and sextupole errors can  be identified in the SIS18 synchrotron [11] in simulations,  and tunes and chromaticities as well as resonance dia-  grams are reproduced in good agreement with the accel-  erator simulation providing training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The contribution is structured as follows: Section II  introduces the DLMN model, its training procedure is  described in Section III and simulation results for the  SIS18 synchrotron are reported in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A conclu-  sion is given in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  DLMN MODEL  Crucial to the objective of creating an accurate repre-  sentation of the accelerator is the chosen modelling ap-  proach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In this work, the modelling approach considers  only drift spaces and transverse magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The  particle beam is reduced to a single particle representing  its centroid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The equation of motion for single particle  dynamics can be solved approximately in the framework  of Hamiltonian dynamics [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The thin-lens approxi-  mation consists of consecutive updates to position and  momentum, known as drifts and kicks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The quality of  the approximation depends on the order of the symplec-  tic integrator, the arrangement of drifts and kicks, and  symplectic integrators up to arbitrary order are known  [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The particle tracking algorithms in MAD-X [14]  and SixTrackLib [15] for instance, are based on this ap-  proach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Similar to layers of neurons forming neural networks,  the accelerator model consists of a concatenation of sim-  ple building blocks, the drifts and kicks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The transfer  map of a single lattice element Ml arises from drifts D  and kicks K  Ml = Dl  1 ◦ Kl  1 ◦ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' ◦ Dl  i ◦ Kl  i  ,  (1)  and the transfer map between two locations in the lat-  tice Ml→m like beam-position monitors is given by their  concatenation  Ml→m = Ml ◦ Ml+1 ◦ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' ◦ Mm  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  (2)  This enables its implementation in the framework of  PINNs and allows to leverage existing tooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The model is capable of representing lattice magnets  including linear fringe fields, but lacks rf cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Drift  spaces are modelled without truncation and, thus, in-  clude non-linear effects like natural amplitude detuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Chromatic detuning due to finite momentum spread of  the beam and non-linear effects like amplitude detun-  ing, cause motion of the beam centroid to deviate from  motion of a single particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The resolution of magnetic  field errors correspondingly depends on transversal emit-  tances as well as momentum spread of the beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Fur-  thermore, this limits the meaningful simulation time to  less than a synchrotron period and thus, we negelect rf-  cavities in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Collective effects like space charge,  wakefields or electron clouds are neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' An advanced  implementation of the DLMN model could account for  these collective effects, as they can be included in terms  of automatic differentiation as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  TRAINING PROCEDURE  Training describes the process of fitting the accelerator  model to measurement data acquired by beam-position  monitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The optimal fit parameters reveal insights  into the distribution of field errors since they rep-  resent magnetic multipole components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Besides the  model, central to training are the training data itself,  a metric quantifying the discrepancy between model  predictions and training data, referred to as loss L,  and an optimization algorithm suited to minimize L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In case of successful training, the model is capable of  reproducing the measurements forming the training set  and generalization beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Throughout the article we  refer to the accelerator model being subject to training  as the model, whereas the source of training data, which  is either a simulated or real machine, is referred to  as accelerator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The capability of the model to predict  correct trajectories from initial conditions not included  into the training set is confirmed by additional data in a  validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  3  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Training Data  The training set consists of measured centroid trajec-  tories, which shall be reproduced by the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In or-  der to predict the motion of the beam centroid an initial  condition must be given as input to the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In ma-  chine experiments, an initial condition can be created by  means of a kicker deflecting the beam from its equilib-  rium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The kicker affects the beam in both planes  and the transversal momentum of the beam centroid is  inferred from the kicker voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Additionally, the beam  energy may be offset by slightly mismatching the rf fre-  quency with respect to the revolution time at the current  magnetic rigidity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A set of training data T is obtained  by varying the kick strength and / or the rf frequency,  while the beam position monitors are used to observe the  beam centroid motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Convergence speed is found to increase if training is  performed in two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In the first stage, initial condi-  tions used for training  T1 = {−∆px, ∆px} × {−∆py, ∆py}  (3)  comprise horizontal ∆px resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' vertical ∆py excitation  amplitude via the kicker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  This allows a first estimate  of gradient errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In the second stage, off-momentum  initial conditions are used for training,  T2 = {−∆px, ∆px} × {−∆py, ∆py} × {−δ, δ}  (4)  enabling identification of sextupole errors and chro-  maticities with high fidelity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Since deviations between centroid motion and single par-  ticle motion due to chromatic and amplitude detuning  grow over time, the number of turns M shall be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In addition, the computational complexity of tracking  grows with M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Observation for more than one turn is es-  sential to include the periodicity of a synchrotron, which  enables a magnetic field error to influence the centroid  motion globally regardless of its location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In case a single  turn is used for training, we find the algorithm underes-  timates the relevance of field errors located close to the  end of the turn, as they affect only few BPM readings  downstream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In case of SIS18, we find M = 3 to be a good setting  for the considered accelerator, which is short compared  to the observation time necessary for a tune measurement  required by alternative approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Loss  In order to judge the quality of model predictions  they need to be compared to observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  A metric  L(q(⃗z0), ˆq(⃗z0)) called loss is introduced to quantify the  discrepancy between model output ˆq(⃗z0) and measure-  ment q(⃗z0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In this work, a modified version of the mean-squared er-  ror (MSE), common to machine learning and regression,  is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The loss  L({q, ˆq}r∈R) = 1  M  R  �  r=1  M  �  m=1  N  �  n=1  �  ⃗qr,m,n − ˆ⃗qr,m,n  �2  σr  (5)  compares predicted and measured centroid positions  ⃗q =  �x, y�T at discrete locations of N beam position  monitors over M turns for R initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The nor-  malization factor  σr  �  ⃗z(r)  0  �  = max{Aq  �  ⃗z(r)  0  �  }q∈{x,y}  (6)  is given by the single-particle amplitude  Aq =  �  2βqJq + D2qδ2  ,  (7)  which depends on the initial condition ⃗z(r)  0  ≡ [px, py, δ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Beta-functions βq, dispersions Dq and linearized actions  Jq are computed from the initial accelerator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Since the loss L compares model predictions to  measurements, it depends on the magnetic multipole  strengths of the model ⃗k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The optimal multipole  strengths ⃗k∗ : L(⃗k) ≥ L(⃗k∗)∀⃗k ∈ D over some set of field  strengths D entail that the model reproduces measured  trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Thus, a comparison of the converged mul-  tipole strengths to those of the untrained initial model  reveals magnetic field errors present in the accelerator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  For a single FODO cell in thin-lens approximation, the  eigenvalues of the Hessian of the loss L with respect to  quadrupole strengths can be calculated analytically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' For  not too large gradient errors, the Hessian is positive-  definite and thus optimization of L poses a convex op-  timization problem, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' a unique extremum exists on D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In case of non-linear beam dynamics, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' non-linearities  originating from truncation free drifts and lattice sex-  tupoles powered to correct chromaticity, this finding is  not altered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A scan of the loss L as a function of model  quadrupole strengths show a unique minimum in case the  model matches the quadrupole strengths of the acceler-  ator, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This emphasizes that minimization of  L is a well-posed problem in presence of non-linearities:  the proposed method can, hence, be applied to non-linear  beam dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Optimization  The DLMN model is trained by minimizing the loss  over the training data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Since the model is differen-  tiable, gradient-based optimization algorithms, which are  established in various high-dimensional fit problems of  machine learning, can be employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In simulations, the  4  50  0  50  1st quad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' k1/k1 / %  100  50  0  50  100  2nd quad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' k1/k1 / %  10  3  10  2  10  1  100  101  loss  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Loss of SIS18 cell vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' gradient errors of first and sec-  ond quadrupole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The training set consists of a single condition  {px, py, δ} = {10−3, 10−3, 0}  ADAM [10] algorithm outperformed options like plain  gradient descent, Adagrad [16] or Adadelta [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The  ADAM optimizer is capable of dealing with sparse gra-  dients and parameters whose gradients differ in size by  orders of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The derivatives of the loss with  respect to model parameters are obtained by automatic  differentiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Automatic differentiation [18] leverages that the model  consists of a concatenation of simple maps, the drift and  kicks, which can be differentiated analytically in closed  form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The derivatives of the whole model are then cal-  culated by exploitation of the chain rule, which allows  to break down their calculation to a concatenation of  the analytic derivatives of drift and kicks, similar to the  concatenation of drifts and kicks yielding the particle  tracking simulation in the first place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Since the scalar  loss function is differentiated w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  many multipole  strengths characterizing each kick, we employ reverse-  mode automatic differentiation, which is more efficient  than forward-mode automatic differentiation in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In contrast to numerical differentiation based on finite  differences, automatic differentiation is not prone to  rounding errors and thus, noisy gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The deriva-  tion of an analytic expression for loss derivatives is in-  feasible because of expression swelling, which causes the  number of terms to grow exponentially with the number  of drifts and kicks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The DLMN model as well as the training procedure  are implemented in the Julia programming language [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Automatic differentiation is used via the library [20], an  implementation of the ADAM algorithm is taken from  [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Additionally, the learning rate of the optimizer is  decreased exponentially as a function of iterations over  the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Both learning rate, also known as step size, and its de-  cay rate form two hyperparameters of the training pro-  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Properties of SIS18 and key beam parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Parameter  Value  Circumference  216 m  Momentum compaction αC  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='4 × 10−2  Transition energy  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='5  Synchrotron tune Qs  > 100 turns  Betatron tunes Qx, Qy  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='4  Natural (absolute) chromaticity ξ(nat)  x  , ξ(nat)  y  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='43 / -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='89  Magnetic Rigidity (Bρ)max  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='5 T m  Ion  proton  Energy E  5 GeV  Energy Spred σE/E  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='6 × 10−4  Transverse Emittances ϵ4-rms  norm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='9 µm  cedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A tree-structured Parzen estimator [22] imple-  mented in [23] is employed for their optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' We  find that the hyperparameters need rather limited tun-  ing and optimal values are identified within few iterations  of the Parzen estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  APPLICATION TO SIS18 IN SIMULATIONS  The DLMN model is applied to the SIS18 at GSI in  simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The SIS18 is a 216 m long synchrotron de-  signed to accelerate ions ranging from protons to ura-  nium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' It features twelve identical cells, where each cell  hosts two bending magnets, two quadrupoles as well as  two sextupole magnets, c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Key properties are  listed in Table I, and a more detailed description is given  in [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The simulated synchrotron features various combina-  tions of gradient and sextupole errors, and provides  beam-position monitor readings of the beam centroid po-  sition as outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The recovery of field errors hidden in  the accelerator simulation is limited by the models ap-  proximation of the beam by a single particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Thus, the  resolution of gradient and sextupole errors is evaluated  in dependence of transverse emittance and energy spread  of the beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Training is performed on a detailed simulation of SIS18  based on the MAD-X / SixTrackLib codes, where the  former is used for matching of tunes and chromaticities  and the latter for 6D particle tracking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The simulation  model consists of lattice magnets including linear fringe  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Furthermore, the simulation includes an rf cavity  enabling a bunched beam necessary for usage of the beam  position monitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The beam consists of protons injected  by the UNILAC [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Key beam parameters can be found  in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Comparable emittances can be achieved with  ion beams by employing the existing electron cooler [26,  27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In Subsection IV A the possible resolution of gradient  and sextupole errors in dependence of beam parameters  is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Subsection IV B covers the case in which  the model lacks a degree of freedom at the location of  a field error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The simultaneous identification of a set of  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='8  energy spread (E)/E / 10  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  1rms  norm / m (both planes)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='8  energy spread (E)/E / 10  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='0  1rms  norm / m (both planes)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='1  k1 / k1 / %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='1  1  10  k2 / k2 / %  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Resolution of gradient and sextupole errors in dependence of beam transverse emittance and energy spread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A gradient  k1l =5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='2 × 10−3 m−1 and a sextupole k2l =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='6 × 10−2 /m2 field error are introduced to the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The dashed line marks the  normalized 1-rms emittance of the UNILAC proton beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  0  5  10  15  [m]  0  10  20  30  [m]  x  y  Dx  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A 18 m long cell of SIS18 drawn to scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Bending  magnets are shown in blue, quadrupoles in yellow and sex-  tupoles in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  distributed field errors is presented in Subsection IV C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Physical plausibility of the model predictions is under-  pinned by correct prediction of tunes and chromaticities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Resolution  The resolution of magnetic multipole components is  limited by the approximation of the beam centroid by  a single particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Due to adiabatic damping, the trans-  verse beam size is smallest at high energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Thus, non-  linear effects such as amplitude detuning become less  influential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  To benefit from this effect, training data  is collected at flat-top energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  A single gradient er-  ror k1l=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='2 × 10−3 m−1 together with a single sextupole  error k2l=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='6 × 10−2 m−2 are introduced to the accel-  erator, causing a shift in tune ∆Qx/Qx ≈1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='2 × 10−3  and chromaticity ∆ξx/ξx ≈1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='7 × 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Training is per-  formed for different transverse emittances as well as en-  ergy spreads and the achieved resolution of field errors is  quantified by the discrepancy  Di =  ����  kacc  i  − kmodel  i  kacc  i  ����  (8)  between the models multipole strength and its ac-  tual counterpart in the accelerator, which is displayed  in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The discrepancy in both gradient and sex-  tupole strengths is determined primarily by the beam en-  ergy spread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Additionally, the discrepancy in sextupole  strengths grows beyond 10 % in case the normalized 1-  rms emittance exceeds 10 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The beam size of the pro-  ton beam is suited for resolving sextupole components in  the order of magnitude k2l ≈10−2 m−2 with a discrep-  ancy of D2 < 10 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Therefore, it is suited to identify un-  documented sextupole contributions related to the main  dipoles in SIS18, but resolution is reduced significantly  in case of heavy-ion beams featuring larger transverse  emittances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Orbit Distortion  In addition to field errors, another source of deviations  between accelerator and model is distortion of the closed  orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Besides moving the center of betatron oscillations,  a displacement d of the closed orbit with respect to the  geometric centre of a magnet induces multipole compo-  nents of lower orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In case the magnet is a 2(n+1)-pole  6  the dominant feed-down contribution acts like a (2n)-  pole, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' an orbit distortion inside a sextupole field k2  induces a gradient component ksext  1  ,  ∆px = k2L  2 (x + d)2  = k2L  2 x2 + k2Ld  � �� �  ksext  1  x + k2L  2 d2  (9)  This effective ksext  1  yields a corresponding tune shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Therefore, training in presence of feed-down yields an  effective model, whose multipole components may differ  from those given a series expansion around a magnets  geometric center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In order to train the model in presence of orbit dis-  tortions, BPM readings are aligned to zero mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The  remaining deviations originate from feed-down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' We in-  vestigate the effect of a closed orbit bump inside a single  sextupole, for the scenario that sextupoles are used to  correct chromaticity to zero in both transverse planes in  SIS18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The degrees of freedom of the model comprise the  focusing strengths of the quadrupoles, which will be ad-  justed during the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The orbit bump leads  to an effective gradient error at the location of the sex-  tupole, which cannot be resolved by training because the  model lacks a gradient degree of freedom at the sextupole  location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Instead, training is capable to predict global proper-  ties, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' the tunes in both planes, by adjusting the clos-  est quadrupole degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The tune shift induced  by the orbit excursion is resolved accurately, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In  contrast to all other quadrupole strengths, the strength  of the neighboring quadrupole does incorporate the gra-  dient error induced by the orbit bump in the sextupole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Training adjusts the degree of freedom closest to the er-  ror and thus, localization of the cell hosting the error is  possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' A large orbit bump induces an additional dipole  error due to feed-down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Since the focusing strengths as  degrees of freedom cannot reproduce the closed orbit,  resolution worsens for large bump excursions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Random Field Errors  Besides systematic field errors, also random contribu-  tions due to fabrication errors and misalignments are  likely to be distributed across the accelerator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' During op-  eration of SIS18, measurements of global properties like  tunes and chromaticities differ from predictions by the  existing accelerator model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This discrepancy is large es-  pecially in the case of chromaticities and depends on the  excitation current of the dipole magnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Therefore, it is  of interest to investigate the applicability of the DLMN  model to quantify sextupole components present in the  accelerator ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Random gradient and sextupole errors are added to the  24 main quadrupoles and 24 bending magnets of SIS18 in  2  0  2  feeddown ksext  1  / 10  3 m  1  2  0  2  k1 neigh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' quad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' / 10  3 m  1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='434  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='435  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='436  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='437  ver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' tune Qy  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Training results for a closed orbit distortion sce-  nario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The final quadrupole deviation of the closest neighbor-  ing quadrupole is compared to the gradient feed-down induced  by the orbit bump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The vertical tune predicted by the model  is compared to the actual accelerator tune (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  the simulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The error multipole strengths are  sampled from a normal distribution with standard devi-  ation σquad and σsext for gradient and sextupole errors,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The magnitude is chosen such that each er-  ror perturbs betatron tune Q and (absolute) chromaticity  ξ by  ∆Qx  Qx  (σquad) = 10−3,  ∆ξx  ξx,nat  (σsext) = 8 · 10−2 ,  likewise for the vertical plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The DLMN model is tasked to identify normal dis-  tributed gradient and sextupole errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Its degrees of  freedom comprise sextupole strengths of the main dipoles  and gradient strengths of the lattice quadrupoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Train-  ing is capable of successfully minimizing the loss over  the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Simultaneously, the discrepancy in mul-  tipole strength is significantly decreased for quadrupole  as well as sextupole strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The switch of training  sets causes a peak in multipole deviations as the ADAM  algorithm needs to adapt its step size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Training on off-  momentum trajectories enables improved resolution of  sextupoles eventually, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Observation of off-  momentum trajectories is therefore essential to model  sextupole components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The evolution of tunes and chromaticities predicted by  the DLMN model converge in both planes against their  counterparts present in the accelerator simulation that  generated the training data in the first place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The reso-  lution of tunes exceeds typical measurement uncertainties  of these quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The DLMN model is found to be capable of predicting  the magnitude of distributed gradient and sextupole er-  rors present in SIS18 in simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The field errors are  7  0  1000  2000  # epoch  10  10  10  8  10  6  10  4  10  2  k1L / m  1  0  1000  2000  # epoch  10  6  10  4  10  2  k2L / m  2  0  1000  2000  # epoch  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='26  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='28  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='30  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='32  Qx  0  1000  2000  # epoch  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='40  x  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='41  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='42  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='43  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='45  Qy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='50  y  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Training results in case of normal distributed gradient and sextupole errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The maximum deviation between gradient  and sextupole strengths between model and accelerator during training is shown in blue, gray lines represent individual multipole  strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' Tunes Q and chromaticities ξ in both planes converge against those present in the accelerator, denoted by dashed  lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  correctly identified for an accelerator setup both at nat-  ural chromaticity as well as for corrected chromaticity,  ξx,y → 0, where strong systematic sextupole fields are  present in the lattice sextupoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The field errors identi-  fied during training can potentially explain observed dis-  crepancies in tune and chromaticity in real accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  The training works just as well for other betatron tunes  than the indicated SIS18 working point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In general, these  random field errors drive non-systematic betatron reso-  nances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In a dedicated study, the betatron tune has been  varied scanning through such a regular sextupole reso-  nance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  As a result of the study, the resolution of the  identified gradient and sextupole errors was found to be  rather independent of the nearby resonance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  Therefore, the trained DLMN model can be applied  to support operations for precise control of tunes and  chromaticities, as well as resonance compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  CONCLUSION  In order to identify magnetic field errors, this work  combines conventional modelling approaches in beam dy-  namics with training techniques designed for artificial  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The proposed Deep Lie Map Network  (DLMN) model enables identification of field errors based  on observations of beam centroid motion by means of  beam position monitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This data-driven modelling ap-  proach yields an effective model of the accelerator, which  encapsulates location and magnitude of magnetic field er-  rors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' It can therefore be used to compute resonance dia-  grams and driving terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In contrast to methods like the  LOCO algorithm [1], the non-linear tune response matrix  [3] or measurement of the resonance driving terms [2], the  proposed method does not require the time-consuming  systematic installation of closed-orbit bumps around the  synchrotron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The trained DLMN model predicts tunes  and chromaticities in good agreement with the accelera-  8  tor being subject to training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In the simulated example  case of SIS18, the training procedure has been demon-  strated to quantify gradient and sextupole errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In  principle, the developed training procedure can be ap-  plied to higher-order field errors like octupoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  In contrast to a physics-informed neural network [6],  the DLMN approach inherently incorporates the sym-  plectic structure of beam dynamics and is guaranteed  to be a valid solution to the equations of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' The  DLMN model parameters are physically meaningful mag-  netic multipole components and can, therefore, be inter-  preted at any stage of the training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' This war-  rants further use of the trained effective model in estab-  lished tools and (tracking) codes of accelerator physics  such as, for instance, MAD-X and SixTrackLib.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' When  modelling large accelerator rings, the present approach in  thin-lens approximation may require a larger amount of  concatenated drifts and kicks to obtain highly resolved  field errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content=' In order to reduce the computing time in  the context of automatic differentiation as required for  the gradient-descent training algorithm, further research  could refine the developed Lie map network by modelling  thick elements based on the Truncated Power Series Al-  gebra technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
+page_content='  DLMN model training yields the potential to reduce  the need for beam time dedicated to identify unknown  magnetic field errors and establish an effective machine  model, which may increase availability and performance  of synchrotrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JNE4T4oBgHgl3EQfIgz1/content/2301.04914v1.pdf'}
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+MMRG, HydrateTech, & Mari´c Labs - Preprint
+Molecular dynamics predictions of transport properties for
+carbon dioxide hydrates under pre-nucleation conditions
+using TIP4P/Ice water and EPM2, TraPPE, and Zhang carbon
+dioxide potentials
+Andr´e Guerra
+, Samuel Mathews
+, Jennifer Tram Su, Milan Mari´c
+, Phillip Servio
+,
+Alejandro D. Rey
+*
+Department of Chemical Engineering, McGill University, Montr´eal, QC, Canada
+(1) Introduction: New technologies that leverage gas hydrates phenomena include carbon cap-
+ture and sequestrations. These processes are often semi-continuous and require regulation of the
+system’s flow properties for proper operation. Accurate computational models for the viscosity
+of carbon dioxide hydrate systems at pre-nucleation conditions can be important for process de-
+sign and control of such technologies. (2) Methods: This work validates the viscosity predictions
+of molecular dynamics simulations using previously measured experimental data. The TIP4P/Ice
+force field was used to model water, while the EPM2, TraPPE, and Zhang force fields were used for
+carbon dioxide. The Green-Kubo and Einstein formulations of viscosity and diffusivity were used
+in this work. (3) Results: All force fields overpredicted viscosity when compared to experimental
+data, but EPM2 resulted in lower discrepancies. Additionally, EPM2 was determined to model
+molecular behavior expected from the macroscopic trends in viscosity with respect to temperature
+and pressure. (4) Conclusions: The EPM2 force field more accurately predicted the viscosity of
+carbon dioxide hydrates systems at pre-nucleation conditions relative to TraPPE and Zhang.
+1.
+Introduction
+Among the Arctic permafrost and the subsea sediments of Earth’s continental margins are ice-like
+crystalline solids[11]. What separates these compounds from normal forms of ice (e.g., hexagonal)
+are gas inclusions - guest gas molecules that reside within the cavities formed by the lattice structure.
+Known as gas hydrates, these non-stoichiometric compounds form when gaseous molecules and
+water freeze at high pressures and low temperatures. Depending on these conditions, as well as the
+identity of the gas molecule, hydrate properties may vary, and structurally take on one of three main
+forms: sI, sII, or sH, which differ in size, structure, and number of occupancies[57]. Water molecules
+maintain the hydrate structure through hydrogen bonds, while the entrapped molecules provide
+stability through weak van der Waals interactions[11].
+In the past two decades, new technologies that utilize the formation of gas hydrates to accom-
+plish a process have been proposed.
+Some examples include pre- and post-combustion carbon
+capture[1, 41, 50], gas separations[19, 20], transport and storage of natural gas[26, 60], and wa-
+ter desalination[66]. These technologies mostly leverage the high gas-to-solid volume ratio of gas
+hydrates (up to 184:1), and the hydrate cages size selectivity to guest species to accomplish their
+process[19, 76]. Due to the semi-continuous nature of these new technologies and the absence of
+oil emulsions in their systems, recent studies have explored the dynamic viscosity of methane and
+*Correspondence E-mail: alejandro.rey@mcgill.ca
+arXiv:2301.01757v1  [physics.app-ph]  4 Jan 2023
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+carbon dioxide hydrate systems in aqueous systems[29, 58]. Rheological studies of these systems
+require highly specialized and expensive equipment to be conducted, in addition to difficult experi-
+mental conditions to be achieved. As a result, the use of computational methods to predict transport
+properties, like dynamic viscosity and diffusivity, is desirable.
+Computational methods such as Density Functional Theory (DFT) and Molecular Dynamics (MD)
+can provide insight into molecular structure and transport phenomena that are otherwise difficult, if
+not impossible, to obtain experimentally. DFT is well suited for atomic-scale quantum calculations
+to examine a material’s static properties, while MD is preferred for nanoscale dynamic processes
+such as transport properties. However, results from computational methods are best interpreted
+and utilized in combination with experimental data. Our research group has developed an inte-
+grated experimental-computational platform for investigating the material sciences of gas hydrate
+systems[28]. This has led to contributions in interfacial phenomena[61–63] and physical and trans-
+port properties of gas hydrate systems[27, 83–86, 95, 96]. In this work, we implement the platform
+to study the transport properties of carbon dioxide hydrate systems as predicted by molecular dy-
+namics. We use experimental data to validate the dynamic viscosity predictions by our models. The
+experimental data is presented elsewhere[29].
+Molecular dynamics simulations implement molecular trajectories by integrating Newton’s equa-
+tions of motion.
+Atomic interactions are mapped by force fields, which are parametrized mod-
+els that represent the potential energy of an atomic system as a function of the individual atomic
+positions[74]. This potential energy arises from the sum of bonded and non-bonded interactions.
+Bonded forces describe how covalent bonds behave, including changes in bond length, bond angle,
+and bond torsion along dihedrals. These are often modeled as harmonic oscillators. Non-bonded
+forces arise between non-covalently bonded atoms, including electrostatic Coulombic interactions
+and repulsive van der Waals forces, modeled by Coulomb’s law and the Lennard-Jones 12/6 poten-
+tial model, respectively. For simplicity, these N-body interactions are approximated as a pairwise
+additive model. By tracking how an atomic system evolves over time, MD simulations rely on sta-
+tistical mechanical principles of the ensemble and the ergodic hypothesis to predict macroscopic
+material properties, such as viscosity and diffusivity, from nanoscale interactions.
+Molecular simulations have been used to investigate gas hydrate systems including the
+nucleation[30, 34, 37, 47, 64, 87, 90, 91, 94] and dissociation[5, 15, 17, 18, 35, 65, 77] of hydrates, the mo-
+bility of guest species between cages[9, 22, 73, 82], surface effects on nucleation[6–8, 10, 48], and nucle-
+ation inhibition mechanisms by poly(vinyl pyrrolidone) and poly(vinyl caprolactam)[44, 46, 54, 89].
+A recent review by Qi et al.[72] expands on recent advances in gas hydrate research accomplished
+by the use of molecular simulations.
+The transport properties of gas hydrate systems have not
+been explored to the same extent. Recently, our research has conducted molecular simulations to
+model methane hydrate systems and to predict their dynamic viscosity[27]. These predictions were
+compared to experimental results for model validation. This previous work has demonstrated the
+TIP4P/Ice water model to improve the dynamic viscosity prediction of subcooled water over the
+widely used TIP4P/2005[27].
+The scope of this study is to examine the performance of equilibrium molecular dynamics vis-
+cosity predictions of carbon dioxide hydrate system at pre-nucleation conditions. This is achieved
+through comparison with experimental data and by conducting various hydrogen bond analyses.
+In this work, we use the TIP4P/Ice force field potential to model water molecules, and we test the
+performance of three widely accepted carbon dioxide force field potentials EPM2[31], TraPPE[71],
+and Zhang[93]. The Green-Kubo and Einstein formulations are used on a rigorously equilibrated
+large molecular system (5472-9072 atoms) to predict their dynamic viscosity and diffusivity, respec-
+2
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+tively. Additionally, the Stokes-Einstein formulation for viscosity is introduced and its performance
+is evaluated in this context.
+2.
+Tools and Methods
+2.1.
+Software Packages
+Molecular dynamics (MD) simulations were conducted using the Large-scale Atomic/Molecular
+Massively Parallel Simulator (LAMMPS) package, an open-source code developed and maintained
+by Sandia National Laboratory and Temple University[78].
+Atom trajectories are dynamically
+tracked via the integration of Newton’s equations of motion coupled with varying interatomic
+potentials. When analyzed, these interacting particles serve as a predictive model for macroscopic
+material properties.
+MD simulations in LAMMPS require an initial configuration of atoms and
+molecules. These configurations were developed using the PACKMOL[56] and Moltemplate[36]
+packages. PACKMOL is a packing optimization algorithm that places atoms according to spatial
+constraints set by the user (in this work, a separation tolerance of 2.5 ˚A). As opposed to the standard
+population commands in LAMMPS, these constraints give rise to structural complexity while reduc-
+ing repulsive inter-molecular forces, effectively lessening the computational power required during
+the initial part of the simulation process. Moltemplate is a cross-platform molecule builder that
+prepares MD systems by assigning atoms and molecules their corresponding parameters according
+to the desired force field potential. Atomic mass, charges, and molecule bond and angle parameters
+associated with the Optimizing Potentials for Liquid Simulations All-Atom TIP4P/Ice force field
+were assigned for water, while parameters associated with the Elementary Physical Model (EPM2),
+Transferable Potential for Phase Equilibria (TraPPE), and Zhang force fields were assigned for car-
+bon dioxide. Finally, MDAnalysis is a python library developed to handle and analyze molecular
+trajectories, which was used by this work to conduct hydrogen bond analyses.
+2.2.
+Simulation Design
+2.2.1.
+Force Field Potentials
+The Optimizing Potentials for Liquid Simulations All-Atom (OPLS-AA) force field was used to
+model all water molecules. Compared to the coarse-grained version united-atom (UA) form, the
+all-atom form represents hydrogen atoms explicitly, making it better suited for simulating gas hy-
+drate systems due to the high presence of hydrogen bonding[38–40]. In particular, the TIP4P/Ice
+four-site water model was specifically designed for estimating properties of water in its solid-state
+form[2]. A recent study considering methane hydrates demonstrated that this model had improved
+performance at predicting transport properties of water at low temperatures over the TIP4P/2005
+model[27].
+Carbon dioxide was modeled using the three-site models TraPPE[71], Zhang[93], and EPM2[31].
+The Zhang model is considered the best all-around performing force field potential for predicting
+the transport properties of pure carbon dioxide, including thermodynamic property predictions[3].
+EPM2 and TraPPE were the next best-performing force field potentials. The Zhang model parame-
+ters were optimized to accurately predict liquid volumetric properties and phase-equilibria[93]. The
+EPM2 model is an improvement on the rigid EPM model by introducing a flexible bond angle poten-
+tial, which more accurately predicts the liquid-vapor coexistence curve for pure carbon dioxide[31].
+3
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+Finally, the TraPPE model was developed to expand the applicability of pure-component models to
+multi-component mixtures involving n-alkanes[71].
+2.2.2.
+LAMMPS Input
+The TIP4P/Ice water model was used to simulate all systems. These systems consisted of 2976
+molecules, which is one order of magnitude greater than the classic system of 256 molecules that suf-
+fers from finite size effects[13]. The systems were defined by the full atom style, the lj/cut/tip4p/long
+pairstyle with 12 ˚A OM site and coulombic cut-off lengths, and the pppm/tip4p kspace space style
+with a dimensionless relative force accuracy of 1 × 10−4. Bond and angle styles were modeled as har-
+monic, while interatomic interactions between dissimilar non-bonded atoms were calculated through
+the Lorenz-Berthelot arithmetic mixing rules. Three molecular representations of carbon dioxide
+were used. The TraPPE and Zhang models (rigid C=O bond angle) and EPM2 model (semi-flexible
+C=O bond angle). Water molecule bonds and angles were kept rigid via the shake command. This
+command is not recommended to constrain angles at 180 degrees as it results in numerical solver
+difficulties[78].
+As a linear molecule, carbon dioxide molecules modeled by TraPPE and Zhang
+had their bonds and angles kept rigid via the rigid commands, which treat all atoms in a molecule
+as one moving body. All rigid models had their bond and angle harmonic constants set to 1000
+kcal/mol/rad2 to ensure rigidity during the minimization step. To advance the molecular trajectories,
+Newton’s equations of motion were numerically integrated using the Velocity Verlet algorithm with
+a 2-femtosecond timestep. Table 1 details the list of parameters for the TIP4P/Ice, EPM2, TraPPE,
+and Zhang force fields.
+4
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+Table 1: Molecular force field parameters implemented in LAMMPS in this work.
+Attribute, Units
+Zhang [93]
+TraPPE [71]
+EPM2 [31]
+TIP4P/Ice [2]
+O mass, g/mol
+15.999
+15.999
+15.999
+15.9994
+H mass, g/mol
+-
+-
+-
+1.008
+C mass, g/mol
+12.011
+12.011
+12.011
+-
+O charge, e
+−0.2944
+−0.35
+−0.3256
+−1.1794
+H charge, e
+-
+-
+-
+0.5897
+C charge, e
+0.5888
+0.7
+0.6512
+-
+OH bond ro, ˚A
+-
+-
+-
+0.9572
+CO bond ro, ˚A
+1.163
+1.1672
+1.149
+-
+OCO angle θ
+180◦
+180◦
+180◦
+-
+HOH angle θ
+-
+-
+-
+104.52◦
+OM distance, ˚A
+-
+-
+-
+0.1577
+H-H LJ ϵ,
+kcal/mol
+-
+-
+-
+0
+C-C LJ ϵ,
+kcal/mol
+0.057131
+0.053477
+0.055713
+-
+O-O LJ ϵ,
+kcal/mol
+0.163711
+0.15647
+0.159455
+0.21084
+C-C LJ σ, ˚A
+2.7918
+2.8
+2.757
+-
+O-O LJ σ, ˚A
+3.0
+3.05
+3.033
+3.1668
+H-H LJ σ, ˚A
+-
+-
+-
+0
+rc, ˚A
+12
+12
+12
+12
+Notes: H: hydrogen, O: oxygen, C: carbon, O-O: oxygen-oxygen interactions, H-H: hydrogen-hydrogen interactions,
+charge units in multiples of an electron charge (e), M is the massless fourth site in the TIP4P water model, rc: cutoff
+distance of Coulombic and Lennard-Jones (LJ) interactions, σ: distance for zero potential energy in LJ potential, ϵ is the
+depth of the LJ potential well.
+2.2.3.
+Carbon Dioxide Hydrate Systems
+The pre-nucleation gas hydrate systems defined in this study consisted of carbon dioxide and
+water. For a binary mixture, the Gibbs phase rule imposes two degrees of freedom. In this study, they
+were taken up by temperature and pressure, leaving the carbon dioxide liquid concentration fixed at
+every condition. Carbon dioxide concentrations in water at low temperatures can be described in an
+analogous way as methane systems were examined by Lekvam and Bishnoi [4, 12, 42, 45]. Here, a
+modified version of Henry’s law for higher pressures is used. Henry’s law has been used to describe
+the liquid solubility of carbon dioxide in water for hydrate systems due to the small effect of pressure
+on solubility at low temperatures[33, 75]. For application in systems at higher pressures, Krichevsky
+and Kasarnovsky present a modification to Henry’s law as shown in Equation 1[42].
+ln
+� f2
+x2
+�
+= ln(H2,1) + ¯v∞
+2 (P − PS
+1 )
+RT
+(1)
+Where for the gas species, f2 is the fugacity, x2 is its liquid concentration, and H2,1 is Henry’s law
+constant. As well, PS
+1 is the partial saturation pressure of the liquid, ¯v∞
+2 is the partial molar volume
+of the gas at infinite dilution, R is the gas constant, P is the pressure, and T is the temperature.
+5
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+The fugacity of carbon dioxide in water is calculated using the Trebble-Bishnoi equation of state
+(EOS)[81]. As this model has been extensively studied, it will not be included here. The partial molar
+volume, ¯v∞
+2 , and Henry’s law constant, H2,1, for carbon dioxide are provided by Di et al.[14] and
+Carroll et al.[12]. Each carbon dioxide system consisted of between 1426 to 2976 molecules depending
+on the liquid concentration calculated.
+2.3.
+Equilibration Procedure
+Accurate transport property estimations require appropriately designed simulations. To this end,
+Maginn et al.[55] present an equilibration procedure based on best practices for transport property
+estimations from MD simulations. Molecules were randomly assigned an initial velocity based on the
+Maxwell-Boltzmann distribution at the desired temperature. All systems studied in this work were
+then equilibrated through a series of simulations in different ensembles. First, the isobaric-isothermal
+(NPT) ensemble was performed for 25 ns, during which the system’s potential energy and density
+were monitored. Sufficient equilibration was attained when these parameters stabilized within their
+expected range[2, 69]. Following this step, the canonical (NVT) ensemble with the Nos´e-Hoover
+thermostat was performed for 50 ns. The system’s density and pressure were monitored throughout
+the equilibration run to ensure no considerable deviation of the thermodynamic state of the system
+from the previous NPT step. Following best practices, it is recommended to use the NVT ensemble
+to estimate transport properties as opposed to the NPT ensemble. In maintaining pressure in an
+NPT ensemble, volume corrections cause disturbances to the dynamics of the system. Additionally,
+properties such as diffusivity and viscosity that are calculated using the Green-Kubo autocorrelation
+functions, are particularly sensitive to these disturbances due to their dependence on velocity and
+pressure[55]. Furthermore, the temperature and pressure were modulated using damping factors of
+100*dt and 1000*dt, respectively, where “dt” is the simulation timestep (2 fs). These were introduced
+to reduce the disturbances induced by ensemble dynamics.
+2.4.
+Replicate Production Runs
+In equilibrium molecular dynamics, the simulated systems that are referred to as ”production
+runs” are equilibrated and are the systems from which property calculations can be confidently per-
+formed. The ideal ensemble for production runs would be the NVE, in which no barostat or ther-
+mostat is implemented. This ensures no disturbances are introduced into the system from these
+dynamic control algorithms. However, the use of the NVE ensemble is problematic to maintain equi-
+librium conditions (i.e., maintaining the desired pressure-temperature condition). For the context of
+transport property estimations, previous work has shown that the estimations of viscosity and dif-
+fusivity are indistinguishable between NVE and NVT systems[21, 68]. As a consequence of this, this
+work implements NVT production runs for transport property calculations after the conclusion of
+the equilibration procedure described above.
+In order to reduce the effect of variability of the autocorrelation functions used to calculate viscos-
+ity and diffusivity (described below) on the calculated values, this work implements bootstrap statis-
+tical analysis for its production runs. Once the system has been equilibrated as described above, ten
+(n = 10) replicate NVT systems were created, each using a different random number generator seed
+for assignment of the temperature at each pressure-temperature condition. This creates a sample of
+ten replicate simulations at each desired condition, all of which were simulated in LAMMPS for 1.5 ns
+for production run calculations to be performed. From the results of the array of systems, a statistical
+6
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+bootstrap with replacement (N = 10, 000) was performed for each pressure-temperature condition.
+Unless otherwise specified, all transport properties presented in this work are averages from the
+N = 10, 000 bootstrap procedure. This statistical averaging takes advantage of the inverse propor-
+tionality between the calculated values’ uncertainty and the number of replicates (u ∝ 1/√n)[70].
+Moreover, the bootstrap procedure performed here allows for the calculated values to be presented
+with their standard errors. Finally, the replicate simulations benefit from the computational speed
+of parallel simulations versus one long simulation, which has been shown to converge to the same
+value[53, 92].
+2.5.
+Viscosity and Diffusivity Formulations
+Molecular dynamic simulations rely on the fundamental principles of statistical mechanics, which
+draw the connection between a system’s microstates and its macroscopic material properties[78].
+Viscosity and diffusivity in particular are studied in this work and can be estimated from fluc-
+tuations in pressure and velocity, respectively. These relations are described by the equilibrium
+Green-Kubo (GK) time autocorrelation relation and its differential counterpart, the Einstein (Eins)
+formulation[25, 43]. Equation 2 presents the relation between viscosity and the off-diagonal elements
+of the pressure tensor. In Equation 3, the Einstein formulation is used to calculate the diffusivity us-
+ing the mean squared displacement (MSD) of molecules. Often, this method is chosen over the GK
+integral definition due to its relative stability and shorter time requirement for convergence[55].
+ηGK =
+V
+kBT
+� ∞
+0 ⟨Pαβ(t) · Pαβ(0)⟩dt
+(2)
+DEins = 1
+6 lim
+t→∞
+d
+dt MSD
+(3)
+Where kB is the Boltzmann constant, dα is the number of dimensions in the simulation (dα = 3 in
+this work), Pαβ is an off-diagonal element of the pressure tensor, MSD ≡ |ri(t) − ri(0)|2 is the mean
+squared displacement of molecules, and ri is the position of the ith molecule.
+This work also tests the application of the Stokes-Einstein formulation of viscosity (Eq. 5). This
+formulation utilizes the Stokes-Einstein relation for the diffusivity of spherical particles in low Re
+flow (Eq. 4) and the Einstein formulation of diffusivity described above (Eq. 3). This formulation
+benefits from the relative stability of the Einstein diffusivity formulation compared to the Green-
+Kubo viscosity, but it introduces the particle and flow assumptions of the Stokes-Einstein relation
+(Eq. 4), which may be poor assumptions here.
+D = kBT
+6πηr
+(4)
+ηSE =
+kBTdt
+πrMSD
+(5)
+Where MSD ≡ |ri(t) − ri(0)|2 is the mean squared displacement of molecules, r is molecular radius,
+and ri is the position of the ith molecule.
+7
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+3.
+Results and Discussion
+3.1.
+Equilibration
+The systems simulated in this work have been equilibrated through an extensive procedure,
+which has been introduced. This procedure entails a systematic approach to equilibration using
+successive simulations starting with the NPT ensemble and followed by the NVT ensemble and sim-
+ulating the system for long enough to identify an approach to equilibrium conditions and diffuse
+regime. This procedure takes into consideration key indicators of equilibrium including a linear
+mean squared displacement (MSD) profile, a linear root mean squared displacement (RMSD) pro-
+file, a final RMSD that is much larger than the simulation box size, a linear log-log plot of MSD vs.
+time, velocity time-autocorrelation that converges to zero, and a diffuse RMSD self-plot. Together
+these indicate a diffuse regime system from which transport properties can be calculated with in-
+creased confidence[55]. The results presented below were obtained from fully equilibrated systems
+as identified by the equilibration procedure and the key indicators above. A detailed discussion on
+the equilibration procedure and equilibrium indicators used in this work were presented elsewhere
+for similar systems[27].
+3.2.
+Transport Properties
+The dynamic viscosity of the systems simulated in this work was calculated using the Green-
+Kubo (GK) and Stokes-Einstein (SE) formulations presented above in equations 2 and 5, respectively.
+The systems were designed using three different carbon dioxide force fields (EPM2, TraPPE, and
+Zhang), as described above, and simulated across combinations of three pressures (0, 2, 3 MPag)
+and temperatures (0, 4, 8 ◦C), which span the hydrate-liquid region of the thermodynamic phase
+diagram of carbon dioxide hydrates. These are conditions that exhibit positive hydrate nucleation
+pressure driving forces, which in combination with equilibrium molecular dynamics define a pre-
+nucleation condition. In other words, carbon dioxide hydrates are thermodynamically favored to
+form under these conditions and theoretically will form if enough time is provided. The timescale of
+the simulations here is in the order of 75 nanoseconds, which is assumed to be too short for sustained
+hydrate growth.
+Figure 1 presents the results from the GK formulation of dynamic viscosity for the conditions and
+force fields examined in this work. Table 2 presents the average percentage difference between pre-
+dicted viscosity and experimentally measured values for each force field and viscosity formulation
+used. In Figure 1(a), the molecular dynamics predictions of viscosity were presented with experi-
+mental rheometry data collected elsewhere[29]. It is evident that the molecular predictions resulted
+in overestimated values compared to the experimental data in all cases (conditions and force field
+combinations). Panel (b) quantifies this discrepancy between predicted and experimental viscosity
+with the residual fractions (i.e., the percentage difference in fraction format) between these values
+for all cases. From the residual fractions, it is evident that the EPM2 and TraPPE predictions outper-
+formed the Zhang predictions in most cases. Additionally, the effect of pressure and temperature on
+the predictions is also apparent. The lowest residual fractions were associated with the atmospheric
+pressure systems, and the residuals increased with pressure for all force fields examined. Moreover,
+predictions at zero degrees celsius had a lower variance between force fields. This is likely a result
+of the phase dynamics at the lowest point in the subcooled water region examined in this work. The
+hydrogen bond interactions under these conditions are likely to be dominated by phase equilibrium
+8
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+over viscous dissipating forces.
+(a)
+(b)
+Fig. 1: The (a) Green-Kubo viscosity of carbon dioxide hydrate systems and (b) the fractional residual dif-
+ference between simulation and experimental values. Repeated simulations produced samples of each con-
+dition’s prediction value of size n = 10; these samples were bootstrapped with replacement (N = 10,000) to
+calculate mean values which are presented here. Vertical bars are standard errors from bootstrap statistics.
+Experimental (Exp) values are from previous work presented elsewhere by Guerra et al.[29]. Blue: 0 MPag,
+Orange: 2 MPag, Green: 3 MPag
+Table 2: Average percentage difference between viscosity predicted by the molecular simulations and the
+experimental measurements.
+GK, %
+SE, %
+±0.05
+±0.05
+EPM2
+61.0
+79.0
+TraPPE
+65.4
+57.2
+Zhang
+71.7
+73.2
+This work set out to examine the applicability of the SE formulation for one main reason - to
+attempt to leverage the stability of the commonly used Einstein formulation for diffusivity. The un-
+stable variations in the pressure tensor used in the formulations for viscosity make predictions less
+reliable than diffusivity, which instead uses the relatively more stable MSD. Ultimately, the formu-
+lations for viscosity require a longer simulation time to allow for the stabilization of the pressure
+tensor elements time-autocorrelations[55]. Figure 2 presents analogous results as Figure 1 above, but
+the viscosity predictions were obtained from the SE formulation of viscosity.
+Panel (a) in Figure 2 presents the dynamic viscosity predictions from each force field examined
+across the temperature-pressure conditions mentioned above and the experimental viscosity col-
+lected by a shear rheometer presented elsewhere[29]. As in the case of the GK predictions, the SE
+viscosity predictions overestimate experimental values in all conditions and all force fields (Table 2).
+Panel (b) quantifies the discrepancy between SE predictions and experimental viscosity with the
+9
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+residual fractions between these values. From the residual fractions, the SE formulation of viscosity
+resulted in an increase in variability of the predictions between the force fields. Although similar
+trends in temperature and pressure as in the GK predictions are apparent, the performance of the
+force fields varies across conditions. The EPM2 force field resulted in lower residual fractions than
+others, in most cases, but at elevated temperature and pressure, it greatly underperformed compared
+to the other force fields. Additionally, the bootstrapped predicted values exhibit greater standard
+errors (shown as vertical bars) than the GK predictions. This indicates the limitations of the Stokes-
+Einstein relation used in the SE formulation. The Stokes-Einstein relation assumption of spherical
+particles is likely too aggressive for the molecular system simulated in this work causing greater
+deviations. Provided these results, the hypothetical stability advantage of the Stokes-Einstein formu-
+lation over the GK prediction is greatly diminished by the SE assumptions, rendering it inappropriate
+for this application.
+(a)
+(b)
+Fig. 2: The (a) Stokes-Einstein viscosity of carbon dioxide hydrate systems and (b) the fractional residual
+difference between simulation and experimental values. Repeated simulations produced samples of each con-
+dition’s prediction value of size n = 10; these samples were bootstrapped with replacement (N = 10,000) to
+calculate mean values which are presented here. Vertical bars are standard errors from bootstrap statistics.
+Experimental (Exp) values are from previous work presented elsewhere by Guerra et al.[29]. Blue: 0 MPag,
+Orange: 2 MPag, Green: 3 MPag
+This study also presents in Figure 3 the calculated diffusivity of the molecular systems simulated
+here. Although we are not aware of direct experimental data that would be representative of and
+comparable to the simulated systems here, experimental data for pure water is included in Figure 3
+to offer a baseline comparison. The positive effect of temperature is evident for all force fields exam-
+ined, however, their relative performance is uncertain without experimental data. Despite the lack
+of direct experimental data for validation, the results from the dynamic viscosity analysis above can
+be used to infer the performance impact on diffusivity predictions due to the inverse proportional-
+ity between these two transport properties (Eq. 4). It is likely that the EPM2 force field and lower
+pressure conditions provide improved predictions of diffusivity, as they generally did for viscosity.
+10
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+Fig. 3: The Einstein diffusivity formulation for carbon dioxide hydrate systems. Repeated simulations pro-
+duced samples of each condition’s prediction value of size n = 10; these samples were bootstrapped with
+replacement (N = 10,000) to calculate mean values which are presented here. Vertical bars are standard errors
+from bootstrap statistics. Exp: linear regression of experimental data for water[16, 23, 32, 59, 79]. Blue: 0 MPag,
+Orange: 2 MPag, Green: 3 MPag
+3.3.
+Hydrogen Bond Analyses
+The molecular transport and interactions in aqueous systems are known to be dominated by
+hydrogen bonds (H-bonds)[51], which are a major contributor to the bulk property of dynamic
+viscosity[49, 80, 88]. H-bond librations were recently indirectly measured by quantifying the stretch
+of OH covalent bonds involved in hydrogen bonding in water through infrared absorption as a rela-
+tive measurement of viscosity[67]. Due to the role of H-bonds in the context of transport properties,
+this work has conducted several H-bond analyses to support the observations discussed above and
+further quantify the performance of the molecular systems simulated and the effect of carbon dioxide
+force field choice. In all analyses below, the geometric criteria for an H-bond were (1) donor-acceptor
+distance less than 3 ˚A, and (2) donor-hydrogen-acceptor angle greater than 150◦.
+3.3.1.
+Hydrogen Bond Structure
+This work conducted Gaussian kernel estimations of the probability density function (PDF) of
+H-bond length and angle to determine the effect of carbon dioxide force field potentials on the aver-
+age H-bond structure as a possible source of deviations of viscosity predictions when compared to
+experimental values. The simulations designed and conducted here resulted in negligible variance in
+H-bond length and angle. The average H-bond length for all force fields and temperature-pressure
+conditions was 2.75 ˚A with a variance of 1.43×10−5 ˚A. The average H-bond angle was 167.5◦ with a
+variance of 0.14◦. Figure 4 presents the PDFs for the EPM2 system simulated at 0◦C and 0 MPag with
+the most probable bond angle and length indicated by horizontal and vertical lines, respectively. This
+indicates that on average the simulated H-bond structure, as defined by the bond length and angle,
+was not affected by force field potential choice nor the temperature-pressure condition. Thus, the
+variance in viscosity predictions cannot be attributed to H-bond structure effects. The elimination of
+the H-bond structure as a piezo-viscous driving force is an important result as it significantly reduces
+the parametric space to be considered.
+11
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+Fig. 4: Surface of the probability distribution functions of hydrogen bond length and angle for the EPM2 system
+simulated at 0◦C and 0 MPag. The most probable values are indicated by the annotation and the vertical and
+horizontal lines. The colour bar indicates the fractional presence of the H-bond length and angles.
+3.3.2.
+Hydrogen Bond Lifetime
+The H-bond lifetime quantifies the average length of time that an H-bond remains intact and is
+proportional to the system’s viscous interactions. It is calculated by the autocorrelation of the binary
+states (1 or 0) of an H-bond, which indicates whether the H-bond is present (1) or not (0). Detailed de-
+scriptions of the algorithm used to quantify H-bond lifetimes have been described elsewhere[24, 52].
+This work uses the Python package MDAnalysis, which contains an implementation of the H-bond
+lifetime algorithm. MDAnalysis used the molecular trajectories from the production NVT simula-
+tions described above with an output frequency of 2 femtoseconds for a total of 20 picoseconds. The
+H-bond autocorrelation data were fit to an exponential function to determine the system’s average
+time constant for H-bond lifetimes. The results are presented in Figure 5.
+(a) EMP2
+(b) TraPPE
+(c) Zhang
+Fig. 5: The average lifetimes of hydrogen bonds in each molecular simulation conducted in this work.
+12
+
+McGill180
+0.175
+175
+0.150
+leg]l
+170
+0.125
+I bond angle,
+0.100
+165
+0.075
+160
+0.050
+H
+2.75 A
+155
+167.76 deg
+0.025
+150
+0.000
+2.5
+2.6
+2.7
+2.8
+2.9
+3.0
+H bond length, [A]MMRG, HydrateTech, & Mari´c Labs - Preprint
+The macroscopic response to positive trends in temperature and pressure is the reduction and
+increase in liquid viscosity, respectively. As previously discussed, H-bond interactions are the main
+molecular scale contributor to macroscopic dynamic viscosity. Thus, longer H-bond lifetimes are
+associated with higher viscosity, while shorter H-bond lifetimes are associated with lower viscosity.
+Based on the results presented in Figure 5, the EPM2 force field systems exhibited the molecular be-
+havior expected from macroscopic trends in temperature and pressure in terms of H-bond lifetimes,
+while TraPPE and Zhang do not. This indicates the EPM2 force field to be a better model for the
+expected molecular behavior in the context of viscosity prediction of carbon dioxide hydrate systems
+at pre-nucleation conditions.
+3.3.3.
+Hydrogen Bond Density
+The hydrogen bond density of the simulated systems was calculated and is presented in Table 3.
+The H-bond density was calculated as the average number of hydrogen bonds normalized by the to-
+tal number of molecules in the simulation. As previously discussed, the concentration of the molec-
+ular systems in this work is dictated by their thermodynamic state (temperature and pressure) and
+are described by equation 1. As a result, simulations have a varying total number of molecules to
+achieve the required concentration, and thus the hydrogen density was normalized to allow direct
+comparison between conditions. In these results, the hydrogen bond density of EPM2 systems de-
+creased with increasing temperature. As previously discussed, hydrogen bonding and viscosity are
+directly related, additionally the expected macroscopic response to increased temperature is reduced
+viscosity. Thus, the decrease in hydrogen bond density with temperature is expected at the molecu-
+lar level. This was only measured to be the case for the EPM2 systems. Moreover, the macroscopic
+response to increased pressure is increased viscosity, and the EPM2 systems also demonstrated this
+behaviour while TraPPE and Zhang systems did not. These observations offer further support to the
+H-bond lifetime analysis discussed above.
+Table 3: Hydrogen bond density for each carbon dioxide force field examined in each temperature-pressure
+condition.
+Temperature
+Pressure
+EPM2, n
+TraPPE, n
+Zhang, n
+Mean
+◦C
+MPag
+±0.0005
+±0.0005
+±0.0005
+±0.0005
+0
+0
+1.512
+1.518
+1.514
+1.515
+4
+0
+1.264
+1.505
+1.520
+1.430
+8
+0
+0.876
+1.503
+1.516
+1.298
+0
+2
+1.760
+1.488
+1.491
+1.579
+4
+2
+1.491
+1.491
+1.495
+1.492
+8
+2
+1.025
+1.492
+1.484
+1.334
+0
+3
+2.501
+1.459
+1.474
+1.811
+4
+3
+2.111
+1.468
+1.478
+1.685
+8
+3
+1.467
+1.462
+1.473
+1.467
+Notes: The numbers of hydrogen bonds presented here are normalized by the total number of molecules in each simula-
+tion:
+�
+n = NH−bonds
+Nmolecules
+�
+for direct comparison across conditions and force fields.
+13
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+4.
+Conclusions and Future Work
+This work designed molecular simulations of carbon dioxide hydrate systems at pre-nucleation
+conditions through molecular dynamics. The TIP4P/Ice force field potential was used to model wa-
+ter molecules, while three commonly accepted force fields for carbon dioxide (EPM2, TraPPE, and
+Zhang) were examined for their performance in the context of transport property predictions of hy-
+drate systems. Dynamic viscosity predicted by the molecular simulations was directly compared
+to previously collected experimental data to evaluate force field performance. Two formulations of
+viscosity were used - Green-Kubo and Stokes-Einstein. Generally, the Stokes-Einstein predictions
+suffered from high variation in predictions which likely stems from the unsuitability of the Stokes-
+Einstein assumptions for the systems simulated here. On average, the predicted viscosity for EPM2
+systems were 61% higher than experimental data, for TraPPE they were 65% higher, and for Zhang
+they were 72% higher. The EPM2 force field resulted in generally more accurate predictions of vis-
+cosity than other force fields. Diffusivity predictions were reported and their relationship viscosity
+was discussed. Experimental data for diffusivity is necessary for further validation of the simulation
+predictions.
+This work conducted a hydrogen bond analysis to examine possible molecular sources for the
+discrepancies between predicted dynamic viscosity and experimental data. The probability density
+functions of hydrogen bond length and angle were calculated to determine structural differences
+between the simulated systems. It was concluded that the molecular structure of hydrogen bonds
+did not appreciably change between simulations, indicating that hydrogen bond structure was not
+a likely source for the viscosity prediction discrepancies. The hydrogen bond lifetime analysis con-
+ducted in this work indicated that the EPM2 model exhibited trends in time constants with respect
+to temperature and pressure which were as expected by the relationship between hydrogen bond
+interaction and viscosity. Moreover, this result was supported by the normalized hydrogen density
+analysis, which indicated that the number of hydrogen bonds in EPM2 force field decreased with
+temperature while TraPPE and Zhang did not.
+The observations and conclusions from this work indicate the opportunity for a re-parametrization
+of the carbon dioxide EPM2 force field for the context of transport property predictions of pre-
+nucleation gas hydrate systems to improve its prediction accuracy. A re-parametrized force field
+may prove useful to engineering applications in process design and control of carbon capture and
+sequestration technologies that make use of computational estimates of carbon dioxide hydrate
+slurry/suspension viscosity. This work can serve as a guide for future re-parametrization efforts,
+indicating the accuracy of current force field models, parameters to be adjusted and the baseline
+experimental data that should be used. Finally, the results presented in this work offer a quantitative
+characterization and comprehensive fundamental molecular scale analysis of pre-nucleation carbon
+dioxide hydrate systems and further our understanding of the material physics of this hydrate
+precursor material.
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+URL https://doi.org/10.1021/acs.energyfuels.2c01024.
+Acknowledgments
+The authors acknowledge the support from the Digital Research Alliance of Canada, Calcul Que-
+bec, and WestGrid through computational resource grants, expertise, and technical support.
+Funding
+Financial support for the work presented here was received from the Natural Sciences and En-
+gineering Research Council of Canada (NSERC) through the Canada Graduate Scholarship Doctoral
+(CGS-D) award (A.G.), NSERC Discovery Grant number 206269 (P.S.), NSERC Discovery Grant num-
+ber 206259 (M.M), NSERC Discovery Grant number 223086 (A.D.R.), Fonds de Recherche du Qu´ebec
+Nature et technologies (FRQNT) bourse de doctorat en recherche (S.M.), from the McGill Engineering
+Doctoral Award (MEDA) (A.G. and S.M.), and the James McGill Professorship (A.D.R.).
+23
+
+McGillMMRG, HydrateTech, & Mari´c Labs - Preprint
+Supplementary Materials
+Here, we provide all supplementary materials used in our analysis.
+24
+
+McGill
\ No newline at end of file
diff --git a/LdAzT4oBgHgl3EQfyv4r/content/tmp_files/load_file.txt b/LdAzT4oBgHgl3EQfyv4r/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..54a65071f3731392a4ed85ceda36eb43f31760f4
--- /dev/null
+++ b/LdAzT4oBgHgl3EQfyv4r/content/tmp_files/load_file.txt
@@ -0,0 +1,1950 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf,len=1949
+page_content='MMRG, HydrateTech, & Mari´c Labs - Preprint  Molecular dynamics predictions of transport properties for  carbon dioxide hydrates under pre-nucleation conditions  using TIP4P/Ice water and EPM2, TraPPE, and Zhang carbon  dioxide potentials  Andr´e Guerra  , Samuel Mathews  , Jennifer Tram Su, Milan Mari´c  , Phillip Servio  ,  Alejandro D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Rey Department of Chemical Engineering, McGill University, Montr´eal, QC, Canada  (1) Introduction: New technologies that leverage gas hydrates phenomena include carbon cap-  ture and sequestrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These processes are often semi-continuous and require regulation of the  system’s flow properties for proper operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Accurate computational models for the viscosity  of carbon dioxide hydrate systems at pre-nucleation conditions can be important for process de-  sign and control of such technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' (2) Methods: This work validates the viscosity predictions  of molecular dynamics simulations using previously measured experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The TIP4P/Ice  force field was used to model water, while the EPM2, TraPPE, and Zhang force fields were used for  carbon dioxide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The Green-Kubo and Einstein formulations of viscosity and diffusivity were used  in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' (3) Results: All force fields overpredicted viscosity when compared to experimental  data, but EPM2 resulted in lower discrepancies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Additionally, EPM2 was determined to model  molecular behavior expected from the macroscopic trends in viscosity with respect to temperature  and pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' (4) Conclusions: The EPM2 force field more accurately predicted the viscosity of  carbon dioxide hydrates systems at pre-nucleation conditions relative to TraPPE and Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Introduction  Among the Arctic permafrost and the subsea sediments of Earth’s continental margins are ice-like  crystalline solids[11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' What separates these compounds from normal forms of ice (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=', hexagonal)  are gas inclusions - guest gas molecules that reside within the cavities formed by the lattice structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Known as gas hydrates, these non-stoichiometric compounds form when gaseous molecules and  water freeze at high pressures and low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Depending on these conditions, as well as the  identity of the gas molecule, hydrate properties may vary, and structurally take on one of three main  forms: sI, sII, or sH, which differ in size, structure, and number of occupancies[57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Water molecules  maintain the hydrate structure through hydrogen bonds, while the entrapped molecules provide  stability through weak van der Waals interactions[11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  In the past two decades, new technologies that utilize the formation of gas hydrates to accom-  plish a process have been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Some examples include pre- and post-combustion carbon  capture[1, 41, 50], gas separations[19, 20], transport and storage of natural gas[26, 60], and wa-  ter desalination[66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These technologies mostly leverage the high gas-to-solid volume ratio of gas  hydrates (up to 184:1), and the hydrate cages size selectivity to guest species to accomplish their  process[19, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Due to the semi-continuous nature of these new technologies and the absence of  oil emulsions in their systems, recent studies have explored the dynamic viscosity of methane and  Correspondence E-mail: alejandro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='rey@mcgill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='ca  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='01757v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='app-ph]  4 Jan 2023  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  carbon dioxide hydrate systems in aqueous systems[29, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Rheological studies of these systems  require highly specialized and expensive equipment to be conducted, in addition to difficult experi-  mental conditions to be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As a result, the use of computational methods to predict transport  properties, like dynamic viscosity and diffusivity, is desirable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Computational methods such as Density Functional Theory (DFT) and Molecular Dynamics (MD)  can provide insight into molecular structure and transport phenomena that are otherwise difficult, if  not impossible, to obtain experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' DFT is well suited for atomic-scale quantum calculations  to examine a material’s static properties, while MD is preferred for nanoscale dynamic processes  such as transport properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' However, results from computational methods are best interpreted  and utilized in combination with experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Our research group has developed an inte-  grated experimental-computational platform for investigating the material sciences of gas hydrate  systems[28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This has led to contributions in interfacial phenomena[61–63] and physical and trans-  port properties of gas hydrate systems[27, 83–86, 95, 96].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In this work, we implement the platform  to study the transport properties of carbon dioxide hydrate systems as predicted by molecular dy-  namics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' We use experimental data to validate the dynamic viscosity predictions by our models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The  experimental data is presented elsewhere[29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Molecular dynamics simulations implement molecular trajectories by integrating Newton’s equa-  tions of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Atomic interactions are mapped by force fields, which are parametrized mod-  els that represent the potential energy of an atomic system as a function of the individual atomic  positions[74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This potential energy arises from the sum of bonded and non-bonded interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Bonded forces describe how covalent bonds behave, including changes in bond length, bond angle,  and bond torsion along dihedrals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These are often modeled as harmonic oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Non-bonded  forces arise between non-covalently bonded atoms, including electrostatic Coulombic interactions  and repulsive van der Waals forces, modeled by Coulomb’s law and the Lennard-Jones 12/6 poten-  tial model, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' For simplicity, these N-body interactions are approximated as a pairwise  additive model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' By tracking how an atomic system evolves over time, MD simulations rely on sta-  tistical mechanical principles of the ensemble and the ergodic hypothesis to predict macroscopic  material properties, such as viscosity and diffusivity, from nanoscale interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Molecular simulations have been used to investigate gas hydrate systems including the  nucleation[30, 34, 37, 47, 64, 87, 90, 91, 94] and dissociation[5, 15, 17, 18, 35, 65, 77] of hydrates, the mo-  bility of guest species between cages[9, 22, 73, 82], surface effects on nucleation[6–8, 10, 48], and nucle-  ation inhibition mechanisms by poly(vinyl pyrrolidone) and poly(vinyl caprolactam)[44, 46, 54, 89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  A recent review by Qi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' [72] expands on recent advances in gas hydrate research accomplished  by the use of molecular simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  The transport properties of gas hydrate systems have not  been explored to the same extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Recently, our research has conducted molecular simulations to  model methane hydrate systems and to predict their dynamic viscosity[27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These predictions were  compared to experimental results for model validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This previous work has demonstrated the  TIP4P/Ice water model to improve the dynamic viscosity prediction of subcooled water over the  widely used TIP4P/2005[27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  The scope of this study is to examine the performance of equilibrium molecular dynamics vis-  cosity predictions of carbon dioxide hydrate system at pre-nucleation conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This is achieved  through comparison with experimental data and by conducting various hydrogen bond analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  In this work, we use the TIP4P/Ice force field potential to model water molecules, and we test the  performance of three widely accepted carbon dioxide force field potentials EPM2[31], TraPPE[71],  and Zhang[93].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The Green-Kubo and Einstein formulations are used on a rigorously equilibrated  large molecular system (5472-9072 atoms) to predict their dynamic viscosity and diffusivity, respec-  2  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Additionally, the Stokes-Einstein formulation for viscosity is introduced and its performance  is evaluated in this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Tools and Methods  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Software Packages  Molecular dynamics (MD) simulations were conducted using the Large-scale Atomic/Molecular  Massively Parallel Simulator (LAMMPS) package, an open-source code developed and maintained  by Sandia National Laboratory and Temple University[78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Atom trajectories are dynamically  tracked via the integration of Newton’s equations of motion coupled with varying interatomic  potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' When analyzed, these interacting particles serve as a predictive model for macroscopic  material properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  MD simulations in LAMMPS require an initial configuration of atoms and  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These configurations were developed using the PACKMOL[56] and Moltemplate[36]  packages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' PACKMOL is a packing optimization algorithm that places atoms according to spatial  constraints set by the user (in this work, a separation tolerance of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5 ˚A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As opposed to the standard  population commands in LAMMPS, these constraints give rise to structural complexity while reduc-  ing repulsive inter-molecular forces, effectively lessening the computational power required during  the initial part of the simulation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Moltemplate is a cross-platform molecule builder that  prepares MD systems by assigning atoms and molecules their corresponding parameters according  to the desired force field potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Atomic mass, charges, and molecule bond and angle parameters  associated with the Optimizing Potentials for Liquid Simulations All-Atom TIP4P/Ice force field  were assigned for water, while parameters associated with the Elementary Physical Model (EPM2),  Transferable Potential for Phase Equilibria (TraPPE), and Zhang force fields were assigned for car-  bon dioxide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Finally, MDAnalysis is a python library developed to handle and analyze molecular  trajectories, which was used by this work to conduct hydrogen bond analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Simulation Design  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Force Field Potentials  The Optimizing Potentials for Liquid Simulations All-Atom (OPLS-AA) force field was used to  model all water molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Compared to the coarse-grained version united-atom (UA) form, the  all-atom form represents hydrogen atoms explicitly, making it better suited for simulating gas hy-  drate systems due to the high presence of hydrogen bonding[38–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In particular, the TIP4P/Ice  four-site water model was specifically designed for estimating properties of water in its solid-state  form[2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' A recent study considering methane hydrates demonstrated that this model had improved  performance at predicting transport properties of water at low temperatures over the TIP4P/2005  model[27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Carbon dioxide was modeled using the three-site models TraPPE[71], Zhang[93], and EPM2[31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  The Zhang model is considered the best all-around performing force field potential for predicting  the transport properties of pure carbon dioxide, including thermodynamic property predictions[3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  EPM2 and TraPPE were the next best-performing force field potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The Zhang model parame-  ters were optimized to accurately predict liquid volumetric properties and phase-equilibria[93].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The  EPM2 model is an improvement on the rigid EPM model by introducing a flexible bond angle poten-  tial, which more accurately predicts the liquid-vapor coexistence curve for pure carbon dioxide[31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  3  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  Finally, the TraPPE model was developed to expand the applicability of pure-component models to  multi-component mixtures involving n-alkanes[71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  LAMMPS Input  The TIP4P/Ice water model was used to simulate all systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These systems consisted of 2976  molecules, which is one order of magnitude greater than the classic system of 256 molecules that suf-  fers from finite size effects[13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The systems were defined by the full atom style, the lj/cut/tip4p/long  pairstyle with 12 ˚A OM site and coulombic cut-off lengths, and the pppm/tip4p kspace space style  with a dimensionless relative force accuracy of 1 × 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Bond and angle styles were modeled as har-  monic, while interatomic interactions between dissimilar non-bonded atoms were calculated through  the Lorenz-Berthelot arithmetic mixing rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Three molecular representations of carbon dioxide  were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The TraPPE and Zhang models (rigid C=O bond angle) and EPM2 model (semi-flexible  C=O bond angle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Water molecule bonds and angles were kept rigid via the shake command.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This  command is not recommended to constrain angles at 180 degrees as it results in numerical solver  difficulties[78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  As a linear molecule, carbon dioxide molecules modeled by TraPPE and Zhang  had their bonds and angles kept rigid via the rigid commands, which treat all atoms in a molecule  as one moving body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' All rigid models had their bond and angle harmonic constants set to 1000  kcal/mol/rad2 to ensure rigidity during the minimization step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' To advance the molecular trajectories,  Newton’s equations of motion were numerically integrated using the Velocity Verlet algorithm with  a 2-femtosecond timestep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Table 1 details the list of parameters for the TIP4P/Ice, EPM2, TraPPE,  and Zhang force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  4  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  Table 1: Molecular force field parameters implemented in LAMMPS in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Attribute, Units  Zhang [93]  TraPPE [71]  EPM2 [31]  TIP4P/Ice [2]  O mass, g/mol  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='999  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='999  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='999  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='9994  H mass, g/mol 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='008  C mass, g/mol  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='011  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='011  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='011 O charge, e  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2944  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='35  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3256  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1794  H charge, e 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5897  C charge, e  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5888  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='6512 OH bond ro, ˚A 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='9572  CO bond ro, ˚A  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='163  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1672  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='149 OCO angle θ  180◦  180◦  180◦ HOH angle θ 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='52◦  OM distance, ˚A 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1577  H-H LJ ϵ,  kcal/mol 0  C-C LJ ϵ,  kcal/mol  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='057131  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='053477  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='055713 O-O LJ ϵ,  kcal/mol  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='163711  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='15647  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='159455  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='21084  C-C LJ σ, ˚A  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='7918  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='757 O-O LJ σ, ˚A  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='033  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1668  H-H LJ σ, ˚A 0  rc, ˚A  12  12  12  12  Notes: H: hydrogen, O: oxygen, C: carbon, O-O: oxygen-oxygen interactions, H-H: hydrogen-hydrogen interactions,  charge units in multiples of an electron charge (e), M is the massless fourth site in the TIP4P water model, rc: cutoff  distance of Coulombic and Lennard-Jones (LJ) interactions, σ: distance for zero potential energy in LJ potential, ϵ is the  depth of the LJ potential well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Carbon Dioxide Hydrate Systems  The pre-nucleation gas hydrate systems defined in this study consisted of carbon dioxide and  water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' For a binary mixture, the Gibbs phase rule imposes two degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In this study, they  were taken up by temperature and pressure, leaving the carbon dioxide liquid concentration fixed at  every condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Carbon dioxide concentrations in water at low temperatures can be described in an  analogous way as methane systems were examined by Lekvam and Bishnoi [4, 12, 42, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Here, a  modified version of Henry’s law for higher pressures is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Henry’s law has been used to describe  the liquid solubility of carbon dioxide in water for hydrate systems due to the small effect of pressure  on solubility at low temperatures[33, 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' For application in systems at higher pressures, Krichevsky  and Kasarnovsky present a modification to Henry’s law as shown in Equation 1[42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  ln  � f2  x2  �  = ln(H2,1) + ¯v∞  2 (P − PS  1 )  RT  (1)  Where for the gas species, f2 is the fugacity, x2 is its liquid concentration, and H2,1 is Henry’s law  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As well, PS  1 is the partial saturation pressure of the liquid, ¯v∞  2 is the partial molar volume  of the gas at infinite dilution, R is the gas constant, P is the pressure, and T is the temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  5  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  The fugacity of carbon dioxide in water is calculated using the Trebble-Bishnoi equation of state  (EOS)[81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As this model has been extensively studied, it will not be included here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The partial molar  volume, ¯v∞  2 , and Henry’s law constant, H2,1, for carbon dioxide are provided by Di et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' [14] and  Carroll et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='[12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Each carbon dioxide system consisted of between 1426 to 2976 molecules depending  on the liquid concentration calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Equilibration Procedure  Accurate transport property estimations require appropriately designed simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' To this end,  Maginn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' [55] present an equilibration procedure based on best practices for transport property  estimations from MD simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Molecules were randomly assigned an initial velocity based on the  Maxwell-Boltzmann distribution at the desired temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' All systems studied in this work were  then equilibrated through a series of simulations in different ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' First, the isobaric-isothermal  (NPT) ensemble was performed for 25 ns, during which the system’s potential energy and density  were monitored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Sufficient equilibration was attained when these parameters stabilized within their  expected range[2, 69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Following this step, the canonical (NVT) ensemble with the Nos´e-Hoover  thermostat was performed for 50 ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The system’s density and pressure were monitored throughout  the equilibration run to ensure no considerable deviation of the thermodynamic state of the system  from the previous NPT step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Following best practices, it is recommended to use the NVT ensemble  to estimate transport properties as opposed to the NPT ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In maintaining pressure in an  NPT ensemble, volume corrections cause disturbances to the dynamics of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Additionally,  properties such as diffusivity and viscosity that are calculated using the Green-Kubo autocorrelation  functions, are particularly sensitive to these disturbances due to their dependence on velocity and  pressure[55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Furthermore, the temperature and pressure were modulated using damping factors of  100*dt and 1000*dt, respectively, where “dt” is the simulation timestep (2 fs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These were introduced  to reduce the disturbances induced by ensemble dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Replicate Production Runs  In equilibrium molecular dynamics, the simulated systems that are referred to as ”production  runs” are equilibrated and are the systems from which property calculations can be confidently per-  formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The ideal ensemble for production runs would be the NVE, in which no barostat or ther-  mostat is implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This ensures no disturbances are introduced into the system from these  dynamic control algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' However, the use of the NVE ensemble is problematic to maintain equi-  librium conditions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=', maintaining the desired pressure-temperature condition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' For the context of  transport property estimations, previous work has shown that the estimations of viscosity and dif-  fusivity are indistinguishable between NVE and NVT systems[21, 68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As a consequence of this, this  work implements NVT production runs for transport property calculations after the conclusion of  the equilibration procedure described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  In order to reduce the effect of variability of the autocorrelation functions used to calculate viscos-  ity and diffusivity (described below) on the calculated values, this work implements bootstrap statis-  tical analysis for its production runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Once the system has been equilibrated as described above, ten  (n = 10) replicate NVT systems were created, each using a different random number generator seed  for assignment of the temperature at each pressure-temperature condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This creates a sample of  ten replicate simulations at each desired condition, all of which were simulated in LAMMPS for 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5 ns  for production run calculations to be performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' From the results of the array of systems, a statistical  6  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  bootstrap with replacement (N = 10, 000) was performed for each pressure-temperature condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Unless otherwise specified, all transport properties presented in this work are averages from the  N = 10, 000 bootstrap procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This statistical averaging takes advantage of the inverse propor-  tionality between the calculated values’ uncertainty and the number of replicates (u ∝ 1/√n)[70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Moreover, the bootstrap procedure performed here allows for the calculated values to be presented  with their standard errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Finally, the replicate simulations benefit from the computational speed  of parallel simulations versus one long simulation, which has been shown to converge to the same  value[53, 92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Viscosity and Diffusivity Formulations  Molecular dynamic simulations rely on the fundamental principles of statistical mechanics, which  draw the connection between a system’s microstates and its macroscopic material properties[78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Viscosity and diffusivity in particular are studied in this work and can be estimated from fluc-  tuations in pressure and velocity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These relations are described by the equilibrium  Green-Kubo (GK) time autocorrelation relation and its differential counterpart, the Einstein (Eins)  formulation[25, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Equation 2 presents the relation between viscosity and the off-diagonal elements  of the pressure tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In Equation 3, the Einstein formulation is used to calculate the diffusivity us-  ing the mean squared displacement (MSD) of molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Often, this method is chosen over the GK  integral definition due to its relative stability and shorter time requirement for convergence[55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  ηGK =  V  kBT  � ∞  0 ⟨Pαβ(t) · Pαβ(0)⟩dt  (2)  DEins = 1  6 lim  t→∞  d  dt MSD  (3)  Where kB is the Boltzmann constant, dα is the number of dimensions in the simulation (dα = 3 in  this work), Pαβ is an off-diagonal element of the pressure tensor, MSD ≡ |ri(t) − ri(0)|2 is the mean  squared displacement of molecules, and ri is the position of the ith molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  This work also tests the application of the Stokes-Einstein formulation of viscosity (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This  formulation utilizes the Stokes-Einstein relation for the diffusivity of spherical particles in low Re  flow (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 4) and the Einstein formulation of diffusivity described above (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This formulation  benefits from the relative stability of the Einstein diffusivity formulation compared to the Green-  Kubo viscosity, but it introduces the particle and flow assumptions of the Stokes-Einstein relation  (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 4), which may be poor assumptions here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  D = kBT  6πηr  (4)  ηSE =  kBTdt  πrMSD  (5)  Where MSD ≡ |ri(t) − ri(0)|2 is the mean squared displacement of molecules, r is molecular radius,  and ri is the position of the ith molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  7  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Results and Discussion  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Equilibration  The systems simulated in this work have been equilibrated through an extensive procedure,  which has been introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This procedure entails a systematic approach to equilibration using  successive simulations starting with the NPT ensemble and followed by the NVT ensemble and sim-  ulating the system for long enough to identify an approach to equilibrium conditions and diffuse  regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This procedure takes into consideration key indicators of equilibrium including a linear  mean squared displacement (MSD) profile, a linear root mean squared displacement (RMSD) pro-  file, a final RMSD that is much larger than the simulation box size, a linear log-log plot of MSD vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  time, velocity time-autocorrelation that converges to zero, and a diffuse RMSD self-plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Together  these indicate a diffuse regime system from which transport properties can be calculated with in-  creased confidence[55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The results presented below were obtained from fully equilibrated systems  as identified by the equilibration procedure and the key indicators above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' A detailed discussion on  the equilibration procedure and equilibrium indicators used in this work were presented elsewhere  for similar systems[27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Transport Properties  The dynamic viscosity of the systems simulated in this work was calculated using the Green-  Kubo (GK) and Stokes-Einstein (SE) formulations presented above in equations 2 and 5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  The systems were designed using three different carbon dioxide force fields (EPM2, TraPPE, and  Zhang), as described above, and simulated across combinations of three pressures (0, 2, 3 MPag)  and temperatures (0, 4, 8 ◦C), which span the hydrate-liquid region of the thermodynamic phase  diagram of carbon dioxide hydrates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These are conditions that exhibit positive hydrate nucleation  pressure driving forces, which in combination with equilibrium molecular dynamics define a pre-  nucleation condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In other words, carbon dioxide hydrates are thermodynamically favored to  form under these conditions and theoretically will form if enough time is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The timescale of  the simulations here is in the order of 75 nanoseconds, which is assumed to be too short for sustained  hydrate growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Figure 1 presents the results from the GK formulation of dynamic viscosity for the conditions and  force fields examined in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Table 2 presents the average percentage difference between pre-  dicted viscosity and experimentally measured values for each force field and viscosity formulation  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In Figure 1(a), the molecular dynamics predictions of viscosity were presented with experi-  mental rheometry data collected elsewhere[29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' It is evident that the molecular predictions resulted  in overestimated values compared to the experimental data in all cases (conditions and force field  combinations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Panel (b) quantifies this discrepancy between predicted and experimental viscosity  with the residual fractions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=', the percentage difference in fraction format) between these values  for all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' From the residual fractions, it is evident that the EPM2 and TraPPE predictions outper-  formed the Zhang predictions in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Additionally, the effect of pressure and temperature on  the predictions is also apparent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The lowest residual fractions were associated with the atmospheric  pressure systems, and the residuals increased with pressure for all force fields examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Moreover,  predictions at zero degrees celsius had a lower variance between force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This is likely a result  of the phase dynamics at the lowest point in the subcooled water region examined in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The  hydrogen bond interactions under these conditions are likely to be dominated by phase equilibrium  8  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  over viscous dissipating forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 1: The (a) Green-Kubo viscosity of carbon dioxide hydrate systems and (b) the fractional residual dif-  ference between simulation and experimental values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Repeated simulations produced samples of each con-  dition’s prediction value of size n = 10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' these samples were bootstrapped with replacement (N = 10,000) to  calculate mean values which are presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Vertical bars are standard errors from bootstrap statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Experimental (Exp) values are from previous work presented elsewhere by Guerra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='[29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Blue: 0 MPag,  Orange: 2 MPag, Green: 3 MPag  Table 2: Average percentage difference between viscosity predicted by the molecular simulations and the  experimental measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  GK, %  SE, %  ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='05  ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='05  EPM2  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='0  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='0  TraPPE  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='4  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2  Zhang  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2  This work set out to examine the applicability of the SE formulation for one main reason - to  attempt to leverage the stability of the commonly used Einstein formulation for diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The un-  stable variations in the pressure tensor used in the formulations for viscosity make predictions less  reliable than diffusivity, which instead uses the relatively more stable MSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Ultimately, the formu-  lations for viscosity require a longer simulation time to allow for the stabilization of the pressure  tensor elements time-autocorrelations[55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Figure 2 presents analogous results as Figure 1 above, but  the viscosity predictions were obtained from the SE formulation of viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Panel (a) in Figure 2 presents the dynamic viscosity predictions from each force field examined  across the temperature-pressure conditions mentioned above and the experimental viscosity col-  lected by a shear rheometer presented elsewhere[29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As in the case of the GK predictions, the SE  viscosity predictions overestimate experimental values in all conditions and all force fields (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Panel (b) quantifies the discrepancy between SE predictions and experimental viscosity with the  9  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  residual fractions between these values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' From the residual fractions, the SE formulation of viscosity  resulted in an increase in variability of the predictions between the force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Although similar  trends in temperature and pressure as in the GK predictions are apparent, the performance of the  force fields varies across conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The EPM2 force field resulted in lower residual fractions than  others, in most cases, but at elevated temperature and pressure, it greatly underperformed compared  to the other force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Additionally, the bootstrapped predicted values exhibit greater standard  errors (shown as vertical bars) than the GK predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This indicates the limitations of the Stokes-  Einstein relation used in the SE formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The Stokes-Einstein relation assumption of spherical  particles is likely too aggressive for the molecular system simulated in this work causing greater  deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Provided these results, the hypothetical stability advantage of the Stokes-Einstein formu-  lation over the GK prediction is greatly diminished by the SE assumptions, rendering it inappropriate  for this application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 2: The (a) Stokes-Einstein viscosity of carbon dioxide hydrate systems and (b) the fractional residual  difference between simulation and experimental values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Repeated simulations produced samples of each con-  dition’s prediction value of size n = 10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' these samples were bootstrapped with replacement (N = 10,000) to  calculate mean values which are presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Vertical bars are standard errors from bootstrap statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Experimental (Exp) values are from previous work presented elsewhere by Guerra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='[29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Blue: 0 MPag,  Orange: 2 MPag, Green: 3 MPag  This study also presents in Figure 3 the calculated diffusivity of the molecular systems simulated  here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Although we are not aware of direct experimental data that would be representative of and  comparable to the simulated systems here, experimental data for pure water is included in Figure 3  to offer a baseline comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The positive effect of temperature is evident for all force fields exam-  ined, however, their relative performance is uncertain without experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Despite the lack  of direct experimental data for validation, the results from the dynamic viscosity analysis above can  be used to infer the performance impact on diffusivity predictions due to the inverse proportional-  ity between these two transport properties (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' It is likely that the EPM2 force field and lower  pressure conditions provide improved predictions of diffusivity, as they generally did for viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  10  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 3: The Einstein diffusivity formulation for carbon dioxide hydrate systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Repeated simulations pro-  duced samples of each condition’s prediction value of size n = 10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' these samples were bootstrapped with  replacement (N = 10,000) to calculate mean values which are presented here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Vertical bars are standard errors  from bootstrap statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Exp: linear regression of experimental data for water[16, 23, 32, 59, 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Blue: 0 MPag,  Orange: 2 MPag, Green: 3 MPag  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Hydrogen Bond Analyses  The molecular transport and interactions in aqueous systems are known to be dominated by  hydrogen bonds (H-bonds)[51], which are a major contributor to the bulk property of dynamic  viscosity[49, 80, 88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' H-bond librations were recently indirectly measured by quantifying the stretch  of OH covalent bonds involved in hydrogen bonding in water through infrared absorption as a rela-  tive measurement of viscosity[67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Due to the role of H-bonds in the context of transport properties,  this work has conducted several H-bond analyses to support the observations discussed above and  further quantify the performance of the molecular systems simulated and the effect of carbon dioxide  force field choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In all analyses below, the geometric criteria for an H-bond were (1) donor-acceptor  distance less than 3 ˚A, and (2) donor-hydrogen-acceptor angle greater than 150◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Hydrogen Bond Structure  This work conducted Gaussian kernel estimations of the probability density function (PDF) of  H-bond length and angle to determine the effect of carbon dioxide force field potentials on the aver-  age H-bond structure as a possible source of deviations of viscosity predictions when compared to  experimental values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The simulations designed and conducted here resulted in negligible variance in  H-bond length and angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The average H-bond length for all force fields and temperature-pressure  conditions was 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='75 ˚A with a variance of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='43×10−5 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The average H-bond angle was 167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5◦ with a  variance of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='14◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Figure 4 presents the PDFs for the EPM2 system simulated at 0◦C and 0 MPag with  the most probable bond angle and length indicated by horizontal and vertical lines, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This  indicates that on average the simulated H-bond structure, as defined by the bond length and angle,  was not affected by force field potential choice nor the temperature-pressure condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Thus, the  variance in viscosity predictions cannot be attributed to H-bond structure effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The elimination of  the H-bond structure as a piezo-viscous driving force is an important result as it significantly reduces  the parametric space to be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  11  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 4: Surface of the probability distribution functions of hydrogen bond length and angle for the EPM2 system  simulated at 0◦C and 0 MPag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The most probable values are indicated by the annotation and the vertical and  horizontal lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The colour bar indicates the fractional presence of the H-bond length and angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Hydrogen Bond Lifetime  The H-bond lifetime quantifies the average length of time that an H-bond remains intact and is  proportional to the system’s viscous interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' It is calculated by the autocorrelation of the binary  states (1 or 0) of an H-bond, which indicates whether the H-bond is present (1) or not (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Detailed de-  scriptions of the algorithm used to quantify H-bond lifetimes have been described elsewhere[24, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  This work uses the Python package MDAnalysis, which contains an implementation of the H-bond  lifetime algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' MDAnalysis used the molecular trajectories from the production NVT simula-  tions described above with an output frequency of 2 femtoseconds for a total of 20 picoseconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The  H-bond autocorrelation data were fit to an exponential function to determine the system’s average  time constant for H-bond lifetimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The results are presented in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  (a) EMP2  (b) TraPPE  (c) Zhang  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' 5: The average lifetimes of hydrogen bonds in each molecular simulation conducted in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  12  McGill180  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='175  175  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='150  leg]l  170  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='125  I bond angle,  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='100  165  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='075  160  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='050  H  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='75 A  155  167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='76 deg  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='025  150  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='000  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='0  H bond length, [A]MMRG, HydrateTech, & Mari´c Labs - Preprint  The macroscopic response to positive trends in temperature and pressure is the reduction and  increase in liquid viscosity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As previously discussed, H-bond interactions are the main  molecular scale contributor to macroscopic dynamic viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Thus, longer H-bond lifetimes are  associated with higher viscosity, while shorter H-bond lifetimes are associated with lower viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Based on the results presented in Figure 5, the EPM2 force field systems exhibited the molecular be-  havior expected from macroscopic trends in temperature and pressure in terms of H-bond lifetimes,  while TraPPE and Zhang do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This indicates the EPM2 force field to be a better model for the  expected molecular behavior in the context of viscosity prediction of carbon dioxide hydrate systems  at pre-nucleation conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Hydrogen Bond Density  The hydrogen bond density of the simulated systems was calculated and is presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  The H-bond density was calculated as the average number of hydrogen bonds normalized by the to-  tal number of molecules in the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As previously discussed, the concentration of the molec-  ular systems in this work is dictated by their thermodynamic state (temperature and pressure) and  are described by equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As a result, simulations have a varying total number of molecules to  achieve the required concentration, and thus the hydrogen density was normalized to allow direct  comparison between conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' In these results, the hydrogen bond density of EPM2 systems de-  creased with increasing temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' As previously discussed, hydrogen bonding and viscosity are  directly related, additionally the expected macroscopic response to increased temperature is reduced  viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Thus, the decrease in hydrogen bond density with temperature is expected at the molecu-  lar level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This was only measured to be the case for the EPM2 systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Moreover, the macroscopic  response to increased pressure is increased viscosity, and the EPM2 systems also demonstrated this  behaviour while TraPPE and Zhang systems did not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' These observations offer further support to the  H-bond lifetime analysis discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Table 3: Hydrogen bond density for each carbon dioxide force field examined in each temperature-pressure  condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Temperature  Pressure  EPM2, n  TraPPE, n  Zhang, n  Mean  C  MPag  ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='0005  ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='0005  ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content='467  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='462  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='473  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='467  Notes: The numbers of hydrogen bonds presented here are normalized by the total number of molecules in each simula-  tion:  �  n = NH−bonds  Nmolecules  �  for direct comparison across conditions and force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  13  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Conclusions and Future Work  This work designed molecular simulations of carbon dioxide hydrate systems at pre-nucleation  conditions through molecular dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The TIP4P/Ice force field potential was used to model wa-  ter molecules, while three commonly accepted force fields for carbon dioxide (EPM2, TraPPE, and  Zhang) were examined for their performance in the context of transport property predictions of hy-  drate systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Dynamic viscosity predicted by the molecular simulations was directly compared  to previously collected experimental data to evaluate force field performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Two formulations of  viscosity were used - Green-Kubo and Stokes-Einstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Generally, the Stokes-Einstein predictions  suffered from high variation in predictions which likely stems from the unsuitability of the Stokes-  Einstein assumptions for the systems simulated here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' On average, the predicted viscosity for EPM2  systems were 61% higher than experimental data, for TraPPE they were 65% higher, and for Zhang  they were 72% higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The EPM2 force field resulted in generally more accurate predictions of vis-  cosity than other force fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Diffusivity predictions were reported and their relationship viscosity  was discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Experimental data for diffusivity is necessary for further validation of the simulation  predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  This work conducted a hydrogen bond analysis to examine possible molecular sources for the  discrepancies between predicted dynamic viscosity and experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The probability density  functions of hydrogen bond length and angle were calculated to determine structural differences  between the simulated systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' It was concluded that the molecular structure of hydrogen bonds  did not appreciably change between simulations, indicating that hydrogen bond structure was not  a likely source for the viscosity prediction discrepancies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The hydrogen bond lifetime analysis con-  ducted in this work indicated that the EPM2 model exhibited trends in time constants with respect  to temperature and pressure which were as expected by the relationship between hydrogen bond  interaction and viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Moreover, this result was supported by the normalized hydrogen density  analysis, which indicated that the number of hydrogen bonds in EPM2 force field decreased with  temperature while TraPPE and Zhang did not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  The observations and conclusions from this work indicate the opportunity for a re-parametrization  of the carbon dioxide EPM2 force field for the context of transport property predictions of pre-  nucleation gas hydrate systems to improve its prediction accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' A re-parametrized force field  may prove useful to engineering applications in process design and control of carbon capture and  sequestration technologies that make use of computational estimates of carbon dioxide hydrate  slurry/suspension viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' This work can serve as a guide for future re-parametrization efforts,  indicating the accuracy of current force field models, parameters to be adjusted and the baseline  experimental data that should be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Finally, the results presented in this work offer a quantitative  characterization and comprehensive fundamental molecular scale analysis of pre-nucleation carbon  dioxide hydrate systems and further our understanding of the material physics of this hydrate  precursor material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  References  [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Aaron and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Tsouris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Separation of co2 from flue gas: A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Separation Science and  Technology, 40:321–348, 1 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' ISSN 0149-6395.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content=' An optimized molecular potential for carbon dioxide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Journal of Chemical  Physics, 122, 6 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content=' Microcanonical molecular simulations of methane hydrate  nucleation and growth: evidence that direct nucleation to si hydrate is among the multiple  22  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  nucleation pathways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content=', 17:8870–8876, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content=' Piezo-elasticity and stability limits of monocrystal methane gas  hydrates: Atomistic-continuum characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' The Canadian Journal of Chemical Engineering,  n/a, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
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+page_content='24433.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  [96] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Rey, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Servio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Multiscale piezoelasticity of methane gas hydrates: From  bonds to cages to lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' Energy & Fuels, 0:null, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1021/acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='energyfuels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2c01024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='1021/acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='energyfuels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='2c01024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Acknowledgments  The authors acknowledge the support from the Digital Research Alliance of Canada, Calcul Que-  bec, and WestGrid through computational resource grants, expertise, and technical support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  Funding  Financial support for the work presented here was received from the Natural Sciences and En-  gineering Research Council of Canada (NSERC) through the Canada Graduate Scholarship Doctoral  (CGS-D) award (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='), NSERC Discovery Grant number 206269 (P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' ), NSERC Discovery Grant num-  ber 206259 (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='M), NSERC Discovery Grant number 223086 (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' ), Fonds de Recherche du Qu´ebec  Nature et technologies (FRQNT) bourse de doctorat en recherche (S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' ), from the McGill Engineering  Doctoral Award (MEDA) (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' ), and the James McGill Professorship (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  23  McGillMMRG, HydrateTech, & Mari´c Labs - Preprint  Supplementary Materials  Here, we provide all supplementary materials used in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
+page_content='  24  McGill' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdAzT4oBgHgl3EQfyv4r/content/2301.01757v1.pdf'}
diff --git a/QdAyT4oBgHgl3EQfU_c5/content/tmp_files/2301.00134v1.pdf.txt b/QdAyT4oBgHgl3EQfU_c5/content/tmp_files/2301.00134v1.pdf.txt
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+ 
+ 
+  
+Abstract—The Internet of Things (IoT) is a system that 
+connects physical computing devices, sensors, software, and 
+other technologies. Data can be collected, transferred, and 
+exchanged with other devices over the network without 
+requiring human interactions. One challenge the development of 
+IoT faces is the existence of anomaly data in the network. 
+Therefore, research on anomaly detection in the IoT 
+environment has become popular and necessary in recent years. 
+This survey provides an overview to understand the current 
+progress of the different anomaly detection algorithms and how 
+they can be applied in the context of the Internet of Things. In 
+this survey, we categorize the widely used anomaly detection 
+machine learning and deep learning techniques in IoT into three 
+types: clustering-based, classification-based, and deep learning-
+based. For each category, we introduce some state-of-the-art 
+anomaly detection methods and evaluate the advantages and 
+limitations of each technique. 
+I. INTRODUCTION 
+The Internet of Things (IoT) is a rapidly expanding 
+network that connects hardware, software, and devices 
+through complex interconnections, enabling data collection 
+and exchange [1]. As the number of IoT users and applications 
+grows across various sectors, new challenges arise in the 
+security and privacy of devices in the IoT network. One area 
+of study in modern IoT data analytics is detecting anomalous 
+data or outliers in data streams. Anomalous data, also known 
+as anomalies or outliers, are unusual or unexpected patterns or 
+behaviors in data that can indicate a problem or rare event. 
+Errors or rare observations can cause anomalies. Errors can 
+result from malicious attacks, compromising the entire IoT 
+network if not detected and addressed. Rare observations are 
+unusual events that may occur during the operation of the IoT 
+network and may need to be monitored or alerted. Anomaly 
+detection in the IoT is important for promptly identifying and 
+addressing problems or unusual events. For example, 
+anomalies in sensor data may indicate a malfunctioning 
+device, while anomalies in network traffic data may indicate a 
+cyber-attack. Anomaly detection can also identify unusual 
+patterns in industrial processes or detect fraud or abnormal 
+behavior in financial transactions. 
+Machine learning techniques have been widely used for 
+anomaly detection in the IoT, as they can analyze large 
+amounts of data efficiently and accurately. There are a variety 
+of machine learning techniques that have been applied to 
+anomaly detection in the IoT, including supervised learning 
+techniques, such as support vector machines (SVMs) and 
+decision trees, and unsupervised learning techniques, such as 
+ 
+ 
+clustering algorithms and autoencoders [2]-[4]. These 
+techniques can be applied to a wide range of data types, 
+including sensor data, network traffic data, and financial 
+transaction data. Identifying patterns in IoT data streams 
+through various anomaly detection techniques can be useful 
+for identifying malicious data, preventing network attacks, and 
+detecting unusual operations in the IoT environment. 
+Recently, several techniques have been commonly used for 
+anomaly detection in IoT, such as statistical-based [2], 
+proximity-based [3] or Machine Learning (ML)-based 
+approaches and Deep Learning (DL)-based [4].  
+One challenge in using machine learning for anomaly 
+detection in the IoT is the large amount of data generated by 
+IoT devices. This data can be noisy, high-dimensional, and 
+heterogeneous, making it difficult for machine learning 
+models to detect anomalies accurately. Additionally, the 
+dynamic nature of the IoT means that the data patterns and 
+relationships may change over time, requiring the machine 
+learning model to be re-trained or updated regularly. Another 
+challenge in anomaly detection in the IoT is the limited 
+availability of labeled training data. In many cases, obtaining 
+a large enough dataset containing both normal and anomalous 
+examples is challenging to train a machine-learning model 
+effectively. This can be especially problematic when abnormal 
+events are rare or hard to predict. Despite these challenges, 
+machine learning techniques have shown promise for anomaly 
+detection in the IoT. However, existing literature reviews on 
+anomaly detection in the IoT using machine learning 
+techniques often focus on a particular industrial application. 
+For example, Ghosh et al. [4] primarily focus on outlier 
+detection in wireless sensor networks, while Deorankar et al. 
+[5] provide a survey on preventing cyberattacks. This leaves a 
+research gap in providing a comprehensive overview of 
+anomaly detection in the IoT and a list of state-of-the-art 
+machine-learning techniques based on different algorithms. 
+This survey aims to address this research gap by outlining 
+the current approaches to anomaly detection in IoT data and 
+discussing the contributions and shortcomings of the presented 
+works. This includes a review of the various machine learning 
+techniques that have been applied to anomaly detection in the 
+IoT, as well as a discussion of the challenges and limitations 
+of these techniques. In this paper, we will focus on ML-based 
+and DL-based techniques because of their ability to process 
+and analyze a large amount of data. The techniques will be 
+categorized into three types: clustering-based, classification-
+Exploring the Use of Data-Driven Approaches for Anomaly 
+Detection in the Internet of Things (IoT) Environment 
+Eleonora Achiluzzi, Menglu Li, Md Fahd Al Georgy, and Rasha Kashef  
+Toronto Metropolitan University 
+{eachiluzzi, menglu.li, mgeorgy, rkashef} @ryerson.ca 
+
+ 
+ 
+based, and deep learning-based. The state-of-the-art anomaly 
+detection algorithms for each kind will be discussed.  
+The remainder of this paper is organized as follows: 
+Section 2 introduces the background of anomaly detection in 
+IoT applications using machine learning techniques. Section 3 
+presents the current clustering-based anomaly detection 
+approaches. Section 4 highlights classification-based anomaly 
+detection approaches on IoT. Section 5 presents selected deep 
+learning-based anomaly detection approaches in the literature. 
+Conclusions ad future directions are summarized in Section 6. 
+II. BACKGROUND 
+A. Anomaly Detection 
+Nonconforming patterns in big data are referred to as 
+anomalies or outliers. The procedure of discovering patterns in 
+a dataset whose behaviour is not what we predicted or 
+expected is called anomaly detection. In general, anomaly 
+refers to the outliers in a dataset, originating as part of the data 
+cleansing process. However, anomaly or outlier detection can 
+effectively detect irregular things in real-world problems, such 
+as fraud detection, intrusion or damage detection, or even 
+abnormal health condition identification [6]. Outliers can be 
+classified into three categories: global outliers, contextual 
+outliers, and collective outliers. 
+• Global outliers: A data instance can be considered a 
+global outlier if it significantly differs concerning the 
+remainder of the data set [7]. 
+• Contextual outliers: A data instance is termed a 
+contextual outlier if it is anomalous in a selected context 
+but not otherwise [7]. 
+• Collective outliers: This outlier refers to a collection of 
+related data instances classified as anomalous with 
+respect to the remainder of the data set [7]. 
+Anomalous data in a computer network could indicate a 
+hacked computer exposing sensitive data to an unauthorized 
+user [8]. Anomalies in the IoT environment may occur for two 
+major reasons: performance and security-related [8]. 
+• Performance-related anomaly: This anomaly may occur 
+due to network device malfunctions, such as sensor faults 
+or unusual operations. 
+• Security-related anomaly: This anomaly may occur due 
+to malicious IoT traffic attempting to obstruct and 
+compromise 
+a 
+targeted 
+system. 
+Security-related 
+anomalies can be organized into six categories: infection, 
+exploding, probe, cheat, traverse, and concurrency [8]. 
+Infection anomalies attempt to infect and damage a 
+targeted system employing viruses or worms. Exploding 
+anomalies attempt to deluge a system with bugs. A 
+common example of an exploding anomaly is buffer 
+overflow attacks. The third category, probe, attempts to 
+collect information to expose the vulnerabilities of the 
+targeted system, such as portmappers [8]. Cheat attacks 
+are characterized by using abnormal callers, such as 
+internet protocol or media access control spoofing [8]. 
+The fourth category, traverse, attempts to match each 
+possible key of a compromised system. A common 
+example of a traverse anomaly is brute force attacks. 
+Concurrency attacks exploit a targeted system by sending 
+identical mass requests above the system's capacities [8]. 
+Distributed Denial of Service (DDoS) and Botnet attacks 
+are common examples of concurrency attacks. 
+Anomaly detection techniques can be utilized to detect and 
+remove performance and security-related anomaly attacks in 
+the IoT environment; however, anomaly detection presents 
+challenges. Some common challenges in anomaly detection 
+techniques include managing noise data and efficiently 
+classifying normal behaviours from anomalous [9][10]. Noise 
+may contribute to misinterpreting normal and anomalous data 
+instances and must be removed before anomaly detection. The 
+distinction between normal and abnormal data instances is 
+often ambiguous and difficult to define. 
+B. Machine learning for anomaly detection 
+Machine learning (ML), as a subset of artificial 
+intelligence (AI), is a computer algorithm that can accomplish 
+tasks without being explicitly programmed [11]. Machine 
+learning builds a mathematical model based on the features of 
+the historical data, and the model gets trained and updated 
+when exposed to new sample data. After training, computer 
+programs can learn, adjust actions, and make decisions 
+automatically without human assistance. Recently, the number 
+of applications of machine learning techniques has increased 
+because they can help programmers implement computer 
+programs faster, simpler, and more accurately [12]. Especially 
+society produces overloaded data, and it is impossible to 
+process and analyze all types of data by humans. Machine 
+learning can process large amounts of data in a short time, and 
+ML can even extract the features of relevant data in disordered 
+datasets [12]. Another main advantage of machine learning is 
+that ML keeps learning from the new training data and can 
+improve and update itself if the algorithm produces 
+unexpected outputs. Machine learning techniques are widely 
+used to achieve classification, anomaly detection, and 
+prediction tasks. Face/emotion recognition [13], sentiment 
+analysis [14], and marketing recommendation systems [15] are 
+well-known applications of ML in daily life. Because of the 
+advantages of machine learning mentioned previously and the 
+characteristic of anomaly detection, which involves analyzing 
+and extracting the underlying patterns between a large amount 
+of data, Machine learning is also one of the most popular 
+techniques to detect anomalies. The ML techniques for 
+anomaly detection can be categorized into three types: 
+clustering-, classification-, and deep learning-based. 
+• Clustering-based algorithm: These algorithms apply the 
+unsupervised learning technique, which uses unlabeled 
+data to train the model. Therefore, each data point in the 
+training set is unknown whether it is normal or abnormal. 
+The main assumption for clustering-based algorithms to 
+detect anomalies is that most of the instances in the 
+dataset are normal, and normal data have some 
+characteristics in common, so the anomaly points seem 
+to be unfit for most of the dataset.  The most widely used 
+clustering-based anomaly detection techniques are K-
+mean clustering, Expectation-Maximization (EM), and 
+FindCBLOF (Cluster-based Local Outlier Factor) [16]. 
+• Classification-based 
+algorithm: 
+They 
+apply 
+the 
+supervised learning technique, which requires each data 
+
+ 
+ 
+point to have a label as “normal” or “abnormal.” The 
+labelled data are passed to a classifier for training 
+purposes. The classification-based algorithms operate 
+anomaly detection under a general assumption also, 
+which is that a classifier that can distinguish between 
+normal points and anomalies can be learned in the given 
+feature spaces [16]. Bayesian Networks and Support 
+Vector Machines are examples of classification-based 
+anomaly detection algorithms [16].   
+• Deep learning-based algorithm: These algorithms are 
+based on artificial neural networks, both supervised and 
+unsupervised learning. The neural network contains 
+multiple layers to extract higher features from the input 
+dataset. The widely used architectures for deep learning-
+based algorithms to detect outliers are Multi-Layer 
+Perceptron (MLP), Convolutional Neural Networks 
+(CNN), and Recurrent Neural Networks (RNN). 
+A summary of ML approaches for anomaly detection is 
+presented in Table 1. 
+TABLE I.  
+SUMMARY OF DIFFERENT TYPES OF MACHINE LEARNING 
+TECHNIQUES FOR ANOMALY DETECTION 
+ML 
+Technique 
+Advantage 
+Disadvantage 
+Clustering-
+based 
+• Able to operate for 
+unlabelled data. 
+• Easy to understand. 
+ 
+• Hardly 
+adapt 
+to 
+dynamic 
+network 
+environments 
+Classification-
+based 
+• Supports 
+multi-class 
+identification, 
+so 
+that 
+different types of anomalies 
+can be distinguished. 
+• The testing phase is fast 
+because the model has 
+already been pre-computed. 
+ 
+• Unavailability 
+of 
+labelled data. 
+Deep learning-
+based 
+• Can extract high levels 
+of 
+underlying 
+features 
+between training data. 
+• RNN model can analyze 
+data in real time. 
+• The computational 
+complexity is high. 
+ 
+C. IoT 
+The Internet of Things (IoT) refers to the network of 
+multipurpose devices connected to the internet. Data is 
+collected from the devices, aggregated, processed, or stored, 
+and exchanged between the devices [17]. A typical IoT system 
+may include sensors, communication interfaces, advanced 
+algorithms, and a cloud interface [17]. IoT applications are 
+useful for various disciplines, such as energy, healthcare, 
+education, and transportation. Some common applications for 
+IoT devices include but are not limited to autonomous 
+vehicles, smart contracts, and smart home appliances. The IoT 
+allows conventional devices to become intelligent and 
+autonomous [18]; however, the expanding IoT network 
+imposes new challenges as billions of new devices are 
+interconnected [17]. Identifying outliers in real-time IoT data 
+analytics is essential for the security and privacy of IoT 
+devices. The architecture of the Internet of Things contains 
+four layers, as Fig. 1 indicates, including: 
+• Sensing Layer: it is integrated with hardware, such as 
+sensors, to receive and record data [19][20]. 
+• Networking Layer: This layer provides basic networking 
+communication and data sharing over the wireless or wired 
+network infrastructure [19][20]. 
+• Service Layer: It creates and manages services, achieving 
+applications and users’ requirements [19][20]. 
+• Interface Layer: This layer allows interaction between users 
+and applications [19][20].  
+ 
+Figure 1. 
+The multi-layer architecture of IoT [19] 
+III. CLUSTERING-BASED ANOMALY DETECTION  
+Clustering is an unsupervised machine learning approach 
+that aims to group input datasets into clusters, such that the 
+objects in a cluster are similar to one another and dissimilar 
+from objects in a separate cluster. Clustering-based methods 
+are widely used for anomaly detection in IoT applications. 
+Many works have been conducted to prove the effectiveness 
+and accuracy of integrating clustering techniques to detect 
+outliers in an input dataset. For instance, Alguliyev et al. [21] 
+proposed a hybrid model to detect anomalies accurately in big 
+data by combining particle swarm optimization (PSO) and K-
+means algorithms. This work presents a novel weighted 
+clustering method, such that inter-cluster distances are 
+maximized, and intra-cluster distances are minimized [21]. 
+The proposed method eliminates the presence of predefined 
+cluster centers and many local minimum points. The proposed 
+method is only tested using one dataset, and experimental 
+results prove that it is superior to the traditional K-means 
+algorithm in performance and clustering accuracy. Clustering 
+algorithms typically require an inputted set of parameters by 
+the user. K-means clustering assumes clusters of spherical 
+shapes; therefore, Rahman et al. [22] present a novel density-
+based clustering algorithm for outlier detection that is 
+parameter independent and can cluster data of arbitrary shapes. 
+The proposed parameter-independent density-based clustering 
+(PIDC) algorithm works in two stages. The first stage 
+identifies outliers in the datasets using unique closest 
+neighbour concepts and removes the detected outliers. Then, 
+the records are passed into the second stage for density-based 
+clustering. This work is tested using six datasets, and a 
+
+Application
+Application
+Contract
+Interface
+Interface
+frontend
+API
+layer
+Servicebus
+Service
+Service
+Service
+division
+integration
+integration
+Service
+S
+Service
+repository
+E
+layer
+C
+Service bus
+U
+R
+Business logic
+Social network
+WLAN
+Network
+Mobilenetwork
+layer
+Internet
+Database
+WSN
+Datasensingacquisitionprotocols
+Sensing
+layer
+RFIDtags
+Intelligentsensors
+RFIDreaders
+BLEdevices
+WSNs 
+ 
+comparative analysis is conducted to evaluate the performance 
+of the proposed algorithm to five common clustering methods. 
+The proposed algorithm performs well on high-dimensional 
+datasets with outliers; however, it exhibits high computational 
+complexity. 
+Anomaly detection in IoT applications often includes real-
+time data requiring prompt outlier detection. The fast arrival 
+of data requires fast computation with minimal memory usage 
+[23]. In this context, Bah et al. [23] present a novel hybrid 
+model called Micro-Cluster with Minimal Probing (MCMP) 
+by combining Micro-Cluster Outlier Detection (MCOD) and 
+Thresh_LEAP methods to address these challenges. This work 
+aims to minimize the computational speed and memory 
+consumption 
+while 
+detecting 
+distance-based 
+outliers 
+accurately. Micro-clusters store neighbouring data points to 
+minimize distance-based computations [23], improving time 
+and memory consumption. The principle of minimal probing 
+from Thresh_LEAP was used for objects outside the micro-
+clusters and improved to compute the significance of inliers. 
+When the proposed algorithm is applied to large real-world 
+and synthetic datasets, it minimizes computational cost and 
+memory consumption; however, when dealing with objects 
+outside the micro-clusters, their approach misidentifies some 
+crucial outliers. 
+Cluster-based Local Outlier Factor (LOF) algorithm 
+effectively detects local outliers, however, computing the LOF 
+at each data point adds computational overhead. In addition, if 
+the K-distance neighbourhood surrounding an outlier contains 
+outliers misidentified as normal points, then the outlier may be 
+incorrectly identified as normal. Yang et al. [24] present a 
+Neighbour Entropy Local Outlier Factor (NELOF) outlier 
+detection algorithm, utilizing an improved Self-Organizing 
+Feature Map (SOFM) algorithm to cluster the dataset. The 
+improved SOFM algorithm uses the Canopy algorithm to 
+avoid the random selection of neurons and adjusts the neurons 
+dynamically. The improved SOFM algorithm proves superior 
+to the traditional SOFM algorithm, significantly decreasing the 
+number of dead neurons. Furthermore, this work replaces the 
+K-distance 
+neighbourhood 
+with 
+relative 
+K-distance 
+neighbourhoods to reduce the influence of outliers in K-
+distance neighbourhoods [24]. The proposed NELOF 
+algorithm was tested with seven different datasets and proved 
+to outperform the LOF algorithm in execution time and 
+accuracy; however, this work does not explore the 
+effectiveness of the proposed algorithm on high-dimensional 
+datasets. 
+Since anomaly detection is critical for time-sensitive IoT 
+applications that include high-dimensional data, Lyu et al. [25] 
+present a Fog-Empowered anomaly detection method using 
+hyperellipsoidal clustering (HyCARCE). Fog computing is 
+presented as an alternative to Cloud computing to provide off-
+loading for the Cloud [25]. In the Fog architecture, the end 
+nodes or sensors transmit data directly to the Fog nodes for 
+clustering and anomaly detection, improving detection 
+response and time delay by minimizing the computational 
+overhead at the sensors and the Cloud. The advantages of 
+using HyCARCE for data clustering include its ability to 
+automatically select the number of clusters and its 
+accommodating to different data distributions, such as linear 
+or hyperspherical. The proposed method is applied to two real-
+world and two synthetic datasets, and it is proven to detect 
+outliers and anomalous clusters in the dataset accurately and 
+in a timely manner. This work does not address privacy and 
+security concerns due to the exchange of information in the 
+Fog architecture. 
+A. Summary of selected algorithms 
+A summary of selected clustering-based approaches for 
+anomaly detection is presented in Table 2. 
+ 
+TABLE II.  
+SUMMARY OF SELECTED CLUSTERING-BASED ANOMALY DETECTION APPROACH ON IOT 
+Model & Year 
+Contributions 
+Limitations 
+ 
+PSO & K-means (2019) 
+[21] 
+ 
+• Combines PSO and K-means algorithms to develop a novel 
+weighted clustering method for anomaly detection. 
+• Their method eliminates the presence of predefined cluster 
+centers and multiple minimum points while improving accuracy. 
+• The proposed method is only tested for one dataset. 
+• The performance of the proposed method is only 
+compared to the traditional K-means algorithm. 
+PIDC (2018) [22] 
+• A novel density-based clustering algorithm which is parameter 
+independent can detect clusters of arbitrary shapes. 
+ 
+• High computational complexity. 
+ 
+MCMP (2019) [23] 
+ 
+• Proposes a novel MCMP approach reducing computational 
+speed and memory consumption during outlier detection. 
+• Able to compute the significance of inliers. 
+• The proposed approach misidentifies some crucial 
+outliers when dealing with objects outside the micro-
+clusters. 
+NELOF 
+& 
+SOFM 
+clustering 
+algorithm 
+(2019) [24] 
+• An improved SOFM clustering algorithm that utilizes the 
+Canopy algorithm to avoid the random selection of neurons. 
+• A relative K-distance neighbourhood to reduce the influence of 
+outliers that exist in the K-distance neighbourhood. 
+• The performance of the proposed method is only 
+compared to LOF in the analysis. 
+• Does not explore the effectiveness of the proposed 
+algorithm on high-dimensional datasets. 
+HyCARCE (2017) [25] 
+• A novel Fog-Empowered detection using HyCARCE. 
+• Sensor data is sent to the Fog nodes to reduce detection time 
+• Supports location-awareness of anomalies. 
+• Does not address privacy and security concerns from 
+information exchange in the Fog nodes. 
+ 
+
+ 
+ 
+IV. CLASSIFICATION-BASED ANOMALY DETECTION  
+In machine learning, there are many techniques that we can 
+use to classify things. In a typical classification-based 
+problem, there is a balanced number of positives and negatives 
+in the dataset. So, we train the model on a balanced number of 
+positives and negatives. In anomaly detection problems, there 
+are fewer positive examples than negative ones. The positive 
+examples (anomalous data) might be lesser than 5% of the total 
+data. The main task of classification is to identify the category 
+or class label of new instances from a data set. Classifying the 
+algorithm, called a classifier, depends on the learning from a 
+training dataset. The training dataset contains data that is 
+correctly classified into accurate class labels. Similarly, for 
+anomaly detection, classification algorithms will try to classify 
+data into two broad categories – normal and abnormal. Some 
+common classification techniques for detecting anomalies are 
+discussed below: 
+• Classification Tree: It is like a tree pattern graph, also 
+known as a prediction model or decision tree. The internal 
+nodes are called test properties, each branch signifies the test 
+results, and the final leaves indicate the class to which the test 
+data belongs. The two most used algorithms are ID3 and C4.5 
+[26]. Classification tree approaches, when compared to naïve 
+Bayes classification, the result obtained from decision trees 
+was found to be more accurate [27]. 
+• Support Vector Machine (SVM): SVM is popular in 
+recognizing patterns and is widely used in intrusion detection 
+systems. “When compared to neural networks in the KDD cup 
+data set, it was found that SVM outperformed NN in terms of 
+false alarm rate and accuracy in most attacks” [28]. 
+• Naïve Bayes network: To take benefit of the structural 
+connection between the random variables, we can use a 
+probabilistic graph model - Naïve Bayesian Networks. The 
+model delivers a solution to the question if only a limited 
+number of observed events are known, then what is the 
+likelihood of a specific kind of attack. Let's compare the 
+decision tree and Bayesian techniques, although the precision 
+of the decision tree is far better. The computational time of the 
+Bayesian network is found to be low [27]. 
+• Genetic Algorithm: Genetic Algorithm (GA) was first 
+introduced in the computational biology field. However, the 
+GA is applied for intrusion detection to develop a set of 
+classification rubrics from the network audit data. The 
+substantial properties of GA are its strength against noise and 
+self-learning competencies [29].  
+• HADES- IoT is a novel host-based anomaly detection and 
+prevention approach. The model is based on whitelisting 
+legitimate processes on an IoT device. The notion of this 
+method is that simple programs that are recognized to run on 
+an “uninfected” off-the-shelf device are allowed to run. To 
+build a whitelist of benign programs, profiling must be 
+performed once for each device. The devices with enabled 
+Telnet service by default (e.g., SimpleHome IP camera) are 
+potentially vulnerable to Mirai” [30]. In the proposed model 
+(HADES-IoT), even such a default misconfiguration does not 
+cause harm since the execution of any unauthorized binary is 
+terminated upon its spawning. 
+A. Summary of selected algorithms 
+A summary of selected classification-based approaches for 
+anomaly detection is presented in Table 3. 
+V. DEEP LEARNING-BASED ANOMALY DETECTION  
+Deep learning, based on artificial neural networks to 
+process data, has demonstrated its ability to extract features 
+and high accuracy for classification tasks. Therefore, applying 
+deep learning-based algorithms on the Internet of Things 
+environment to detect anomalies is also popular. Several 
+selected deep learning-based algorithms are elaborated on in 
+the following literature. One of the common examples of 
+detecting anomalies in the IoT is detecting network attacks. 
+Some network intrusion detection systems (NIDS) have 
+problems with adaptation to dynamic network environments, 
+unavailability of labelled data, and high false-positive rates. 
+Therefore, Van et al. [36] proposed using deep learning 
+algorithms to implement network intrusion detection systems. 
+Two types of deep learning models are mentioned in their 
+paper: the Restricted Boltzmann Machines (RBM) and 
+Autoencoder (AE). The authors constructed a stacked RBM 
+and AE as two Deep Belief Network (DBN) structures and 
+compared their performance on detection intrusion. For the 
+stacked RBM, which uses a probability distribution, the hidden 
+layer of each RBM is set to be the input layer of the next RBM 
+of the stack. The stacked AE can extract features of network 
+data by unsupervised learning so that it can solve the challenge 
+of the unavailability of labelled data. For the experiment, Van 
+et al. [36] used the same dataset that contains four types of 
+network attacks to test the ability of two DBM models. The 
+results show the Stacked AE outperforms the Stacked RBM on 
+the accuracy of intrusion detection; however, the training time 
+and execution time of the stacked RBM are much longer than 
+the Stacked AE model. Almiani et al. [37] proposed a deep 
+learning-based intrusion detection system in the IoT 
+environment. Their model contains two major components: 
+the traffic analysis engine and the classification engine. The 
+traffic analysis engine is used to pre-process the traffic data, 
+such as symbolic-to-numeric transformation, feature reduction 
+and normalization. Then, the processed data is fed into the 
+classification engine, which adopts two deep recurrent neural 
+networks (RNN) to respond fast in a real-time environment. 
+The two RNN work as two filters of attack detection. The 
+traffic data classified as normal by the first RNN layer will be 
+passed to the second RNN detection layer to identify whether 
+it is an anomaly. The same dataset is used to train the two 
+layers of RNN. The only difference is the training set for the 
+first RNN contains both normal and abnormal data, while the 
+training set for the second RNN only has normal traffic data.  
+Almiani et al. [37] compare their proposed model with other 
+baseline models for anomaly detection accuracy and execution 
+time, which indicates the proposed RNN model has a high 
+sensitivity to detect abnormal attacks in a competitive 
+computational overhead. The scalability and distribution of 
+resources are the characteristics of the Internet of Things. 
+Therefore, any anomaly detection model that depends on a 
+centralized cloud will fail to handle the IoT requirements [38]. 
+ 
+ 
+
+ 
+ 
+TABLE III.  
+SUMMARY OF SELECTED CLASSIFICATION-BASED ANOMALY DETECTION APPROACH ON IOT 
+Model & 
+Year 
+Contributions 
+Limitations 
+Naive Bayes 
++ decision 
+Tree 
+(2010) 
+[31] 
+• The model performs balance detections and keeps false positives 
+at an acceptable limit for different network attacks. 
+• The method minimized the rate of false positives and maximized 
+balanced detection rates. [28] 
+• The model requires much improvement in detecting false 
+positives to remote-to-user attacks. 
+HADES-IOT 
+(2019) [30] 
+• The generic model can be easily adapted to any Linux kernel 
+version. The method is said to be resilient against attackers and 
+focused on disabling its protection mechanisms. 
+• HADES-IoT terminates any executable not included in the 
+whitelist both of them upon its execution and stops the attack. 
+ 
+• Researchers initially utilized features provided by Linux, such 
+as KProbe1 or inotify. After examining several IoT devices (D-
+Link IP Camera, SimpleHome IP camera), they found that these 
+features are not supported. 
+• As the challenge is to distinguish unidentified processes in 
+real-time right after their spawning, the Linux process scheduler 
+is another limiting factor. 
+• The model is based on the whitelisting approach. This may be 
+viewed as impractical because some benign programs may be 
+missed during profiling. 
+One Class and 
+Two Class 
+SVM 
+(2012) [32] 
+• The first-class SVM is used for detecting abnormality scores. 
+Secondly, the detector is retrained when certain new data records are 
+included in the existing dataset. 
+• A prior failure history is not required, and the model continually 
+learns from the observed failure events. 
+• It has no performance measure of computational complexity. 
+DT + SVM 
+(2007) [33] 
+• The data set is first passed through the tree, and node information 
+is generated and passed along with the original set of attributes 
+through SVM to obtain the final output. [30] 
+• This approach delivers equivalent results to SVM. 
+Ensemble 
+approach [33] 
+• To make the final decision, information is combined from 
+different individual classifiers.  
+• Provided the best performance for Probe and R2L classes. 
+• Selecting base classifiers is critical and cannot be done 
+automatically. 
+k-Means 
++ID3 (2010) 
+[34] 
+• Proposed a hybrid technique which combines clustering and 
+classification.  
+• The K-mean clustering can be applied to the normal training data 
+points to form clusters. Then the decision tree will be performed on 
+each cluster. 
+• The proposed algorithm outperforms the individual k-Means and 
+the ID3 method. 
+• This approach is limited to a specific dataset. 
+k-Medoids 
++Naïve Bayes 
+(2012) [35] 
+• Similar data instances are grouped by using the k- Medoids 
+clustering technique. 
+• It can increase detection accuracy rate and reduction in false 
+alarm rates. 
+• It is challenging to predict naïve Bayes classifiers in different 
+settings. 
+SVM 
++ 
+k-
+medoids 
+(2012)[35] 
+• Proposed a hybrid technique which combines k-medoids 
+clustering and SVM classification.  
+• The proposed anomaly detection technique reaches a higher 
+accuracy than the baseline algorithms. [32] 
+• Time complexity is more when the dataset is very large. 
+N.g. et al. [38] proposed Vector Convolutional Deep Learning 
+(VCDL) model to detect anomalies in IoT traffic, which 
+applies an emerging distributed intelligence approach called 
+“fog computing.” The proposed model contains three layers of 
+components. The first layer is IoT devices which are 
+distributed. The second layer is the fog layer—multiple work 
+fog nodes connected to the IoT devices and train each VCDL 
+model in a distributed manner. The master fog node in the fog 
+layer will collect and share the best set of parameters with the 
+worker nodes. Therefore, the traffic data will be fed into the 
+corresponding worker node and be classified as either normal 
+or attack. The classification result will be passed to the cloud 
+layer, the third layer of the proposed framework. The cloud 
+layer is used to validate the information from the entire fog 
+layer. The experiment results indicate that the proposed 
+distributed VCDL framework can detect anomaly traffic data 
+with high accuracy and less detection time than the centralized 
+detection model.   
+The IoT system always involves real-time data or time-
+series data. Therefore, several pieces of research focus on 
+detecting anomalies in time series data collected by IoT 
+devices. For example, Liu et al. [39] worked on detecting 
+outlier data in the indoor climate control system. There are two 
+kinds of anomalies: point anomaly, which indicates a single 
+outlier value hugely different from other data, and contextual 
+anomaly, which refers to a series of inappropriate data points. 
+Liu et al. [39] proposed a neural network-based model to detect 
+these two kinds of anomalies, which combines the autoencoder 
+(AE) and the long short-term memory (LSTM) model. The 
+structure of AE is similar to the regular Feed Forward Neural 
+Network with a reduced number of neurons in hidden layers 
+so that the output of the AE can be very close to the input. The 
+LSTM model can extract features of sequential data and 
+capture the relationship between neighbouring input data [39]. 
+Therefore, the AE component in the proposed model works to 
+detect point anomalies, while the LSTM component detects 
+the contextual anomaly. The proposed model demonstrated the 
+accuracy of the anomaly detection algorithm could be 
+improved by integrating the neural network models. 
+
+ 
+ 
+A. Summary of selected algorithms 
+A summary of selected deep learning-based approaches for 
+anomaly detection on IoT is presented in Table 4, which 
+includes the contributions and drawbacks of each algorithm. 
+VI. CONCLUSION AND FUTURE DIRECTIONS 
+The Internet of Things (IoT) has recently become popular as 
+a system connecting physical hardware, such as computing 
+devices, sensors, and other technologies. Over the IoT 
+network, data can be collected, transferred, and exchanged 
+with other devices without requiring human interactions, and 
+it always involves processing and analyzing a massive 
+amount of data. Therefore, the security and operation status 
+of the IoT network is important, and it is essential to detect 
+any unusual behaviours known as anomalies. The anomaly in 
+the IoT environment can be categorized as performance-
+related or security-related. The performance-related anomaly 
+can be represented as sensor faults or unusual events. The 
+security-related anomaly is usually caused by malicious 
+attacks. In this paper, we provided a survey on the state-of-
+the-art anomaly detection algorithms in the IoT environment 
+using machine learning techniques because machine learning 
+technology has a strong ability to deal with the big data 
+involved in the IoT. We categorize the machine learning-
+related algorithms to detect anomalies into three types: 
+clustering-based, classification-based, and deep learning-
+based. For each detection algorithm, we select a significant 
+number of research papers, discuss the advantages of the 
+chosen method, and mention each existing method's 
+limitations. We also notice that although much work has been 
+done through independent algorithms, deploying hybrid 
+approaches can provide better results and overcome the 
+shortcoming of one method over the other. We believe that 
+this survey paper provides an in-depth knowledge of these 
+commonly used approaches and will help make decisions on 
+choosing a particular technique for an anomaly detection 
+problem in the IoT environment. Future direction involves the 
+use of multi-level learning [41], semantic learning [42], 
+ensemble learning [43], hybrid learning [44], and distributed 
+computing [45]-[46] for anomaly detection.  
+TABLE IV.  
+SUMMARY OF SELECTED DEEP LEARNING-BASED ANOMALY DETECTION APPROACH ON IOT 
+Model & Year 
+Contributions 
+Limitations 
+DBN (2017) [36] 
+• Gives two examples of deep learning-based models for 
+anomaly detection. 
+• Provides comparisons in anomaly detection accuracy 
+and computational performance for the two selected 
+models. 
+• Does not choose a non-deep learning-based anomaly 
+detection model as the baseline to demonstrate the ability of deep 
+learning.  
+• The types of intrusions that the proposed models can detect 
+are limited. 
+2-RNN (2020) [37] 
+• Proposed a two-layer RNN model to increase the 
+anomaly detection accuracy on a challenging dataset. 
+• The proposed model can effectively detect in real-time 
+environments with a competitive computational overhead. 
+ 
+• Only apply a sample dataset in the experiment to test the 
+effectiveness of the proposed model. 
+VCDL (2020) [38] 
+• Trains the Vector Convolutional Deep Learning model 
+in a distributed manner. 
+• Able to detect the anomaly traffic in parallel. 
+• Achieve detection performance with high accuracy. 
+• Only applies a sample dataset in the experiment to test the 
+effectiveness of the proposed model. 
+• The model does not work for detecting multiclass anomalies. 
+AE-LSTM (2020) [39] 
+• Integrates two types of neural network models to detect 
+different types of anomalies. 
+• The proposed anomaly detection algorithm can be 
+performed in a real-time situation. 
+• They may not be able to detect anomalies with different 
+patterns. 
+• It has no performance measure of computational complexity. 
+CNN-based monitoring 
+detection (2019) [40] 
+• Proposed two CNN-based models to detect two types of 
+abnormal situations in the operating environment of power 
+equipment. 
+• It outperforms the traditional CNN network for 
+detecting personnel or fire smoke in images. 
+• The purpose of the anomaly detection algorithm is very 
+specific. The model cannot detect other abnormal cases in the 
+operating environment. 
+• In the experiment, only images are used for testing. The 
+ability of anomaly detection on video is not proven. 
+ 
+REFERENCES 
+[1] B. Farahani, F. Firouzi, V. Chang, M. Badaroglu, N. Constant, and K. 
+Mankodiya, "Towards Fog-Driven IoT eHealth: Promises and 
+Challenges of IoT in Medicine and Healthcare," Future Generation 
+Computer Systems, vol. 78, 2018, pp. 659-676. 
+[2] N. Nesa, T. Ghosh and I. Banerjee, "Outlier detection in sensed data 
+using statistical learning models for IoT," in 2018 IEEE Wireless 
+Communications and Networking Conference (WCNC), Barcelona, 
+2018, pp. 1-6, doi: 10.1109/WCNC.2018.8376988. 
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+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf,len=733
+page_content='Abstract—The Internet of Things (IoT) is a system that  connects physical computing devices, sensors, software, and  other technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Data can be collected, transferred, and  exchanged with other devices over the network without  requiring human interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' One challenge the development of  IoT faces is the existence of anomaly data in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Therefore, research on anomaly detection in the IoT  environment has become popular and necessary in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  This survey provides an overview to understand the current  progress of the different anomaly detection algorithms and how  they can be applied in the context of the Internet of Things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In  this survey, we categorize the widely used anomaly detection  machine learning and deep learning techniques in IoT into three  types: clustering-based, classification-based, and deep learning-  based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' For each category, we introduce some state-of-the-art  anomaly detection methods and evaluate the advantages and  limitations of each technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' INTRODUCTION  The Internet of Things (IoT) is a rapidly expanding  network that connects hardware, software, and devices  through complex interconnections, enabling data collection  and exchange [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' As the number of IoT users and applications  grows across various sectors, new challenges arise in the  security and privacy of devices in the IoT network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' One area  of study in modern IoT data analytics is detecting anomalous  data or outliers in data streams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Anomalous data, also known  as anomalies or outliers, are unusual or unexpected patterns or  behaviors in data that can indicate a problem or rare event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Errors or rare observations can cause anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Errors can  result from malicious attacks, compromising the entire IoT  network if not detected and addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Rare observations are  unusual events that may occur during the operation of the IoT  network and may need to be monitored or alerted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Anomaly  detection in the IoT is important for promptly identifying and  addressing problems or unusual events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' For example,  anomalies in sensor data may indicate a malfunctioning  device, while anomalies in network traffic data may indicate a  cyber-attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Anomaly detection can also identify unusual  patterns in industrial processes or detect fraud or abnormal  behavior in financial transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Machine learning techniques have been widely used for  anomaly detection in the IoT, as they can analyze large  amounts of data efficiently and accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' There are a variety  of machine learning techniques that have been applied to  anomaly detection in the IoT, including supervised learning  techniques, such as support vector machines (SVMs) and  decision trees, and unsupervised learning techniques, such as  clustering algorithms and autoencoders [2]-[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' These  techniques can be applied to a wide range of data types,  including sensor data, network traffic data, and financial  transaction data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Identifying patterns in IoT data streams  through various anomaly detection techniques can be useful  for identifying malicious data, preventing network attacks, and  detecting unusual operations in the IoT environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Recently, several techniques have been commonly used for  anomaly detection in IoT, such as statistical-based [2],  proximity-based [3] or Machine Learning (ML)-based  approaches and Deep Learning (DL)-based [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  One challenge in using machine learning for anomaly  detection in the IoT is the large amount of data generated by  IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This data can be noisy, high-dimensional, and  heterogeneous, making it difficult for machine learning  models to detect anomalies accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Additionally, the  dynamic nature of the IoT means that the data patterns and  relationships may change over time, requiring the machine  learning model to be re-trained or updated regularly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Another  challenge in anomaly detection in the IoT is the limited  availability of labeled training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In many cases, obtaining  a large enough dataset containing both normal and anomalous  examples is challenging to train a machine-learning model  effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This can be especially problematic when abnormal  events are rare or hard to predict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Despite these challenges,  machine learning techniques have shown promise for anomaly  detection in the IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' However, existing literature reviews on  anomaly detection in the IoT using machine learning  techniques often focus on a particular industrial application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  For example, Ghosh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [4] primarily focus on outlier  detection in wireless sensor networks, while Deorankar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  [5] provide a survey on preventing cyberattacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This leaves a  research gap in providing a comprehensive overview of  anomaly detection in the IoT and a list of state-of-the-art  machine-learning techniques based on different algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  This survey aims to address this research gap by outlining  the current approaches to anomaly detection in IoT data and  discussing the contributions and shortcomings of the presented  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This includes a review of the various machine learning  techniques that have been applied to anomaly detection in the  IoT, as well as a discussion of the challenges and limitations  of these techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In this paper, we will focus on ML-based  and DL-based techniques because of their ability to process  and analyze a large amount of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The techniques will be  categorized into three types: clustering-based, classification-  Exploring the Use of Data-Driven Approaches for Anomaly  Detection in the Internet of Things (IoT) Environment  Eleonora Achiluzzi, Menglu Li, Md Fahd Al Georgy, and Rasha Kashef  Toronto Metropolitan University  {eachiluzzi, menglu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='li, mgeorgy, rkashef} @ryerson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='ca  based, and deep learning-based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The state-of-the-art anomaly  detection algorithms for each kind will be discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The remainder of this paper is organized as follows:  Section 2 introduces the background of anomaly detection in  IoT applications using machine learning techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Section 3  presents the current clustering-based anomaly detection  approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Section 4 highlights classification-based anomaly  detection approaches on IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Section 5 presents selected deep  learning-based anomaly detection approaches in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Conclusions ad future directions are summarized in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' BACKGROUND  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Anomaly Detection  Nonconforming patterns in big data are referred to as  anomalies or outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The procedure of discovering patterns in  a dataset whose behaviour is not what we predicted or  expected is called anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In general, anomaly  refers to the outliers in a dataset, originating as part of the data  cleansing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' However, anomaly or outlier detection can  effectively detect irregular things in real-world problems, such  as fraud detection, intrusion or damage detection, or even  abnormal health condition identification [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Outliers can be  classified into three categories: global outliers, contextual  outliers, and collective outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Global outliers: A data instance can be considered a  global outlier if it significantly differs concerning the  remainder of the data set [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Contextual outliers: A data instance is termed a  contextual outlier if it is anomalous in a selected context  but not otherwise [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Collective outliers: This outlier refers to a collection of  related data instances classified as anomalous with  respect to the remainder of the data set [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Anomalous data in a computer network could indicate a  hacked computer exposing sensitive data to an unauthorized  user [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Anomalies in the IoT environment may occur for two  major reasons: performance and security-related [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Performance-related anomaly: This anomaly may occur  due to network device malfunctions, such as sensor faults  or unusual operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Security-related anomaly: This anomaly may occur due  to malicious IoT traffic attempting to obstruct and  compromise  a  targeted  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Security-related  anomalies can be organized into six categories: infection,  exploding, probe, cheat, traverse, and concurrency [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Infection anomalies attempt to infect and damage a  targeted system employing viruses or worms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Exploding  anomalies attempt to deluge a system with bugs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' A  common example of an exploding anomaly is buffer  overflow attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The third category, probe, attempts to  collect information to expose the vulnerabilities of the  targeted system, such as portmappers [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Cheat attacks  are characterized by using abnormal callers, such as  internet protocol or media access control spoofing [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The fourth category, traverse, attempts to match each  possible key of a compromised system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' A common  example of a traverse anomaly is brute force attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content="  Concurrency attacks exploit a targeted system by sending  identical mass requests above the system's capacities [8]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Distributed Denial of Service (DDoS) and Botnet attacks  are common examples of concurrency attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Anomaly detection techniques can be utilized to detect and  remove performance and security-related anomaly attacks in  the IoT environment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' however, anomaly detection presents  challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Some common challenges in anomaly detection  techniques include managing noise data and efficiently  classifying normal behaviours from anomalous [9][10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Noise  may contribute to misinterpreting normal and anomalous data  instances and must be removed before anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  distinction between normal and abnormal data instances is  often ambiguous and difficult to define.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Machine learning for anomaly detection  Machine learning (ML), as a subset of artificial  intelligence (AI), is a computer algorithm that can accomplish  tasks without being explicitly programmed [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Machine  learning builds a mathematical model based on the features of  the historical data, and the model gets trained and updated  when exposed to new sample data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' After training, computer  programs can learn, adjust actions, and make decisions  automatically without human assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Recently, the number  of applications of machine learning techniques has increased  because they can help programmers implement computer  programs faster, simpler, and more accurately [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Especially  society produces overloaded data, and it is impossible to  process and analyze all types of data by humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Machine  learning can process large amounts of data in a short time, and  ML can even extract the features of relevant data in disordered  datasets [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Another main advantage of machine learning is  that ML keeps learning from the new training data and can  improve and update itself if the algorithm produces  unexpected outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Machine learning techniques are widely  used to achieve classification, anomaly detection, and  prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Face/emotion recognition [13], sentiment  analysis [14], and marketing recommendation systems [15] are  well-known applications of ML in daily life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Because of the  advantages of machine learning mentioned previously and the  characteristic of anomaly detection, which involves analyzing  and extracting the underlying patterns between a large amount  of data, Machine learning is also one of the most popular  techniques to detect anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The ML techniques for  anomaly detection can be categorized into three types:  clustering-, classification-, and deep learning-based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Clustering-based algorithm: These algorithms apply the  unsupervised learning technique, which uses unlabeled  data to train the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Therefore, each data point in the  training set is unknown whether it is normal or abnormal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The main assumption for clustering-based algorithms to  detect anomalies is that most of the instances in the  dataset are normal, and normal data have some  characteristics in common, so the anomaly points seem  to be unfit for most of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The most widely used  clustering-based anomaly detection techniques are K-  mean clustering, Expectation-Maximization (EM), and  FindCBLOF (Cluster-based Local Outlier Factor) [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Classification-based  algorithm:  They  apply  the  supervised learning technique, which requires each data  point to have a label as “normal” or “abnormal.” The  labelled data are passed to a classifier for training  purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The classification-based algorithms operate  anomaly detection under a general assumption also,  which is that a classifier that can distinguish between  normal points and anomalies can be learned in the given  feature spaces [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Bayesian Networks and Support  Vector Machines are examples of classification-based  anomaly detection algorithms [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Deep learning-based algorithm: These algorithms are  based on artificial neural networks, both supervised and  unsupervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The neural network contains  multiple layers to extract higher features from the input  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The widely used architectures for deep learning-  based algorithms to detect outliers are Multi-Layer  Perceptron (MLP), Convolutional Neural Networks  (CNN), and Recurrent Neural Networks (RNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  A summary of ML approaches for anomaly detection is  presented in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  SUMMARY OF DIFFERENT TYPES OF MACHINE LEARNING  TECHNIQUES FOR ANOMALY DETECTION  ML  Technique  Advantage  Disadvantage  Clustering-  based  Able to operate for  unlabelled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Easy to understand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Hardly  adapt  to  dynamic  network  environments  Classification-  based  Supports  multi-class  identification,  so  that  different types of anomalies  can be distinguished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The testing phase is fast  because the model has  already been pre-computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Unavailability  of  labelled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Deep learning-  based  Can extract high levels  of  underlying  features  between training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  RNN model can analyze  data in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The computational  complexity is high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' IoT  The Internet of Things (IoT) refers to the network of  multipurpose devices connected to the internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Data is  collected from the devices, aggregated, processed, or stored,  and exchanged between the devices [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' A typical IoT system  may include sensors, communication interfaces, advanced  algorithms, and a cloud interface [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' IoT applications are  useful for various disciplines, such as energy, healthcare,  education, and transportation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Some common applications for  IoT devices include but are not limited to autonomous  vehicles, smart contracts, and smart home appliances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The IoT  allows conventional devices to become intelligent and  autonomous [18];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' however, the expanding IoT network  imposes new challenges as billions of new devices are  interconnected [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Identifying outliers in real-time IoT data  analytics is essential for the security and privacy of IoT  devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The architecture of the Internet of Things contains  four layers, as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' 1 indicates, including:  Sensing Layer: it is integrated with hardware, such as  sensors, to receive and record data [19][20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Networking Layer: This layer provides basic networking  communication and data sharing over the wireless or wired  network infrastructure [19][20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Service Layer: It creates and manages services, achieving  applications and users’ requirements [19][20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Interface Layer: This layer allows interaction between users  and applications [19][20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The multi-layer architecture of IoT [19]  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' CLUSTERING-BASED ANOMALY DETECTION  Clustering is an unsupervised machine learning approach  that aims to group input datasets into clusters, such that the  objects in a cluster are similar to one another and dissimilar  from objects in a separate cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Clustering-based methods  are widely used for anomaly detection in IoT applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Many works have been conducted to prove the effectiveness  and accuracy of integrating clustering techniques to detect  outliers in an input dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' For instance, Alguliyev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [21]  proposed a hybrid model to detect anomalies accurately in big  data by combining particle swarm optimization (PSO) and K-  means algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This work presents a novel weighted  clustering method, such that inter-cluster distances are  maximized, and intra-cluster distances are minimized [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed method eliminates the presence of predefined  cluster centers and many local minimum points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The proposed  method is only tested using one dataset, and experimental  results prove that it is superior to the traditional K-means  algorithm in performance and clustering accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Clustering  algorithms typically require an inputted set of parameters by  the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' K-means clustering assumes clusters of spherical  shapes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' therefore, Rahman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [22] present a novel density-  based clustering algorithm for outlier detection that is  parameter independent and can cluster data of arbitrary shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed parameter-independent density-based clustering  (PIDC) algorithm works in two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The first stage  identifies outliers in the datasets using unique closest  neighbour concepts and removes the detected outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Then,  the records are passed into the second stage for density-based  clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This work is tested using six datasets,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' and a  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Application  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Application  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Contract  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Interface  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Interface  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='frontend  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='API  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='layer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Servicebus  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Service  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Service  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
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+page_content='RFIDtags  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='Intelligentsensors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='RFIDreaders  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='BLEdevices  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='WSNs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='comparative analysis is conducted to evaluate the performance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='of the proposed algorithm to five common clustering methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed algorithm performs well on high-dimensional  datasets with outliers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' however, it exhibits high computational  complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Anomaly detection in IoT applications often includes real-  time data requiring prompt outlier detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The fast arrival  of data requires fast computation with minimal memory usage  [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In this context, Bah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [23] present a novel hybrid  model called Micro-Cluster with Minimal Probing (MCMP)  by combining Micro-Cluster Outlier Detection (MCOD) and  Thresh_LEAP methods to address these challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This work  aims to minimize the computational speed and memory  consumption  while  detecting  distance-based  outliers  accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Micro-clusters store neighbouring data points to  minimize distance-based computations [23], improving time  and memory consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The principle of minimal probing  from Thresh_LEAP was used for objects outside the micro-  clusters and improved to compute the significance of inliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  When the proposed algorithm is applied to large real-world  and synthetic datasets, it minimizes computational cost and  memory consumption;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' however, when dealing with objects  outside the micro-clusters, their approach misidentifies some  crucial outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Cluster-based Local Outlier Factor (LOF) algorithm  effectively detects local outliers, however, computing the LOF  at each data point adds computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In addition, if  the K-distance neighbourhood surrounding an outlier contains  outliers misidentified as normal points, then the outlier may be  incorrectly identified as normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [24] present a  Neighbour Entropy Local Outlier Factor (NELOF) outlier  detection algorithm, utilizing an improved Self-Organizing  Feature Map (SOFM) algorithm to cluster the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  improved SOFM algorithm uses the Canopy algorithm to  avoid the random selection of neurons and adjusts the neurons  dynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The improved SOFM algorithm proves superior  to the traditional SOFM algorithm, significantly decreasing the  number of dead neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Furthermore, this work replaces the  K-distance  neighbourhood  with  relative  K-distance  neighbourhoods to reduce the influence of outliers in K-  distance neighbourhoods [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The proposed NELOF  algorithm was tested with seven different datasets and proved  to outperform the LOF algorithm in execution time and  accuracy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' however, this work does not explore the  effectiveness of the proposed algorithm on high-dimensional  datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Since anomaly detection is critical for time-sensitive IoT  applications that include high-dimensional data, Lyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [25]  present a Fog-Empowered anomaly detection method using  hyperellipsoidal clustering (HyCARCE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Fog computing is  presented as an alternative to Cloud computing to provide off-  loading for the Cloud [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In the Fog architecture, the end  nodes or sensors transmit data directly to the Fog nodes for  clustering and anomaly detection, improving detection  response and time delay by minimizing the computational  overhead at the sensors and the Cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The advantages of  using HyCARCE for data clustering include its ability to  automatically select the number of clusters and its  accommodating to different data distributions, such as linear  or hyperspherical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The proposed method is applied to two real-  world and two synthetic datasets, and it is proven to detect  outliers and anomalous clusters in the dataset accurately and  in a timely manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This work does not address privacy and  security concerns due to the exchange of information in the  Fog architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Summary of selected algorithms  A summary of selected clustering-based approaches for  anomaly detection is presented in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  SUMMARY OF SELECTED CLUSTERING-BASED ANOMALY DETECTION APPROACH ON IOT  Model & Year  Contributions  Limitations  PSO & K-means (2019)  [21]  Combines PSO and K-means algorithms to develop a novel  weighted clustering method for anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Their method eliminates the presence of predefined cluster  centers and multiple minimum points while improving accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed method is only tested for one dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The performance of the proposed method is only  compared to the traditional K-means algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  PIDC (2018) [22]  A novel density-based clustering algorithm which is parameter  independent can detect clusters of arbitrary shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  High computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  MCMP (2019) [23]  Proposes a novel MCMP approach reducing computational  speed and memory consumption during outlier detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Able to compute the significance of inliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed approach misidentifies some crucial  outliers when dealing with objects outside the micro-  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  NELOF  &  SOFM  clustering  algorithm  (2019) [24]  An improved SOFM clustering algorithm that utilizes the  Canopy algorithm to avoid the random selection of neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  A relative K-distance neighbourhood to reduce the influence of  outliers that exist in the K-distance neighbourhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The performance of the proposed method is only  compared to LOF in the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Does not explore the effectiveness of the proposed  algorithm on high-dimensional datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  HyCARCE (2017) [25]  A novel Fog-Empowered detection using HyCARCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Sensor data is sent to the Fog nodes to reduce detection time  Supports location-awareness of anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Does not address privacy and security concerns from  information exchange in the Fog nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' CLASSIFICATION-BASED ANOMALY DETECTION  In machine learning, there are many techniques that we can  use to classify things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In a typical classification-based  problem, there is a balanced number of positives and negatives  in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' So, we train the model on a balanced number of  positives and negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In anomaly detection problems, there  are fewer positive examples than negative ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The positive  examples (anomalous data) might be lesser than 5% of the total  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The main task of classification is to identify the category  or class label of new instances from a data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Classifying the  algorithm, called a classifier, depends on the learning from a  training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The training dataset contains data that is  correctly classified into accurate class labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Similarly, for  anomaly detection, classification algorithms will try to classify  data into two broad categories – normal and abnormal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Some  common classification techniques for detecting anomalies are  discussed below:  Classification Tree: It is like a tree pattern graph, also  known as a prediction model or decision tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The internal  nodes are called test properties, each branch signifies the test  results, and the final leaves indicate the class to which the test  data belongs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The two most used algorithms are ID3 and C4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='5  [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Classification tree approaches, when compared to naïve  Bayes classification, the result obtained from decision trees  was found to be more accurate [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Support Vector Machine (SVM): SVM is popular in  recognizing patterns and is widely used in intrusion detection  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' “When compared to neural networks in the KDD cup  data set, it was found that SVM outperformed NN in terms of  false alarm rate and accuracy in most attacks” [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Naïve Bayes network: To take benefit of the structural  connection between the random variables, we can use a  probabilistic graph model - Naïve Bayesian Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  model delivers a solution to the question if only a limited  number of observed events are known, then what is the  likelihood of a specific kind of attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=" Let's compare the  decision tree and Bayesian techniques, although the precision  of the decision tree is far better." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The computational time of the  Bayesian network is found to be low [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Genetic Algorithm: Genetic Algorithm (GA) was first  introduced in the computational biology field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' However, the  GA is applied for intrusion detection to develop a set of  classification rubrics from the network audit data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  substantial properties of GA are its strength against noise and  self-learning competencies [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  HADES- IoT is a novel host-based anomaly detection and  prevention approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The model is based on whitelisting  legitimate processes on an IoT device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The notion of this  method is that simple programs that are recognized to run on  an “uninfected” off-the-shelf device are allowed to run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' To  build a whitelist of benign programs, profiling must be  performed once for each device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The devices with enabled  Telnet service by default (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=', SimpleHome IP camera) are  potentially vulnerable to Mirai” [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In the proposed model  (HADES-IoT), even such a default misconfiguration does not  cause harm since the execution of any unauthorized binary is  terminated upon its spawning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Summary of selected algorithms  A summary of selected classification-based approaches for  anomaly detection is presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' DEEP LEARNING-BASED ANOMALY DETECTION  Deep learning, based on artificial neural networks to  process data, has demonstrated its ability to extract features  and high accuracy for classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Therefore, applying  deep learning-based algorithms on the Internet of Things  environment to detect anomalies is also popular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Several  selected deep learning-based algorithms are elaborated on in  the following literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' One of the common examples of  detecting anomalies in the IoT is detecting network attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Some network intrusion detection systems (NIDS) have  problems with adaptation to dynamic network environments,  unavailability of labelled data, and high false-positive rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Therefore, Van et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [36] proposed using deep learning  algorithms to implement network intrusion detection systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Two types of deep learning models are mentioned in their  paper: the Restricted Boltzmann Machines (RBM) and  Autoencoder (AE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The authors constructed a stacked RBM  and AE as two Deep Belief Network (DBN) structures and  compared their performance on detection intrusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' For the  stacked RBM, which uses a probability distribution, the hidden  layer of each RBM is set to be the input layer of the next RBM  of the stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The stacked AE can extract features of network  data by unsupervised learning so that it can solve the challenge  of the unavailability of labelled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' For the experiment, Van  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [36] used the same dataset that contains four types of  network attacks to test the ability of two DBM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  results show the Stacked AE outperforms the Stacked RBM on  the accuracy of intrusion detection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' however, the training time  and execution time of the stacked RBM are much longer than  the Stacked AE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Almiani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [37] proposed a deep  learning-based intrusion detection system in the IoT  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Their model contains two major components:  the traffic analysis engine and the classification engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  traffic analysis engine is used to pre-process the traffic data,  such as symbolic-to-numeric transformation, feature reduction  and normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Then, the processed data is fed into the  classification engine, which adopts two deep recurrent neural  networks (RNN) to respond fast in a real-time environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The two RNN work as two filters of attack detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  traffic data classified as normal by the first RNN layer will be  passed to the second RNN detection layer to identify whether  it is an anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The same dataset is used to train the two  layers of RNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The only difference is the training set for the  first RNN contains both normal and abnormal data, while the  training set for the second RNN only has normal traffic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Almiani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [37] compare their proposed model with other  baseline models for anomaly detection accuracy and execution  time, which indicates the proposed RNN model has a high  sensitivity to detect abnormal attacks in a competitive  computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The scalability and distribution of  resources are the characteristics of the Internet of Things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Therefore, any anomaly detection model that depends on a  centralized cloud will fail to handle the IoT requirements [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  SUMMARY OF SELECTED CLASSIFICATION-BASED ANOMALY DETECTION APPROACH ON IOT  Model &  Year  Contributions  Limitations  Naive Bayes  + decision  Tree  (2010)  [31]  The model performs balance detections and keeps false positives  at an acceptable limit for different network attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The method minimized the rate of false positives and maximized  balanced detection rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [28]  The model requires much improvement in detecting false  positives to remote-to-user attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  HADES-IOT  (2019) [30]  The generic model can be easily adapted to any Linux kernel  version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The method is said to be resilient against attackers and  focused on disabling its protection mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  HADES-IoT terminates any executable not included in the  whitelist both of them upon its execution and stops the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Researchers initially utilized features provided by Linux, such  as KProbe1 or inotify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' After examining several IoT devices (D-  Link IP Camera, SimpleHome IP camera), they found that these  features are not supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  As the challenge is to distinguish unidentified processes in  real-time right after their spawning, the Linux process scheduler  is another limiting factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The model is based on the whitelisting approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' This may be  viewed as impractical because some benign programs may be  missed during profiling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  One Class and  Two Class  SVM  (2012) [32]  The first-class SVM is used for detecting abnormality scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Secondly, the detector is retrained when certain new data records are  included in the existing dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  A prior failure history is not required, and the model continually  learns from the observed failure events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  It has no performance measure of computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  DT + SVM  (2007) [33]  The data set is first passed through the tree, and node information  is generated and passed along with the original set of attributes  through SVM to obtain the final output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [30]  This approach delivers equivalent results to SVM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Ensemble  approach [33]  To make the final decision, information is combined from  different individual classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Provided the best performance for Probe and R2L classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Selecting base classifiers is critical and cannot be done  automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  k-Means  +ID3 (2010)  [34]  Proposed a hybrid technique which combines clustering and  classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The K-mean clustering can be applied to the normal training data  points to form clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Then the decision tree will be performed on  each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed algorithm outperforms the individual k-Means and  the ID3 method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  This approach is limited to a specific dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  k-Medoids  +Naïve Bayes  (2012) [35]  Similar data instances are grouped by using the k- Medoids  clustering technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  It can increase detection accuracy rate and reduction in false  alarm rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  It is challenging to predict naïve Bayes classifiers in different  settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  SVM  +  k-  medoids  (2012)[35]  Proposed a hybrid technique which combines k-medoids  clustering and SVM classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed anomaly detection technique reaches a higher  accuracy than the baseline algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [32]  Time complexity is more when the dataset is very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [38] proposed Vector Convolutional Deep Learning  (VCDL) model to detect anomalies in IoT traffic, which  applies an emerging distributed intelligence approach called  “fog computing.” The proposed model contains three layers of  components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The first layer is IoT devices which are  distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The second layer is the fog layer—multiple work  fog nodes connected to the IoT devices and train each VCDL  model in a distributed manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The master fog node in the fog  layer will collect and share the best set of parameters with the  worker nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Therefore, the traffic data will be fed into the  corresponding worker node and be classified as either normal  or attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The classification result will be passed to the cloud  layer, the third layer of the proposed framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The cloud  layer is used to validate the information from the entire fog  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The experiment results indicate that the proposed  distributed VCDL framework can detect anomaly traffic data  with high accuracy and less detection time than the centralized  detection model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The IoT system always involves real-time data or time-  series data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Therefore, several pieces of research focus on  detecting anomalies in time series data collected by IoT  devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' For example, Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [39] worked on detecting  outlier data in the indoor climate control system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' There are two  kinds of anomalies: point anomaly, which indicates a single  outlier value hugely different from other data, and contextual  anomaly, which refers to a series of inappropriate data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' [39] proposed a neural network-based model to detect  these two kinds of anomalies, which combines the autoencoder  (AE) and the long short-term memory (LSTM) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  structure of AE is similar to the regular Feed Forward Neural  Network with a reduced number of neurons in hidden layers  so that the output of the AE can be very close to the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  LSTM model can extract features of sequential data and  capture the relationship between neighbouring input data [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Therefore, the AE component in the proposed model works to  detect point anomalies, while the LSTM component detects  the contextual anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The proposed model demonstrated the  accuracy of the anomaly detection algorithm could be  improved by integrating the neural network models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Summary of selected algorithms  A summary of selected deep learning-based approaches for  anomaly detection on IoT is presented in Table 4, which  includes the contributions and drawbacks of each algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' CONCLUSION AND FUTURE DIRECTIONS  The Internet of Things (IoT) has recently become popular as  a system connecting physical hardware, such as computing  devices, sensors, and other technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Over the IoT  network, data can be collected, transferred, and exchanged  with other devices without requiring human interactions, and  it always involves processing and analyzing a massive  amount of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Therefore, the security and operation status  of the IoT network is important, and it is essential to detect  any unusual behaviours known as anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The anomaly in  the IoT environment can be categorized as performance-  related or security-related.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The performance-related anomaly  can be represented as sensor faults or unusual events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  security-related anomaly is usually caused by malicious  attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' In this paper, we provided a survey on the state-of-  the-art anomaly detection algorithms in the IoT environment  using machine learning techniques because machine learning  technology has a strong ability to deal with the big data  involved in the IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' We categorize the machine learning-  related algorithms to detect anomalies into three types:  clustering-based, classification-based, and deep learning-  based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=" For each detection algorithm, we select a significant  number of research papers, discuss the advantages of the  chosen method, and mention each existing method's  limitations." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' We also notice that although much work has been  done through independent algorithms, deploying hybrid  approaches can provide better results and overcome the  shortcoming of one method over the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' We believe that  this survey paper provides an in-depth knowledge of these  commonly used approaches and will help make decisions on  choosing a particular technique for an anomaly detection  problem in the IoT environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' Future direction involves the  use of multi-level learning [41], semantic learning [42],  ensemble learning [43], hybrid learning [44], and distributed  computing [45]-[46] for anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  SUMMARY OF SELECTED DEEP LEARNING-BASED ANOMALY DETECTION APPROACH ON IOT  Model & Year  Contributions  Limitations  DBN (2017) [36]  Gives two examples of deep learning-based models for  anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Provides comparisons in anomaly detection accuracy  and computational performance for the two selected  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Does not choose a non-deep learning-based anomaly  detection model as the baseline to demonstrate the ability of deep  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The types of intrusions that the proposed models can detect  are limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  2-RNN (2020) [37]  Proposed a two-layer RNN model to increase the  anomaly detection accuracy on a challenging dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed model can effectively detect in real-time  environments with a competitive computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Only apply a sample dataset in the experiment to test the  effectiveness of the proposed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  VCDL (2020) [38]  Trains the Vector Convolutional Deep Learning model  in a distributed manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Able to detect the anomaly traffic in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Achieve detection performance with high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  Only applies a sample dataset in the experiment to test the  effectiveness of the proposed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The model does not work for detecting multiclass anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  AE-LSTM (2020) [39]  Integrates two types of neural network models to detect  different types of anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The proposed anomaly detection algorithm can be  performed in a real-time situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  They may not be able to detect anomalies with different  patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  It has no performance measure of computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  CNN-based monitoring  detection (2019) [40]  Proposed two CNN-based models to detect two types of  abnormal situations in the operating environment of power  equipment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  It outperforms the traditional CNN network for  detecting personnel or fire smoke in images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  The purpose of the anomaly detection algorithm is very  specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The model cannot detect other abnormal cases in the  operating environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content='  In the experiment, only images are used for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
+page_content=' The  ability of anomaly detection on video is not proven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QdAyT4oBgHgl3EQfU_c5/content/2301.00134v1.pdf'}
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+Learning by Sorting: Self-supervised Learning
+with Group Ordering Constraints
+Nina Shvetsova1,3
+Felix Petersen2
+Anna Kukleva3
+Bernt Schiele3
+Hilde Kuehne1,4
+1Goethe University Frankfurt, 2Stanford University, 3Max-Planck-Institute for Informatics, 4MIT-IBM Watson AI Lab
+shvetsov@uni-frankfurt.de
+Abstract
+Contrastive learning has become a prominent ingredi-
+ent in learning representations from unlabeled data. How-
+ever, existing methods primarily consider pairwise rela-
+tions. This paper proposes a new approach towards self-
+supervised contrastive learning based on Group Ordering
+Constraints (GroCo). The GroCo loss leverages the idea of
+comparing groups of positive and negative images instead
+of pairs of images. Building on the recent success of dif-
+ferentiable sorting algorithms, group ordering constraints
+enforce that the distances of all positive samples (a posi-
+tive group) are smaller than the distances of all negative
+images (a negative group); thus, enforcing positive samples
+to gather around an anchor. This leads to a more holistic
+optimization of the local neighborhoods. We evaluate the
+proposed setting on a suite of competitive self-supervised
+learning benchmarks and show that our method is not only
+competitive to current methods in the case of linear prob-
+ing but also leads to higher consistency in local represen-
+tations, as can be seen from a significantly improved k-NN
+performance across all benchmarks.
+1. Introduction
+Self-supervised learning has become a topic of grow-
+ing interest over the last years as it allows models to learn
+representations from large-scale data without any need for
+annotation.
+Recently, self-supervised contrastive meth-
+ods [3,10,17,26,51,56] notably narrowed the gap to the su-
+pervised learning performance. These methods rely on the
+concept of the pairwise contrastive loss, which is based on
+the idea that an image, serving as anchor, and an augmenta-
+tion of the same image, a so-called positive pair, should be
+close to each other in a projection space, while a pair made
+up of an anchor image and a different image, a so-called
+negative pair, should be far away from each other. This con-
+cept of bringing positive pairs in embedding space closer
+together was further extended in various frameworks, such
+Update
+Contrastive Loss
+Group Ordering Constraints (GroCo) Loss
+all pos. distances < all neg. distances
+Update
+Distance
+Distance
+Figure 1.
+Pairwise contrastive loss compared to the proposed
+group ordering constraints loss: While pairwise loss only consid-
+ers pairwise distances, groupwise sorting allows us to enforce that
+a group of positive samples is closer to the anchor than a group of
+negative ones and, thus, to improve the representation of the local
+neighborhood.
+as BYOL [23], SwAV [8], and many more [4,9,13,19,58].
+However, the idea of the pairwise contrastive loss is lim-
+ited by the fact that it only considers individual positive
+pairs. This means that it can not align the embedding space
+based on more than two positive data points. Several at-
+tempts have been made to address this issue, e.g., combin-
+ing the contrastive idea with concepts based on local neigh-
+borhoods, such as clustering as in the case of SwAV [8],
+or minimizing distances between multiple positives pairs
+for the same instance together as in the case of Whiten-
+ing [19]. Another limitation of the contrastive loss is that
+it requires a large number of negatives in order to be effec-
+tive [10]. Some methods tackle this issue by leveraging a
+large batch size [10], memory banks [26], or negative min-
+ing [52]. However, here, a drawback is that, as the embed-
+ding space is optimized with respect to all negatives, even
+1
+arXiv:2301.02009v1  [cs.CV]  5 Jan 2023
+
+Positives
+Negatives
+Negative Positions
+Positive Positions
+Group of Negatives
+Group of Positives
+Distance to 
+Anchor:
+0.8
+0.4
+0.6
+0.2
+Differentiable Odd-even
+Sorting Network:
+(Sorts input values in ascending order 
+by swapping neighboring elements)
+0.0
+0.6
+0.4
+1.0
+0.9
+0.1
+0
+0
+0.1
+0.3
+0.6
+0
+0
+0.6
+0.3
+0.1
+0
+0
+0.1
+0.9
+Differentiable Permutation Matrix: 
+(Probability of elements to be swapped 
+to rank [1,2,3,4])
+Swaps between x - not ok
+Swaps within group -  ok
+1.0
+0.4
+0.6
+0.0
+Group Ordering Constraints (GroCo) loss:
+Sum over negative and positive positions 
+and compute BCE
+∑ Negative 
+Positions
+1.0
+1.0
+0.0
+0.0
+∑ Positive 
+Positions
+0.0
+0.0
+1.0
+1.0
+Negative 
+GT
+Positive 
+GT
+Projection
+Space:
+BCE
+loss
+[1]         [2]        [3]        [4]  
+Anchor
+Encoder
+Figure 2. Overview of the proposed group ordering constraints loss: We first compute the distance of groups of positive as well as
+negative samples with respect to an anchor. The distances are sorted via a differentiable odd-even-sorting network in non-descending
+order, computing the swapping probability for samples. The result is a differentiable permutation matrix, in which the row values can be
+thought of as the probabilities of sorting the elements into the corresponding positions. We can ignore swap operations within groups, and
+only need to consider swapping operations between groups. We, therefore, sum over the positive and negative columns of the permutation
+matrix and compute the BCE between the row-wise entries and the expected ground truth.
+negatives that are far away from the anchor will contribute
+to the optimization of the representation. Other methods
+were proposed to address this issue, such as hard nega-
+tive selection by controlling the hardness of examples [47]
+or negative selection by sparse support vectors [50]. Yet,
+these methods still require manual selection of the hardness
+level [47] or incur an additional optimization cost [50].
+In this paper, we propose a novel approach to address
+those points by shifting away from the concept of a pairwise
+contrastive loss and instead propose to train the network
+based on Group Ordering Constraints (GroCo)—namely,
+the idea that the group of multiple positives should be closer
+to an anchor image than any negative from the group of neg-
+atives. We illustrate this idea and comparison with the pair-
+wise contrastive loss in Figure 1. With group constraints,
+we do not treat positive and negative pairs individually, as
+in contrastive loss, but rather as groups, and effectively con-
+strain only those elements that are placed in the group over-
+lap area with respect to the distance to the anchor point.
+To enforce the group ordering constraints in the projec-
+tion space, we propose the idea of learning by sorting: we
+suggest sorting positives and negatives by distance to the
+anchor image in a differentiable way and swapping them if
+they are in the wrong order. To create an end-to-end train-
+ing pipeline, we leverage recent advances in differentiable
+sorting [16, 24, 41, 42]. Specifically, we utilize a differen-
+tiable sorting algorithm to obtain a differentiable permu-
+tation matrix for sorting a list of distances to the positive
+and negative images, as shown in Figure 2. If we would
+know the full ground truth orderings among positives and
+negatives, such as which positive sample should be closer
+to the anchor than another positive sample, we could cre-
+ate a ground truth permutation matrix, and calculate how
+much the predicted permutation matrix would deviate from
+the ground truth one [16, 24, 41, 42]. Since this assump-
+tion is not given in practice and we do not know the ground
+truth distance ordering within the positive or the negative
+groups, we propose the GroCo loss, a relaxed formulation
+of the original sorting supervision that captures how many
+negative elements appear in the positive positions and vice
+versa. Compared to the pairwise contrastive loss, the result-
+ing group ordering focuses on optimizing the local neigh-
+borhood around an anchor image, rather than optimizing all
+data points at once. Moreover, without any additional mod-
+ifications, our group ordering loss directly focuses on the
+strongest positive and negative examples.
+To show the capabilities of the proposed approach, we
+evaluate it on a suite of competitive self-supervised learn-
+ing benchmarks, namely in the context of linear probing, k-
+NN classification, as well as image retrieval. Our evaluation
+demonstrates that models trained via group ordering con-
+straints obtain competitive performance in linear evaluation
+compared to other contrastive learning frameworks, some
+of them even trained with significantly larger batch sizes
+and/or an additional teacher network. Further, we demon-
+strate the superior ability of the proposed method in the
+context of shaping local neighborhoods by evaluating the
+nearest neighbor classification capabilities by outperform-
+ing any other state-of-the-art method on this task.
+We summarize the contributions of this work as follows1:
+• We propose a new concept for self-supervised repre-
+sentation learning based on learning by sorting.
+• We leverage recently proposed differentiable sorting
+methods to derive the contrastive group ordering con-
+straints (GroCo) loss.
+• We demonstrate that the proposed method achieves
+competitive performance in linear separability of em-
+beddings and is especially suitable to model the lo-
+cal neighborhoods and outperforms current top-level
+state-of-the-art frameworks on a wide range of nearest-
+neighbor tasks.
+1The code will be made publicly available.
+2
+
+2. Related Work
+2.1. Self-supervised Representation Learning
+Self-supervised learning aims to learn a robust represen-
+tation from data without human annotation. Various learn-
+ing objectives were developed for self-supervised learning
+from images including image colorization [60], inpaint-
+ing [40], puzzle solving [37], and rotation prediction [22].
+Over the last years, methods [8, 10, 13, 23, 26] that en-
+force the model to be robust to different image distor-
+tions achieved great performance improvements in self-
+supervised learning. Such methods generally rely on sam-
+pling two augmented views of the image—a positive pair—
+and minimize the distance between those in the embedding
+space. Contrastive methods [10–12,26] are a great example
+of those approaches. To prevent the model from learning a
+trivial solution for any input, contrastive methods also in-
+troduce the concept of a negative pair, i.e., two different im-
+age, and contrast positive pairs against negative pairs. The
+InfoNCE loss, which is often referred to as a contrastive
+loss, is the most prominent method in many self-supervised
+learning scenarios [1, 10, 26, 46]. Earlier contrastive meth-
+ods relied on the triplet loss [49], which considers one pos-
+itive and one negative example for the anchor image. In
+contrastive learning, many components and extensions have
+been investigated: data augmentation strategies [10, 54],
+projection head design [11], hard negative sampling [47],
+increasing the richness of positives with nearest neigh-
+bours [17], or mitigating effect of false negatives [28]. In
+this work, we propose a novel contrastive method—learning
+by sorting—which features properties not inherent to other
+contrastive learning methods: we primarily consider those
+positives and negatives that are placed (sorted) incorrectly
+in the embedding space, thereby implicitly considering the
+strongest positive and negative examples.
+There are also methods [13, 23] that do not rely on
+negatives and only maximize agreement between positive
+views. Such methods prevent collapsing of the representa-
+tion space by using asymmetric architectures applied to dif-
+ferent views [13,23], an additional teacher network [9,23],
+stop gradient [9,13,23], feature whitening [19], or informa-
+tion maximization [4, 58]. Another set of methods [2, 7, 8]
+utilizes clustering of the latent embeddings. However, so
+far, methods mostly rely on similarity maximization be-
+tween only two sampled views. SwAV [8] also considered
+sampling more augmentations in a multi-crop setting, where
+two full-size augmented images are sampled together with
+several smaller crops, and Whitening [19] utilized more
+full-resolution samples. However, even in these cases, the
+loss was still computed by considering pairs of views inde-
+pendently. In contrast, we propose optimizing the embed-
+ding space based on group ordering constraints.
+2.2. Differentiable Sorting and Ranking
+Differentiable sorting and ranking methods provide a
+pipeline that allows training neural networks with order-
+ing supervision in an end-to-end fashion with gradient de-
+scent [5, 16, 24, 41, 42, 44]. The sorting operator can be
+seen as a function returning a permutation matrix that in-
+dicates the permutation necessary to sort the sequence of
+values (the matrix that multiplied with a input vector returns
+a sorted output vector.) In this context, differentiable sort-
+ing refers to relaxing the (hard) permutation matrix to a dif-
+ferentiable permutation matrix via continuous relaxations.
+The differentiable permutation matrix for a given sequence
+of values, which could, e.g., be scores predicted by a neural
+network, can then be used to compute the loss by compari-
+son to a ground truth permutation matrix. Recently, multi-
+ple methods for relaxing the permutation matrix have been
+proposed, including an argsort approximation by unimodal
+row-stochastic matrices [24, 44], a formulation of entropy-
+regularized optimal transport [16], as well as networks of
+differentiable swap operations (differentiable sorting net-
+works) [41,42]. The latter method composes the full permu-
+tation matrix as a product of permutation matrices that arise
+from comparing only two elements at a time (usually neigh-
+bors) and either swapping them or not swapping them. In-
+spired by the idea of swapping the neighboring elements in
+the sequence, our approach learns representations by com-
+paring neighboring elements in the embedding space.
+In terms of applications, differentiable sorting has been
+leveraged in various contexts, including recommender sys-
+tems [33], image patch selection [15], selection experts in
+multi-task learning [25], and attention mechanisms [59]. To
+the best of our knowledge, the proposed method is the first
+work to leverage ordering supervision for self-supervised
+learning of visual representations.
+3. Method
+Given a dataset of images {xi}M
+i=1 ⊆ X, our goal is to
+learn an encoder g : X → Rd that extracts image represen-
+tations that later might be used for downstream tasks.
+3.1. Training Pipeline
+Similar to other contrastive methods, our approach con-
+siders several augmented views of the same image as pos-
+itive examples, which should be close together in an em-
+bedding space, and different images as negative examples,
+which should be apart in an embedding space. Our model
+starts from sampling mini-batches of B images and gener-
+ates m ≥ 2 randomly augmented views per each image,
+resulting in m · B data points. If m = 2 we are close to the
+original pairwise contrastive learning setup [4, 10, 13, 28,
+58]. The augmented views are processed with the encoder
+network g(·), that extracts data representation vectors from
+views. Then, an MLP projection head h(·) maps represen-
+3
+
+tations to the latent space where distances between views
+are calculated. For each data point serving as an anchor xa,
+we have m − 1 positive examples {xp
+i }m−1
+i=1 (which results
+in 1 positive example in the classical setup of m = 2) and
+m·(B−1) negative examples {xn
+i }m·(B−1)
+i=1
+. We use the co-
+sine distance to measure the distance between data points:
+d(x, y) = −
+x⊤y
+∥x∥∥.y∥.
+3.2. Group Ordering Constraints (GroCo)
+In order to consider not only pairs of views but instead
+groups of multiple positives at once, we extend the con-
+trastive loss to the idea that the group of positives should
+be closer to the anchor image than the group of negatives in
+the embedding space. This idea directly results in group
+ordering constraints (GroCo).
+To simplify the notation,
+we denote the distance between data point xa and its pos-
+itive xp
+i and negative examples xn
+i as dp
+i = d(xa, xp
+i ) and
+dn
+i = d(xa, xn
+i ). If we assume that K positives xp
+1, ..., xp
+K
+are ordered with respect to their distances to the anchor
+xa as dp
+1 ≤ ... ≤ dp
+K and N negatives xn
+1, ..., xn
+N as
+dn
+1 ≤ ... ≤ dn
+N, then we define the group ordering con-
+straints as
+dp
+1 ≤ ... ≤ dp
+K <<< dn
+1 ≤ ... ≤ dn
+N.
+(1)
+As can be seen in Equation 1, all elements in the groups
+are considered in the constraints; however, for training,
+the relevant constraint is the (bold) < in the center. This
+constraint differs from pairwise contrastive loss constraints,
+which 1) consider positives individually and 2) consider all
+negatives even if they are far away from the anchor and are
+thus less relevant. Our constraints also differ from the triplet
+loss, which considers only one positive and one negative ex-
+ample, while we are working with groups.
+3.3. Learning by Sorting
+Inspired by recent advances in differentiable sorting [41,
+42], we design a loss that fulfills our group ordering con-
+straints based on differentiable sorting. Our training pro-
+cedure can be seen as sorting positives and negatives in the
+embedding space with respect to an anchor image and swap-
+ping them if they are in the incorrect order; therefore, we
+call the approach learning by sorting.
+3.3.1
+Differentiable Sorting Networks
+In the following, we review the differentiable sorting algo-
+rithm called differentiable sorting networks [41] as it is a
+core element of our loss function. We note that “networks”
+in “sorting networks” is not related to the term “neural net-
+works” and that a differentiable sorting network is a func-
+tion with no trainable parameters. Sorting networks are a
+family of sorting algorithms from classic computer science
+literature [30]. An example of this is the odd-even sort-
+ing network. By relaxing the conditional swap operator to
+0.8
+0.4
+0.6
+0.2
+0.2
+0.6
+0.2
+0.6
+0.4
+0.8
+0.4
+0.8
+0.2
+0.4
+0.8
+0.6
+0.2
+0.4
+0.6
+0.8
+step 1
+step 2
+step 3
+step 4
+0.9
+0.1
+0
+0
+0.1
+0.3
+0.6
+0
+0
+0.6
+0.3
+0.1
+0
+0
+0.1
+0.9
+P1
+Input:
+P2
+P3
+P4
+f(0.6-0.2) f(0.2-0.6)
+0
+0
+f(0.2-0.6) f(0.6-0.2)
+0
+0
+0
+0
+f(0.8-0.4) f(0.4-0.8)
+0
+0
+f(0.4-0.8) f(0.8-0.4)
+P = P4 ⦁ P3 ⦁  P2 ⦁  P1 
+P1=
+Differentiable Odd-even Sorting Network
+ differentiable conditional swap operation  
+Output: differentiable 
+permutation matrix P
+-1
+0
+1
+1
+x
+p
+f(x) = 1/𝜋 arctan(βx) + 0.5
+f(x)
+β= 0.5
+β= 1.0
+β= 2.0
+Figure 3. Overview of a differentiable sorting network with the
+odd-even sorting algorithm. The network compares neighboring
+elements that start from odd and even indices alternatively in each
+step and apply a differentiable swap operation if elements are in
+the wrong order. The conditional swap operations on each step s
+also define a differentiable permutation matrix Ps. The network
+output is a complete differentiable permutation matrix P, defined
+as the multiplication of matrices of each step.
+a differentiable conditional swap, sorting networks can be
+made differentiable by relaxation to differentiable sorting
+networks [41].
+We consider differentiable sorting networks based on
+the odd-even sorting network to sort an input sequence of
+K + N elements in non-descending order as shown in Fig-
+ure 3. The differentiable sorting network is defined as a
+composition of functions, where each function refers to one
+step of sorting, and where pairs of elements of the input se-
+quence are compared and swapped if they are in the wrong
+order via a conditional swap operation. For the odd-even
+sorting network network, the algorithm compares neigh-
+bored elements on odd and even indices alternatingly in
+each step, and requires K + N steps to sort a given input
+sequence of length K + N.
+The conditional swap operation for elements (di, dj)
+where i < j can be defined as d′
+i = min(di, dj), d′
+j =
+max(di, dj), and the differentiable relaxation [42] of this
+operation is defined as:
+d′
+i = softmin(di, dj) = dif(dj − di) + djf(di − dj)
+d′
+j = softmax(di, dj) = dif(di − dj) + djf(dj − di) (2)
+where f(x) =
+1
+π arctan(βx) + 0.5 [42]. The hyperpa-
+rameter β > 0 denotes an inverse temperature, and when
+β → ∞ the relaxation converges to the discrete swap op-
+eration. The differentiable conditional swap operation for
+the elements (di, dj) can be defined as a permutation ma-
+trix Pswap(di,dj) ∈ R(K+N)×(K+N) is an identity matrix
+4
+
+except for entries Pii, Pij, Pjj, Pji, which are defined as:
+Pii = Pjj = f(dj − di),
+Pij = Pji = f(di − dj).
+(3)
+The permutation matrix Ps for step s is the product of matri-
+ces corresponding to parallel (and thus independent) swap
+operations in this step Ps = �
+i∈R Pswap(di,di+1), where R
+is the set of odd indices if s is odd and the set of even in-
+dices if s is even. The complete permutation matrix P is
+defined as P = PK+N · ... · P1.
+In the discrete case, each row of a permutation matrix has
+exactly one entry of 1, which indicate the position where the
+element that corresponds to this row should be placed. In
+the relaxed version, row values can be seen as a distribution
+over possible positions of the element [43]. For training
+with sorting supervision, where the correct order of input
+values is known, we can create a ground truth matrix Q and
+define the loss as L =
+1
+(K+N)2
+�
+i,j BCE(Pij, Qij) where
+BCE refers to binary cross-entropy.
+3.3.2
+GroCo Loss
+If we would know the ground truth order of positives and
+negatives, we could create a ground truth permutation ma-
+trix and calculate a loss.
+However, as we rely on ran-
+dom augmentations, we do not know the ground truth order
+among positives and among negatives. Thus, we propose
+a solution to obtain a loss to fulfil our group ordering con-
+straints.
+Let us again assume that positives are ordered with re-
+spect to their distances to the anchor image as dp
+1 ≤ ... ≤
+dp
+K and negatives as dn
+1 ≤ ... ≤ dn
+N. As shown in Figure 3,
+we concatenate positive and negative distances in a list:
+[dp
+1, ..., dp
+K, dn
+1, ..., dn
+N].
+(4)
+Even though we have ordered elements in the positive and
+negative sub-list, we still don’t know if the constraint dp
+i <
+dn
+j is fulfilled for any 1 ≤ i ≤ K and 1 ≤ j ≤ N.
+Here, we apply a differentiable sorting network to the
+list and obtain a differentiable permutation matrix for sort-
+ing the list in non-descending order. Values in a permu-
+tation matrix row can be seen as probabilities to sort the
+corresponding element to the different positions, e.g., P11
+would be the probability for assigning the first element in
+the list (dp
+1) to position 1, P12 to position 2, etc. Therefore,
+a sum of the first K elements in a row can be considered as
+a probability being sorted inside the first K elements. Thus,
+for a permutation matrix of size (K + N) × (K + N) the
+sum of the first K columns results in probabilities of being
+sorted in positive places and the later columns (from K + 1
+to K +N) in negative places. We define a loss that enforces
+positives to be sorted in the positive places and negatives in
+the negatives places, as
+L =
+1
+2(K + N)
+K+N
+�
+i=1
+�
+BCE
+� K
+�
+k=1
+Pik, 1i≤K
+�
++
++ BCE
+� K+N
+�
+k=K+1
+Pik, 1i>K
+�
+�
+(5)
+where 1 is an indicator function.
+As illustrated in Figure 2, our loss is a relaxation of the
+sorting supervision that considers only two types of swap
+operations: swap operations within the group of positive
+and negative samples, which should not contribute to the
+loss, and swap operations between the groups, which vi-
+olate the positive-negative ordering assumption and which
+we want to use as the optimization criterion.
+Role of Pre-ordering. Practically, we pre-order positives
+and negatives inside the groups in a non-differentiable way
+before inputting them into the differentiable sorting net-
+work. Though even without it, the loss will still contrast
+positives to negatives, we believe that pre-ordering fulfills
+the idea behind GroCO. When we input pre-ordered ele-
+ments, the sorting network performs comparisons of neigh-
+boring elements swapping them if they are in the wrong
+order, or if everything is sorted correctly, comparing the
+strongest positive with the strongest negative. In this way,
+elements are considered as a group, and borders of the
+groups or their overlapping parts are used in the loss.
+Number of Negatives. Since the only strongest negatives
+(that are sorted incorrectly) mostly participate in the compu-
+tation of the loss function, we may use only top-N strongest
+negatives almost without losing any learning signal. We
+will show in the ablation study that N = 10 is enough.
+Role of β.
+The inverse temperature β in differentiable
+swap operation corresponds to the degree of relaxation of
+the swap operation that converges to a discrete case when
+β → ∞ (Figure 3). Therefore with lower β the swap oper-
+ation is more “soft”, which means that the variance in gra-
+dients is smaller, which is beneficial for optimization, but
+a relaxation error accumulated by steps is larger, and vice
+versa in the case of larger β. With higher β even a small
+difference between values results in a high probability for
+a swap or not swap operation, resulting in a smaller margin
+between the positive and negatives group. With lower β we
+push positive and negative groups further apart.
+4. Experimental Evaluation
+4.1. Implementation Details
+Unless stated otherwise, we use the following setup for
+all of our experiments:
+5
+
+Augmentation. To create m augmented views per image
+(considering m = 2, 3, 4), we follow the DINO augmen-
+tation setup [9]. Since computational cost grows linearly
+with an increasing number of augmentations, we addition-
+ally considered the multi-crop augmentation strategy pro-
+posed in SwAV [8]. The idea is to sample low-resolution
+local views along with the standard 224×224 ones. We use
+2× 224 + 6× 96 scheme, where with two global 224× 224
+augmented views, we also sampled six local 96 × 96 views,
+giving eight views per image. In this case, we follow “local-
+to-global” correspondence idea [8, 9] and use only global
+views as positives for both local and global anchor images.
+Model. To be consistent with previous works [8,10,13,23]
+we use Resnet50 [27] as the encoder g(·) and an MLP
+block consisting of three fully connected layers with a size
+of 2048 and followed by a batch normalization layer [29]
+as the projection head h(·). All batch normalization lay-
+ers except the last one are followed by a ReLU activa-
+tion. The dimensionality of the representation space and
+the latent space are both 2 048 as in [13]. We also adopt
+the stop gradient operation, which is widely used in dif-
+ferent self-supervised learning methods [9, 10, 23]; specifi-
+cally, we perform stop gradient during distance computation
+d(xa, x·
+i) = d(xa, stop grad(x·
+i)). While we found that
+it is not strictly necessary for a successful training of our
+model, we observed that stop gradient makes the training
+process more stable and allows training the model with a
+much larger variation of hyperparameters while maintain-
+ing stable performance.
+Training. Following previous works [8,10,13,23], we use
+the train set of the ImageNet ILSVRC-2012 dataset [48] for
+self-supervised training without any human annotation. We
+train our model with the SGD optimizer [57] with a learn-
+ing rate of 24.0 × (batch size/1024) × (100/#epochs) and
+weight decay of 10−6. By default, we use the top N = 10
+strongest negative examples and an inverse temperature of
+β = 1. Due to resource constraints, we train our model
+with a batch size of 1 024 with mixed precision. We use
+a 10 epoch linear warm-up and a cosine schedule without
+restarts [34].
+Using an 8-GPU (NVIDIA A6000 GPUs)
+server, training for 100 epochs with m = 2 views per image
+takes approximately 22 hours.
+4.2. Evaluation Procedure
+Linear Probing. First, we follow the standard protocol and
+evaluated the learned embedding space by linear evalua-
+tion [8,10,13,23], which captures the linear separability of
+classes in the representation space. For this, we train a lin-
+ear classifier on frozen representations in a fully-supervised
+way using the ImageNet train set. We follow the standard
+protocol [13] to train the linear classifier.
+k-NN Evaluation.
+To analyze local properties of the
+learned representation, namely how often neighbored data
+Method
+Batch
+Views
+Linear Probing (Top-1)
+Size
+100 ep
+200 ep
+400 ep
+Max-Margin [50]
+256
+2×224
+63.8
+-
+-
+MoCo v2† [12]
+256
+2×224
+67.4
+69.9
+71.0
+SimSiam [13]
+256
+2×224
+68.1
+70.0
+70.8
+VICReg [4]
+2048
+2×224
+68.6
+-
+-
+Barlow Twins [58]
+2048
+2×224
+68.7
+-
+-
+SimCLR† [10]
+4096
+2×224
+66.5
+68.3
+69.8
+SwAV† [8]
+4096
+2×224
+66.5
+69.1
+70.7
+BYOL† [23]
+4096
+2×224
+66.5
+70.6
+73.2
+Whitening [19]
+4096
+4×224
+69.4
+-
+72.6
+GroCo (ours)
+1024
+2×224
+69.2
+70.4
+71.0
+GroCo (ours)
+1024
+4×224
+69.6
+70.4
+71.4
+SwAV [8]
+4096
+2×224 + 6×96
+72.1
+73.9
+74.6
+GroCo (ours)
+1024
+2×224 + 6×96
+71.6
+73.0
+73.7
+Table 1. Comparison with state-of-the-art in linear probing
+on ImageNet. We report results for training for 100, 200, and
+400 epochs. Backbone=Resnet50. †denotes results from Sim-
+Siam [13] improved reproductions.
+points correspond to the same semantic class, we further
+evaluate our method by nearest neighbor classification, pre-
+dicting the object class by a simple weighted k nearest
+neighbor classifier (k-NN) with k = {1, 10, 20} based on
+cosine distance as in [8, 9]. We again use the ImageNet
+train set for supervision and test on the ImageNet val set.
+4.3. Comparison to State-of-the-Art
+We start with a comparison of the proposed method to
+state-of-the-art self-supervised learning methods in linear
+probing and k-NN evaluation on the ImageNet [48] and for
+image retrieval on the revised Oxford and Paris dataset [45].
+Linear Probing. In the case of linear probing (Table 1),
+we observe that our method outperforms almost all base-
+lines in classical (not multi-crop) settings.
+Our method
+demonstrates state-of-the-art performance in 100 epochs
+training, outperforming contrastive baselines SimCLR [10]
+and MoCo v2 [12] by +2% and information maximiza-
+tion methods Barlow Twins and VICReg by +1% in 100
+epochs setup. Moreover, our method outperforms SimCLR
+and clustering-based SwAV [8] in all other settings as well.
+Also, we even observe competitive performance compared
+to BYOL [23] and Whitening [19] methods that use ×4
+larger batch size and/or an additional teacher network. We
+also observe performance improvement by utilizing mul-
+tiple positive examples during training. In the multi-crop
+2 × 224 + 6 × 224 settings, our method is on par with
+clustering-based SwAV, which utilizes ×4 larger batch size.
+k-NN Evaluation. We further evaluate the k-NN perfor-
+mance of our methods compared to multiple state-of-the-art
+methods with officially released weights in Table 2. We ob-
+serve that the proposed method excels in all settings, outper-
+forming all methods by more than 4% in the no multi-crop
+scenario. The method further greatly improves performance
+by leveraging multiple positive examples. Finally, by uti-
+6
+
+Method
+Batch
+Views
+k-NN (weighted, k=20)
+Size
+100 ep
+200 ep
+400 ep
+MoCo v2 [12]
+256
+2×224
+-
+55.6
+-
+SimSiam [13]
+256
+2×224
+57.4
+-
+-
+SimCLR [10]
+4096
+2×224
+53.8
+57.2
+59.2
+SwAV [8]
+4096
+2×224
+-
+-
+61.3
+GroCo (ours)
+1024
+2×224
+60.5
+62.7
+63.6
+GroCo (ours)
+1024
+4×224
+61.8
+63.6
+65.0
+SwAV [8]
+4096
+2×224 + 6×96
+61.7
+63.7
+64.9
+GroCo (ours)
+1024
+2×224 + 6×96
+62.2
+64.4
+65.2
+Table 2.
+Comparison with state-of-the-art in k-NN perfor-
+mance on ImageNet. We evaluate k-NN performance (Top-1)
+on officially released weights of baseline models trained for 100,
+200, and 400 epochs. We used a simple weighted k-NN with k=20.
+Backbone=Resnet50.
+Method
+Epochs
+Batch
+Views
+Oxford
+Paris
+Size
+M
+H
+M
+H
+SimSiam [13]
+100
+256
+2×224
+26.89
+7.04
+46.92
+19.31
+MoCo v2 [12]
+200
+256
+2×224
+23.28
+5.07
+42.8
+17.33
+SimCLR [10]
+400
+4096
+2×224
+23.27
+4.56
+46.93
+20.19
+SwAV [8]
+400
+4096
+2×224
+28.01
+8.35
+46.23
+17.4
+GroCo (ours)
+400
+1024
+2×224
+31.77
+9.08
+54.79
+25.77
+Table 3. Comparison with state-of-the-art in image retrieval.
+We evaluate image retrieval performance on Medium (M) and
+Hard (H) splits of revisited Oxford and Paris datasets [45]. We
+evaluate nearest neighbor retrieval performance with ImageNet-
+trained encoders and report Mean Average Precision.
+lizing local-to-global correspondences our method outper-
+forms the SwAV method that uses ×4 larger batch size.
+Image Retrieval.
+To further demonstrate the potential
+of the proposed methods in nearest neighbors-based tasks,
+we additionally evaluate ImageNet-trained self-supervised
+learning methods in image retrieval on the revisited Oxford
+and Paris datasets [45] in Table 3. We report the Mean Av-
+erage Precision for the Medium (M) and Hard (H) splits of
+the datasets as in [9]. We observe that our method outper-
+forms all other methods in this task, confirming its good
+local properties of learned representations.
+4.4. Comparison to the Pairwise Contrastive Loss
+To evaluate the properties of the proposed method in a
+direct comparison with the pairwise contrastive loss formu-
+lation, we compared our method to the classical contrastive
+learning method SimCLR [10], which uses the most popu-
+lar InfoNCE loss [38] in training. Since SimCLR originally
+uses only two augmentations per image, we extend it to a
+group of positives scenario by applying contrastive loss be-
+tween all possible positive pairs (see supplement). For a
+fair comparison, we reproduced SimCLR with the 3-layers
+MLP projection head (as in our method) [11].
+Representation Learning Performance. First, we evalu-
+ated the learned representations based on the numbers of
+positive samples in Table 4. We consider four scenarios.
+Method
+Views
+k-NN Evaluation
+Linear Eval.
+k=1
+k=10
+k=20
+Top-1
+Top-5
+SimCLR
+2×224
+-
+-
+-
+64.3
+-
+SimCLR†
+2×224
+46.0
+51.5
+51.9
+65.7
+86.7
+SimCLR†
+3×224
+44.7
+50.0
+50.6
+65.8
+86.8
+SimCLR†
+4×224
+46.3
+52.1
+52.6
+66.5
+87.1
+SimCLR†
+2×224+6×96
+46.6
+51.4
+52.0
+67.2
+87.7
+GroCo (ours)
+2×224
+55.3
+60.3
+60.5
+69.2
+88.4
+GroCo (ours)
+3×224
+55.8
+61.2
+61.6
+69.5
+88.8
+GroCo (ours)
+4×224
+56.4
+61.5
+61.8
+69.6
+88.9
+GroCo (ours)
+2×224+6×96
+57.0
+61.9
+62.2
+71.6
+90.4
+Table 4. Comparison with SimCLR as a contrastive baseline
+on ImageNet. Results are reported for k-NN and linear probing.
+The best results are bolded. Backbone=Resnet50, #epochs=100,
+batch size=1024. †denotes our reproduction.
+First, in the 2 × 224 scenario, we sample only two augmen-
+tations per image, and therefore we have only one positive
+example per data point. In this case, our loss works simi-
+larly to SimCLR in a way that it is minimizing the distance
+between the positive example and the anchor, however, our
+loss still considers negatives as a group and utilizes only the
+nearest negative elements that are sorted incorrectly, there-
+fore focusing on local properties of representation space.
+While outperforming SimCLR baseline by +3% (Top-1) in
+linear probing, our method also advances in k-NN evalu-
+ation by more than +10% (k=20), demonstrating that our
+loss helps to learn better representation not only in terms of
+linear separability but also in terms of local structure. We
+further consider settings with 3×224, 4×224, and 2×224 +
+6×9 views. We observe that SimCLR shows mixed results
+from utilizing more views: while it benefits in linear evalu-
+ation, performance is not stable in k-NN, for 3×224 perfor-
+mance is lower and for 2×224 + 6×9 is the same. However,
+our method clearly profits from utilizing more positives in
+both evaluations, resulting in +1.7% in k-NN +2.4% in lin-
+ear evaluation for 2×224 + 6×9 setup.
+Transfer Performance. We further evaluated how well per-
+formance transfers on other datasets. In Table 5 we com-
+pare Imagenet pre-trained models in k-NN evaluation and
+linear transfer and on 11 many-shot classification datasets,
+including FGVC Aircraft [35], Caltech-101 [21], Stanford
+Cars [31], CIFAR10 [32], CIFAR-100 [32], DTD [14], Ox-
+ford 102 Flowers [36], Food-101 [6], Oxford-IIIT Pets [39],
+SUN397 [53] and Pascal VOC2007 [20]. For linear transfer
+evaluation, we follow the experimental protocol provided
+in [18] without any modification. We observe that the pro-
+posed method is on par with SimCLR in linear evaluation.
+In zero-shot k-NN evaluation, our method excels in 10 out
+of 11 datasets, in particular improving performance on the
+Pets dataset by +15%, and on the Aircraft and Food datasets
+by +4%. This shows that the improved k-NN performance
+transfers to downstream tasks as well.
+7
+
+Method
+Evaluation
+Aircraft
+Caltech101
+Cars
+Cifar10
+Cifar100
+DTD
+Flowers
+Food
+Pets
+SUN397
+VOC2007
+Average
+SimCLR†
+k-NN (weighted, k=20)
+19.5
+75.8
+15.2
+85.1
+63.3
+70.9
+73.1
+47.9
+60.6
+46.3
+70.0
+57.06
+GroCo (ours)
+k-NN (weighted, k=20)
+23.7
+79.3
+17.5
+85.4
+63.6
+69.3
+77.7
+52.8
+75.9
+50.1
+73.7
+60.81
+SimCLR†
+Linear transfer
+42.51
+85.10
+43.19
+90.86
+74.54
+75.11
+91.59
+68.20
+77.92
+58.43
+78.74
+71.47
+GroCo (ours)
+Linear transfer
+45.90
+86.44
+42.63
+89.26
+70.72
+72.77
+88.41
+66.72
+84.29
+58.51
+81.34
+71.55
+Table 5. Comparison with SimCLR as a contrastive baseline in transfer performance on 11 classification datasets. Models are
+pre-trained on Imagenet. Backbone=Resnet50, #epochs=100, batch size=1024, views=2x224. †denotes our reproduction.
+k-NN Evaluation
+Linear Probing
+k=1
+k=10
+k=20
+Top-1
+Top-5
+Triplet Loss (margin=0.8)
+46.8
+52.5
+52.8
+63.9
+85.4
+Triplet Loss (margin=1.6)
+47.9
+53.4
+53.7
+64.2
+85.3
+Triplet Loss (margin=+∞)
+47.9
+53.3
+53.8
+64.3
+85.3
+GroCo (Ours)
+54.7
+59.5
+60.0
+68.5
+88.2
+(a) Ordering supervision.
+k-NN Evaluation
+Linear Probing
+k=1
+k=10
+k=20
+Top-1
+Top-5
+Randomly ordered
+54.1
+59.2
+59.4
+68.4
+88.2
+Pre-ordered (Ours)
+54.7
+59.5
+60.0
+68.5
+88.2
+(b) Pre-ordering in the groups.
+Inverse temp.
+Number of negatives N
+β
+5
+10
+20
+k-NN
+Lin.p.
+k-NN
+Lin.p.
+k-NN
+Lin.p.
+0.25
+58.9
+67.9
+-
+-
+-
+-
+0.5
+59.1
+67.5
+59.8
+68.5
+-
+-
+1
+58.8
+67.7
+60.0
+68.5
+54.4
+65.2
+2
+-
+-
+60.0
+68.3
+56.2
+65.7
+4
+-
+-
+-
+-
+59.2
+67.7
+8
+-
+-
+-
+-
+58.6
+67.7
+(c) An inverse temperature β, a number of negatives N.
+Batch Size
+k-NN Evaluation
+Linear Probing
+k=1
+k=10
+k=20
+Top-1
+Top-5
+256
+52.2
+56.8
+56.8
+67.2
+87.7
+512
+53.1
+57.9
+58.1
+67.7
+87.8
+1024
+54.7
+59.5
+60.0
+68.5
+88.2
+(d) Batch size.
+Table 6. Ablation Experiments. For (c), we report k-NN perfor-
+mance with k=20, and linear probing performance (Top-1), de-
+noted as Lin.p.
+The best results are bolded.
+Options used to
+obtain the main results are highlighted.
+Backbone=Resnet50,
+Views=2×224, #epochs=100, Weight Decay=0.5e-6.
+4.5. Ablation Study
+Finally, we analyze the design choices of our method.
+Ordering Supervision. First, we compare the group order-
+ing supervision via differentiable sorting with a triplet loss
+formulation L = max (dp
+i − dn
+j + r, 0), where r is a mar-
+gin. For a fair comparison, we consider all positive and the
+10 strongest negative samples and evaluate different margin
+parameters in Table 6a. Here, sorting is superior to a triplet
+loss with hard margin selection.
+Pre-ordering in Groups. We analyze the impact of pre-
+ordering elements within the negative and positive groups
+before forwarding them to the sorting network in Table 6b.
+We observe that our methods achieve competitive perfor-
+mance even without pre-ordering; however, pre-ordering
+strengthens our method further.
+Inverse Temperature, Number of Negatives. In Table 6c,
+we examine the influence of the number of nearest neigh-
+bor negatives N used in the loss, as well as the value of
+the inverse temperature parameter β (Equation 2). We ob-
+serve that usage of too many negatives may not be benefi-
+cial for the model. Since our loss focuses on negatives that
+are sorted incorrectly, increasing the number of negatives at
+some point does not bring any new learning signal (because
+more distant is unlikely to be sorted incorrectly). However,
+a larger N results in more steps of the sorting network, in-
+creasing the degree of relaxation. Using a larger inverse
+temperature β (leading to a lower degree of relaxation in the
+swap operation) we can gain some performance; however,
+the variance of the gradients is larger with a larger β, which
+is not beneficial for optimization. We found that N = 10
+and β = 1 is the most efficient configuration.
+Batch Size. The large batch size might be an important fac-
+tor in obtaining good performance for many self-supervised
+learning methods. We find that our method is quite robust
+for training with smaller batch sizes (Table 6d).
+Training Time. We also consider the training time of our
+model compared to SimCLR baseline. To eliminate the in-
+fluence of distributed training, we measure the average time
+of training iteration on one GPU. We find that the iteration
+time of both models is comparable, 514ms for SimCLR vs
+526ms for the proposed methods for a batch size of 128.
+5. Conclusion
+In this paper, we proposed an alternative approach
+to the common pairwise contrastive learning formulation.
+Namely, we proposed the group ordering constraints, that
+consider positives and negatives as groups and enforce the
+group of positives to be closer to the anchor image than the
+negative group. To enforce these constraints, we leveraged
+recent progress in the context of differentiable sorting ap-
+proaches and formulated a group ordering loss based on the
+given sorting supervision. Our evaluation showed that the
+proposed framework, does not only compete with current
+contrastive loss baselines, but actually outperforms standard
+contrastive learning with regards to all k-NN-based metrics.
+8
+
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+Supplementary Material
+In the supplementary material, we first discuss relations be-
+tween the GroCo loss, the contrastive loss, and the triplet
+loss in Section A. Then we provide additional experimen-
+tal evaluation results in Section B and qualitative analysis
+in Section C. Then we describe odd-even sorting networks
+in Section D. Finally, we cover additional implementation
+details in Section E.
+A. Discussion of GroCo/Contrastive/Triplet
+Loss Relations
+In this section, we discuss the similarities and differences
+between the GroCo loss, the contrastive loss, and the triplet
+loss. For comparison purposes, let’s consider a simplified
+version of losses when there is only one positive example xp
+and one negative example xn for the anchor xa. We denote
+the distance from the anchor xa to the positive sample xp as
+dp = −
+xa⊤xp
+∥xa∥∥xp∥ and the distance from the anchor xa to the
+negative sample xn as dn = −
+xa⊤xn
+∥xa∥∥xn∥. Then contrastive
+InfoNCE loss (with respect to the anchor xa) is defined as:
+LContrastive = − log
+exp(−dp/τ)
+exp(−dp/τ) + exp(−dn/τ)
+= log (1 + exp(−(dn − dp)/τ)),
+(6)
+where τ is a temperature hyperparameter (Figure 4a).
+The triplet loss is defined as:
+LT riplet = max (dp − dn + r, 0) =
+= max (r − (dn − dp), 0),
+(7)
+where r is a margin hyperparameter (Figure 4b).
+For the GroCo loss, a permutation matrix P ∈ R2×2
+corresponds to only one conditional swap operation and is
+defined as:
+P11 = P22 = f(dn − dp) = 1
+π arctan(β(dn − dp)) + 0.5,
+P12 = P21 = f(dp − dn) = 1
+π arctan(β(dp − dn)) + 0.5,
+(8)
+where β is an inverse temperature. Therefore, the GroCo
+loss is defined as:
+LGroCo = 1
+4
+�
+−2 log
+� 1
+π arctan(β(dn − dp)) + 0.5
+�
+−
+−2 log
+�
+1 − 1
+π arctan(β(dp − dn)) − 0.5
+��
+=
+= − log
+� 1
+π arctan(β(dn − dp)) + 0.5
+�
+,
+(9)
+where β is an inverse temperature hyperparameter (Fig-
+ure 4c).
+In Figure 4, we show the loss curves with different values
+of respective hyperparameters. We note that in this simpli-
+fied example with only one positive and only one negative,
+all three losses try to maximize the difference between the
+distances to the positive and negative examples (dn − dp).
+The temperature τ, the margin r, or the inverse tempera-
+ture β define the flatness of the loss curve depending on the
+difference (dn − dp).
+However, in the case with more negative/positive ex-
+amples for the anchor image, different losses integrate
+information from multiple negatives/positives in different
+ways. For triplet loss, there are various strategies to sam-
+ple one positive example and one negative example for the
+anchor image [49, 55].
+The complete loss is defined as
+the sum (or average) of the losses for the chosen triplets
+�
+ij max (r − (dn
+i − dp
+j), 0). On the other hand, the con-
+trastive loss aggregates multiple negatives by contrasting
+the positive example to all negative examples, resulting in
+sum under logarithm: log (1 + �
+i exp(−(dn
+i − dp)/τ)).
+And in contrast to an explicit sum over a predefined num-
+ber of negatives, the GroCo loss aggregates multiple posi-
+tives and negatives via the permutation matrix, condition-
+ally swapping neighboring elements, and later applies the
+group ordering supervision, enforcing the distance between
+positive and negative groups.
+B. Additional Experimental Results
+In this section, we provide additional experimental eval-
+uations:
+Augmentation Strategy. In Table 7a we evaluate the per-
+formance of the model with respect to different augmenta-
+tion strategies for view sampling. We follow two setups:
+1) the augmentation strategy as used in the SimCLR [10]
+method with a random resized crop, color jittering, and
+gaussian blur, grayscaling and horizontal flip and 2) the aug-
+mentation strategy as used in the DINO [9] method that ex-
+tends the SimCLR list of augmentations with solarization.
+SimCLR augmentations are considered as “stronger” com-
+pared to DINO augmentations since they include a larger
+range of cropping sizes (8% -100% of original image com-
+pared to 14%-100% in DINO augmentations) and larger
+range values in color jittering. We observe that the stronger
+SimCLR [10] augmentations are more beneficial for the
+SimCLR method than the weaker DINO augmentations,
+while for the proposed method, the DINO augmentation
+strategy is more beneficial.
+However, the difference be-
+tween augmentation strategies diminishes with increasing
+number of training epochs and is no longer measurable at
+400 epochs. For a fair comparison, we use the SimCLR
+augmentation strategy in all reproductions of the SimCLR
+method reported in the main paper.
+11
+
+log (1 + exp(−(dn − dp)/τ))
+2
+1
+0
+1
+2
+dn
+dp
+0
+5
+10
+15
+20
+Loss
+LContrastive,
+= 0.1
+LContrastive,
+= 0.5
+LContrastive,
+= 1
+(a) Contrastive InfoNCE loss
+max (r − (dn − dp), 0)
+2
+1
+0
+1
+2
+dn
+dp
+0
+1
+2
+3
+4
+Loss
+LTriplet, r = 0.8
+LTriplet, r = 1.6
+LTriplet, r = 2
+(b) Triplet loss
+− log( 1
+π arctan(β(dn − dp)) + 0.5)
+2
+1
+0
+1
+2
+dn
+dp
+0
+1
+2
+3
+Loss
+LGroCo,
+= 0.25
+LGroCo,
+= 1
+LGroCo,
+= 4
+(c) GroCo loss
+Figure 4. Comparison of the contrastive loss, the triplet loss, and the GroCo loss in a simple scenario with only one positive example and
+one negative example for an anchor image. We denote the distance from the anchor to the positive sample as dp and the distance from the
+anchor to the negative sample as dn. We note that in the simple case of only one positive and one negative, all three losses try to maximize
+the difference between the distances to the positive and negative examples (dn − dp). The temperature τ, the margin r, or the inverse
+temperature β define the flatness of the loss curve depending on the difference (dn − dp).
+Method
+Augmentations
+Epochs
+k-NN Evaluation
+Linear Evaluation
+k=1
+k=10
+k=20
+Top-1
+Top-5
+SimCLR
+as in SimCLR [9]
+100
+46.0
+51.5
+51.9
+65.7
+86.7
+SimCLR
+as in DINO [9]
+100
+43.3
+48.6
+49.1
+63.7
+85.4
+GroCo
+as in SimCLR [9]
+100
+54.0
+59.0
+59.4
+68.4
+88.3
+GroCo
+as in DINO [9]
+100
+55.3
+60.3
+60.5
+69.2
+88.4
+GroCo
+as in SimCLR [9]
+200
+56.7
+61.6
+61.8
+69.8
+89.1
+GroCo
+as in DINO [9]
+200
+57.7
+62.4
+62.7
+70.4
+89.5
+GroCo
+as in SimCLR [9]
+400
+58.3
+63.3
+63.8
+71.1
+89.7
+GroCo
+as in DINO [9]
+400
+58.7
+63.4
+63.6
+71.0
+89.7
+(a) Augmentation strategy
+Projection dim
+Embedding dim
+k-NN Evaluation
+Linear Probing
+k=1
+k=10
+k=20
+Top-1
+Top-5
+128
+2048
+53.7
+58.5
+58.7
+68.1
+88.0
+512
+2048
+55.2
+59.8
+60.1
+69.0
+88.5
+2048
+2048
+55.3
+60.3
+60.5
+69.2
+88.4
+(b) Projection dimentionality
+k-NN Evaluation
+Linear Probing
+k=1
+k=10
+k=20
+Top-1
+Top-5
+10 random negatives
+39.5
+45.0
+45.3
+60.1
+82.7
+top-10 strongest negatives
+55.3
+60.3
+60.5
+69.2
+88.4
+(c) Importance of negatives
+Method
+Space
+k-NN Evaluation
+k=1
+k=10
+k=20
+SimCLR
+Projection Space
+35.8
+41.6
+42.3
+SimCLR
+Representation Space
+46.0
+51.5
+51.9
+GroCo
+Projection Space
+51.4
+56.9
+57.3
+GroCo
+Representation Space
+55.3
+60.3
+60.5
+(d) k-NN evaluation
+Table 7. Additional Experiments. The best results are bolded.
+Options used to obtain the main results are highlighted. Back-
+bone=Resnet50, Views=2×224, #epochs=100.
+Projection Dimensionality.
+We also ablate our method
+with respect to the dimensionality of the projection space
+(or the latent space), where distances between samples are
+computed to calculate a training loss. Table 7b shows that
+increasing dimensionality of the projection space increases
+performance in general, which is more noticeable for the
+k-NN performance. Note that we do not change the dimen-
+sionality of the embedding space (output space of the en-
+coder that is used for the k-NN evaluation and linear evalu-
+ation), which is always 2048-dimensional.
+Importance of Negatives. We also evaluate the importance
+of utilizing strong negatives for the successful training of
+our model. We train the model using ten random negatives
+instead of the top-10 strongest negatives as a negative group
+and report performance in Table 7c. We observe that lever-
+aging the strongest negatives increases performance across
+all metrics, demonstrating the importance of hard negatives
+during training with the GroCo loss, similarly as the con-
+trastive loss benefits from hard negative sampling [47].
+k-NN in Projection Space. We also evaluate the k-NN per-
+formance in the projection space (or the latent space) where
+the training loss is applied. We compare k-NN performance
+in the projection and representation spaces in Table 7d. We
+observe that for both methods, k-NN performance is higher
+if we use embeddings from the representation space even
+though we train the model to compare embeddings in the
+projection space. This could be explained by the fact that
+the embedding space contains more general image represen-
+tations since the representations in projection space could
+be overfitted to the respective augmentations and there be-
+come agnostic to some image attributes (like color, since we
+train the model to match views with different color jittering
+parameters).
+12
+
+Algorithm 1 Python pseudocode of an odd-even sorting
+network for sorting an array of numbers in non-descending
+order
+# arr: array to sort
+# n: length of array
+for s in range(1, n + 1):
+if s % 2 == 1:
+for i in range(0, n - 1, 2):
+if arr[i] > arr[i+1]:
+arr[i], arr[i+1] = arr[i+1], arr[i]
+else:
+for i in range(1, n - 1, 2):
+if arr[i] > arr[i+1]:
+arr[i], arr[i+1] = arr[i+1], arr[i]
+2
+4
+1
+6
+6
+1
+1
+6
+4
+2
+2
+4
+1
+2
+4
+6
+1
+2
+4
+6
+step 1
+step 2
+step 3
+step 4
+Input:
+6
+4
+2
+1
+Output:
+[1]
+[2]
+[3]
+[4]
+Figure 5. An illustration of an odd-even sorting network for sort-
+ing four elements in non-descending order with an example of
+sorting of [6, 1, 4, 2] array.
+C. Qualitative Analysis of Learned Represen-
+tation Space
+We also additionally perform a qualitative analysis of
+learned representation. In Figure 6, we visualize represen-
+tations for images from four classes of different types of
+cats and four classes of different types of dogs. We find that
+our method produces much more visually separable clusters
+with respect to “inter-class” variations (cats vs dogs) and
+“intra-class” variations (between different classes of cats)
+than the SimCLR baseline.
+D. Odd-even Sorting Network
+An odd-even sorting network, or odd-even sort, is a sort-
+ing algorithm from classic computer science literature [30].
+Sorting networks, or networks for sorting, are a family of
+sorting algorithms that consist of the fixed sequence of com-
+parisons, in a sense that the next comparisons (elements on
+which positions are compared) does not depend on the re-
+sult of previous comparisons. An odd-even sorting network
+is a simple example of this family of algorithms. The odd-
+even sorting network compares neighbored elements start-
+ing from odd and even indices alternating on each step,
+and requires n steps to sort a sequence of n elements. We
+present a pseudocode of the odd-even sorting network in
+Algorithm 1. We also additionally illustrate the odd-even
+sorting process in Figure 5.
+E. Implementation Details
+E.1. Linear Evaluation Details
+For linear evaluation, we train a linear classifier on
+frozen representations in a fully-supervised way, using the
+training set of ImageNet for training and the validation set
+for evaluation.
+We follow the training protocol of Sim-
+CLR [10] and SimSiam [13] and train a linear classifier for
+90 epochs using the LARS optimizer [57] with the batch
+size of 4096, the momentum of 0.9, the linear rate of 1.6
+(following the rule: learning rate = 0.1 × batch size/256),
+without a warmup and weight decay. Following [10] and
+[13], we use weak data augmentation (only random crop-
+ping with horizontal flipping) and apply gradient stopping
+on the input of the classifier to prevent updating the encoder.
+E.2. SimCLR with Multiple Positives
+To train SimCLR with more than one positive view per
+anchor, we apply contrastive loss for all possible positive
+pairs, considering all views from other images in the batch
+as negatives (with a batch of B examples with have m(B −
+1) negatives views). Let xb
+i denote the i’th view of the b’th
+image in a batch, and Pxb
+i denote a set of positive samples
+for the anchor xb
+i, and Nxb
+i denote a set of positive samples
+for the anchor xb
+i. Then, the loss is calculated as
+LSimCLR = 1
+B
+B
+�
+b=1
+1
+m
+m
+�
+i=1
+1
+���Pxb
+i
+���
+�
+y∈Pxb
+i
+− log
+�
+exp(−d(xb
+i, y)/τ)
+exp(−d(xb
+i, y)/τ) + �
+z∈Nxb
+i exp(−d(xb
+i, z)/τ)
+�
+,
+(10)
+where τ is a temperature parameter. This extension of the
+SimCLR framework for m > 2 views per image is the same
+as used in the SwAV evaluations [8]. Note that in the multi-
+crop scenario, we use only full-resolution global views as
+positive examples following “local-global” correspondence
+idea [8,9].
+13
+
+(a) SimCLR
+(b) GroCo (ours)
+Figure 6. t-SNE visualization of learned representations of Imagenet validation images from four classes of different types of cats (Egyptian
+cat, Persian cat, Siamese cat, Tabby cat) and four classes different types of dogs (Pomeranian dog, African hunting dog, Tibetan mastiff,
+English setter) for the SimCLR method and the proposed method. For visualization we use models with Resnet50 encoder trained for 100
+epochs with a batch size of 1024 and 2 × 224 views.
+14
+
+24
+15
+5
+0
+600
+5
+-10
+-15
+-20
+-15
+-10
+5-
+0
+5
+1524
+15
+Egyptian cat
+Persian cat
+5
+Siamese cat
+Tabby cat
+Pomeranian dog
+African hunting dog
+5
+Tibetan mastiff
+English setter
+-10
+15
+-20
+-15
+of-
+5-
+0
+5
+1515
+5
+600
+5
+-10
+15
+20
+20
+15
+-10
+5-
+0
+5
+1
+1515
+Egyptian cat
+5
+Persian cat
+Siamese cat
+0-
+Tabby cat
+Pomeranian dog
+5-
+African hunting dog
+Tibetan mastiff
+-10
+English setter
+-15
+-20 
+-20
+-15
+of-
+5-
+5
+1
+15
\ No newline at end of file
diff --git a/R9A0T4oBgHgl3EQfDv_g/content/tmp_files/load_file.txt b/R9A0T4oBgHgl3EQfDv_g/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..28b18409d59d32168ac41769d5580c65d830b69b
--- /dev/null
+++ b/R9A0T4oBgHgl3EQfDv_g/content/tmp_files/load_file.txt
@@ -0,0 +1,1039 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf,len=1038
+page_content='Learning by Sorting: Self-supervised Learning  with Group Ordering Constraints  Nina Shvetsova1,3  Felix Petersen2  Anna Kukleva3  Bernt Schiele3  Hilde Kuehne1,4  1Goethe University Frankfurt, 2Stanford University, 3Max-Planck-Institute for Informatics, 4MIT-IBM Watson AI Lab  shvetsov@uni-frankfurt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='de  Abstract  Contrastive learning has become a prominent ingredi-  ent in learning representations from unlabeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' How-  ever, existing methods primarily consider pairwise rela-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This paper proposes a new approach towards self-  supervised contrastive learning based on Group Ordering  Constraints (GroCo).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The GroCo loss leverages the idea of  comparing groups of positive and negative images instead  of pairs of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Building on the recent success of dif-  ferentiable sorting algorithms, group ordering constraints  enforce that the distances of all positive samples (a posi-  tive group) are smaller than the distances of all negative  images (a negative group);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' thus, enforcing positive samples  to gather around an anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This leads to a more holistic  optimization of the local neighborhoods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We evaluate the  proposed setting on a suite of competitive self-supervised  learning benchmarks and show that our method is not only  competitive to current methods in the case of linear prob-  ing but also leads to higher consistency in local represen-  tations, as can be seen from a significantly improved k-NN  performance across all benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Introduction  Self-supervised learning has become a topic of grow-  ing interest over the last years as it allows models to learn  representations from large-scale data without any need for  annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Recently, self-supervised contrastive meth-  ods [3,10,17,26,51,56] notably narrowed the gap to the su-  pervised learning performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' These methods rely on the  concept of the pairwise contrastive loss, which is based on  the idea that an image, serving as anchor, and an augmenta-  tion of the same image, a so-called positive pair, should be  close to each other in a projection space, while a pair made  up of an anchor image and a different image, a so-called  negative pair, should be far away from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This con-  cept of bringing positive pairs in embedding space closer  together was further extended in various frameworks, such  Update  Contrastive Loss  Group Ordering Constraints (GroCo) Loss  all pos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' distances < all neg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' distances  Update  Distance  Distance  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Pairwise contrastive loss compared to the proposed  group ordering constraints loss: While pairwise loss only consid-  ers pairwise distances, groupwise sorting allows us to enforce that  a group of positive samples is closer to the anchor than a group of  negative ones and, thus, to improve the representation of the local  neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  as BYOL [23], SwAV [8], and many more [4,9,13,19,58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  However, the idea of the pairwise contrastive loss is lim-  ited by the fact that it only considers individual positive  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This means that it can not align the embedding space  based on more than two positive data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Several at-  tempts have been made to address this issue, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', combin-  ing the contrastive idea with concepts based on local neigh-  borhoods, such as clustering as in the case of SwAV [8],  or minimizing distances between multiple positives pairs  for the same instance together as in the case of Whiten-  ing [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Another limitation of the contrastive loss is that  it requires a large number of negatives in order to be effec-  tive [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Some methods tackle this issue by leveraging a  large batch size [10], memory banks [26], or negative min-  ing [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' However, here, a drawback is that, as the embed-  ding space is optimized with respect to all negatives, even  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='02009v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='CV]  5 Jan 2023  Positives  Negatives  Negative Positions  Positive Positions  Group of Negatives  Group of Positives  Distance to  Anchor:  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  Differentiable Odd-even  Sorting Network:  (Sorts input values in ascending order  by swapping neighboring elements)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  Differentiable Permutation Matrix:  (Probability of elements to be swapped  to rank [1,2,3,4])  Swaps between x - not ok  Swaps within group -  ok  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  Group Ordering Constraints (GroCo) loss:  Sum over negative and positive positions  and compute BCE  ∑ Negative  Positions  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  ∑ Positive  Positions  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  Negative  GT  Positive  GT  Projection  Space:  BCE  loss  [1]         [2]        [3]        [4]  Anchor  Encoder  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Overview of the proposed group ordering constraints loss: We first compute the distance of groups of positive as well as  negative samples with respect to an anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The distances are sorted via a differentiable odd-even-sorting network in non-descending  order, computing the swapping probability for samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The result is a differentiable permutation matrix, in which the row values can be  thought of as the probabilities of sorting the elements into the corresponding positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We can ignore swap operations within groups, and  only need to consider swapping operations between groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We, therefore, sum over the positive and negative columns of the permutation  matrix and compute the BCE between the row-wise entries and the expected ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  negatives that are far away from the anchor will contribute  to the optimization of the representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Other methods  were proposed to address this issue, such as hard nega-  tive selection by controlling the hardness of examples [47]  or negative selection by sparse support vectors [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Yet,  these methods still require manual selection of the hardness  level [47] or incur an additional optimization cost [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  In this paper, we propose a novel approach to address  those points by shifting away from the concept of a pairwise  contrastive loss and instead propose to train the network  based on Group Ordering Constraints (GroCo)—namely,  the idea that the group of multiple positives should be closer  to an anchor image than any negative from the group of neg-  atives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We illustrate this idea and comparison with the pair-  wise contrastive loss in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' With group constraints,  we do not treat positive and negative pairs individually, as  in contrastive loss, but rather as groups, and effectively con-  strain only those elements that are placed in the group over-  lap area with respect to the distance to the anchor point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  To enforce the group ordering constraints in the projec-  tion space, we propose the idea of learning by sorting: we  suggest sorting positives and negatives by distance to the  anchor image in a differentiable way and swapping them if  they are in the wrong order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To create an end-to-end train-  ing pipeline, we leverage recent advances in differentiable  sorting [16, 24, 41, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Specifically, we utilize a differen-  tiable sorting algorithm to obtain a differentiable permu-  tation matrix for sorting a list of distances to the positive  and negative images, as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' If we would  know the full ground truth orderings among positives and  negatives, such as which positive sample should be closer  to the anchor than another positive sample, we could cre-  ate a ground truth permutation matrix, and calculate how  much the predicted permutation matrix would deviate from  the ground truth one [16, 24, 41, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Since this assump-  tion is not given in practice and we do not know the ground  truth distance ordering within the positive or the negative  groups, we propose the GroCo loss, a relaxed formulation  of the original sorting supervision that captures how many  negative elements appear in the positive positions and vice  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Compared to the pairwise contrastive loss, the result-  ing group ordering focuses on optimizing the local neigh-  borhood around an anchor image, rather than optimizing all  data points at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Moreover, without any additional mod-  ifications, our group ordering loss directly focuses on the  strongest positive and negative examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  To show the capabilities of the proposed approach, we  evaluate it on a suite of competitive self-supervised learn-  ing benchmarks, namely in the context of linear probing, k-  NN classification, as well as image retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Our evaluation  demonstrates that models trained via group ordering con-  straints obtain competitive performance in linear evaluation  compared to other contrastive learning frameworks, some  of them even trained with significantly larger batch sizes  and/or an additional teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Further, we demon-  strate the superior ability of the proposed method in the  context of shaping local neighborhoods by evaluating the  nearest neighbor classification capabilities by outperform-  ing any other state-of-the-art method on this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We summarize the contributions of this work as follows1:  We propose a new concept for self-supervised repre-  sentation learning based on learning by sorting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We leverage recently proposed differentiable sorting  methods to derive the contrastive group ordering con-  straints (GroCo) loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We demonstrate that the proposed method achieves  competitive performance in linear separability of em-  beddings and is especially suitable to model the lo-  cal neighborhoods and outperforms current top-level  state-of-the-art frameworks on a wide range of nearest-  neighbor tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  1The code will be made publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Related Work  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Self-supervised Representation Learning  Self-supervised learning aims to learn a robust represen-  tation from data without human annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Various learn-  ing objectives were developed for self-supervised learning  from images including image colorization [60], inpaint-  ing [40], puzzle solving [37], and rotation prediction [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Over the last years, methods [8, 10, 13, 23, 26] that en-  force the model to be robust to different image distor-  tions achieved great performance improvements in self-  supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Such methods generally rely on sam-  pling two augmented views of the image—a positive pair—  and minimize the distance between those in the embedding  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Contrastive methods [10–12,26] are a great example  of those approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To prevent the model from learning a  trivial solution for any input, contrastive methods also in-  troduce the concept of a negative pair, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', two different im-  age, and contrast positive pairs against negative pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The  InfoNCE loss, which is often referred to as a contrastive  loss, is the most prominent method in many self-supervised  learning scenarios [1, 10, 26, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Earlier contrastive meth-  ods relied on the triplet loss [49], which considers one pos-  itive and one negative example for the anchor image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In  contrastive learning, many components and extensions have  been investigated: data augmentation strategies [10, 54],  projection head design [11], hard negative sampling [47],  increasing the richness of positives with nearest neigh-  bours [17], or mitigating effect of false negatives [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In  this work, we propose a novel contrastive method—learning  by sorting—which features properties not inherent to other  contrastive learning methods: we primarily consider those  positives and negatives that are placed (sorted) incorrectly  in the embedding space, thereby implicitly considering the  strongest positive and negative examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  There are also methods [13, 23] that do not rely on  negatives and only maximize agreement between positive  views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Such methods prevent collapsing of the representa-  tion space by using asymmetric architectures applied to dif-  ferent views [13,23], an additional teacher network [9,23],  stop gradient [9,13,23], feature whitening [19], or informa-  tion maximization [4, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Another set of methods [2, 7, 8]  utilizes clustering of the latent embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' However, so  far, methods mostly rely on similarity maximization be-  tween only two sampled views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' SwAV [8] also considered  sampling more augmentations in a multi-crop setting, where  two full-size augmented images are sampled together with  several smaller crops, and Whitening [19] utilized more  full-resolution samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' However, even in these cases, the  loss was still computed by considering pairs of views inde-  pendently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In contrast, we propose optimizing the embed-  ding space based on group ordering constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Differentiable Sorting and Ranking  Differentiable sorting and ranking methods provide a  pipeline that allows training neural networks with order-  ing supervision in an end-to-end fashion with gradient de-  scent [5, 16, 24, 41, 42, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The sorting operator can be  seen as a function returning a permutation matrix that in-  dicates the permutation necessary to sort the sequence of  values (the matrix that multiplied with a input vector returns  a sorted output vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=') In this context, differentiable sort-  ing refers to relaxing the (hard) permutation matrix to a dif-  ferentiable permutation matrix via continuous relaxations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The differentiable permutation matrix for a given sequence  of values, which could, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', be scores predicted by a neural  network, can then be used to compute the loss by compari-  son to a ground truth permutation matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Recently, multi-  ple methods for relaxing the permutation matrix have been  proposed, including an argsort approximation by unimodal  row-stochastic matrices [24, 44], a formulation of entropy-  regularized optimal transport [16], as well as networks of  differentiable swap operations (differentiable sorting net-  works) [41,42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The latter method composes the full permu-  tation matrix as a product of permutation matrices that arise  from comparing only two elements at a time (usually neigh-  bors) and either swapping them or not swapping them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In-  spired by the idea of swapping the neighboring elements in  the sequence, our approach learns representations by com-  paring neighboring elements in the embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  In terms of applications, differentiable sorting has been  leveraged in various contexts, including recommender sys-  tems [33], image patch selection [15], selection experts in  multi-task learning [25], and attention mechanisms [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To  the best of our knowledge, the proposed method is the first  work to leverage ordering supervision for self-supervised  learning of visual representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Method  Given a dataset of images {xi}M  i=1 ⊆ X, our goal is to  learn an encoder g : X → Rd that extracts image represen-  tations that later might be used for downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Training Pipeline  Similar to other contrastive methods, our approach con-  siders several augmented views of the same image as pos-  itive examples, which should be close together in an em-  bedding space, and different images as negative examples,  which should be apart in an embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Our model  starts from sampling mini-batches of B images and gener-  ates m ≥ 2 randomly augmented views per each image,  resulting in m · B data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' If m = 2 we are close to the  original pairwise contrastive learning setup [4, 10, 13, 28,  58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The augmented views are processed with the encoder  network g(·), that extracts data representation vectors from  views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Then, an MLP projection head h(·) maps represen-  3  tations to the latent space where distances between views  are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For each data point serving as an anchor xa,  we have m − 1 positive examples {xp  i }m−1  i=1 (which results  in 1 positive example in the classical setup of m = 2) and  m·(B−1) negative examples {xn  i }m·(B−1)  i=1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We use the co-  sine distance to measure the distance between data points:  d(x, y) = −  x⊤y  ∥x∥∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='y∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Group Ordering Constraints (GroCo)  In order to consider not only pairs of views but instead  groups of multiple positives at once, we extend the con-  trastive loss to the idea that the group of positives should  be closer to the anchor image than the group of negatives in  the embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This idea directly results in group  ordering constraints (GroCo).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  To simplify the notation,  we denote the distance between data point xa and its pos-  itive xp  i and negative examples xn  i as dp  i = d(xa, xp  i ) and  dn  i = d(xa, xn  i ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' If we assume that K positives xp  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', xp  K  are ordered with respect to their distances to the anchor  xa as dp  1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' ≤ dp  K and N negatives xn  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', xn  N as  dn  1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' ≤ dn  N, then we define the group ordering con-  straints as  dp  1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' ≤ dp  K <<< dn  1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' ≤ dn  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  (1)  As can be seen in Equation 1, all elements in the groups  are considered in the constraints;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' however, for training,  the relevant constraint is the (bold) < in the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This  constraint differs from pairwise contrastive loss constraints,  which 1) consider positives individually and 2) consider all  negatives even if they are far away from the anchor and are  thus less relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Our constraints also differ from the triplet  loss, which considers only one positive and one negative ex-  ample, while we are working with groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Learning by Sorting  Inspired by recent advances in differentiable sorting [41,  42], we design a loss that fulfills our group ordering con-  straints based on differentiable sorting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Our training pro-  cedure can be seen as sorting positives and negatives in the  embedding space with respect to an anchor image and swap-  ping them if they are in the incorrect order;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' therefore, we  call the approach learning by sorting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  Differentiable Sorting Networks  In the following, we review the differentiable sorting algo-  rithm called differentiable sorting networks [41] as it is a  core element of our loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We note that “networks”  in “sorting networks” is not related to the term “neural net-  works” and that a differentiable sorting network is a func-  tion with no trainable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Sorting networks are a  family of sorting algorithms from classic computer science  literature [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' An example of this is the odd-even sort-  ing network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' By relaxing the conditional swap operator to  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  step 1  step 2  step 3  step 4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  P1  Input:  P2  P3  P4  f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2) f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6)  0  0  f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6) f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2)  0  0  0  0  f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4) f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8)  0  0  f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8) f(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4)  P = P4 ⦁ P3 ⦁  P2 ⦁  P1  P1=  Differentiable Odd-even Sorting Network  differentiable conditional swap operation  Output: differentiable  permutation matrix P  1  0  1  1  x  p  f(x) = 1/𝜋 arctan(βx) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  f(x)  β= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  β= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  β= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Overview of a differentiable sorting network with the  odd-even sorting algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The network compares neighboring  elements that start from odd and even indices alternatively in each  step and apply a differentiable swap operation if elements are in  the wrong order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The conditional swap operations on each step s  also define a differentiable permutation matrix Ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The network  output is a complete differentiable permutation matrix P, defined  as the multiplication of matrices of each step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  a differentiable conditional swap, sorting networks can be  made differentiable by relaxation to differentiable sorting  networks [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We consider differentiable sorting networks based on  the odd-even sorting network to sort an input sequence of  K + N elements in non-descending order as shown in Fig-  ure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The differentiable sorting network is defined as a  composition of functions, where each function refers to one  step of sorting, and where pairs of elements of the input se-  quence are compared and swapped if they are in the wrong  order via a conditional swap operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For the odd-even  sorting network network, the algorithm compares neigh-  bored elements on odd and even indices alternatingly in  each step, and requires K + N steps to sort a given input  sequence of length K + N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The conditional swap operation for elements (di, dj)  where i < j can be defined as d′  i = min(di, dj), d′  j =  max(di, dj), and the differentiable relaxation [42] of this  operation is defined as:  d′  i = softmin(di, dj) = dif(dj − di) + djf(di − dj)  d′  j = softmax(di, dj) = dif(di − dj) + djf(dj − di) (2)  where f(x) =  1  π arctan(βx) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5 [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The hyperpa-  rameter β > 0 denotes an inverse temperature, and when  β → ∞ the relaxation converges to the discrete swap op-  eration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The differentiable conditional swap operation for  the elements (di, dj) can be defined as a permutation ma-  trix Pswap(di,dj) ∈ R(K+N)×(K+N) is an identity matrix  4  except for entries Pii, Pij, Pjj, Pji, which are defined as:  Pii = Pjj = f(dj − di),  Pij = Pji = f(di − dj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  (3)  The permutation matrix Ps for step s is the product of matri-  ces corresponding to parallel (and thus independent) swap  operations in this step Ps = �  i∈R Pswap(di,di+1), where R  is the set of odd indices if s is odd and the set of even in-  dices if s is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The complete permutation matrix P is  defined as P = PK+N · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' · P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  In the discrete case, each row of a permutation matrix has  exactly one entry of 1, which indicate the position where the  element that corresponds to this row should be placed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In  the relaxed version, row values can be seen as a distribution  over possible positions of the element [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For training  with sorting supervision, where the correct order of input  values is known, we can create a ground truth matrix Q and  define the loss as L =  1  (K+N)2  �  i,j BCE(Pij, Qij) where  BCE refers to binary cross-entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  GroCo Loss  If we would know the ground truth order of positives and  negatives, we could create a ground truth permutation ma-  trix and calculate a loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  However, as we rely on ran-  dom augmentations, we do not know the ground truth order  among positives and among negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Thus, we propose  a solution to obtain a loss to fulfil our group ordering con-  straints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Let us again assume that positives are ordered with re-  spect to their distances to the anchor image as dp  1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' ≤  dp  K and negatives as dn  1 ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' ≤ dn  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' As shown in Figure 3,  we concatenate positive and negative distances in a list:  [dp  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', dp  K, dn  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', dn  N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  (4)  Even though we have ordered elements in the positive and  negative sub-list, we still don’t know if the constraint dp  i <  dn  j is fulfilled for any 1 ≤ i ≤ K and 1 ≤ j ≤ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Here, we apply a differentiable sorting network to the  list and obtain a differentiable permutation matrix for sort-  ing the list in non-descending order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Values in a permu-  tation matrix row can be seen as probabilities to sort the  corresponding element to the different positions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=', P11  would be the probability for assigning the first element in  the list (dp  1) to position 1, P12 to position 2, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Therefore,  a sum of the first K elements in a row can be considered as  a probability being sorted inside the first K elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Thus,  for a permutation matrix of size (K + N) × (K + N) the  sum of the first K columns results in probabilities of being  sorted in positive places and the later columns (from K + 1  to K +N) in negative places.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We define a loss that enforces  positives to be sorted in the positive places and negatives in  the negatives places, as  L =  1  2(K + N)  K+N  �  i=1  �  BCE  � K  �  k=1  Pik, 1i≤K  �  +  + BCE  � K+N  �  k=K+1  Pik, 1i>K  �  �  (5)  where 1 is an indicator function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  As illustrated in Figure 2, our loss is a relaxation of the  sorting supervision that considers only two types of swap  operations: swap operations within the group of positive  and negative samples, which should not contribute to the  loss, and swap operations between the groups, which vi-  olate the positive-negative ordering assumption and which  we want to use as the optimization criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Role of Pre-ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Practically, we pre-order positives  and negatives inside the groups in a non-differentiable way  before inputting them into the differentiable sorting net-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Though even without it, the loss will still contrast  positives to negatives, we believe that pre-ordering fulfills  the idea behind GroCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' When we input pre-ordered ele-  ments, the sorting network performs comparisons of neigh-  boring elements swapping them if they are in the wrong  order, or if everything is sorted correctly, comparing the  strongest positive with the strongest negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In this way,  elements are considered as a group, and borders of the  groups or their overlapping parts are used in the loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Number of Negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Since the only strongest negatives  (that are sorted incorrectly) mostly participate in the compu-  tation of the loss function, we may use only top-N strongest  negatives almost without losing any learning signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  will show in the ablation study that N = 10 is enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Role of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The inverse temperature β in differentiable  swap operation corresponds to the degree of relaxation of  the swap operation that converges to a discrete case when  β → ∞ (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Therefore with lower β the swap oper-  ation is more “soft”, which means that the variance in gra-  dients is smaller, which is beneficial for optimization, but  a relaxation error accumulated by steps is larger, and vice  versa in the case of larger β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' With higher β even a small  difference between values results in a high probability for  a swap or not swap operation, resulting in a smaller margin  between the positive and negatives group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' With lower β we  push positive and negative groups further apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Experimental Evaluation  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Implementation Details  Unless stated otherwise, we use the following setup for  all of our experiments:  5  Augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To create m augmented views per image  (considering m = 2, 3, 4), we follow the DINO augmen-  tation setup [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Since computational cost grows linearly  with an increasing number of augmentations, we addition-  ally considered the multi-crop augmentation strategy pro-  posed in SwAV [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The idea is to sample low-resolution  local views along with the standard 224×224 ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We use  2× 224 + 6× 96 scheme, where with two global 224× 224  augmented views, we also sampled six local 96 × 96 views,  giving eight views per image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In this case, we follow “local-  to-global” correspondence idea [8, 9] and use only global  views as positives for both local and global anchor images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To be consistent with previous works [8,10,13,23]  we use Resnet50 [27] as the encoder g(·) and an MLP  block consisting of three fully connected layers with a size  of 2048 and followed by a batch normalization layer [29]  as the projection head h(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' All batch normalization lay-  ers except the last one are followed by a ReLU activa-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The dimensionality of the representation space and  the latent space are both 2 048 as in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We also adopt  the stop gradient operation, which is widely used in dif-  ferent self-supervised learning methods [9, 10, 23];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' specifi-  cally, we perform stop gradient during distance computation  d(xa, x·  i) = d(xa, stop grad(x·  i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' While we found that  it is not strictly necessary for a successful training of our  model, we observed that stop gradient makes the training  process more stable and allows training the model with a  much larger variation of hyperparameters while maintain-  ing stable performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Following previous works [8,10,13,23], we use  the train set of the ImageNet ILSVRC-2012 dataset [48] for  self-supervised training without any human annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  train our model with the SGD optimizer [57] with a learn-  ing rate of 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0 × (batch size/1024) × (100/#epochs) and  weight decay of 10−6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' By default, we use the top N = 10  strongest negative examples and an inverse temperature of  β = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Due to resource constraints, we train our model  with a batch size of 1 024 with mixed precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We use  a 10 epoch linear warm-up and a cosine schedule without  restarts [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Using an 8-GPU (NVIDIA A6000 GPUs)  server, training for 100 epochs with m = 2 views per image  takes approximately 22 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Evaluation Procedure  Linear Probing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' First, we follow the standard protocol and  evaluated the learned embedding space by linear evalua-  tion [8,10,13,23], which captures the linear separability of  classes in the representation space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For this, we train a lin-  ear classifier on frozen representations in a fully-supervised  way using the ImageNet train set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We follow the standard  protocol [13] to train the linear classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  To analyze local properties of the  learned representation, namely how often neighbored data  Method  Batch  Views  Linear Probing (Top-1)  Size  100 ep  200 ep  400 ep  Max-Margin [50]  256  2×224  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8 MoCo v2† [12]  256  2×224  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  SimSiam [13]  256  2×224  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  VICReg [4]  2048  2×224  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6 Barlow Twins [58]  2048  2×224  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7 SimCLR† [10]  4096  2×224  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  SwAV† [8]  4096  2×224  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  BYOL† [23]  4096  2×224  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  Whitening [19]  4096  4×224  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  GroCo (ours)  1024  2×224  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  GroCo (ours)  1024  4×224  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  SwAV [8]  4096  2×224 + 6×96  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  GroCo (ours)  1024  2×224 + 6×96  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison with state-of-the-art in linear probing  on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We report results for training for 100, 200, and  400 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Backbone=Resnet50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' †denotes results from Sim-  Siam [13] improved reproductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  points correspond to the same semantic class, we further  evaluate our method by nearest neighbor classification, pre-  dicting the object class by a simple weighted k nearest  neighbor classifier (k-NN) with k = {1, 10, 20} based on  cosine distance as in [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We again use the ImageNet  train set for supervision and test on the ImageNet val set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison to State-of-the-Art  We start with a comparison of the proposed method to  state-of-the-art self-supervised learning methods in linear  probing and k-NN evaluation on the ImageNet [48] and for  image retrieval on the revised Oxford and Paris dataset [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Linear Probing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In the case of linear probing (Table 1),  we observe that our method outperforms almost all base-  lines in classical (not multi-crop) settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Our method  demonstrates state-of-the-art performance in 100 epochs  training, outperforming contrastive baselines SimCLR [10]  and MoCo v2 [12] by +2% and information maximiza-  tion methods Barlow Twins and VICReg by +1% in 100  epochs setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Moreover, our method outperforms SimCLR  and clustering-based SwAV [8] in all other settings as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Also, we even observe competitive performance compared  to BYOL [23] and Whitening [19] methods that use ×4  larger batch size and/or an additional teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  also observe performance improvement by utilizing mul-  tiple positive examples during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In the multi-crop  2 × 224 + 6 × 224 settings, our method is on par with  clustering-based SwAV, which utilizes ×4 larger batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We further evaluate the k-NN perfor-  mance of our methods compared to multiple state-of-the-art  methods with officially released weights in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We ob-  serve that the proposed method excels in all settings, outper-  forming all methods by more than 4% in the no multi-crop  scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The method further greatly improves performance  by leveraging multiple positive examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Finally, by uti-  6  Method  Batch  Views  k-NN (weighted, k=20)  Size  100 ep  200 ep  400 ep  MoCo v2 [12]  256  2×224 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6 SimSiam [13]  256  2×224  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4 SimCLR [10]  4096  2×224  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  SwAV [8]  4096  2×224 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  GroCo (ours)  1024  2×224  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  GroCo (ours)  1024  4×224  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  SwAV [8]  4096  2×224 + 6×96  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  GroCo (ours)  1024  2×224 + 6×96  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Comparison with state-of-the-art in k-NN perfor-  mance on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We evaluate k-NN performance (Top-1)  on officially released weights of baseline models trained for 100,  200, and 400 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We used a simple weighted k-NN with k=20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Backbone=Resnet50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Method  Epochs  Batch  Views  Oxford  Paris  Size  M  H  M  H  SimSiam [13]  100  256  2×224  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='89  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='04  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='92  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='31  MoCo v2 [12]  200  256  2×224  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='28  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='07  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='33  SimCLR [10]  400  4096  2×224  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='27  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='56  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='93  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='19  SwAV [8]  400  4096  2×224  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='01  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='35  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='23  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  GroCo (ours)  400  1024  2×224  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='77  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='08  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='79  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='77  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison with state-of-the-art in image retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We evaluate image retrieval performance on Medium (M) and  Hard (H) splits of revisited Oxford and Paris datasets [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  evaluate nearest neighbor retrieval performance with ImageNet-  trained encoders and report Mean Average Precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  lizing local-to-global correspondences our method outper-  forms the SwAV method that uses ×4 larger batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Image Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  To further demonstrate the potential  of the proposed methods in nearest neighbors-based tasks,  we additionally evaluate ImageNet-trained self-supervised  learning methods in image retrieval on the revisited Oxford  and Paris datasets [45] in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We report the Mean Av-  erage Precision for the Medium (M) and Hard (H) splits of  the datasets as in [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We observe that our method outper-  forms all other methods in this task, confirming its good  local properties of learned representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison to the Pairwise Contrastive Loss  To evaluate the properties of the proposed method in a  direct comparison with the pairwise contrastive loss formu-  lation, we compared our method to the classical contrastive  learning method SimCLR [10], which uses the most popu-  lar InfoNCE loss [38] in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Since SimCLR originally  uses only two augmentations per image, we extend it to a  group of positives scenario by applying contrastive loss be-  tween all possible positive pairs (see supplement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For a  fair comparison, we reproduced SimCLR with the 3-layers  MLP projection head (as in our method) [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Representation Learning Performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' First, we evalu-  ated the learned representations based on the numbers of  positive samples in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We consider four scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Method  Views  k-NN Evaluation  Linear Eval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k=1  k=10  k=20  Top-1  Top-5  SimCLR  2×224 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3 SimCLR†  2×224  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  SimCLR†  3×224  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  SimCLR†  4×224  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  SimCLR†  2×224+6×96  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  GroCo (ours)  2×224  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  GroCo (ours)  3×224  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  GroCo (ours)  4×224  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  GroCo (ours)  2×224+6×96  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison with SimCLR as a contrastive baseline  on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Results are reported for k-NN and linear probing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The best results are bolded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Backbone=Resnet50, #epochs=100,  batch size=1024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' †denotes our reproduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  First, in the 2 × 224 scenario, we sample only two augmen-  tations per image, and therefore we have only one positive  example per data point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In this case, our loss works simi-  larly to SimCLR in a way that it is minimizing the distance  between the positive example and the anchor, however, our  loss still considers negatives as a group and utilizes only the  nearest negative elements that are sorted incorrectly, there-  fore focusing on local properties of representation space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  While outperforming SimCLR baseline by +3% (Top-1) in  linear probing, our method also advances in k-NN evalu-  ation by more than +10% (k=20), demonstrating that our  loss helps to learn better representation not only in terms of  linear separability but also in terms of local structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  further consider settings with 3×224, 4×224, and 2×224 +  6×9 views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We observe that SimCLR shows mixed results  from utilizing more views: while it benefits in linear evalu-  ation, performance is not stable in k-NN, for 3×224 perfor-  mance is lower and for 2×224 + 6×9 is the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' However,  our method clearly profits from utilizing more positives in  both evaluations, resulting in +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7% in k-NN +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4% in lin-  ear evaluation for 2×224 + 6×9 setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Transfer Performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We further evaluated how well per-  formance transfers on other datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In Table 5 we com-  pare Imagenet pre-trained models in k-NN evaluation and  linear transfer and on 11 many-shot classification datasets,  including FGVC Aircraft [35], Caltech-101 [21], Stanford  Cars [31], CIFAR10 [32], CIFAR-100 [32], DTD [14], Ox-  ford 102 Flowers [36], Food-101 [6], Oxford-IIIT Pets [39],  SUN397 [53] and Pascal VOC2007 [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For linear transfer  evaluation, we follow the experimental protocol provided  in [18] without any modification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We observe that the pro-  posed method is on par with SimCLR in linear evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  In zero-shot k-NN evaluation, our method excels in 10 out  of 11 datasets, in particular improving performance on the  Pets dataset by +15%, and on the Aircraft and Food datasets  by +4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This shows that the improved k-NN performance  transfers to downstream tasks as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  7  Method  Evaluation  Aircraft  Caltech101  Cars  Cifar10  Cifar100  DTD  Flowers  Food  Pets  SUN397  VOC2007  Average  SimCLR†  k-NN (weighted, k=20)  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='06  GroCo (ours)  k-NN (weighted, k=20)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='81  SimCLR†  Linear transfer  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='51  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='10  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='19  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='86  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='54  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='11  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='59  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='20  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='92  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='43  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='74  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='47  GroCo (ours)  Linear transfer  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='90  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='44  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='63  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='26  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='72  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='77  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='41  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='72  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='29  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='51  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='34  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='55  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison with SimCLR as a contrastive baseline in transfer performance on 11 classification datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Models are  pre-trained on Imagenet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Backbone=Resnet50, #epochs=100, batch size=1024, views=2x224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' †denotes our reproduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN Evaluation  Linear Probing  k=1  k=10  k=20  Top-1  Top-5  Triplet Loss (margin=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8)  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  Triplet Loss (margin=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  Triplet Loss (margin=+∞)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  GroCo (Ours)  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  (a) Ordering supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN Evaluation  Linear Probing  k=1  k=10  k=20  Top-1  Top-5  Randomly ordered  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content='4  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  Pre-ordered (Ours)  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  (b) Pre-ordering in the groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Inverse temp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Number of negatives N  β  5  10  20  k-NN  Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN  Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN  Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='25  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content='5 1  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  2 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content='2  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  4 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  8 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  (c) An inverse temperature β, a number of negatives N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Batch Size  k-NN Evaluation  Linear Probing  k=1  k=10  k=20  Top-1  Top-5  256  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  512  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  1024  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  (d) Batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Ablation Experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For (c), we report k-NN perfor-  mance with k=20, and linear probing performance (Top-1), de-  noted as Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The best results are bolded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Options used to  obtain the main results are highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Backbone=Resnet50,  Views=2×224, #epochs=100, Weight Decay=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5e-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Ablation Study  Finally, we analyze the design choices of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Ordering Supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' First, we compare the group order-  ing supervision via differentiable sorting with a triplet loss  formulation L = max (dp  i − dn  j + r, 0), where r is a mar-  gin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For a fair comparison, we consider all positive and the  10 strongest negative samples and evaluate different margin  parameters in Table 6a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Here, sorting is superior to a triplet  loss with hard margin selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Pre-ordering in Groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We analyze the impact of pre-  ordering elements within the negative and positive groups  before forwarding them to the sorting network in Table 6b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We observe that our methods achieve competitive perfor-  mance even without pre-ordering;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' however, pre-ordering  strengthens our method further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Inverse Temperature, Number of Negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In Table 6c,  we examine the influence of the number of nearest neigh-  bor negatives N used in the loss, as well as the value of  the inverse temperature parameter β (Equation 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We ob-  serve that usage of too many negatives may not be benefi-  cial for the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Since our loss focuses on negatives that  are sorted incorrectly, increasing the number of negatives at  some point does not bring any new learning signal (because  more distant is unlikely to be sorted incorrectly).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' However,  a larger N results in more steps of the sorting network, in-  creasing the degree of relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Using a larger inverse  temperature β (leading to a lower degree of relaxation in the  swap operation) we can gain some performance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' however,  the variance of the gradients is larger with a larger β, which  is not beneficial for optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We found that N = 10  and β = 1 is the most efficient configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Batch Size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The large batch size might be an important fac-  tor in obtaining good performance for many self-supervised  learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We find that our method is quite robust  for training with smaller batch sizes (Table 6d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Training Time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We also consider the training time of our  model compared to SimCLR baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To eliminate the in-  fluence of distributed training, we measure the average time  of training iteration on one GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We find that the iteration  time of both models is comparable, 514ms for SimCLR vs  526ms for the proposed methods for a batch size of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Conclusion  In this paper, we proposed an alternative approach  to the common pairwise contrastive learning formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Namely, we proposed the group ordering constraints, that  consider positives and negatives as groups and enforce the  group of positives to be closer to the anchor image than the  negative group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' To enforce these constraints, we leveraged  recent progress in the context of differentiable sorting ap-  proaches and formulated a group ordering loss based on the  given sorting supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Our evaluation showed that the  proposed framework, does not only compete with current  contrastive loss baselines, but actually outperforms standard  contrastive learning with regards to all k-NN-based metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  8  References  [1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong  Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Vatt:  Transformers for multimodal self-supervised learning from  raw video, audio and text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' NeurIPS, 34:24206–24221, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  3  [2] Yuki Markus Asano, Christian Rupprecht, and Andrea  Vedaldi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Self-labelling via simultaneous clustering and  representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='05371,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' 3  [3] Philip Bachman, R Devon Hjelm, and William Buchwalter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Learning representations by maximizing mutual information  across views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' NeurIPS, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' 1  [4] Adrien Bardes, Jean Ponce, and Yann LeCun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Vi-  creg: Variance-invariance-covariance regularization for self-  supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' arXiv preprint arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='04906, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content=' Then we provide additional experimen-  tal evaluation results in Section B and qualitative analysis  in Section C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content=' Finally, we cover additional implementation  details in Section E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Discussion of GroCo/Contrastive/Triplet  Loss Relations  In this section, we discuss the similarities and differences  between the GroCo loss, the contrastive loss, and the triplet  loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For comparison purposes, let’s consider a simplified  version of losses when there is only one positive example xp  and one negative example xn for the anchor xa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We denote  the distance from the anchor xa to the positive sample xp as  dp = −  xa⊤xp  ∥xa∥∥xp∥ and the distance from the anchor xa to the  negative sample xn as dn = −  xa⊤xn  ∥xa∥∥xn∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Then contrastive  InfoNCE loss (with respect to the anchor xa) is defined as:  LContrastive = − log  exp(−dp/τ)  exp(−dp/τ) + exp(−dn/τ)  = log (1 + exp(−(dn − dp)/τ)),  (6)  where τ is a temperature hyperparameter (Figure 4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The triplet loss is defined as:  LT riplet = max (dp − dn + r, 0) =  = max (r − (dn − dp), 0),  (7)  where r is a margin hyperparameter (Figure 4b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  For the GroCo loss, a permutation matrix P ∈ R2×2  corresponds to only one conditional swap operation and is  defined as:  P11 = P22 = f(dn − dp) = 1  π arctan(β(dn − dp)) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5,  P12 = P21 = f(dp − dn) = 1  π arctan(β(dp − dn)) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5,  (8)  where β is an inverse temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Therefore, the GroCo  loss is defined as:  LGroCo = 1  4  �  −2 log  � 1  π arctan(β(dn − dp)) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  �  −  −2 log  �  1 − 1  π arctan(β(dp − dn)) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  ��  =  = − log  � 1  π arctan(β(dn − dp)) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  �  ,  (9)  where β is an inverse temperature hyperparameter (Fig-  ure 4c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  In Figure 4, we show the loss curves with different values  of respective hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We note that in this simpli-  fied example with only one positive and only one negative,  all three losses try to maximize the difference between the  distances to the positive and negative examples (dn − dp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The temperature τ, the margin r, or the inverse tempera-  ture β define the flatness of the loss curve depending on the  difference (dn − dp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  However, in the case with more negative/positive ex-  amples for the anchor image, different losses integrate  information from multiple negatives/positives in different  ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For triplet loss, there are various strategies to sam-  ple one positive example and one negative example for the  anchor image [49, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  The complete loss is defined as  the sum (or average) of the losses for the chosen triplets  �  ij max (r − (dn  i − dp  j), 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' On the other hand, the con-  trastive loss aggregates multiple negatives by contrasting  the positive example to all negative examples, resulting in  sum under logarithm: log (1 + �  i exp(−(dn  i − dp)/τ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  And in contrast to an explicit sum over a predefined num-  ber of negatives, the GroCo loss aggregates multiple posi-  tives and negatives via the permutation matrix, condition-  ally swapping neighboring elements, and later applies the  group ordering supervision, enforcing the distance between  positive and negative groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Additional Experimental Results  In this section, we provide additional experimental eval-  uations:  Augmentation Strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In Table 7a we evaluate the per-  formance of the model with respect to different augmenta-  tion strategies for view sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We follow two setups:  1) the augmentation strategy as used in the SimCLR [10]  method with a random resized crop, color jittering, and  gaussian blur, grayscaling and horizontal flip and 2) the aug-  mentation strategy as used in the DINO [9] method that ex-  tends the SimCLR list of augmentations with solarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  SimCLR augmentations are considered as “stronger” com-  pared to DINO augmentations since they include a larger  range of cropping sizes (8% -100% of original image com-  pared to 14%-100% in DINO augmentations) and larger  range values in color jittering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We observe that the stronger  SimCLR [10] augmentations are more beneficial for the  SimCLR method than the weaker DINO augmentations,  while for the proposed method, the DINO augmentation  strategy is more beneficial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  However, the difference be-  tween augmentation strategies diminishes with increasing  number of training epochs and is no longer measurable at  400 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For a fair comparison, we use the SimCLR  augmentation strategy in all reproductions of the SimCLR  method reported in the main paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  11  log (1 + exp(−(dn − dp)/τ))  2  1  0  1  2  dn  dp  0  5  10  15  20  Loss  LContrastive,  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  LContrastive,  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  LContrastive,  = 1  (a) Contrastive InfoNCE loss  max (r − (dn − dp), 0)  2  1  0  1  2  dn  dp  0  1  2  3  4  Loss  LTriplet, r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  LTriplet, r = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  LTriplet, r = 2  (b) Triplet loss  − log( 1  π arctan(β(dn − dp)) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5)  2  1  0  1  2  dn  dp  0  1  2  3  Loss  LGroCo,  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='25  LGroCo,  = 1  LGroCo,  = 4  (c) GroCo loss  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Comparison of the contrastive loss, the triplet loss, and the GroCo loss in a simple scenario with only one positive example and  one negative example for an anchor image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We denote the distance from the anchor to the positive sample as dp and the distance from the  anchor to the negative sample as dn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We note that in the simple case of only one positive and one negative, all three losses try to maximize  the difference between the distances to the positive and negative examples (dn − dp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The temperature τ, the margin r, or the inverse  temperature β define the flatness of the loss curve depending on the difference (dn − dp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Method  Augmentations  Epochs  k-NN Evaluation  Linear Evaluation  k=1  k=10  k=20  Top-1  Top-5  SimCLR  as in SimCLR [9]  100  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  SimCLR  as in DINO [9]  100  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  GroCo  as in SimCLR [9]  100  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  GroCo  as in DINO [9]  100  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  GroCo  as in SimCLR [9]  200  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  GroCo  as in DINO [9]  200  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  GroCo  as in SimCLR [9]  400  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  GroCo  as in DINO [9]  400  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  (a) Augmentation strategy  Projection dim  Embedding dim  k-NN Evaluation  Linear Probing  k=1  k=10  k=20  Top-1  Top-5  128  2048  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  512  2048  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  2048  2048  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  (b) Projection dimentionality  k-NN Evaluation  Linear Probing  k=1  k=10  k=20  Top-1  Top-5  10 random negatives  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='7  top-10 strongest negatives  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  (c) Importance of negatives  Method  Space  k-NN Evaluation  k=1  k=10  k=20  SimCLR  Projection Space  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='8  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  SimCLR  Representation Space  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='0  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  GroCo  Projection Space  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  GroCo  Representation Space  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='5  (d) k-NN evaluation  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Additional Experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The best results are bolded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Options used to obtain the main results are highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Back-  bone=Resnet50, Views=2×224, #epochs=100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Projection Dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We also ablate our method  with respect to the dimensionality of the projection space  (or the latent space), where distances between samples are  computed to calculate a training loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Table 7b shows that  increasing dimensionality of the projection space increases  performance in general, which is more noticeable for the  k-NN performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Note that we do not change the dimen-  sionality of the embedding space (output space of the en-  coder that is used for the k-NN evaluation and linear evalu-  ation), which is always 2048-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Importance of Negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We also evaluate the importance  of utilizing strong negatives for the successful training of  our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We train the model using ten random negatives  instead of the top-10 strongest negatives as a negative group  and report performance in Table 7c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We observe that lever-  aging the strongest negatives increases performance across  all metrics, demonstrating the importance of hard negatives  during training with the GroCo loss, similarly as the con-  trastive loss benefits from hard negative sampling [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  k-NN in Projection Space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We also evaluate the k-NN per-  formance in the projection space (or the latent space) where  the training loss is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We compare k-NN performance  in the projection and representation spaces in Table 7d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  observe that for both methods, k-NN performance is higher  if we use embeddings from the representation space even  though we train the model to compare embeddings in the  projection space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This could be explained by the fact that  the embedding space contains more general image represen-  tations since the representations in projection space could  be overfitted to the respective augmentations and there be-  come agnostic to some image attributes (like color, since we  train the model to match views with different color jittering  parameters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  12  Algorithm 1 Python pseudocode of an odd-even sorting  network for sorting an array of numbers in non-descending  order  # arr: array to sort  # n: length of array  for s in range(1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' n + 1):  if s % 2 == 1:  for i in range(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' n - 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' 2):  if arr[i] > arr[i+1]:  arr[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' arr[i+1] = arr[i+1],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' arr[i]  else:  for i in range(1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' n - 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' 2):  if arr[i] > arr[i+1]:  arr[i],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' arr[i+1] = arr[i+1],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' arr[i]  2  4  1  6  6  1  1  6  4  2  2  4  1  2  4  6  1  2  4  6  step 1  step 2  step 3  step 4  Input:  6  4  2  1  Output:  [1]  [2]  [3]  [4]  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' An illustration of an odd-even sorting network for sort-  ing four elements in non-descending order with an example of  sorting of [6, 1, 4, 2] array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Qualitative Analysis of Learned Represen-  tation Space  We also additionally perform a qualitative analysis of  learned representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' In Figure 6, we visualize represen-  tations for images from four classes of different types of  cats and four classes of different types of dogs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We find that  our method produces much more visually separable clusters  with respect to “inter-class” variations (cats vs dogs) and  “intra-class” variations (between different classes of cats)  than the SimCLR baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Odd-even Sorting Network  An odd-even sorting network, or odd-even sort, is a sort-  ing algorithm from classic computer science literature [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  Sorting networks, or networks for sorting, are a family of  sorting algorithms that consist of the fixed sequence of com-  parisons, in a sense that the next comparisons (elements on  which positions are compared) does not depend on the re-  sult of previous comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' An odd-even sorting network  is a simple example of this family of algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' The odd-  even sorting network compares neighbored elements start-  ing from odd and even indices alternating on each step,  and requires n steps to sort a sequence of n elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We  present a pseudocode of the odd-even sorting network in  Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' We also additionally illustrate the odd-even  sorting process in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Implementation Details  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Linear Evaluation Details  For linear evaluation, we train a linear classifier on  frozen representations in a fully-supervised way, using the  training set of ImageNet for training and the validation set  for evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  We follow the training protocol of Sim-  CLR [10] and SimSiam [13] and train a linear classifier for  90 epochs using the LARS optimizer [57] with the batch  size of 4096, the momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='9, the linear rate of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='6  (following the rule: learning rate = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='1 × batch size/256),  without a warmup and weight decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Following [10] and  [13], we use weak data augmentation (only random crop-  ping with horizontal flipping) and apply gradient stopping  on the input of the classifier to prevent updating the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' SimCLR with Multiple Positives  To train SimCLR with more than one positive view per  anchor, we apply contrastive loss for all possible positive  pairs, considering all views from other images in the batch  as negatives (with a batch of B examples with have m(B −  1) negatives views).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Let xb  i denote the i’th view of the b’th  image in a batch, and Pxb  i denote a set of positive samples  for the anchor xb  i, and Nxb  i denote a set of positive samples  for the anchor xb  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Then, the loss is calculated as  LSimCLR = 1  B  B  �  b=1  1  m  m  �  i=1  1  ���Pxb  i  ���  �  y∈Pxb  i  − log  �  exp(−d(xb  i, y)/τ)  exp(−d(xb  i, y)/τ) + �  z∈Nxb  i exp(−d(xb  i, z)/τ)  �  ,  (10)  where τ is a temperature parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' This extension of the  SimCLR framework for m > 2 views per image is the same  as used in the SwAV evaluations [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' Note that in the multi-  crop scenario, we use only full-resolution global views as  positive examples following “local-global” correspondence  idea [8,9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  13  (a) SimCLR  (b) GroCo (ours)  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' t-SNE visualization of learned representations of Imagenet validation images from four classes of different types of cats (Egyptian  cat, Persian cat, Siamese cat, Tabby cat) and four classes different types of dogs (Pomeranian dog, African hunting dog, Tibetan mastiff,  English setter) for the SimCLR method and the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content=' For visualization we use models with Resnet50 encoder trained for 100  epochs with a batch size of 1024 and 2 × 224 views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
+page_content='  14  24  15  5  0  600  5  10  15  20  15  10  5-  0  5  1524  15  Egyptian cat  Persian cat  5  Siamese cat  Tabby cat  Pomeranian dog  African hunting dog  5  Tibetan mastiff  English setter  10  15  20  15  of-  5-  0  5  1515  5  600  5  10  15  20  20  15  10  5-  0  5  1  1515  Egyptian cat  5  Persian cat  Siamese cat  0-  Tabby cat  Pomeranian dog  5-  African hunting dog  Tibetan mastiff  10  English setter  15  20  20  15  of-  5-  5  1  15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9A0T4oBgHgl3EQfDv_g/content/2301.02009v1.pdf'}
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+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='11466v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='mtrl-sci]  26 Jan 2023  Hydrogen atom/molecule adsorption on 2D  metallic porphyrin: A first-principles study  Raphael M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Tromer,†,‡ Isaac M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Felix,¶ Levi C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Felix,†,‡ Leonardo D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Machado,¶  Cristiano F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Woellner,§ and Douglas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Galvao∗,†  †Applied Physics Department, State University of Campinas, Campinas, SP, 13083-970,  Brazil  ‡Center for Computational Engineering and Sciences, State University of Campinas,  Campinas, SP, 13083-970, Brazil  ¶Departamento de F´ısica Te´orica e Experimental, Universidade Federal do Rio Grande do  Norte, Natal, RN, 59072-970, Brazil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  §Physics Department, Federal University of Paran´a, UFPR, Curitiba, PR, 81531-980,  Brazil  E-mail: galvao@ifi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='unicamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='br  Abstract  Hydrogen is a promising element for applications in new energy sources like fuel  cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' One key issue for such applications is storing hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' And, to improve stor-  age capacity, understanding the interaction mechanism between hydrogen and possible  storage materials is critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' This work uses DFT simulations to comprehensively in-  vestigate the adsorption mechanism of H/H2 on the 2D metallic porphyrins with one  transition metal in its center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Our results suggest that the mechanism for adsorption of  H (H2) is chemisorption (physisorption).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The maximum adsorption energy for atomic  hydrogen was −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7 eV for 2D porphyrins embedded with vanadium or chromium atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  1  Our results also revealed charge transfer of up −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='43 e to chemisorbed H atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In con-  trast, the maximum adsorption energy calculated for molecular hydrogen was −122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  meV for 2D porphyrins embedded with scandium atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Furthermore, charge transfer  was minimal for physisorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Finally, we also determined that uniaxial strain has a  minimal effect on the adsorption properties of 2D metallic porphyrins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Introduction  The use of nanostructured systems in applications is predicated on obtaining new 2D mate-  rials and then understanding and manipulating their electrical,1 thermal,2–5 magnetic prop-  erties,6 among others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Since Andre Geim and Konstantin Novoselov extracted a graphene layer from graphite  by a simple exfoliation process,7 many methods have been proposed to allow the synthe-  sis of new 2D8–13 nanostructured materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Among these materials, there is a preference  for systems that are organic and that do not cause pollution when discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='14,15 In this  quest for future materials, one common objective is to find solids that support the use of  alternative energy sources, which aim to replace fossil fuels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='16,17 One such alternative fuel is  hydrogen, and intense research has been carried out to investigate nanostructured systems  that could serve as hosts for its storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Many materials have been proposed for hydrogen  storage applications, such as covalent organic frameworks (COFs)18,19 and metal-organic  frameworks (MOFs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='20,21 Still, to improve hydrogen storage cells, understanding the inter-  action of nanostructured systems with hydrogen is vitally important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  In addition to applications in hydrogen storage,22–25 MOFs have also been used as cat-  alysts in hydrogen evolution reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='26–29 A type of system commonly used for the latter  purpose are MOFs constructed from porphyrin molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='26–28 To assemble these systems,  various experimental techniques have been used to link the porphyrin molecules through  covalent bonds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='26–28 Other porphyrin systems have been investigated recently, including two-  dimensional (2D) porphyrins that contain metal atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='30,31 Still, this type of 2D system has  2  yet to be investigated for possible uses in hydrogen storage applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  In this work, we investigate the interaction between 2D porphyrin metallic systems and  hydrogen atoms and molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The 2D porphyrin systems were assembled from a unit cell  containing a porphyrin molecule with one transition metal in the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We considered  2D porphyrin systems with ten different transition metals embedded in the center, each  corresponding to one of the ten elements of period 4 of the periodic table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' For each 2D  metallic porphyrin system, we calculated the adsorption energy with H/H2, for both relaxed  and strained systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We verified that the interaction between 2D-porphyrin and hydrogen  atoms (molecules) corresponds to chemisorption (physisorption).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Methodology  As mentioned above, we investigated the interaction between an H atom and an H2 molecule  with 2D porphyrin systems containing one transition metal atom from period 4 of the periodic  table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The following metals were considered: scandium (Sc), titanium (Ti), vanadium (V),  chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu), and zinc  (Zn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Here, we use the name 2D-por-M to refer to the investigated structures in general, and  we replace M by an element symbol to refer to a specific structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' For example, 2D-por-Sc  refers to a 2D porphyrin system containing a scandium atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  The first step of our calculations consisted in optimizing all 2D-por-M structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Our  calculations were based on the density functional theory (DFT) formalism, as implemented  in the Quantum Espresso (QE) software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='32 In the approach used, the wavefunctions were  expanded in the plane wave basis set and pseudopotentials were used to represent the core  electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='33,34 To choose the calculation parameters, we carried out convergence tests for  the total energy against the number of k-points and the cut-off energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' After these tests,  we set the cut-off energy to 75 Ry and used a 10 × 10 × 1 k-point mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  The van der  Waals vdw-df is a functional which was used to describe the exchange-correlation term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='35–37  3  During optimization, ions and lattice vectors were varied simultaneously, and we assumed  that convergence had been achieved when the force on each atom was less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='05 eV/˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  After all 2D-por-M structures were optimized, we investigated their interaction with H atoms  and H2 molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' For these calculations, the initial position for H/H2 was always located  above the transition metal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Preliminary tests indicated that electrostatic interactions were  stronger when a hydrogen atom/molecule was placed in this region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  For the calculations with hydrogen atoms, in the initial step, we placed a H atom  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0 ˚A  above one of the considered metals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Then we optimized the 2D-por-M structure  and the hydrogen position, with the constraint that H was only allowed to move in the  direction perpendicular to the 2D plane (z-direction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Note that we also tested an initial  distance of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0 ˚A, but found that this change did not affect the final optimized distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  For the calculations with hydrogen molecules, in the initial step we placed a H2 molecule  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0 ˚A above one of the considered metals, with a vertical orientation (the H-H bond was  perpendicular to the surface).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' During the optimization process, the hydrogen atom that was  initially closer to the metal was constrained to only move along the z-direction, whereas the  other hydrogen was allowed to move in all directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  After the 2D-por-M structure with a hydrogen atom or molecule is optimized, the ad-  sorption energy is obtained using this expression:1,38  Ead = E2D−por−M+H/H2 − E2D−por−M − EH/H2,  (1)  where E2D−por−M+H/H2 is the total energy of a system where 2D-por-M and H/H2 are inter-  acting, E2D−por−M is the energy of an isolated 2D-por-M system, and EH/H2 is the energy of  an isolated H atom/H2 molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  We also calculate the formation energy per atom for the various 2D-por-M structures  using the following expression:  Ef = (E2D−por−M − NCEC − NNEN − EM)/Nt,  (2)  4  where E2D−por−M is the energy of an isolated 2D-por-M system, NC/NN is the number of car-  bon/nitrogen atoms in the unit cell, EC/N/M is the energy of an isolated carbon/nitrogen/metal  atom, and Nt is the total number of the atoms in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Results and discussion  Figure 1 presents the 2D metallic porphyrin (2D-por-M) structure for the transition metals  M present in period 4 of the periodic table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' For the ten different transition metals considered  here, the optimized lattice was a square (Lx = Ly = L) with L values ranging from 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='37 and  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='52 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Hence, the difference between lattice vectors is minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We also observed that the  transition metal remained at the 2D plane (xy) for all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' As a result, the electrostatic  potential is the same above and below the 2D plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Here, we do not consider isomeric  effects on the magnetic properties, as Singh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' did for metallic 2d-porphyrin-vanadium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='30  Figure 1: Structure of the 2D metallic porphyrin, with the square unit cell highlighted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The  central metallic atom varied in our calculations, and we considered ten transition metals  from period 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Table 1 presents the formation energy per atom obtained using expression 2 for the  optimized 2D-por-M structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Note that the calculated values are very close, with a  slight difference of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='3 eV/atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Consequently, the energy necessary to obtain all the  structures investigated here is quite similar, although experimental procedures could vary  5  C  N  Sc Ti V Cr Mn  Fe Co Ni Cu Znfor different metallic atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='12,39–42  Table 1: In the first column, we have the metallic element attached to the porphyrin struc-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In the second column, we have the corresponding formation energy per atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  2D-por-M  Ef(eV/atom)  Sc  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  Ti  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  V  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  Cr  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  Mn  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  Fe  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  Co  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  Ni  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  Cu  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Zn  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='9  Figure 2 displays the spin-polarized density of states for the optimized 2D-por-M struc-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The µ value in each graph indicates the corresponding total magnetic moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' It can  be observed that all structures are metallic, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=', without a bandgap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Furthermore, notice  that structures containing metals with intermediate atomic numbers present high magnetic  moment, whereas those with smaller or higher atomic numbers have either null or insignif-  icant magnetic moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Finally, for systems with high µ value, an apparent asymmetry in  the DOS between spin up and down states occurs, which is due to unpaired electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Let us now discuss the interaction between the optimized 2D-por-M structures and H  atoms/H2 molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' As mentioned in the methods section, we initially placed the H atom (or  H2 molecule) above the metal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Then, for the H atom, we constrained the hydrogen to relax  only in the z-direction, that is, the direction perpendicular to the plane of 2D-por-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' For  the H2 molecule, we constrained the atom closer to the plane and allowed the other atoms to  move freely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Figure 7 in the supplementary material displays the optimized structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' After  optimization, we calculated the adsorption energy using expression 1, and we present the  results for H and H2 in column 2 from tables 2 and 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The adsorption energy is  negative for both H and H2, due to the attractive electrostatic interaction between 2D-por-M  and hydrogen, with larger negative energy values indicating stronger mutual attraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  6  Spin up               Spin down  2  1  0  1  2  E – EFermi (eV)  E – EFermi  (eV)  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  2  1  0  1  2  Sc (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Ti (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  V (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6μB)  Cr (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7μB)  Mn (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1μB)  Co (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Fe (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2μB)  Cu (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1μB)  Zn (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2μB)  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  Figure 2: Spin-polarized Density of states for 2D metallic porphyrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  7  For an H atom interacting with 2D-por-M, the adsorption energy varies between -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  eV (for Cu) and -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7 eV (for V and Cr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Column 3 of table 2 presents the corresponding  equilibrium distance for H atoms, which varies between 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='44 ˚A (for Co) and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='84 ˚A (for Sc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Together, these results denote that H atoms chemisorb on 2D-por-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We also analyzed the  charge transfer between H atoms and 2D-por-M, and the results are presented in column 4  of table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Note that negative values indicate charge transfer from 2D-por-M to a hydrogen,  and the opposite is true for positive values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Overall, we observe high charge transfer for  calculations with H atoms, confirming the occurrence of chemisorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Additionally, we  observe a tendency for higher charge transfer in systems containing metals with higher elec-  tropositivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='43 For instance, the least electronegative metal investigated here (Sc) produced  the largest charge transfer (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='43 e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  For H2 molecules, adsorption energy values range from -33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4 meV (for Co) to -122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5 meV  (for Sc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' All other structures present adsorption energies around -50/-60 meV, as we see  in column 2 of table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Concerning the equilibrium distance between metal atoms and H2  molecules, values are presented in column 3 of table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' When comparing these results with  those previously discussed for H atoms, we observe considerably larger equilibrium distances  for H2 molecules, varying between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='64 ˚A (for Ti) and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='21 ˚A (for Mn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Together, these  results indicate that H2 molecules are physisorbed on 2D-por-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In this case, interactions are  mainly due to Van der Waals forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Charge transfer results for H2 molecules are presented in  column 4 of table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Transferred charge values are much smaller in this instance, supporting  our argument that physisorption occurs for H2 molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Note that our results regarding  the H/H2 charge transfer process are in agreement with the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='38,44  The last columns of tables 2 and 3 shows the total magnetic moment of the system after  H or H2 adsorbed on 2D-por-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Comparing these results with those presented in figure  2, we observe that the adsorbed H atom affects the magnetic moment value considerably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  In contrast, the total magnetic moment remains practically unaffected with H2 adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  For chemisorption, the magnetic moment value changes because the charge transfer process  8  changes the electronic distribution of the monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Table 2: In the first column, we have the transition metal element considered in the calcu-  lation (M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Columns 2 and 3 present adsorption energies and equilibrium distance between  H and transition metal, while columns 4 and 5 show the charge transferred to H (negative  values) or from H (positive values) and, the total magnetic moment in the structure after  adsorption of H on 2D-por-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  M  [Ead-H](eV)  RH−M (˚A)  qH(e)  µH (µB)  Sc  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='84  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Ti  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  V  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6  Cr  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  Mn  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='53  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Fe  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='49  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='07  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Co  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Ni  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='3  Cu  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='53  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Zn  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  In order to gain insight into the electronic density distribution after adsorption, we cal-  culated the charge density difference of (i) an H atom on 2D-por-Cr and (ii) an H2 molecule  on 2D-por-Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We show the electron density of 2D-por-Cr and 2D-por-Sc because the former  presents the highest interaction energy with H and the latter with H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Moreover, the results  from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 3 illustrate well typical charge distributions obtained for the other structures  Figure 3-a)/b) presents the results for the H atom/H2 molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 3-a) and 3-b) we  used isosurface values of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='008e/V3 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0008e/V3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In addition, the blue/red  regions represent electron depletion/accumulation after adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 3-a), we note electron depletion at the Cr atom and accumulation at the hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  This result agrees with that presented in table 2, which indicated a charge transfer of −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='24 e  from 2D-por-Cr to the H atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We typically observed charge accumulation in the hydrogen  when chemisorption occurred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 3-b), we first note the charge transfer is tiny for  physisorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Looking at the H2 molecule, we observe the formation of a dipole, with  charge accumulation (red) at the H atom near the metal and depletion (blue) at the other  one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Notice that the blue region is larger than the red one, as the total charge in the molecule  9  Table 3: In the first column, we have the transition metal element considered in the calcu-  lation (M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Columns 2 and 3 present adsorption energies and equilibrium distance between  H2 and transition metal, while columns 4 and 5 show the charge transferred to H2 (negative  values) or from H2 (positive values) and, the total magnetic moment in the structure after  adsorption of H on 2D-por-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  M  [Ead-H2](meV)  RH2−M (˚A)  qH2 (e)  µH2 (µB)  Sc  122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Ti  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  V  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='8  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='003  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6  Cr  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  Mn  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  Fe  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  Co  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='004  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Ni  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  Cu  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  Zn  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  is positive (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='009e according to table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We also present the total density of states after  H/H2 adsorption in Figures 8 and 9 of the Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' These results reveal  that all investigated systems remain metallic after hydrogen adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  a)                                    b)  Figure 3: Charge density difference map (a) for a hydrogen atom adsorbed on 2D-por-Cr  and (b) for a hydrogen molecule adsorbed on 2D-por-Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The red and blue colors represent  electron accumulation and depletion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  10  erHAdsorption on strained 2D-por-M  When chemisorption occurs, we observed the that the monolayer: (i) transfers charge to H  and (ii) it had its total magnetic moment reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In contrast, H2 physisorbed on 2D-por-M,  had little charge transfer and total magnetic moment changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In this section, we investigate  how an uniaxial strain applied along the x-direction affects adsorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We did not apply  strain to the y-direction because the system is isotropic in the xy plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Sc  Ti  V  Cr  Mn  Fe  Co  Ni  Cu  Zn  Ead (meV)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  3,0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0  No strain  3% along x  6% along x  9% along x  Figure 4: Adsorption energies for an H atom placed on a strained 2D-por-M monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We  considered different metallic elements and strain values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Figure 4 presents the adsorption energy of an H atom as a function of the applied strain  along the x-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We considered strain values of 3, 6, and 9%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We note that the strain  altered the adsorption energy slightly in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The change is more perceptible for Co,  Ni, Cu, and Zn, where the adsorption energy decreased with the strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Still, the maximum  variation was only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='25 eV (for Zn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Figure 5-a) shows the hydrogen-metal distance as a  function of the applied uniaxial strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In all cases, we observed that this distance remained  nearly unaffected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Figure 5-b) presents the change transfer between an H atom and a metal  against the strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In this case, we observed a slight decrease in the transferred charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  11  Overall, for 2D-por-M structures with an H atom, we observed that adsorption energies  and transferred charges decreased slightly with the strain, whereas the hydrogen-metal dis-  tance remained almost constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Finally, note that the applied strain did not significantly  change the total magnetic moment of the investigated structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  0  3  6  9  strain (%)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1  qH  (e)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='9  R (Å)  a)  b)  Sc          Ti           V           Cr          Mn  Fe          Co          Ni          Cu          Zn  Figure 5: a) Equilibrium distance R between an H atom and 2D-por-M and b) charge in an  H atom (qH) as a function of the uniaxial strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Figure 6 displays adsorption energies for a H2 molecule adsorbed on a strained 2D-por-M  monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We again considered monolayers under 3%, 6%, and 9% strain in the x-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  The results reveal that the strain had little effect on the adsorption energies for all inves-  tigated structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We also found that the applied strain did not modify charge transfer,  H2-metal distance, and magnetic moment values for the structures where physisorption oc-  12  curred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In summary, for structures with H2 molecules adsorbed on 2D-por-M, we found that  the strain had no appreciable effect on all studied quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Sc  Ti  V  Cr  Mn  Fe  Co  Ni  Cu  Zn  140  120  100  80  60  40  Ead (meV)  No strain  3% along x  6% along x  9% along x  Figure 6: Adsorption energies for an H2 molecule placed on a strained 2D-por-M monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  We considered different metallic elements and strain values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Conclusions  In summary, we used density functional theory calculations to study the structural and  electronic properties of an H atom/H2 molecule adsorbed on the 2D metallic porphyrin  with a transition metal in its center (2D-por-M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' We considered all transition metals of  row four of the periodic table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Our results revealed chemisorption of atomic hydrogens on  the monolayer, with adsorption energies ranging from −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5 eV (for Cu) to −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7 eV (for V  and Cr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' In contrast, we found physisorption of molecular hydrogens on 2D-por-M, with  adsorption energies ranging from −33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='4 meV (for Co) to −122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='5 eV (for Sc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  We also  analyzed the charge transferred between the monolayer and H/H2 and found an appreciable  charge transfer in chemisorption (up to −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='43 e for Sc) but a negligible one in physisorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Negative values indicate electron accumulation in the hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Moreover, we observed  13  that chemisorption changed the total magnetic moment moderately, as the charge transfer  process changed the electronic distribution of 2D-por-M, particularly in the cases of Fe and  Zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Finally, we observed that strain slightly changes the properties of monolayers with  hydrogen chemisorbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' However, the strain had practically no effect on the properties of  monolayers where physisorption occurred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  In general, we conclude that 2D-por-M can be useful in applications involving hydrogen  atoms or molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The sizeable mutual interaction between the monolayer and hydrogen  is crucial for applications in hydrogen storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Moreover, it is possible to adjust the charge  transferred to the adsorbed hydrogen by changing the metal in the monolayer, an important  feature for catalysis applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Finally, we found that the considered monolayers have  varied magnetic moments and that these can be changed through hydrogen chemisorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  This characteristic could be useful in spintronic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Acknowledgements  This work was financed in part by the Coordenac˜ao de Aperfei¸coamento de Pessoal de N´ıvel  Superior - Brasil (CAPES) - Finance Code 001, CNPq, and FAPESP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' The authors thank  the Center for Computational Engineering & Sciences (CCES) at Unicamp for financial  support through the FAPESP/CEPID Grant 2013/08293-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' LDM would also like to thank  the support of the High Performance Computing Center at UFRN (NPAD/UFRN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  14  Supplementary Material  H/H2 adsorbed on the 2D-porphyrin-M  Sc  Ti  V  Cr  Mn  Fe  Co  Ni  Cu  Zn  Sc  Ti  V  Cr  Mn  Fe  Co  Ni  Cu  Zn  Z  Y  X  Figure 7: Equilibrium distance for H/H2 atom/molecule adsorbed on the 2D-porphyrin-M  for all transition metal investigated in this manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Density of states of porphyrin metalic  15  Spin up               Spin down  2  1  0  1  2  E – EFermi (eV)  E – EFermi  (eV)  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  2  1  0  1  2  Sc (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Ti (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  V (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6μB)  Cr (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7μB)  Mn (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Co (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Fe (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='3μB)  Cu (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Zn (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  Figure 8: Total density of states for H atom adsorbed on the 2D metallic porphyrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='.  16  Spin up               Spin down  2  1  0  1  2  E – EFermi (eV)  E – EFermi  (eV)  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  2  1  0  1  2  Sc (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Ti (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  V (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='6μB)  Cr (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='7μB)  Mn (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1μB)  Co (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Fe (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2μB)  Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='0μB)  Cu (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='1μB)  Zn (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='2μB)  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  10  5  0  5  10  DOS (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=')  Figure 9: Total density of states for H2 atom adsorbed on the 2D metallic porphyrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='.  17  References  (1) Tromer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Freitas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Felix, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Mortazavi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Machado, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Azevedo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  Pereira, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Electronic, optical and thermoelectric properties of boron-doped ni-  trogenated holey graphene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 2020, 22, 21147–21157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  (2) Kınacı, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Haskins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Sevik, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' C¸a˘gın, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Thermal conductivity of BN-C nanos-  tructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' B 2012, 86, 115410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  (3) Felix, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Pereira, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Thermal conductivity of graphene-hBN superlattice rib-  bons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 2018, 8, 1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  (4) Felix, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Pereira, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Suppression of coherent thermal transport in quasiperiodic  graphene-hBN superlattice ribbons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Carbon 2020, 160, 335–341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  (5) Felix, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Pereira, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Thermal conductivity of Thue–Morse and double-period  quasiperiodic graphene-hBN superlattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Heat Mass Transf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content='  (27) Leng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Ding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Lin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' Jiang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Boosting photocatalytic hydrogen  20  production of porphyrinic MOFs: the metal location in metalloporphyrin matters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' ACS  Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' 2018, 8, 4583–4590.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content='  (28) Aziz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
+page_content=' Ruiz-Salvador, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' Calero, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtFJT4oBgHgl3EQfKyxj/content/2301.11466v1.pdf'}
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+1
+Hardware Prototype of a Time-Encoding
+Sub-Nyquist ADC
+Hila Naaman, Student Member, IEEE, Nimrod Glazer Member, IEEE, Moshe Namer, Daniel Bilik, Shlomi
+Savariego, and Yonina C. Eldar, Fellow, IEEE
+Abstract—Analog-to-digital converters (ADCs) are key com-
+ponents of digital signal processing. Classical samplers in this
+framework are controlled by a global clock. At high sampling
+rates, clocks are expensive and power-hungry, thus increasing the
+cost and energy consumption of ADCs. It is, therefore, desirable
+to sample using a clock-less ADC at the lowest possible rate. An
+integrate-and-fire time-encoding machine (IF-TEM) is a time-
+based power-efficient asynchronous design that is not synced to
+a global clock. Finite-rate-of-innovation (FRI) signals, ubiquitous
+in various applications, have fewer degrees of freedom than
+the signal’s Nyquist rate, enabling sub-Nyquist sampling signal
+models. This work proposes a power-efficient IF-TEM ADC
+architecture and demonstrates sub-Nyquist sampling and FRI
+signal recovery. Using an IF-TEM, we implement in hardware
+the first sub-Nyquist time-based sampler. We offer a feasible
+approach for accurately estimating the FRI parameters from IF-
+TEM data. The suggested hardware and reconstruction approach
+retrieves FRI parameters with an error of up to -25dB while
+operating at rates approximately 10 times lower than the Nyquist
+rate, paving the way to low-power ADC architectures.
+Index Terms—Brain-inspired computing, analog-to-digital con-
+version (ADC), time-based sampling hardware, integrate and fire
+TEM (IF-TEM), sub-Nyquist sampling, finite-rate-of innovation
+(FRI) signals.
+I. INTRODUCTION
+Analog-to-digital converters (ADCs) are electronic hard-
+ware components that facilitate the digital processing of sig-
+nals and communication between computers and the physical
+world [1], [2]. Traditional ADCs, also known as synchronous
+ADCs, are controlled by a global clock that operates at a
+rate that meets the Nyquist rate, requiring the acquisition
+of samples at intervals of 1/2W seconds for signals with a
+frequency no greater than WHz [3]. However, synchronous
+ADCs have several limitations that may make them less
+suitable for certain applications. One limitation is high power
+consumption due to the continuous clock signal, which can
+be a significant disadvantage in energy-constrained systems
+such as battery-powered devices [4]. Another limitation is the
+need for a stable and accurate clock signal, which becomes
+more challenging to achieve as the sampling rate in a high
+speed system increases, especially in noisy or interference-
+prone environments [5]–[7]. Synchronous ADCs also require
+All the authors are with the Faculty of Math and Computer Science, Weizmann
+Institute of Science, Israel. Email: hila.naaman@weizmann.ac.il
+Parts of this work were presented at the international Symposium on Information
+Theory, ISIT, July 2022.
+This research was partially supported by the European Union’s Horizon 2020 research
+and innovation program under grant No. 101000967-ERC-CoDeS, by the Israel Science
+Foundation under grant no. 0100101, and by the QuantERA grant C’MON-QSENS.
+complex clock circuits, which increase the complexity of the
+design and implementation [8], [9]. Consequently, there is a
+need for innovative ADCs that address these limitations by
+reducing both power consumption and sampling rate.
+The integrate-and-fire time encoding machine (IF-TEM),
+an asynchronous energy-efficient event-driven sampler, is a
+promising alternative to conventional ADCs [8], [10]–[13].
+In this architecture, no global clock is required, making the
+IF-TEM sampler low energy. Furthermore, compared to its
+traditional amplitude-based ADCs, TEMs use extremely sim-
+ple, entirely analog, low-power, and small size encoders [10],
+[14]–[16]. An IF-TEM integrates an input signal and then
+compares the integral to a threshold; if the threshold is
+met, the time instances are recorded
+[17]–[22]. The IF-
+TEM sampler has been utilized for ultra-wide-band (UWB)
+communications [23], remote sensing [24], [25], heart activity
+monitoring [26], [27], event-based cameras (also referred to
+as neuromorphic cameras) [28]–[31] and other applications
+such as spiking neural network (SNN) interpretations, leading
+to better knowledge of how to utilize neuromorphic hardware
+and replace power-hungry ADCs [32].
+In [17], it was shown that bandlimited signals sampled by
+an IF-TEM can be perfectly recovered if the average sampling
+rate of the IF-TEM is higher than the signal’s Nyquist sam-
+pling rate. By requiring the bandwidth to be inversely propor-
+tional to the interval between time instances, the reconstruction
+of the original signal closely resembles the reconstruction of a
+bandlimited signal sampled with irregular amplitude samples.
+In [33], it was shown that a spectrally sparse signal could
+be recovered when the average IF-TEM sampling rate is
+below the Nyquist rate with high probability. The introduced
+TEM was affected by frequency-dependent quantization noise,
+which was most significant at high-frequency input signals.
+Reconstruction of signals from time encoding has been gener-
+alized for signals in shift-invariant spaces [34], and finite rate
+of innovation (FRI) signals [21], [22], [35], [36].
+FRI signals are characterized by a small number of degrees
+of freedom that permit sub-Nyquist sampling [1], [37]. Due
+to their prevalence in numerous scientific applications, such
+as radar [38], [39], ultrasound [40]–[42], time-domain optical-
+coherence tomography (TDOCT) [43], and light detection and
+ranging (LIDAR) [44], sampling and recovery of FRI signals,
+particularly through the use of IF-TEMs, is of great interest
+[22], [35], [45], [46]. Most of the FRI sampling literature
+focuses on reducing the ADC’s sampling rate by using the
+signal structure. It ignores other aspects of the ADC, such as
+its power consuming clock [37], [40], [47], [48]. We address
+arXiv:2301.02012v1  [eess.SP]  5 Jan 2023
+
+2
+Fig. 1. Time encoding machine with spike trigger reset. The input is biased by
+b, scaled by κ, and integrated. A time instant is recorded when the threshold
+δ is reached, after which the value of the integrator resets.
+the issue of the synchronous ADCs’ power consumption by
+utilizing the asynchronous IF-TEM sampler, which is energy-
+efficient.
+Time-based sampling of FRI signals can be performed simi-
+larly to conventional FRI sampling techniques, such as kernel-
+based sampling [21], [22], [35], [36], [46], [49]. The authors
+in [22] provided theoretical guarantees for the sampling and
+recovery of FRI signals using an IF-TEM, and proposed
+a sampling method that is more robust in the presence of
+noise than existing techniques. Our work introduces a low-
+power IF-TEM ADC hardware that demonstrates sub-Nyquist
+sampling and FRI signal recovery based on the approach in
+[22]. We use hardware-measured data with time instances
+perturbations up to 35ms. The jittered time instances are
+modeled as t′
+n = tn + ϵn, where tn are the ideal time
+instances and we model the jitter noise as i.i.d. uniformly
+distributed ϵn
+iid
+∼ U[− σ
+2 , σ
+2 ]. Based upon these assumptions
+and the measured time instances from the hardware, it appears
+that the noise level σ fluctuates between 15-70 ms. As present
+reconstruction techniques are incapable of dealing with such
+large perturbations, we modify the method of [22] to introduce
+robustness in the presence of large timing noise.
+Our contribution is twofold: first, we introduce a robust
+sub-Nyquist sampling and reconstruction technique; then, we
+present a hardware implementation of sub-Nyquist TEM sam-
+pling of FRI signals. Prior to acquiring timing information
+with the IF-TEM, similarly to [22], the signal is prefiltered
+using a sampling kernel which eliminates the zeroth frequency
+component of the signal for robust recovery. Our reconstruc-
+tion method relies on the sampling kernel selection as well
+as introducing a new forward model to improve recovery
+from noisy hardware data. Compared to our previous results
+[16], here we present a simpler, straightforward proof for the
+recovery guarantees, which is based on using a partial sum
+of the measurements, resulting in more stable reconstruction.
+We demonstrate that in the presence of noise, the proposed
+reconstruction technique outperforms the method in [22].
+Then, we present the FRI-TEM hardware prototype that can
+be employed in low-power time-of-flight applications. The
+hardware components are designed to accommodate a broad
+spectrum of FRI signal frequencies. The two primary compo-
+nents of the hardware are an integrator and a reset function.
+As long as the input signal is positive, the integrator capacitor
+must operate in its linear domain, which is continually charged
+or increasing. In addition, the IF-TEM thresholding requires a
+Fig. 2. Our IF-TEM hardware sampling: the IF-TEM input signal y(t) (blue),
+the integrator output (green), and the IF-TEM output time instances (red).
+means for a rapid reset. These are achieved by incorporating
+a differentiator and a FET into the reset function.
+We demonstrate the capabilities of the system via several
+FRI signals. Prior to the IF-TEM system, a band-pass filter is
+employed as the sampling kernel. The filter eliminates unnec-
+essary signal information and enables sub-Nyquist sampling.
+The designed hardware samples the filtered signal, resulting
+in time instances. One method of recording time instances or
+their differences is to use an oscilloscope. For estimating the
+FRI parameters, the Fourier coefficients are computed using
+our suggested algorithm, and the parameters are subsequently
+estimated using the annihilating filter technique. We demon-
+strate that it is possible to estimate FRI parameters with sub-
+Nyquist samples, taken at approximately 10 times the rate of
+innovation, which is significantly lower than the Nyquist rate
+of the signal.
+The rest of the paper is organized as follows. In Section
+II, we formulate the problem of sampling and recovering an
+FRI signal using an IF-TEM, and discuss some background
+results. In Section III, we present our robust reconstruction
+algorithm together with simulation results. In Section IV, we
+justify the required hardware specs and comment on the circuit
+challenges, followed by a detailed analog board’s design work
+specifications. Experimental hardware results of IF-TEM sub-
+Nyquist sampling and reconstruction are shown in Section V.
+Finally, we conclude the paper in Section VI.
+II. PRELIMINARY RESULTS PROBLEM FORMULATION
+In this section, we review some previously established
+results in time encoding and FRI, followed by our formulation
+of the theoretical problem of FRI sampling and reconstruction
+utilizing an IF-TEM sampler.
+A. Time Encoding Machine
+We consider an IF-TEM whose operating principle is the
+same as in [22] (see Fig. 1). The input to the IF-TEM is
+a bounded signal y(t), and the output is a series of spikes
+or time instances. An IF-TEM is parameterized by positive
+real numbers b, κ, and δ. A bias b is added to a c-bounded
+signal y(t) such that |y(t)| ≤ c < b < ∞, and the sum
+is integrated and scaled by
+1
+κ. When the resulting signal
+reaches the threshold δ, the time instant tn is recorded, and the
+
+0.7
+[F-TEM input y(t)
+Integrated signal with reset
+[tn]
+0.6
+0.5
+Amplitude
+0.4
+0.3
+0.2
+0.1
+00
+0
+5
+6
+Time [sec]
+×10℃3
+Fig. 3.
+Hardware integrator circuit. Our hardware implementation is com-
+prised of an operational amplifier, a capacitor C and resistors R1 and R2.
+integrator is reset. The IF-TEM process is repeated to record
+subsequent time instants, i.e., if a time instant tn was recorded,
+the next time instant tn+1 satisfies
+1
+κ
+� tn+1
+tn
+(y(s) + b) ds = δ.
+(1)
+Fig. 2 depicts the operational output of our IF-TEM hard-
+ware implementation using real data. The integrator con-
+stant κ is determined from the integrator circuit hardware
+as demonstrated in Fig. 3. The time encodings {tn, n ∈ Z}
+form a discrete representation of the analog signal y(t) and
+the objective is to reconstruct y(t) from them. Typically,
+reconstruction is performed using an alternative set of discrete
+representations {yn, n ∈ Z} defined as
+yn ≜
+� tn+1
+tn
+y(s) ds = −b(tn+1 − tn) + κδ.
+(2)
+The measurements {yn, n ∈ Z} are derived from the time
+encodings {tn, n ∈ Z} and IF-TEM parameters {b, κ, δ}.
+Using (2) and the fact that |y(t)| ≤ c, it can be shown that for
+any two consecutive time instants [18], [50]:
+κδ
+b + c ≤ tn+1 − tn ≤
+κδ
+b − c.
+(3)
+B. FRI Signal Recovery
+Consider an FRI signal of the form
+x(t) =
+L
+�
+ℓ=1
+aℓh(t − τℓ),
+(4)
+where the FRI parameters {(aℓ, τℓ)|τℓ ∈ (0, T], aℓ ∈ R}L
+ℓ=1
+are the unknown amplitudes and delays. We assume that the
+pulse h(t) ∈ L2(R), and the number of FRI pulses L are
+known. Since the analysis of recovering aperiodic FRI signals
+using IF-TEM measurements is similar to that of recovering
+periodic FRI signals [22], in this paper we will concentrate on
+the scenario of recovering T-periodic FRI signals.
+Consider a T-periodic FRI signal, resulted from the linear
+combination of delayed versions of a prototype pulse h(t) ∈
+Fig. 4.
+Sampling setup IF-TEM: Continuous-time signal x(t) is filtered
+through a sampling kernel g(t) and then sampled by using an IF-TEM to
+generate time instances {tn}.
+L2(R), of the form
+x(t) =
+�
+p∈Z
+L
+�
+ℓ=1
+aℓh(t − τℓ − pT),
+(5)
+where the FRI parameters {(aℓ, τℓ)|τℓ ∈ (0, T], aℓ ∈ R}L
+ℓ=1
+correspond to the unknown amplitudes and delays. The rate
+of innovation of x(t) is 2L
+T and hence, 2L measurements are
+sufficient for perfect recovery [1], [37].
+Since x(t) is T-periodic, it has a Fourier series representa-
+tion
+x(t) =
+�
+k∈Z
+ˆx[k]ejkω0t,
+(6)
+where ω0 =
+2π
+T . The Fourier-series coefficients (FSCs) are
+given by
+ˆx[k] = 1
+T
+ˆh(kω0)
+L
+�
+ℓ=1
+aℓe−jkω0τℓ,
+(7)
+where K is a set of integers, ˆh(ω) is the continuous-time
+Fourier transform of h(t) [1]. It is assumed that ˆh(kω0) ̸= 0
+for k ∈ K.
+It was shown in [37], that the parameters {aℓ, τℓ}L
+ℓ=1 can be
+uniquely computed from 2L samples of the FSCs ˆx[k] using
+spectral analysis methods, such as the annihilating filter (AF)
+[1]. Thus, FRI signal reconstruction is reduced to the problem
+of uniquely determining the desired number of FSCs from the
+signal measurements.
+C. Kernel and Sub-Nyquist Sampling
+A crucial component of an FRI sampling architecture is the
+sampling kernel. Generally, sampling kernels with compact
+support are preferable from a hardware implementation per-
+spective. We consider IF-TEM sampling and recovery with
+a compactly supported sum-of-sincs (SoS) kernel for FRI
+signals. Consider an SoS kernel generated by
+ˆg(ω) =
+�
+k∈K
+sinc
+� ω
+ω0
+− k
+�
+.
+(8)
+Based on the robust sampling kernel presented in [22], and
+to maintain the real-valued nature of the filter response and
+output, we select K as
+K = {−K, · · · , −1, 1, · · · , K},
+where
+K ≥ 2L.
+(9)
+The sampling kernel resilience is a result of selecting a support
+set K that is symmetric about zero but does not include zero.
+The filtered signal y(t) = (x ∗ g)(t) is given as
+y(t) =
+�
+k∈K
+ˆx[k]ˆg(kω0)ejkω0t =
+�
+k∈K
+ˆx[k]ejkω0t.
+(10)
+
++4
+B =
+�
+����
+e−jKω0t2 − e−jKω0t1
+· · ·
+e−jω0t2 − e−jω0t1
+ejω0t2 − ejω0t1
+· · ·
+ejKω0t2 − ejKω0t1
+e−jKω0t3 − e−jKω0t2
+· · ·
+e−jω0t3 − e−jω0t2
+ejω0t3 − ejω0t2
+· · ·
+ejKω0t3 − ejKω0t2
+...
+...
+...
+...
+e−jKω0tN − e−jKω0tN−1
+· · ·
+e−jω0tN − e−jω0tN−1
+ejω0tN − ejω0tN−1
+· · ·
+ejKω0tN − ejKω0tN−1
+�
+���� .
+(12)
+In this case, the forward model or the relation between yn’s
+and the desired FSCs is given by
+yn =
+�
+k∈K
+ˆx[k]
+jkω0
+�
+ejkω0tn+1 − ejkω0tn�
+.
+(11)
+It was shown in [22], that y(t) is bounded provided that
+max{aℓ|aℓ ∈ R}L
+ℓ=1 < ∞ and the pulse h(t) is absolutely
+integrable.
+To
+extract
+the
+FSCs
+from
+(11),
+let
+y
+=
+[
+� t2
+t1 y(t)dt,
+� t3
+t2 y(t)dt, · · · ,
+� tN
+tN−1 y(t)dt]⊤, where N is the
+number of time instants in the interval T. The measurements
+y and the FSCs
+ˆx =
+�
+− ˆx[−K]
+jKω0
+, · · · , − ˆx[−1]
+jω0
+, ˆx[1]
+jω0
+, · · · , ˆx[K]
+jKω0
+�⊤
+(13)
+are related as
+y = Bˆx,
+(14)
+where B is given in (12). It was shown in [22], that the matrix
+B has full column rank and is uniquely left invertible. Then
+the Fourier coefficients vector can be computed as
+ˆx = B†y,
+(15)
+where B† denotes the Moore-Penrose inverse. Prefect recon-
+struction is established by [22] when N ≥ 4L + 2 and
+|K| ≥ 2L, as summarized in the following theorem:
+Theorem 1 (Section III.D in [22]). Let x(t) be a T-periodic
+FRI signal of the following form
+x(t) =
+�
+p∈Z
+L
+�
+ℓ=1
+aℓh(t − τℓ − pT),
+where the pulse h(t) ∈ L2(R), and the number of FRI pulses
+L are known. Consider the sampling mechanism shown in Fig.
+4. Let the sampling kernel g(t) satisfy
+ˆg(kω0) =
+�
+1
+if k ∈ K = {−K, · · · , −1, 1, · · · , K},
+0
+otherwise,
+and max
+t
+|(h∗g)(t)| < ∞. The filtered signal y(t) = (x∗g)(t).
+Suppose the IF-TEM parameters {b, κ, δ} are chosen such that
+b > c where c = max
+t
+|y(t)| , and
+b − c
+κδ
+≥ 2K + 2
+T
+.
+(16)
+Then the parameters {aℓ, τℓ}L
+ℓ=1 can be perfectly recovered
+from the IF-TEM outputs if
+1) K ≥ 2L when {tℓ}L
+ℓ=1 are off-grid.
+2) K ≥ L when {tℓ}L
+ℓ=1 are on-grid.
+In practice, our IF-TEM HW circuit introduces noise
+into the signal, which causes the time occurrences tn to
+be perturbed. As a result, unstable recovery occurred when
+the aforementioned algorithm was utilized in the process
+of reconstructing the data from the hardware measurements
+(see Section III for more details). Therefore, a reconstruction
+strategy that is more robust to noise is required.
+D. Problem Formulation
+Consider a T-periodic FRI signal of the form of (5) and
+a sampling mechanism as shown in Fig. 4. The signal x(t)
+is passed through the sampling kernel g(t) as defined in
+(8), and the resulting signal y(t) is sampled using an IF-
+TEM. Both the time encodings{tn}N
+n=1 and the amplitude
+measurements {yn}N
+n=1 correspond to a discrete representation
+of y(t) = (x∗g)(t). In other words, {tn} encodes information
+of the FRI signal. As our objective is to design robust hard-
+ware, the FRI parameters {aℓ, τℓ}L
+ℓ=1 need to be accurately
+estimated from the IF-TEM firings. To this end, together with
+the hardware implementation, a robust recovery algorithm
+is needed. In the following section, we first introduce our
+robust recovery mechanism that perfectly recovers the Fourier
+series coefficients {ˆx[k]}k∈K from IF-TEM observations in
+the absence of noise with as few as 4L + 2 spikes inside an
+interval T. Then, we illustrate the resilience of our method in
+the presence of noise and demonstrate that it outperforms the
+one proposed in [22]. In Section IV, we discuss our hardware
+prototype realizations.
+III. ROBUST SUB-NYQUIST SAMPLING AND
+RECONSTRUCTION OF FRI SIGNALS FROM IF-TEM
+The IF-TEM circuit introduces noise into the signal, which
+perturbs the time instances {tn}. Even in the absence of
+noise, the time instances can only be determined with limited
+precision. The modeled jittered time instances are modeled as
+t′
+n = tn + ϵn,
+(17)
+where tn are the ideal time instances and ϵn
+iid
+∼ U[− σ
+2 , σ
+2 ] is
+the noise jitter. Our experiments on our hardware showed that
+the noise level σ fluctuates between 15 − 70 ms. Since the
+method presented in [22] to reconstruct FRI signals from IF-
+TEM measurements resulted in an inconsistent recovery using
+hardware data, a more noise-tolerant reconstruction method is
+presented next.
+We compare the proposed recovery method with the recon-
+struction described by [22] in the presence of perturbations
+to the measured time instances. Both approaches employ a
+sample kernel lacking the zeroth frequency. While the recon-
+struction approach proposed by [22] used the forward equation
+defined in (11), our new algorithm is based on an alternative
+formulation presented in (20) below.
+
+5
+A. Robust Reconstruction
+This section presents a method for determining the Fourier
+coefficients of the FRI signal that is more robust and improves
+recovery. The recovery approach described in [22], and dis-
+cussed in the previous section, is based on computing the FSCs
+ˆx of the FRI signal x(t) using (15). In the case of noise, this
+leads to a perturbation in the measurements yn as well as
+the matrix B defined in (11) and (12), respectively. In this
+case, while computing the FSCs, the stability of B, which is
+measured by the condition number of the matrix, impacts the
+results. Next, we show that by utilizing a partial summation
+of yn, perfect recovery is achieved similarly to Theorem 1. In
+the noisy scenario, the resulting method is more robust. As
+we show below, when employing a partial summation of yn,
+we end up with a recovery problem similar to (15) but with
+the matrix A defined in (23) replacing B. This matrix has a
+better condition number than B.
+To gain intuition as to why this is the case, we demonstrate
+that for every k ∈ K, utilizing the partial summation for the
+measurements reduces the noise in each element of A by half
+compared to its corresponding element in B. This result is
+summarized in the following lemma.
+Lemma 1. Let [B]nk = ejkω0tn+1 − ejkω0tn be the entries
+of matrix B, where n = 1, · · · , N − 1, k ∈ K. Let [A]nk =
+ejkω0tn+1 be the entries of matrix A, where n = 1, · · · , N −
+1, k ∈ K ∪ {0}. The jittered time instances are modeled as
+t′
+n = tn + ϵn, where tn are the ideal time instances and the
+jitter noise is modeled as ϵn
+iid
+∼ U[− σ
+2 , σ
+2 ], i.i.d. uniformly
+distributed. For every t′
+n and k ∈ K,
+var ([B]nk) = 2var ([A]nk) ,
+(18)
+where var is the variance.
+Proof. By utilizing the fact that t′
+n = tn + ϵn, and using (12)
+and (23), it follows that,
+var ([B]nk) = var
+�
+ejkω0(tn+1+ϵn+1) − ejkω0(tn+ϵn)�
+= |ejkω0tn+1|2 var
+�
+ejkω0ϵn+1�
++ |ejkω0tn|2 var
+�
+ejkω0ϵn�
+= 2var
+�
+ejkω0ϵn�
+= 2var ([A]nk) ,
+(19)
+establishing the lemma.
+It can be intuitively inferred that by utilizing the partial
+summation, the noise in each element of [A]nk becomes
+smaller than the corresponding noise in [B]nk. Consequently,
+the matrix A has a better condition number than B. This
+can be explained by the fact that the condition number of
+a matrix is a measure of the sensitivity of the matrix to small
+perturbations in its elements, and a smaller condition number
+indicates that the matrix is less sensitive to such perturbations.
+Therefore, by reducing the noise in the elements of A using
+the partial summation, we can improve its condition number.
+In the next step, we employ the partial summation of yn to
+present a perfect recovery guarantee for FRI signals by using
+IF-TEM. Instead of recovering the FSCs from yn through the
+forward model (11) with K in (9), which defines the relation
+between yn and the FSCs ˆx[k], we propose an alternative
+model that is based on zn. These are the partial sums of the
+measurements yn defined as
+zn =
+n−1
+�
+i=1
+yi =
+�
+k∈K
+ˆx[k]
+jkω0
+�
+ejkω0tn − ejkω0t1�
+,
+(20)
+where n = 2, · · · , N. Note that (20) can be written as
+zn =
+�
+k∈K
+ˆx[k]
+jkω0
+ejkω0tn + c,
+(21)
+where
+c = −
+�
+k∈K
+ˆx[k]
+jkω0
+ejkω0t1.
+(22)
+Let z = [z2, · · · , zN]T ∈ RN−1 be the vector of partial sums,
+ˆz =
+�
+− ˆx[−K]
+jKω0 , · · · , − ˆx[−1]
+jω0 , c, ˆx[1]
+jω0 , · · · , ˆx[K]
+jKω0
+�⊤
+∈ C(2K+1)
+be the vector of FSCs, with c in the zeroth place, and A ∈
+C(N−1)×(2K+1) be the matrix defined as
+A =
+�
+����
+e−jKω0t2
+· · · 1 · · ·
+ejKω0t2
+e−jKω0t3
+· · · 1 · · ·
+ejKω0t3
+...
+...
+...
+e−jKω0tN
+· · · 1 · · ·
+ejKω0tN
+�
+����.
+(23)
+Then, (21) can be expressed in matrix form as follows:
+z = Aˆz.
+(24)
+Since the set of time instants {tn}N
+n=2 are distinct, and A is
+a Vandermonde matrix, it has full column rank provided that
+N − 1 ≥ 2K + 1. This means that the matrix A has linearly
+independent columns. Therefore, we can perfectly recover the
+vector of FSCs ˆz via
+ˆz = A† z,
+(25)
+where A† denotes the Moore-Penrose inverse of A. Once we
+have ˆz, the FSCs ˆx[k] can be uniquely determined. Using
+ˆz[k] =
+� ˆx[k]
+jω0k,
+if k ∈ K ,
+− �
+k′∈K
+�
+ˆx[k′]
+jk′ω0
+�
+ejk′ω0t1
+if k = 0 .
+(26)
+The vector of FSCs ˆz and the vector of FSCs ˆx are related
+by:
+ˆx = [ˆz[−K], · · · , ˆz[−1], ˆz[1], · · · , ˆz[K]]⊤ ∈ C2K.
+(27)
+This equation allows us to obtain ˆx by selecting the appropri-
+ate elements of ˆz, which is the vector obtained from the partial
+sums of the measurements. Note that the resulting vector ˆx has
+dimensions 2K, which implies that it only contains the FSCs
+for positive and negative frequencies.
+Using the vector ˆz and (27), the vector of FSCs ˆx is
+uniquely determined. This indicates that, in the modified ker-
+nel setup, without zero frequency, the set of FSCs ˆx[k] can be
+uniquely determined from time encodings if N −1 ≥ 2K +1.
+This condition implies that there should be a minimum of
+2K + 2 firing instants within an interval T. For an IF-TEM,
+the minimum firing rate is given as b−c
+κδ (as shown in [22]).
+
+6
+Fig. 5. Perfect reconstruction of an FRI signal from IF-TEM measurements
+with the modified sampling kernel. (a): the input signal and its reconstruction
+for L = 5. (b): the filtered signal y(t) and the time instants tn.
+Hence, for uniqueness recovery, the IF-TEM parameters must
+satisfy the inequality b−c
+κδ ≥ 2K+2
+T
+(see [22] for details).
+A reconstruction algorithm to compute the FRI parameters
+from IF-TEM firings is presented in Algorithm 1. Compared
+to the technique presented in [22], our method requires the
+same number of FSCs in the absence of noise. However, in
+the presence of noise, as is typically the case in real-world
+hardware, the proposed approach yields a lower error for the
+same number of measurements.
+Algorithm 1 Reconstruction of a T-periodic FRI signal.
+Input: N ≥ 2K + 2 spike times {tn}N
+n=1 in a period T.
+1: Let n ← 1
+2: while n ≤ N − 1 do
+3:
+Compute yn = −b(tn+1 − tn) + κδ
+4:
+Compute zn+1 = �n
+i=1 yi
+5:
+n := n + 1.
+6: end while
+7: Compute the vector ˆz = A† z, where A is defined in (23)
+8: Compute the Fourier coefficients vector ˆx from ˆz using
+(27)
+9: Estimate {(aℓ, τℓ)}L
+ℓ=1 using a spectral analysis method
+for K ≥ 2L.
+Output: {(aℓ, τℓ)}L
+ℓ=1.
+B. Numerical evaluation
+In this section, we provide numerical evidence of the valid-
+ity of Algorithm 1 through simulations. We then show that our
+proposed reconstruction technique improves the conditioning
+of the forward transformation, leading to a significant recon-
+struction improvement that is necessary for precise recovery
+Fig. 6. Average condition number of matrices A and B as a function of the
+number of FRI pulses L.
+using real hardware. To validate Theorem 1, we consider h(t)
+as a Dirac impulse with a time period of T = 1 second,
+and L = 5. The amplitudes are selected randomly over the
+range [−1, 1]. The time delays are chosen randomly between
+(0, 1) such that they lie on a grid with a resolution of 0.05.
+The input signal x(t) is filtered using an SoS sampling kernel
+with K = −K, · · · − 1, 1, · · · , K, where K = L. The filtered
+output y(t) is sampled using an IF-TEM where the IF-TEM
+parameters are chosen to satisfy the inequality (16). In this
+particular case, the IF-TEM sampler resulted in 16 firing
+instants in one time period, as shown in Fig. 5(b). As shown
+in Fig.
+5(a), we achieve perfect recovery of the FRI signal
+by using a kernel without zero frequency.
+As the IF-TEM circuit produces noise into the signal, which
+perturbs the time instances {tn}, we consider the jittered time
+instances: t′
+n = tn + ϵn, as defined in (17). We compare the
+proposed recovery method with the reconstruction algorithm
+described by [22] in the presence of perturbations to the
+measured time instances. Each approach employs a sample
+kernel lacking a zeroth frequency. While the reconstruction
+approach proposed by [22] used the forward method defined
+in (11), our method utilized a different forward method defined
+in (20).
+Using the forward operators or matrices A and B (see (14)
+and (24)), the FSCs are recovered in each of the previously
+discussed methods. The matrices A and B are functions of
+the measured time instants and sampling kernel. In Fig. 6,
+the condition numbers of matrices with the same number of
+4L+2 perturbed firing instants are compared as a function of
+the number of FRI signals L. To this aim, 5000 random sets
+of monotonic sequences {tn ∈ [0, T)}N
+n=1 were generated. As
+depicted in Fig. 6, the condition number of matrix A is smaller
+than that of matrix B. This demonstrates that our reconstruc-
+tion algorithm enhances stability and noise resilience.
+We evaluate and compare the relative mean square error
+(MSE) in the estimation of time delays performance for the
+reconstruction accuracy of the presented algorithm with the
+
+0.6
+Original
+(a)
+Recovered
+0.4
+0.2
+Amplitude
+-0.2
+-0.4
+-0.6
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+t
+0.5
+格
+-0.5
+-
+-1.5
+0.1
+0.2
+0.3
+0.4
+0.5
+90
+0.8
+0.1
+0.2
+0.3
+0.4
+0.5
+90
+L'0
+0.8
+60
+1o sps(log scale)
+cond(A)
+cond(B)
+3.5
+Condition Number (
+3
+2.5
+2
+1.5
+4
+6
+8
+10
+12
+14
+Number of pulses L7
+one suggested by [22], where the MSE is given by
+MSE = 10 log
+� L
+�
+ℓ=1
+(τℓ − ˆτℓ)2
+�
+,
+(28)
+and ˆτℓ is the estimated time delay. Specifically, we consider
+the signal x(t) as in (5), with period T = 1 second consisting
+of L = 3 pulses with h(t) a third-order cubic B-spline.
+The off-grid time-delays {τℓ}3
+ℓ=1 and amplitudes {aℓ}3
+ℓ=1 are
+generated at random over intervals (0, T] and [1, 5], respec-
+tively. The IF-TEM parameters are κ = 1, b = 2.5c where
+c = max
+t
+|y(t)|, and δ is chosen to satisfy (16). We consider
+a sum-of-sincs kernel with K = {−K, · · · , −1, 1 · · · , K}
+for the calculation of the Fourier coefficients ˆx[k]. The time
+instances {tn} were perturbed as t′
+n = tn +ϵn where tn is the
+actual time encoding and ϵn is a random variable uniformly
+distributed over [−σ/2, σ/2]. We use an annihilating filter
+with Cadzow denoising to estimate the time-delays in the
+presence of noise. Since Cadzow denoising requires more than
+2L consecutive samples of FSCs, we consider K ≥ 2L + 1
+while excluding the zero. Based on the fact that the proposed
+recovery where 0 /∈ K estimates {ˆx[k]}−1
+k=−K and {ˆx[k]}K
+k=1,
+we apply Cadzow denoising on each of these sequences inde-
+pendently and then apply block annihilation [51] to determine
+the time-delays jointly.
+The MSEs in the estimation of time-delays for different
+numbers of FSCs and perturbation levels are shown in Fig.
+7. We used 500 independent noise and FRI signal realizations
+to compute each MSE value. In Fig. 7(a) and (b) we show
+MSEs for [22] and Algorithm 1, both without zero in the
+sampling kernel, for K = 2L + 1 up to 5L. We observe that
+comparing the approaches, we note a gain of up to 10 dB.
+Since perturbation in the time encoding is also equivalent to
+quantization noise, a lower MSE indicates that our proposed
+approach can operate at lower bits compared to [22].
+IV. ANALOG BOARD AND HARDWARE CHALLENGES
+In this section, we will describe the specifications of our
+FRI-TEM hardware prototype.
+A. FRI-TEM Analog Board
+We begin by discussing the key components of the FRI-
+TEM hardware implementation, as well as various circuit
+design considerations. As shown in Fig. 9 and 10, the analog
+board comprises three sequential stages: the generation of an
+FRI signal, band-pass filtering, and an IF-TEM sampler.
+The FRI signal generator uses an analog approach, which
+is known for its low digital noise and ability to accurately
+simulate real-world applications such as radar and ultrasound
+[52]. The process of signal production involves several com-
+ponents working together to generate and process a signal.
+One possible configuration for a signal generator is to use
+a scope, a splitter, an analog delay generator, and a passive
+radio frequency (RF) combiner. The scope generates an FRI
+pulse (10−500ns wide), that is transmitted through the splitter.
+The splitter receives the pulse and sends it to both the delay
+generator and the combiner (see Fig. 9). The delay generator is
+(a) Without zero approach in [22]
+(b) Without zero Algorithm 1
+Fig. 7. A comparison of [22] and Algorithm 1 for off-grid time delays with
+perturbation in the time encodings: our method has lower error compared to
+[22].
+comprised of a fiber optic cable, a photo-diode encoder, and
+a photo-diode detector. Encoding the signal with the photo-
+diode encoder is the initial step of the delay generator. The
+signal then travels through the fiber optic line, causing a
+delay of at least 4µs. The significance of the fiber optic delay
+implementation originates from its well-known benefits, such
+as the introduction of low digital noise, which more accurately
+simulates practical applications. In order to decode the delayed
+input signal, a photo-diode detector is used to transform the
+signal to an analog signal with the same frequency as the
+original FRI input pulse. In Fig. 9 for instance, the FRI signal
+x(t) (5) consists of two 20MHz pulses separated by a relative
+delay of 4µs. The output of the combiner, x(t), is then sent
+as input to the sampling kernel.
+The filter, also known as the sampling kernel, is used to
+remove the zeroth frequency component of the signal, as
+shown in Fig. 8. For example, if the frequency of the signal
+is 10 Hz, the magnitude of the zeroth frequency component
+would be −30dB. The positioning of the sampling kernel,
+which is essentially a band-pass filter (BPF), is critical for the
+
+5L
+-10
+4L
+-20
+K
+3L
+-30
+-40
+2L+1
+-50
+0.006
+0.017
+0.05
+0.07
+a5L
+-10
+4L
+-20
+K
+3L
+-30
+-40
+2L+1
+-50
+0.006
+0.017
+0.05
+0.07
+a8
+Fig. 8.
+A 1MHz filter Bode plot. The sampling kernel removes the zeroth
+frequency. The magnitude (in blue) and phase (in red) plotted on a logarithmic
+frequency scale.
+sub-Nyquist sampling and reconstruction of FRI signals using
+an IF-TEM (see Section III). In order to accurately recover
+and analyze two pulses of an FRI signal within a noise-free
+setting for a short time period such as T = 10µs, the minimum
+theoretical sampling rate required is 0.4MHz [1], [37]. In order
+to facilitate this fast sampling and reconstruction process, a
+1MHz filter was chosen. Here, an eight-order 1MHz BPF is
+employed, enabling a suitable trade-off between energy usage
+and reconstruction performance.
+The output of the filter, y(t) (10), is then transmitted to the
+IF-TEM sampler. The block diagram of the IF-TEM circuit is
+shown in Fig. 10, and a list of the specific components of the
+IF-TEM circuit can be found in Table I. A prototype of the
+IF-TEM sampler is depicted in Fig. 11.
+The primary IF-TEM components consist of the bias b,
+integrator, comparator, differentiator, and reset function. To
+guarantee sufficient samples for reconstruction, we should
+ensure that the δ threshold is achieved at least as many times
+as the desired sample amount. By adding the bias b to the
+input y(t), the integrator obtains a signal that is always non-
+negative. In this case, integration over a non-negative signal is
+a positive function, and the threshold is always attained. For
+an FRI signal x(t) with L pulses, it can be shown that the
+sampler input filtered signal y(t) is constrained by [22]
+|y(t)| ≤ c = L amax ∥g∥∞∥h∥1,
+(29)
+where g and h are the known filter and pulse shape, respec-
+tively. Consequently, the bias b > c, which is effectively a con-
+stant DC voltage, is selected manually using a potentiometer,
+which is a device that allows the user to adjust the electrical
+resistance in a circuit by turning a knob. By adjusting the
+resistance, the user is able to fine-tune the value of the bias
+to the desired level. It is important to carefully select the
+appropriate bias value in order to ensure that the IF-TEM
+system is able to function properly.
+The output of the integrator is sent to the comparator, which
+compares the integrator voltage to a predefined threshold δ.
+The threshold is a constant DC voltage that is implemented
+in our hardware utilizing a potentiometer that is manually
+regulated and adjustable. The comparator is responsible for
+comparing the voltage produced by the integrator to a pre-
+defined threshold value. When the integrator voltage reaches
+or exceeds the threshold, the comparator’s output changes. If
+the comparator’s input is below the threshold, it will output a
+logical value of ’0’, while if the input is above the threshold,
+the output will be ’1’. In other words, the comparator will
+produce a sequence of logical ’1’ values when the integrator
+voltage hits the threshold. This change in the comparator’s
+output signal indicates that the threshold has been reached
+and triggers the next stage in the IF-TEM process.
+The output of the comparator is sent to the differentiator,
+which generates a short pulse that activates the fast reset
+function. This function is responsible for capturing the time
+instances tn. The reset function consists of an amplifier and a
+field-effect transistor (FET) that work together to quickly and
+completely discharge the integrator capacitor. In greater detail,
+the FET functions as a switch and is controlled by the pulse
+produced by the differentiator, which determines the duration
+of time that the FET is active. This allows the integrator
+capacitor to be fully discharged. The FET has three terminals:
+source, gate, and drain. By providing a voltage of ”1” to the
+gate terminal, the FET can modify the conductivity between
+the drain and source terminals, which allows the current flow
+to be regulated. This results in a rapid and complete discharge
+of the integrator capacitor.
+TABLE I
+LIST OF HARDWARE COMPONENTS
+Device
+Reference
+Manufacturer
+Buffer
+AD899
+Mini-Circuits
+Integrator
+LT1364
+Analog Devices
+Comparator
+TLV3201
+Texas Instruments
+Differentiator
+LT1364
+Analog Devices
+B. Circuit challenges
+To implement an IF-TEM circuit, it is necessary to employ
+an integrator that operates according to (2). Specifically, the
+integrator capacitor must operate in its linear domain, which
+is continuously charged or rising, as long as the input signal
+is positive. Additionally, the IF-TEM thresholding process
+requires a fast reset mechanism. Therefore, our goal is to
+develop an integrator and reset function in which the capacitor
+of the integrator operates in its linear zone and discharges
+rapidly and completely. The main challenge in the implemen-
+tation of the IF-TEM hardware is to design and implement
+such an IF-TEM integrator capacitor, while supporting a wide
+range of input FRI signals without circuit modification. By
+utilizing the differentiator and a FET in the reset function,
+both the entire discharge and rapid discharge of the capacitor
+are accomplished for a variety of FRI signals. Next, we provide
+results from our hardware and compare them to our theoretical
+results from Theorem 1.
+V. HARDWARE EXPERIMENTS
+To determine the potential and feasibility of the devel-
+opment proposed system, we performed experiments on the
+
+OdB
+969
+5
+147
+147
+196
+45
+245
+10Hz
+100
+1. 0k
+10k
+100k
+1.0M
+: -30.22dB, 84.93° @ 10.0H29
+Fig. 9. The FRI-TEM hardware prototype contains a signal generator, a sampling kernel and an IF-TEM sampler. The signal generator consists of a delay
+path of atleast 4µs, which is built from a modulator optic fiber that ends in a Photo-Diode detector. Then, a combiner receives the original signal (single one
+or more) from the generator and the delayed path to create the FRI signal. The generated signal is passed into a BPF of 1MHz which removes the zero
+frequency. Finally, the resulting signal is sampled by an IF-TEM sampler board. Based on Algorithm 1, the FRI signal is recovered.
+Fig. 10. Block diagram of the analog board.
+
+Signal generation
+FIBEF
+AsAnalog
+MODULATOR
+PHoto Diode
+Detector
+TIME (in sec.)
+Time delay generator
+FRI pulse [MHz]
+Splitter
+Combiner
+Sampling kernel
+Signal Sampler
+Reconstruction
+Time Encoding Machine
+@SA MPLLAB
+Combiner
+for FRI signals 
+y(t)
+Signai in
+Delayed Signal In
+0.88
+112
+Recover Signa
+BPF - 1MHz
+IF-TEM circuit
+Removes the zeroth frequencyOptical fiber
+Splitter
+Combiner
+Si(in1)
+Delay Line
+Laser
+Delayed
+(O
+BPF
+-3dB
+Laser Detector
+Sig
+Modulator
+0.22KHz - 1MHz
+[si(in2)
+Threshold
+Integrator
+Comparator
+Inverter
+Amplifier
+DC
+01100
+H言
+Differentiator
++20dB 
+Restorer
+R
+Reset Function
+ FET
+Amplifier
+Blas
++10dB
+0->1
+Switch
+IAH10
+Fig. 11. IF-TEM hardware board.
+Fig. 12. (a). FRI input signal x(t) (green), BPF output y(t) (yellow), and the IF-TEM output resulting in 19 samples (blue). (b). sampling and reconstruction
+using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).
+FRI-TEM hardware system that we built. As depicted in Fig.
+12(a), we consider an FRI input signal, referred to as x(t),
+consisted of two pulses with a width of 100ns and a delay of
+5µs between them. The sampling kernel mentioned in Section
+II-C was utilized in these experiments. The parameters for
+the IF-TEM circuit were set to a value of κ = 3 · 10−8,
+with a bias of b = 3V and a threshold of δ = 1.5V .
+The specific time delays and amplitudes used in this input
+signal were chosen arbitrarily, and the IF-TEM parameters
+were selected to adhere to the constraints outlined in (16).
+As demonstrated in Fig. 12(a), the filtered signal y(t) was
+transmitted to an IF-TEM sampler, which produced 19 time
+instances tn, resulting in a firing rate of 1.9MHz, which is 4.75
+times the rate of innovation and 10.5 times the Nyquist rate.
+It is important to note that a minimum of 4L + 2 = 10 time
+instances are required for off-grid reconstruction. Fig. 12(b)
+illustrates a comparison between the original input signal and
+the estimated signal. This demonstrates that the parameters of
+the FRI system can be robustly estimated while operating at
+a rate that is 10 times lower than the Nyquist rate.
+In Fig. 13(a), Fig. 14(a), and Fig. 15(a), we demonstrate
+sampling and reconstruction of FRI signals with L = 3, 5 for
+h(t) as a Dirac impulse and stream of pulses. The FRI signal
+is represented by the green curve, the filtered signal y(t) is
+shown in yellow, and the time instances tn produced by the
+IF-TEM sampler are depicted in blue. In each of these figures,
+
+IF-TEM sampler Board
+REG4
+REG2
+O
+Differentiator
+GND
+Comparator
+PDUINO
+LEONARDO MODULE
+TEM-DEMQ-VER3
+Filtered Signal y(t)
+GND
+GND
+018
+U1
+12
+Integrator
+GND
+2283922A-Y84-211117
+COMPperator
+INTECRATOR
+Dlfferantiator
+Reset Function
+Threshold S
+Level [Volts]
+Bias Level
+PULSE
+TEST
+[Volts]  b
+ADJUST
+REFERENCE-
+JUST
+GND
+00
+88
+8.2.8
+Time instances tn(a)
+50.09/
+3109/
+5.00V/
+1.00V/
+39.46
+1.0009/
+Stop
+(q)
+True
+- - -Estimate
+0.8
+0.6
+0.4
+0.2 
+1.2
+1.4
+1.6
+1.8
+2
+-183.750mv
+-922.25m
++14.9375V
++3.48750
+.00:
+.00:1
+TIME (in sec.)11
+Fig. 13. (a). FRI input signal x(t) (green), BPF output y(t) (yellow), and the IF-TEM output resulting in 19 samples (blue). (b). sampling and reconstruction
+using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).
+Fig. 14. (a). FRI input signal x(t) (yellow), BPF output y(t) (green), and the IF-TEM output resulting in 21 samples (blue). (b). sampling and reconstruction
+using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).
+Fig. 15. (a). FRI input signal x(t) (green), BPF output y(t) (yellow), and the IF-TEM output resulting in 22 samples (blue). (b). sampling and reconstruction
+using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).
+the number of time instances produced is 19, 21, and 22,
+respectively, resulting in firing rates of 1.9 MHz, 2.1 MHz, and
+2.2 MHz, which are all between 9.5 and 10.5 times the Nyquist
+rate. The reconstructed FRI signals are shown in Figures 13(b),
+14(b), and 15(b). The maximum error in time delay estimation
+is -25 dB. These results indicate that our proposed sampling
+and reconstruction method is suitable for use in radar and
+ultrasonic imaging applications.
+
+(a)
+1009/
+250V/
+5.00V/
+1.00V/
+17.849
+1.000g/
+Stop
+(q)
+True
+- - -Estimate
+0.8
+0.6
+0.4
+0.2
++356.200ml
++893.00mv
++17.0625V
++3.46250v
+0.20.3
+0.405
+0.6
+0.7
+0.80.9
+DC
+1.00:1
+AC
+1.00:1DC
+1.00:1DC
+001
+TIME (in μs.)(a)
+200/2240/35.00V/
+41.00V/
+-185.4
+1.000g/
+Stop
+(q)
+0.4
+True
+- - -Estimate
+0.3
+0.2
+0.1
+-0.1
+-0.2
+-0.3
++325.000mw
++354.00mV
++13.6850
++3.27500V
+0
+0.2
+0.4
+0.6
+0.8
+1
+100.1DC BU
+100:1DCBU
+1.00:1DC BVV
+100.1
+TIME (in μs.)(a)
+150.07
+/含006
+35.00V7
+1.00V7
+50.56
+1.00097
+Stop
+(b)
+-True
+- - -Estimate
+0.8
+0.6
+0.4
+0.2
++176.250m
++172.50ml
++14.9375.
++3.48750
+0.2
+0.4
+0.6
+0.8
+DC
+00:10C
+1.00:1DC
+TIME (in μs.)12
+Fig. 16.
+A comparison between the reconstruction using the hardware
+measurements and the simulation.
+Figure 16 presents a comparison between the reconstruction
+using the hardware measurements and the simulation for the
+amplitudes and time delays of the FRI signals with two pulses.
+This comparison is used to evaluate the performance of the
+proposed hardware prototype and reconstruction method by
+comparing the results obtained from the hardware measure-
+ments with those obtained from the simulation. The evaluation
+involves calculating the error between the reconstructed signals
+obtained from the hardware and simulation, as well as compar-
+ing the estimated FRI parameters. This comparison provides
+insight into the accuracy and reliability of the hardware and
+reconstruction approach. The error in the estimation of the
+time delay is found to be -25 dB, and this result is consistent
+with the findings when using L = 3.5 pulses.
+VI. CONCLUSION
+In this work, we studied the problem of recovering FRI
+signals using an IF-TEM sampler. To this end, we intro-
+duced a hardware prototype of a sub-Nyquist IF-TEM ADC
+and developed a robust reconstruction approach to accurately
+retrieve the FRI parameters. The hardware prototype that
+we introduced is an asynchronous, energy-efficient ADC that
+estimates the FRI parameters using a sub-Nyquist framework,
+which allows it to operate at rates significantly lower than
+the Nyquist rate. We have demonstrated that our proposed
+hardware and reconstruction method can retrieve the FRI
+parameters with a reconstruction error of up to -25 dB
+while operating at rates approximately 10 times lower than
+the Nyquist rate. These results suggest that the proposed
+hardware prototype and reconstruction approach are effective
+and efficient in accurately recovering FRI signals and may be
+useful in various applications, such as radar and ultrasonic
+imaging. In comparison to traditional ADCs, the proposed
+prototype is asynchronous and energy-efficient, which may
+make it particularly attractive for use in energy-constrained
+systems such as battery-powered devices where these factors
+are important considerations.
+In this study, we investigated the problem of recovering FRI
+signals using an IF-TEM sampler. To address this challenge,
+we proposed a hardware prototype of a sub-Nyquist IF-TEM
+ADC and developed a robust reconstruction approach to accu-
+rately retrieve the FRI parameters. The hardware prototype that
+we introduced is an asynchronous, energy-efficient ADC that
+estimates the FRI parameters using a sub-Nyquist framework,
+which allows it to operate at rates significantly lower than
+the Nyquist rate. Our proposed hardware and reconstruction
+method have been demonstrated to be able to retrieve the
+FRI parameters with a reconstruction error of up to -25 dB
+while operating at rates approximately 10 times lower than
+the Nyquist rate. These results suggest that the proposed
+hardware prototype and reconstruction approach are effective
+and efficient in accurately recovering FRI signals and may
+be useful in various applications such as radar and ultrasonic
+imaging. In comparison to traditional ADCs, the proposed
+prototype is asynchronous and energy-efficient, which may
+make it particularly attractive for use in energy-constrained
+systems such as battery-powered devices where these factors
+are important considerations.
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+
diff --git a/StA0T4oBgHgl3EQfD_-h/content/tmp_files/load_file.txt b/StA0T4oBgHgl3EQfD_-h/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,1021 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf,len=1020
+page_content='1  Hardware Prototype of a Time-Encoding  Sub-Nyquist ADC  Hila Naaman, Student Member, IEEE, Nimrod Glazer Member, IEEE, Moshe Namer, Daniel Bilik, Shlomi  Savariego, and Yonina C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Eldar, Fellow, IEEE  Abstract—Analog-to-digital converters (ADCs) are key com-  ponents of digital signal processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Classical samplers in this  framework are controlled by a global clock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' At high sampling  rates, clocks are expensive and power-hungry, thus increasing the  cost and energy consumption of ADCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' It is, therefore, desirable  to sample using a clock-less ADC at the lowest possible rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' An  integrate-and-fire time-encoding machine (IF-TEM) is a time-  based power-efficient asynchronous design that is not synced to  a global clock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Finite-rate-of-innovation (FRI) signals, ubiquitous  in various applications, have fewer degrees of freedom than  the signal’s Nyquist rate, enabling sub-Nyquist sampling signal  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This work proposes a power-efficient IF-TEM ADC  architecture and demonstrates sub-Nyquist sampling and FRI  signal recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Using an IF-TEM, we implement in hardware  the first sub-Nyquist time-based sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We offer a feasible  approach for accurately estimating the FRI parameters from IF-  TEM data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The suggested hardware and reconstruction approach  retrieves FRI parameters with an error of up to -25dB while  operating at rates approximately 10 times lower than the Nyquist  rate, paving the way to low-power ADC architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Index Terms—Brain-inspired computing, analog-to-digital con-  version (ADC), time-based sampling hardware, integrate and fire  TEM (IF-TEM), sub-Nyquist sampling, finite-rate-of innovation  (FRI) signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' INTRODUCTION  Analog-to-digital converters (ADCs) are electronic hard-  ware components that facilitate the digital processing of sig-  nals and communication between computers and the physical  world [1], [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Traditional ADCs, also known as synchronous  ADCs, are controlled by a global clock that operates at a  rate that meets the Nyquist rate, requiring the acquisition  of samples at intervals of 1/2W seconds for signals with a  frequency no greater than WHz [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' However, synchronous  ADCs have several limitations that may make them less  suitable for certain applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' One limitation is high power  consumption due to the continuous clock signal, which can  be a significant disadvantage in energy-constrained systems  such as battery-powered devices [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Another limitation is the  need for a stable and accurate clock signal, which becomes  more challenging to achieve as the sampling rate in a high  speed system increases, especially in noisy or interference-  prone environments [5]–[7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Synchronous ADCs also require  All the authors are with the Faculty of Math and Computer Science, Weizmann  Institute of Science, Israel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Email: hila.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='naaman@weizmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='il  Parts of this work were presented at the international Symposium on Information  Theory, ISIT, July 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  This research was partially supported by the European Union’s Horizon 2020 research  and innovation program under grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 101000967-ERC-CoDeS, by the Israel Science  Foundation under grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 0100101, and by the QuantERA grant C’MON-QSENS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  complex clock circuits, which increase the complexity of the  design and implementation [8], [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Consequently, there is a  need for innovative ADCs that address these limitations by  reducing both power consumption and sampling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The integrate-and-fire time encoding machine (IF-TEM),  an asynchronous energy-efficient event-driven sampler, is a  promising alternative to conventional ADCs [8], [10]–[13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In this architecture, no global clock is required, making the  IF-TEM sampler low energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Furthermore, compared to its  traditional amplitude-based ADCs, TEMs use extremely sim-  ple, entirely analog, low-power, and small size encoders [10],  [14]–[16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' An IF-TEM integrates an input signal and then  compares the integral to a threshold;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' if the threshold is  met, the time instances are recorded  [17]–[22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The IF-  TEM sampler has been utilized for ultra-wide-band (UWB)  communications [23], remote sensing [24], [25], heart activity  monitoring [26], [27], event-based cameras (also referred to  as neuromorphic cameras) [28]–[31] and other applications  such as spiking neural network (SNN) interpretations, leading  to better knowledge of how to utilize neuromorphic hardware  and replace power-hungry ADCs [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In [17], it was shown that bandlimited signals sampled by  an IF-TEM can be perfectly recovered if the average sampling  rate of the IF-TEM is higher than the signal’s Nyquist sam-  pling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' By requiring the bandwidth to be inversely propor-  tional to the interval between time instances, the reconstruction  of the original signal closely resembles the reconstruction of a  bandlimited signal sampled with irregular amplitude samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In [33], it was shown that a spectrally sparse signal could  be recovered when the average IF-TEM sampling rate is  below the Nyquist rate with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The introduced  TEM was affected by frequency-dependent quantization noise,  which was most significant at high-frequency input signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Reconstruction of signals from time encoding has been gener-  alized for signals in shift-invariant spaces [34], and finite rate  of innovation (FRI) signals [21], [22], [35], [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  FRI signals are characterized by a small number of degrees  of freedom that permit sub-Nyquist sampling [1], [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Due  to their prevalence in numerous scientific applications, such  as radar [38], [39], ultrasound [40]–[42], time-domain optical-  coherence tomography (TDOCT) [43], and light detection and  ranging (LIDAR) [44], sampling and recovery of FRI signals,  particularly through the use of IF-TEMs, is of great interest  [22], [35], [45], [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Most of the FRI sampling literature  focuses on reducing the ADC’s sampling rate by using the  signal structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' It ignores other aspects of the ADC, such as  its power consuming clock [37], [40], [47], [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We address  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='02012v1  [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='SP]  5 Jan 2023  2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Time encoding machine with spike trigger reset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The input is biased by  b, scaled by κ, and integrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' A time instant is recorded when the threshold  δ is reached, after which the value of the integrator resets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  the issue of the synchronous ADCs’ power consumption by  utilizing the asynchronous IF-TEM sampler, which is energy-  efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Time-based sampling of FRI signals can be performed simi-  larly to conventional FRI sampling techniques, such as kernel-  based sampling [21], [22], [35], [36], [46], [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The authors  in [22] provided theoretical guarantees for the sampling and  recovery of FRI signals using an IF-TEM, and proposed  a sampling method that is more robust in the presence of  noise than existing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Our work introduces a low-  power IF-TEM ADC hardware that demonstrates sub-Nyquist  sampling and FRI signal recovery based on the approach in  [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We use hardware-measured data with time instances  perturbations up to 35ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The jittered time instances are  modeled as t′  n = tn + ϵn, where tn are the ideal time  instances and we model the jitter noise as i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' uniformly  distributed ϵn  iid  ∼ U[− σ  2 , σ  2 ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Based upon these assumptions  and the measured time instances from the hardware, it appears  that the noise level σ fluctuates between 15-70 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As present  reconstruction techniques are incapable of dealing with such  large perturbations, we modify the method of [22] to introduce  robustness in the presence of large timing noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Our contribution is twofold: first, we introduce a robust  sub-Nyquist sampling and reconstruction technique;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' then, we  present a hardware implementation of sub-Nyquist TEM sam-  pling of FRI signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Prior to acquiring timing information  with the IF-TEM, similarly to [22], the signal is prefiltered  using a sampling kernel which eliminates the zeroth frequency  component of the signal for robust recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Our reconstruc-  tion method relies on the sampling kernel selection as well  as introducing a new forward model to improve recovery  from noisy hardware data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Compared to our previous results  [16], here we present a simpler, straightforward proof for the  recovery guarantees, which is based on using a partial sum  of the measurements, resulting in more stable reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  We demonstrate that in the presence of noise, the proposed  reconstruction technique outperforms the method in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Then, we present the FRI-TEM hardware prototype that can  be employed in low-power time-of-flight applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The  hardware components are designed to accommodate a broad  spectrum of FRI signal frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The two primary compo-  nents of the hardware are an integrator and a reset function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  As long as the input signal is positive, the integrator capacitor  must operate in its linear domain, which is continually charged  or increasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In addition, the IF-TEM thresholding requires a  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Our IF-TEM hardware sampling: the IF-TEM input signal y(t) (blue),  the integrator output (green), and the IF-TEM output time instances (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  means for a rapid reset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' These are achieved by incorporating  a differentiator and a FET into the reset function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  We demonstrate the capabilities of the system via several  FRI signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Prior to the IF-TEM system, a band-pass filter is  employed as the sampling kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The filter eliminates unnec-  essary signal information and enables sub-Nyquist sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The designed hardware samples the filtered signal, resulting  in time instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' One method of recording time instances or  their differences is to use an oscilloscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' For estimating the  FRI parameters, the Fourier coefficients are computed using  our suggested algorithm, and the parameters are subsequently  estimated using the annihilating filter technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We demon-  strate that it is possible to estimate FRI parameters with sub-  Nyquist samples, taken at approximately 10 times the rate of  innovation, which is significantly lower than the Nyquist rate  of the signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Section  II, we formulate the problem of sampling and recovering an  FRI signal using an IF-TEM, and discuss some background  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Section III, we present our robust reconstruction  algorithm together with simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Section IV, we  justify the required hardware specs and comment on the circuit  challenges, followed by a detailed analog board’s design work  specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Experimental hardware results of IF-TEM sub-  Nyquist sampling and reconstruction are shown in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Finally, we conclude the paper in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' PRELIMINARY RESULTS PROBLEM FORMULATION  In this section, we review some previously established  results in time encoding and FRI, followed by our formulation  of the theoretical problem of FRI sampling and reconstruction  utilizing an IF-TEM sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Time Encoding Machine  We consider an IF-TEM whose operating principle is the  same as in [22] (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The input to the IF-TEM is  a bounded signal y(t), and the output is a series of spikes  or time instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' An IF-TEM is parameterized by positive  real numbers b, κ, and δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' A bias b is added to a c-bounded  signal y(t) such that |y(t)| ≤ c < b < ∞, and the sum  is integrated and scaled by  1  κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' When the resulting signal  reaches the threshold δ, the time instant tn is recorded, and the  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='7  [F-TEM input y(t)  Integrated signal with reset  [tn]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='1  00  0  5  6  Time [sec]  ×10℃3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Hardware integrator circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Our hardware implementation is com-  prised of an operational amplifier, a capacitor C and resistors R1 and R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  integrator is reset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The IF-TEM process is repeated to record  subsequent time instants, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=', if a time instant tn was recorded,  the next time instant tn+1 satisfies  1  κ  � tn+1  tn  (y(s) + b) ds = δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (1)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 2 depicts the operational output of our IF-TEM hard-  ware implementation using real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The integrator con-  stant κ is determined from the integrator circuit hardware  as demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The time encodings {tn, n ∈ Z}  form a discrete representation of the analog signal y(t) and  the objective is to reconstruct y(t) from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Typically,  reconstruction is performed using an alternative set of discrete  representations {yn, n ∈ Z} defined as  yn ≜  � tn+1  tn  y(s) ds = −b(tn+1 − tn) + κδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (2)  The measurements {yn, n ∈ Z} are derived from the time  encodings {tn, n ∈ Z} and IF-TEM parameters {b, κ, δ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Using (2) and the fact that |y(t)| ≤ c, it can be shown that for  any two consecutive time instants [18], [50]:  κδ  b + c ≤ tn+1 − tn ≤  κδ  b − c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (3)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' FRI Signal Recovery  Consider an FRI signal of the form  x(t) =  L  �  ℓ=1  aℓh(t − τℓ),  (4)  where the FRI parameters {(aℓ, τℓ)|τℓ ∈ (0, T], aℓ ∈ R}L  ℓ=1  are the unknown amplitudes and delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We assume that the  pulse h(t) ∈ L2(R), and the number of FRI pulses L are  known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Since the analysis of recovering aperiodic FRI signals  using IF-TEM measurements is similar to that of recovering  periodic FRI signals [22], in this paper we will concentrate on  the scenario of recovering T-periodic FRI signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Consider a T-periodic FRI signal, resulted from the linear  combination of delayed versions of a prototype pulse h(t) ∈  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Sampling setup IF-TEM: Continuous-time signal x(t) is filtered  through a sampling kernel g(t) and then sampled by using an IF-TEM to  generate time instances {tn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  L2(R), of the form  x(t) =  �  p∈Z  L  �  ℓ=1  aℓh(t − τℓ − pT),  (5)  where the FRI parameters {(aℓ, τℓ)|τℓ ∈ (0, T], aℓ ∈ R}L  ℓ=1  correspond to the unknown amplitudes and delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The rate  of innovation of x(t) is 2L  T and hence, 2L measurements are  sufficient for perfect recovery [1], [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Since x(t) is T-periodic, it has a Fourier series representa-  tion  x(t) =  �  k∈Z  ˆx[k]ejkω0t,  (6)  where ω0 =  2π  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The Fourier-series coefficients (FSCs) are  given by  ˆx[k] = 1  T  ˆh(kω0)  L  �  ℓ=1  aℓe−jkω0τℓ,  (7)  where K is a set of integers, ˆh(ω) is the continuous-time  Fourier transform of h(t) [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' It is assumed that ˆh(kω0) ̸= 0  for k ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  It was shown in [37], that the parameters {aℓ, τℓ}L  ℓ=1 can be  uniquely computed from 2L samples of the FSCs ˆx[k] using  spectral analysis methods, such as the annihilating filter (AF)  [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Thus, FRI signal reconstruction is reduced to the problem  of uniquely determining the desired number of FSCs from the  signal measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Kernel and Sub-Nyquist Sampling  A crucial component of an FRI sampling architecture is the  sampling kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Generally, sampling kernels with compact  support are preferable from a hardware implementation per-  spective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We consider IF-TEM sampling and recovery with  a compactly supported sum-of-sincs (SoS) kernel for FRI  signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Consider an SoS kernel generated by  ˆg(ω) =  �  k∈K  sinc  � ω  ω0  − k  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (8)  Based on the robust sampling kernel presented in [22], and  to maintain the real-valued nature of the filter response and  output, we select K as  K = {−K, · · · , −1, 1, · · · , K},  where  K ≥ 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (9)  The sampling kernel resilience is a result of selecting a support  set K that is symmetric about zero but does not include zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The filtered signal y(t) = (x ∗ g)(t) is given as  y(t) =  �  k∈K  ˆx[k]ˆg(kω0)ejkω0t =  �  k∈K  ˆx[k]ejkω0t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (10)  +4  B =  �  ����  e−jKω0t2 − e−jKω0t1  · ·  e−jω0t2 − e−jω0t1  ejω0t2 − ejω0t1  · ·  ejKω0t2 − ejKω0t1  e−jKω0t3 − e−jKω0t2  · ·  e−jω0t3 − e−jω0t2  ejω0t3 − ejω0t2  · ·  ejKω0t3 − ejKω0t2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  e−jKω0tN − e−jKω0tN−1  · ·  e−jω0tN − e−jω0tN−1  ejω0tN − ejω0tN−1  · ·  ejKω0tN − ejKω0tN−1  �  ���� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (12)  In this case, the forward model or the relation between yn’s  and the desired FSCs is given by  yn =  �  k∈K  ˆx[k]  jkω0  �  ejkω0tn+1 − ejkω0tn�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (11)  It was shown in [22], that y(t) is bounded provided that  max{aℓ|aℓ ∈ R}L  ℓ=1 < ∞ and the pulse h(t) is absolutely  integrable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  To  extract  the  FSCs  from  (11),  let  y  =  [  � t2  t1 y(t)dt,  � t3  t2 y(t)dt, · · · ,  � tN  tN−1 y(t)dt]⊤, where N is the  number of time instants in the interval T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The measurements  y and the FSCs  ˆx =  �  − ˆx[−K]  jKω0  , · · · , − ˆx[−1]  jω0  , ˆx[1]  jω0  , · · · , ˆx[K]  jKω0  �⊤  (13)  are related as  y = Bˆx,  (14)  where B is given in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' It was shown in [22], that the matrix  B has full column rank and is uniquely left invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Then  the Fourier coefficients vector can be computed as  ˆx = B†y,  (15)  where B† denotes the Moore-Penrose inverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Prefect recon-  struction is established by [22] when N ≥ 4L + 2 and  |K| ≥ 2L, as summarized in the following theorem:  Theorem 1 (Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='D in [22]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Let x(t) be a T-periodic  FRI signal of the following form  x(t) =  �  p∈Z  L  �  ℓ=1  aℓh(t − τℓ − pT),  where the pulse h(t) ∈ L2(R), and the number of FRI pulses  L are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Consider the sampling mechanism shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Let the sampling kernel g(t) satisfy  ˆg(kω0) =  �  1  if k ∈ K = {−K, · · · , −1, 1, · · · , K},  0  otherwise,  and max  t  |(h∗g)(t)| < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The filtered signal y(t) = (x∗g)(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Suppose the IF-TEM parameters {b, κ, δ} are chosen such that  b > c where c = max  t  |y(t)| , and  b − c  κδ  ≥ 2K + 2  T  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (16)  Then the parameters {aℓ, τℓ}L  ℓ=1 can be perfectly recovered  from the IF-TEM outputs if  1) K ≥ 2L when {tℓ}L  ℓ=1 are off-grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  2) K ≥ L when {tℓ}L  ℓ=1 are on-grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In practice, our IF-TEM HW circuit introduces noise  into the signal, which causes the time occurrences tn to  be perturbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As a result, unstable recovery occurred when  the aforementioned algorithm was utilized in the process  of reconstructing the data from the hardware measurements  (see Section III for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Therefore, a reconstruction  strategy that is more robust to noise is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Problem Formulation  Consider a T-periodic FRI signal of the form of (5) and  a sampling mechanism as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The signal x(t)  is passed through the sampling kernel g(t) as defined in  (8), and the resulting signal y(t) is sampled using an IF-  TEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Both the time encodings{tn}N  n=1 and the amplitude  measurements {yn}N  n=1 correspond to a discrete representation  of y(t) = (x∗g)(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In other words, {tn} encodes information  of the FRI signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As our objective is to design robust hard-  ware, the FRI parameters {aℓ, τℓ}L  ℓ=1 need to be accurately  estimated from the IF-TEM firings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' To this end, together with  the hardware implementation, a robust recovery algorithm  is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In the following section, we first introduce our  robust recovery mechanism that perfectly recovers the Fourier  series coefficients {ˆx[k]}k∈K from IF-TEM observations in  the absence of noise with as few as 4L + 2 spikes inside an  interval T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Then, we illustrate the resilience of our method in  the presence of noise and demonstrate that it outperforms the  one proposed in [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Section IV, we discuss our hardware  prototype realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' ROBUST SUB-NYQUIST SAMPLING AND  RECONSTRUCTION OF FRI SIGNALS FROM IF-TEM  The IF-TEM circuit introduces noise into the signal, which  perturbs the time instances {tn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Even in the absence of  noise, the time instances can only be determined with limited  precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The modeled jittered time instances are modeled as  t′  n = tn + ϵn,  (17)  where tn are the ideal time instances and ϵn  iid  ∼ U[− σ  2 , σ  2 ] is  the noise jitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Our experiments on our hardware showed that  the noise level σ fluctuates between 15 − 70 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Since the  method presented in [22] to reconstruct FRI signals from IF-  TEM measurements resulted in an inconsistent recovery using  hardware data, a more noise-tolerant reconstruction method is  presented next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  We compare the proposed recovery method with the recon-  struction described by [22] in the presence of perturbations  to the measured time instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Both approaches employ a  sample kernel lacking the zeroth frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' While the recon-  struction approach proposed by [22] used the forward equation  defined in (11), our new algorithm is based on an alternative  formulation presented in (20) below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  5  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Robust Reconstruction  This section presents a method for determining the Fourier  coefficients of the FRI signal that is more robust and improves  recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The recovery approach described in [22], and dis-  cussed in the previous section, is based on computing the FSCs  ˆx of the FRI signal x(t) using (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In the case of noise, this  leads to a perturbation in the measurements yn as well as  the matrix B defined in (11) and (12), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In this  case, while computing the FSCs, the stability of B, which is  measured by the condition number of the matrix, impacts the  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Next, we show that by utilizing a partial summation  of yn, perfect recovery is achieved similarly to Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In  the noisy scenario, the resulting method is more robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As  we show below, when employing a partial summation of yn,  we end up with a recovery problem similar to (15) but with  the matrix A defined in (23) replacing B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This matrix has a  better condition number than B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  To gain intuition as to why this is the case, we demonstrate  that for every k ∈ K, utilizing the partial summation for the  measurements reduces the noise in each element of A by half  compared to its corresponding element in B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This result is  summarized in the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Let [B]nk = ejkω0tn+1 − ejkω0tn be the entries  of matrix B, where n = 1, · · · , N − 1, k ∈ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Let [A]nk =  ejkω0tn+1 be the entries of matrix A, where n = 1, · · · , N −  1, k ∈ K ∪ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The jittered time instances are modeled as  t′  n = tn + ϵn, where tn are the ideal time instances and the  jitter noise is modeled as ϵn  iid  ∼ U[− σ  2 , σ  2 ], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' uniformly  distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' For every t′  n and k ∈ K,  var ([B]nk) = 2var ([A]nk) ,  (18)  where var is the variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' By utilizing the fact that t′  n = tn + ϵn, and using (12)  and (23), it follows that,  var ([B]nk) = var  �  ejkω0(tn+1+ϵn+1) − ejkω0(tn+ϵn)�  = |ejkω0tn+1|2 var  �  ejkω0ϵn+1�  + |ejkω0tn|2 var  �  ejkω0ϵn�  = 2var  �  ejkω0ϵn�  = 2var ([A]nk) ,  (19)  establishing the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  It can be intuitively inferred that by utilizing the partial  summation, the noise in each element of [A]nk becomes  smaller than the corresponding noise in [B]nk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Consequently,  the matrix A has a better condition number than B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This  can be explained by the fact that the condition number of  a matrix is a measure of the sensitivity of the matrix to small  perturbations in its elements, and a smaller condition number  indicates that the matrix is less sensitive to such perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Therefore, by reducing the noise in the elements of A using  the partial summation, we can improve its condition number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In the next step, we employ the partial summation of yn to  present a perfect recovery guarantee for FRI signals by using  IF-TEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Instead of recovering the FSCs from yn through the  forward model (11) with K in (9), which defines the relation  between yn and the FSCs ˆx[k], we propose an alternative  model that is based on zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' These are the partial sums of the  measurements yn defined as  zn =  n−1  �  i=1  yi =  �  k∈K  ˆx[k]  jkω0  �  ejkω0tn − ejkω0t1�  ,  (20)  where n = 2, · · · , N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Note that (20) can be written as  zn =  �  k∈K  ˆx[k]  jkω0  ejkω0tn + c,  (21)  where  c = −  �  k∈K  ˆx[k]  jkω0  ejkω0t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (22)  Let z = [z2, · · · , zN]T ∈ RN−1 be the vector of partial sums,  ˆz =  �  − ˆx[−K]  jKω0 , · · · , − ˆx[−1]  jω0 , c, ˆx[1]  jω0 , · · · , ˆx[K]  jKω0  �⊤  ∈ C(2K+1)  be the vector of FSCs, with c in the zeroth place, and A ∈  C(N−1)×(2K+1) be the matrix defined as  A =  �  ����  e−jKω0t2  · · 1 · · ·  ejKω0t2  e−jKω0t3  · · 1 · · ·  ejKω0t3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  e−jKω0tN  · · 1 · · ·  ejKω0tN  �  ����.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (23)  Then, (21) can be expressed in matrix form as follows:  z = Aˆz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (24)  Since the set of time instants {tn}N  n=2 are distinct, and A is  a Vandermonde matrix, it has full column rank provided that  N − 1 ≥ 2K + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This means that the matrix A has linearly  independent columns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Therefore, we can perfectly recover the  vector of FSCs ˆz via  ˆz = A† z,  (25)  where A† denotes the Moore-Penrose inverse of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Once we  have ˆz, the FSCs ˆx[k] can be uniquely determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Using  ˆz[k] =  � ˆx[k]  jω0k,  if k ∈ K ,  − �  k′∈K  �  ˆx[k′]  jk′ω0  �  ejk′ω0t1  if k = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (26)  The vector of FSCs ˆz and the vector of FSCs ˆx are related  by:  ˆx = [ˆz[−K], · · · , ˆz[−1], ˆz[1], · · · , ˆz[K]]⊤ ∈ C2K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  (27)  This equation allows us to obtain ˆx by selecting the appropri-  ate elements of ˆz, which is the vector obtained from the partial  sums of the measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Note that the resulting vector ˆx has  dimensions 2K, which implies that it only contains the FSCs  for positive and negative frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Using the vector ˆz and (27), the vector of FSCs ˆx is  uniquely determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This indicates that, in the modified ker-  nel setup, without zero frequency, the set of FSCs ˆx[k] can be  uniquely determined from time encodings if N −1 ≥ 2K +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  This condition implies that there should be a minimum of  2K + 2 firing instants within an interval T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' For an IF-TEM,  the minimum firing rate is given as b−c  κδ (as shown in [22]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  6  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Perfect reconstruction of an FRI signal from IF-TEM measurements  with the modified sampling kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (a): the input signal and its reconstruction  for L = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (b): the filtered signal y(t) and the time instants tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Hence, for uniqueness recovery, the IF-TEM parameters must  satisfy the inequality b−c  κδ ≥ 2K+2  T  (see [22] for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  A reconstruction algorithm to compute the FRI parameters  from IF-TEM firings is presented in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Compared  to the technique presented in [22], our method requires the  same number of FSCs in the absence of noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' However, in  the presence of noise, as is typically the case in real-world  hardware, the proposed approach yields a lower error for the  same number of measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Algorithm 1 Reconstruction of a T-periodic FRI signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Input: N ≥ 2K + 2 spike times {tn}N  n=1 in a period T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  1: Let n ← 1  2: while n ≤ N − 1 do  3:  Compute yn = −b(tn+1 − tn) + κδ  4:  Compute zn+1 = �n  i=1 yi  5:  n := n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  6: end while  7: Compute the vector ˆz = A† z, where A is defined in (23)  8: Compute the Fourier coefficients vector ˆx from ˆz using  (27)  9: Estimate {(aℓ, τℓ)}L  ℓ=1 using a spectral analysis method  for K ≥ 2L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Output: {(aℓ, τℓ)}L  ℓ=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Numerical evaluation  In this section, we provide numerical evidence of the valid-  ity of Algorithm 1 through simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We then show that our  proposed reconstruction technique improves the conditioning  of the forward transformation, leading to a significant recon-  struction improvement that is necessary for precise recovery  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Average condition number of matrices A and B as a function of the  number of FRI pulses L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  using real hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' To validate Theorem 1, we consider h(t)  as a Dirac impulse with a time period of T = 1 second,  and L = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The amplitudes are selected randomly over the  range [−1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The time delays are chosen randomly between  (0, 1) such that they lie on a grid with a resolution of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The input signal x(t) is filtered using an SoS sampling kernel  with K = −K, · · · − 1, 1, · · · , K, where K = L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The filtered  output y(t) is sampled using an IF-TEM where the IF-TEM  parameters are chosen to satisfy the inequality (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In this  particular case, the IF-TEM sampler resulted in 16 firing  instants in one time period, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 5(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  5(a), we achieve perfect recovery of the FRI signal  by using a kernel without zero frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  As the IF-TEM circuit produces noise into the signal, which  perturbs the time instances {tn}, we consider the jittered time  instances: t′  n = tn + ϵn, as defined in (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We compare the  proposed recovery method with the reconstruction algorithm  described by [22] in the presence of perturbations to the  measured time instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Each approach employs a sample  kernel lacking a zeroth frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' While the reconstruction  approach proposed by [22] used the forward method defined  in (11), our method utilized a different forward method defined  in (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Using the forward operators or matrices A and B (see (14)  and (24)), the FSCs are recovered in each of the previously  discussed methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The matrices A and B are functions of  the measured time instants and sampling kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 6,  the condition numbers of matrices with the same number of  4L+2 perturbed firing instants are compared as a function of  the number of FRI signals L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' To this aim, 5000 random sets  of monotonic sequences {tn ∈ [0, T)}N  n=1 were generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As  depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 6, the condition number of matrix A is smaller  than that of matrix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This demonstrates that our reconstruc-  tion algorithm enhances stability and noise resilience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  We evaluate and compare the relative mean square error  (MSE) in the estimation of time delays performance for the  reconstruction accuracy of the presented algorithm with the  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='6  Original  (a)  Recovered  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  Amplitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
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+page_content='9  1  t  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  格  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
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+page_content='5  90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content="5  90  L'0  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='8  60  1o sps(log scale)  cond(A)  cond(B)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  Condition Number (  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5  4  6  8  10  12  14  Number of pulses L7  one suggested by [22], where the MSE is given by  MSE = 10 log  � L  �  ℓ=1  (τℓ − ˆτℓ)2  �  ,  (28)  and ˆτℓ is the estimated time delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Specifically, we consider  the signal x(t) as in (5), with period T = 1 second consisting  of L = 3 pulses with h(t) a third-order cubic B-spline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The off-grid time-delays {τℓ}3  ℓ=1 and amplitudes {aℓ}3  ℓ=1 are  generated at random over intervals (0, T] and [1, 5], respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The IF-TEM parameters are κ = 1, b = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5c where  c = max  t  |y(t)|, and δ is chosen to satisfy (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We consider  a sum-of-sincs kernel with K = {−K, · · · , −1, 1 · · · , K}  for the calculation of the Fourier coefficients ˆx[k].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The time  instances {tn} were perturbed as t′  n = tn +ϵn where tn is the  actual time encoding and ϵn is a random variable uniformly  distributed over [−σ/2, σ/2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We use an annihilating filter  with Cadzow denoising to estimate the time-delays in the  presence of noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Since Cadzow denoising requires more than  2L consecutive samples of FSCs, we consider K ≥ 2L + 1  while excluding the zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Based on the fact that the proposed  recovery where 0 /∈ K estimates {ˆx[k]}−1  k=−K and {ˆx[k]}K  k=1,  we apply Cadzow denoising on each of these sequences inde-  pendently and then apply block annihilation [51] to determine  the time-delays jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The MSEs in the estimation of time-delays for different  numbers of FSCs and perturbation levels are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We used 500 independent noise and FRI signal realizations  to compute each MSE value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 7(a) and (b) we show  MSEs for [22] and Algorithm 1, both without zero in the  sampling kernel, for K = 2L + 1 up to 5L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We observe that  comparing the approaches, we note a gain of up to 10 dB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Since perturbation in the time encoding is also equivalent to  quantization noise, a lower MSE indicates that our proposed  approach can operate at lower bits compared to [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' ANALOG BOARD AND HARDWARE CHALLENGES  In this section, we will describe the specifications of our  FRI-TEM hardware prototype.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' FRI-TEM Analog Board  We begin by discussing the key components of the FRI-  TEM hardware implementation, as well as various circuit  design considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 9 and 10, the analog  board comprises three sequential stages: the generation of an  FRI signal, band-pass filtering, and an IF-TEM sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The FRI signal generator uses an analog approach, which  is known for its low digital noise and ability to accurately  simulate real-world applications such as radar and ultrasound  [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The process of signal production involves several com-  ponents working together to generate and process a signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  One possible configuration for a signal generator is to use  a scope, a splitter, an analog delay generator, and a passive  radio frequency (RF) combiner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The scope generates an FRI  pulse (10−500ns wide), that is transmitted through the splitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The splitter receives the pulse and sends it to both the delay  generator and the combiner (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The delay generator is  (a) Without zero approach in [22]  (b) Without zero Algorithm 1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' A comparison of [22] and Algorithm 1 for off-grid time delays with  perturbation in the time encodings: our method has lower error compared to  [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  comprised of a fiber optic cable, a photo-diode encoder, and  a photo-diode detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Encoding the signal with the photo-  diode encoder is the initial step of the delay generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The  signal then travels through the fiber optic line, causing a  delay of at least 4µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The significance of the fiber optic delay  implementation originates from its well-known benefits, such  as the introduction of low digital noise, which more accurately  simulates practical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In order to decode the delayed  input signal, a photo-diode detector is used to transform the  signal to an analog signal with the same frequency as the  original FRI input pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 9 for instance, the FRI signal  x(t) (5) consists of two 20MHz pulses separated by a relative  delay of 4µs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The output of the combiner, x(t), is then sent  as input to the sampling kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The filter, also known as the sampling kernel, is used to  remove the zeroth frequency component of the signal, as  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' For example, if the frequency of the signal  is 10 Hz, the magnitude of the zeroth frequency component  would be −30dB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The positioning of the sampling kernel,  which is essentially a band-pass filter (BPF), is critical for the  5L  10  4L  20  K  3L  30  40  2L+1  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='07  a5L  10  4L  20  K  3L  30  40  2L+1  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='07  a8  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  A 1MHz filter Bode plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The sampling kernel removes the zeroth  frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The magnitude (in blue) and phase (in red) plotted on a logarithmic  frequency scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  sub-Nyquist sampling and reconstruction of FRI signals using  an IF-TEM (see Section III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In order to accurately recover  and analyze two pulses of an FRI signal within a noise-free  setting for a short time period such as T = 10µs, the minimum  theoretical sampling rate required is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4MHz [1], [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In order  to facilitate this fast sampling and reconstruction process, a  1MHz filter was chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Here, an eight-order 1MHz BPF is  employed, enabling a suitable trade-off between energy usage  and reconstruction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The output of the filter, y(t) (10), is then transmitted to the  IF-TEM sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The block diagram of the IF-TEM circuit is  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 10, and a list of the specific components of the  IF-TEM circuit can be found in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' A prototype of the  IF-TEM sampler is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The primary IF-TEM components consist of the bias b,  integrator, comparator, differentiator, and reset function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' To  guarantee sufficient samples for reconstruction, we should  ensure that the δ threshold is achieved at least as many times  as the desired sample amount.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' By adding the bias b to the  input y(t), the integrator obtains a signal that is always non-  negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In this case, integration over a non-negative signal is  a positive function, and the threshold is always attained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' For  an FRI signal x(t) with L pulses, it can be shown that the  sampler input filtered signal y(t) is constrained by [22]  |y(t)| ≤ c = L amax ∥g∥∞∥h∥1,  (29)  where g and h are the known filter and pulse shape, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Consequently, the bias b > c, which is effectively a con-  stant DC voltage, is selected manually using a potentiometer,  which is a device that allows the user to adjust the electrical  resistance in a circuit by turning a knob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' By adjusting the  resistance, the user is able to fine-tune the value of the bias  to the desired level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' It is important to carefully select the  appropriate bias value in order to ensure that the IF-TEM  system is able to function properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The output of the integrator is sent to the comparator, which  compares the integrator voltage to a predefined threshold δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The threshold is a constant DC voltage that is implemented  in our hardware utilizing a potentiometer that is manually  regulated and adjustable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The comparator is responsible for  comparing the voltage produced by the integrator to a pre-  defined threshold value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' When the integrator voltage reaches  or exceeds the threshold, the comparator’s output changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' If  the comparator’s input is below the threshold, it will output a  logical value of ’0’, while if the input is above the threshold,  the output will be ’1’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In other words, the comparator will  produce a sequence of logical ’1’ values when the integrator  voltage hits the threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This change in the comparator’s  output signal indicates that the threshold has been reached  and triggers the next stage in the IF-TEM process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The output of the comparator is sent to the differentiator,  which generates a short pulse that activates the fast reset  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This function is responsible for capturing the time  instances tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The reset function consists of an amplifier and a  field-effect transistor (FET) that work together to quickly and  completely discharge the integrator capacitor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In greater detail,  the FET functions as a switch and is controlled by the pulse  produced by the differentiator, which determines the duration  of time that the FET is active.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This allows the integrator  capacitor to be fully discharged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The FET has three terminals:  source, gate, and drain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' By providing a voltage of ”1” to the  gate terminal, the FET can modify the conductivity between  the drain and source terminals, which allows the current flow  to be regulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This results in a rapid and complete discharge  of the integrator capacitor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  TABLE I  LIST OF HARDWARE COMPONENTS  Device  Reference  Manufacturer  Buffer  AD899  Mini-Circuits  Integrator  LT1364  Analog Devices  Comparator  TLV3201  Texas Instruments  Differentiator  LT1364  Analog Devices  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Circuit challenges  To implement an IF-TEM circuit, it is necessary to employ  an integrator that operates according to (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Specifically, the  integrator capacitor must operate in its linear domain, which  is continuously charged or rising, as long as the input signal  is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Additionally, the IF-TEM thresholding process  requires a fast reset mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Therefore, our goal is to  develop an integrator and reset function in which the capacitor  of the integrator operates in its linear zone and discharges  rapidly and completely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The main challenge in the implemen-  tation of the IF-TEM hardware is to design and implement  such an IF-TEM integrator capacitor, while supporting a wide  range of input FRI signals without circuit modification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' By  utilizing the differentiator and a FET in the reset function,  both the entire discharge and rapid discharge of the capacitor  are accomplished for a variety of FRI signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Next, we provide  results from our hardware and compare them to our theoretical  results from Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' HARDWARE EXPERIMENTS  To determine the potential and feasibility of the devel-  opment proposed system, we performed experiments on the  OdB  969  5  147  147  196  45  245  10Hz  100  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 0k  10k  100k  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='0M  : -30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='22dB, 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='93° @ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='0H29  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The FRI-TEM hardware prototype contains a signal generator, a sampling kernel and an IF-TEM sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The signal generator consists of a delay  path of atleast 4µs, which is built from a modulator optic fiber that ends in a Photo-Diode detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Then, a combiner receives the original signal (single one  or more) from the generator and the delayed path to create the FRI signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The generated signal is passed into a BPF of 1MHz which removes the zero  frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Finally, the resulting signal is sampled by an IF-TEM sampler board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Based on Algorithm 1, the FRI signal is recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Block diagram of the analog board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Signal generation  FIBEF  AsAnalog  MODULATOR  PHoto Diode  Detector  TIME (in sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=')  Time delay generator  FRI pulse [MHz]  Splitter  Combiner  Sampling kernel  Signal Sampler  Reconstruction  Time Encoding Machine  @SA MPLLAB  Combiner  for FRI signals  y(t)  Signai in  Delayed Signal In  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='88  112  Recover Signa  BPF - 1MHz  IF-TEM circuit  Removes the zeroth frequencyOptical fiber  Splitter  Combiner  Si(in1)  Delay Line  Laser  Delayed  (O  BPF  3dB  Laser Detector  Sig  Modulator  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='22KHz - 1MHz  [si(in2)  Threshold  Integrator  Comparator  Inverter  Amplifier  DC  01100  H言  Differentiator  +20dB  Restorer  R  Reset Function  FET  Amplifier  Blas  +10dB  0->1  Switch  IAH10  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' IF-TEM hardware board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' FRI input signal x(t) (green), BPF output y(t) (yellow), and the IF-TEM output resulting in 19 samples (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' sampling and reconstruction  using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  FRI-TEM hardware system that we built.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' As depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  12(a), we consider an FRI input signal, referred to as x(t),  consisted of two pulses with a width of 100ns and a delay of  5µs between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The sampling kernel mentioned in Section  II-C was utilized in these experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The parameters for  the IF-TEM circuit were set to a value of κ = 3 · 10−8,  with a bias of b = 3V and a threshold of δ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  The specific time delays and amplitudes used in this input  signal were chosen arbitrarily, and the IF-TEM parameters  were selected to adhere to the constraints outlined in (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  As demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 12(a), the filtered signal y(t) was  transmitted to an IF-TEM sampler, which produced 19 time  instances tn, resulting in a firing rate of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='9MHz, which is 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='75  times the rate of innovation and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5 times the Nyquist rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  It is important to note that a minimum of 4L + 2 = 10 time  instances are required for off-grid reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 12(b)  illustrates a comparison between the original input signal and  the estimated signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This demonstrates that the parameters of  the FRI system can be robustly estimated while operating at  a rate that is 10 times lower than the Nyquist rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 13(a), Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 14(a), and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 15(a), we demonstrate  sampling and reconstruction of FRI signals with L = 3, 5 for  h(t) as a Dirac impulse and stream of pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The FRI signal  is represented by the green curve, the filtered signal y(t) is  shown in yellow, and the time instances tn produced by the  IF-TEM sampler are depicted in blue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In each of these figures,  IF-TEM sampler Board  REG4  REG2  O  Differentiator  GND  Comparator  PDUINO  LEONARDO MODULE  TEM-DEMQ-VER3  Filtered Signal y(t)  GND  GND  018  U1  12  Integrator  GND  2283922A-Y84-211117  COMPperator  INTECRATOR  Dlfferantiator  Reset Function  Threshold S  Level [Volts]  Bias Level  PULSE  TEST  [Volts]  b  ADJUST  REFERENCE-  JUST  GND  00  88  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='8  Time instances tn(a)  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='09/  3109/  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='00V/  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='00V/  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='46  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='0009/  Stop  (q)  True  - -Estimate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='8  2  183.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='750mv  922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='25m  +14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='9375V  +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='48750  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='00:  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='00:1  TIME (in sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' )11  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' FRI input signal x(t) (green), BPF output y(t) (yellow), and the IF-TEM output resulting in 19 samples (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' sampling and reconstruction  using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' FRI input signal x(t) (yellow), BPF output y(t) (green), and the IF-TEM output resulting in 21 samples (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' sampling and reconstruction  using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' FRI input signal x(t) (green), BPF output y(t) (yellow), and the IF-TEM output resulting in 22 samples (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' sampling and reconstruction  using IF-TEM hardware: the input signal x(t) (blue) and its reconstruction (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  the number of time instances produced is 19, 21, and 22,  respectively, resulting in firing rates of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='9 MHz, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='1 MHz, and  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='2 MHz, which are all between 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5 times the Nyquist  rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The reconstructed FRI signals are shown in Figures 13(b),  14(b), and 15(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The maximum error in time delay estimation  is -25 dB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' These results indicate that our proposed sampling  and reconstruction method is suitable for use in radar and  ultrasonic imaging applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
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+page_content='00:1DC  TIME (in μs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' )12  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  A comparison between the reconstruction using the hardware  measurements and the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  Figure 16 presents a comparison between the reconstruction  using the hardware measurements and the simulation for the  amplitudes and time delays of the FRI signals with two pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  This comparison is used to evaluate the performance of the  proposed hardware prototype and reconstruction method by  comparing the results obtained from the hardware measure-  ments with those obtained from the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The evaluation  involves calculating the error between the reconstructed signals  obtained from the hardware and simulation, as well as compar-  ing the estimated FRI parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' This comparison provides  insight into the accuracy and reliability of the hardware and  reconstruction approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The error in the estimation of the  time delay is found to be -25 dB, and this result is consistent  with the findings when using L = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='5 pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' CONCLUSION  In this work, we studied the problem of recovering FRI  signals using an IF-TEM sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' To this end, we intro-  duced a hardware prototype of a sub-Nyquist IF-TEM ADC  and developed a robust reconstruction approach to accurately  retrieve the FRI parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The hardware prototype that  we introduced is an asynchronous, energy-efficient ADC that  estimates the FRI parameters using a sub-Nyquist framework,  which allows it to operate at rates significantly lower than  the Nyquist rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' We have demonstrated that our proposed  hardware and reconstruction method can retrieve the FRI  parameters with a reconstruction error of up to -25 dB  while operating at rates approximately 10 times lower than  the Nyquist rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' These results suggest that the proposed  hardware prototype and reconstruction approach are effective  and efficient in accurately recovering FRI signals and may be  useful in various applications, such as radar and ultrasonic  imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In comparison to traditional ADCs, the proposed  prototype is asynchronous and energy-efficient, which may  make it particularly attractive for use in energy-constrained  systems such as battery-powered devices where these factors  are important considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  In this study, we investigated the problem of recovering FRI  signals using an IF-TEM sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' To address this challenge,  we proposed a hardware prototype of a sub-Nyquist IF-TEM  ADC and developed a robust reconstruction approach to accu-  rately retrieve the FRI parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' The hardware prototype that  we introduced is an asynchronous, energy-efficient ADC that  estimates the FRI parameters using a sub-Nyquist framework,  which allows it to operate at rates significantly lower than  the Nyquist rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Our proposed hardware and reconstruction  method have been demonstrated to be able to retrieve the  FRI parameters with a reconstruction error of up to -25 dB  while operating at rates approximately 10 times lower than  the Nyquist rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' These results suggest that the proposed  hardware prototype and reconstruction approach are effective  and efficient in accurately recovering FRI signals and may  be useful in various applications such as radar and ultrasonic  imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' In comparison to traditional ADCs, the proposed  prototype is asynchronous and energy-efficient, which may  make it particularly attractive for use in energy-constrained  systems such as battery-powered devices where these factors  are important considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content='  REFERENCES  [1] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
+page_content=' Eldar, Sampling theory: Beyond bandlimited systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StA0T4oBgHgl3EQfD_-h/content/2301.02012v1.pdf'}
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diff --git a/TdE3T4oBgHgl3EQfaArM/content/tmp_files/load_file.txt b/TdE3T4oBgHgl3EQfaArM/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf,len=1063
+page_content='Draft version January 12, 2023  Typeset using LATEX default style in AASTeX631  Nonlinear Fast Magnetosonic Waves in Solar Prominence Pillars  Leon Ofman,1, 2 Therese A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Kucera,2 and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Richard DeVore2  1Department of Physics  Catholic University of America  Washington, DC 20064, USA  2Heliophysics Science Division  NASA Goddard Space Flight Center  Greenbelt, MD 20771, USA∗  (Accepted January 6, 2023)  Submitted to ApJ  ABSTRACT  We investigate the properties of nonlinear fast magnetosonic (NFM) waves in a solar prominence, mo-  tivated by recent high-resolution and high-cadence Hinode/SOT observations of small-scale oscillations  in a prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' As an example, we analyze the details of the 2012 February 14 Hinode/SOT  observations of quasi-periodic propagating features consistent with NFM waves, imaged in emission in  Ca II and in the far blue wing of Hα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We perform wavelet analysis and find oscillations in the 1-3 min  period range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Guided by these observations, we model the NFM waves with a three-dimensional mag-  netohydrodynamics (3D MHD) model, extending previous 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5D MHD studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The new model includes  the structure of the high-density, low-temperature material of the prominence pillar embedded in the  hot corona, in both potential and non-force-free sheared magnetic field configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The nonlinear  model demonstrates the effects of mode coupling and the propagating density compressions associated  with linear and NFM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The guided fast magnetosonic waves, together with density compressions  and currents, are reproduced in the 3D pillar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We demonstrate or the first time the dynamic  effects of the Lorentz force due to the magnetic shear in the non-force-free field on the pillar structure  and on the propagation of the waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The insights gained from the 3D MHD modeling are useful for  improving coronal seismology of prominence structures that exhibit fast MHD wave activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' INTRODUCTION  Solar prominences (also called filaments;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Tandberg-Hanssen 1995) are highly complex magnetic structures that  extend from the photosphere up into the corona, where they support material that is much denser (n ∼ 1010−12  cm−3) and cooler (T ∼ 1×104 K) than the surrounding plasma (n ∼ 108−9 cm−3, T ∼ 1-2×106 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' High-resolution  observations of prominences have been available in H I Balmer (Hα) and Ca II emission for decades from ground-based  telescopes and, more recently, in various ion emission bands from satellite-borne instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These observations show  that the prominence material is highly dynamic, exhibiting persistent flows, waves, and other oscillations, as well as  MHD instabilities that can lead to its violent eruption (for reviews, see Labrosse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Parenti 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Arregui  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Idealized models of quiescent prominences often assume an equilibrium magnetic structure that supports  the cool material statically within the hot corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The observations indicate that both the magnetic and thermal  structures of prominences are often out of equilibrium, highly dynamic at small scales and gradually evolving at large  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Small-scale propagating and oscillating features in cool prominence threads and low-lying coronal loops have been  studied from space for many years using high-resolution and high-cadence spectral observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Hinode’s Solar Optical  Corresponding author: Leon Ofman  ofman@cua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='edu  ∗ Visiting, Department of Geosciences, Tel Aviv University, Tel Aviv, Israel  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='04503v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='SR]  11 Jan 2023  2  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Telescope (Hinode/SOT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Kosugi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2007) has observed such phenomena in Hα and Ca II emission (Okamoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman & Wang 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Schmieder et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Kucera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018), as has the Interface Region  Imaging Spectrograph (IRIS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' De Pontieu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2014) in chromospheric Mg II emission as spectral lines and slit jaw  images (Kucera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' High-resolution prominence observations by Hinode/SOT show that the prominences  material exhibits constant down-flows, lateral flows, upflows, and dynamic evolution with the observed velocities in  the range 1 − 100 km s−1 consistent with the effects of magneto-fluid instabilities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Berger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Recent  ground-based high-resolution observations using the New Vacuum Solar Telescope (NVST;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2014) report  evidence of small-scale oscillations and waves detected in Hα in quiescent prominences (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Advanced high-resolution resistive 3D MHD modeling of prominence structure evolution shows that the nonlinear  development of the magnetic Rayleigh–Taylor instability produces small scale structures in the prominence material  (Jenkins & Keppens 2022), and possibly can provide an alternative (to waves) interpretation of some of the observed  small-scale oscillating structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The (quasi-) periodic, small-scale, oscillating features, with typical time scales of minutes in prominence threads  and pillars, have been identified and modeled previously as linear fast magnetosonic waves (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Schmieder et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Because the nonlinearity of these waves is evident in the observations in the form of steepening and asymmetric  density compressions, the models were later extended to nonlinear fast magnetosonic (NFM) waves using an MHD  model with two-dimensional spatial variations and three-dimensional vector fields (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5D MHD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' see Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Ofman & Kucera 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The observed waves can be used to deduce the magnetic structure of prominences by applying  techniques of coronal seismology (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Nakariakov & Verwichte 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Anfinogentov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These indirect methods  are invaluable, as the coronal magnetic field is very difficult to measure directly using spectroscopic or other methods,  while force-free extrapolation methods have limited applicability in realistic coronal structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Coronal seismology  remains based primarily on linear MHD wave theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' However, nonlinearity may significantly affect the wave structure,  phase speed, wave dissipation, and couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Thus, interpreting observations of nonlinear waves requires the use of  nonlinear wave theory or nonlinear MHD modeling for improved accuracy of the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Plasma flows, in addition to waves, are often observed in cool prominence threads in emission lines such as Hα  and Ca II (Okamoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Alexander et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Kucera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Parenti 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Diercke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These  flows may affect the oscillations through, for example, changes in the density that affect the phase speed of the waves  and Doppler shifts of the oscillation frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Recently, Kucera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (2018) and Ofman & Kucera (2020) used  Hinode/SOT Ca II spectral lines to study small-scale motions in prominences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The observed propagating fluctuations  were identified as NFM waves using a combination of data analysis and modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The observed NFM waves had  typical periods ∼ 5-11 minutes and wavelengths ∼ 2000 km, while the flows had typical speeds ∼ 15-50 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  main properties of the observed NFM waves, combined with the effects of mass flows in prominence threads, were  replicated by the model (Ofman & Kucera 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The magnetic field strengths in the prominence were estimated to  lie in the range 5-17 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  In the present study, we extend the previous studies of propagating waves in prominences with data analysis and  modeling of a prominence pillar observed on 2012 February 14 from Hinode/SOT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We employ a new, fully three  dimensional (3D) MHD model of small-scale NFM waves in an idealized prominence pillar with more realistic structure  than in the previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The new model allows us to investigate more complex fast magnetosonic wave generation,  propagation, and interaction than in the previous 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5D configurations, for example, by including the effects of magnetic  shear, and for the first time study the effects of non-force free shear magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The results are useful for interpreting  high-resolution Hinode/SOT observations of prominence small-scale oscillations and for making further advancements  in the coronal seismology of solar prominences using MHD waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Our paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In §2 we present new observations of propagating features in a prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  In §3 we describe the new 3D MHD model, along with the initial and boundary conditions used in the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In  §4, we present the numerical results and compare them with observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Finally, the discussion and our conclusions  are given in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' OBSERVATIONS AND DATA ANALYSIS  The studied prominence was observed by Hinode/SOT on 2014 February 14 from 10:48 - 13:15 UT as part of Hinode  Operation Plan (HOP) 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The data consisted of measurements from both the Broadband Filter Instrument (BFI)  and the Narrowband Filter Instrument (NFI) (Kosugi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Tsuneta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The BFI was used to observe  the Ca II H line at 3969 ˚A and the NFI was used to observe the Hα line at 6563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2 ˚A, both with cadences of 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Nonlinear Fast Waves in a Prominence Pillar  3  (a) NSO/GONG H−alpha 11−Feb−2012 11:00:54 UT  450  500  550  600  650  700  Solar−X (arcsec)  500  550  600  650  Solar−Y (arcsec)  (b) Hinode SOT Ca II  14−Feb−2012 12:46:49 UT  840  860  880  900  Solar−X (arcsec)  440  460  480  500  520  Solar−Y (arcsec)  (c) Hinode SOT Hα far blue wing  14−Feb−2012 12:46:58 UT  840  860  880  900  Solar−X (arcsec)  440  460  480  500  520  Solar−Y (arcsec)  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) GONG Hα image showing the prominence on 11 Feb 2012, three days before the prominence was observed on  the limb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The box shows the approximate field of view of the images in (b) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Hinode Ca II image showing the  prominence on the limb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' the box is the field of view shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' An animation that corresponds to this panel is available  online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The video shows the Hinode Ca II emission observed on 14-Feb-2012 in the time interval 10:51:06-13:13:45 UT in an  accelerated time of 16 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) Hα far blue-wing image;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' the box is the field of view shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The Hα line positions for this data set were not well calibrated, but appear to be from near line center and in the  blue wing of the line (about 416 m˚A from line center), making them not useful for Doppler measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The image  field of view is about 112′′ square, and the spatial resolution is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='3′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Maps were processed with the fg prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='pro  routine provided by to the Solar Soft library (https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='lmsal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='com/solarsoft/, Freeland & Handy (1998)) by the  Hinode team, including dark-current subtraction and flat-field removal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Drift and jitter were corrected using an image  cross-correlation (fg rigidalign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='pro) routine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  For context, we inspected observations from the Global Oscillation Network Group to image the on-disk structure  of the prominence in the days preceding its appearance at the limb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' GONG Hα images are provided by a network of  six stations around the globe (Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 1996) with a pixel size of about 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The features observed on the limb were part of a long prominence that extended more or less East-West above the  northern active-region belt and curved equator-ward on the western end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' A portion of that prominence seen against the  solar disk three days before the observations we analyzed is shown in Figure 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The most evident prominence features  seen in Hα are a series of barbs connected by fainter spine flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These barbs evolve over time, and it is difficult  to identify individual barbs near the limb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' However, the appearance of the region at the limb from Hinode/SOT,  Figures 1b (Ca II) and 1c (Hα), is consistent with associating the pillars with barbs that are oriented mostly along  the line of sight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Figure 2 shows time-distance diagrams for the small-scale propagating features (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', ‘pulses’) observed in the Ca II  images in two locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The pulses were measured along a 5-pixel-wide area centered on the solid red and green lines  shown in panels (a) and (d), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Panel (b) shows a series of pulses with plane-of-sky velocities 12-16 km s−1  determined from the slopes of the dashed red lines, which were visually fit to the intensity peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The peaks are about  1 min apart, and the distances between pulses are in the range 1330-2030 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Panel (e) shows another set of pulses  corresponding to the location shown in panel (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These pulses have peaks 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='3 min apart, velocities 8-11 km s−1  obtained from the slopes of the dashed green lines, and distance between pulses in the range 800-1600 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Panels (c)  and (f) show the intensities along the horizontal lines shown in panels (b) and (e) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The variations between  the maximum and minimum intensities of the individual features are about 10% of the total intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Figure 3 shows time-distance diagrams for moving features seen in the Hα blue wing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Shown are a series of pulses  with plane-of-sky velocities 12-16 km s−1, peaks 1-5 min apart with sharp non-sinusoidal peaks indicative of nonlinear  steepening, and distances between pulses of 1000-3000 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The plane-of-the-sky propagation speed is likely reduced  compared to the ‘true’ phase speed due to projection effects, and the value is in qualitative agreement with possible  fast magnetosonic speeds in cool prominence material of the order ∼ 20 km s−1 (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Schmieder et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  variations between the maximum and minimum intensities of the individual features are about 30-60% of the total  intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  We have performed a wavelet analysis (Torrence & Compo 1998) of the oscillations in Ca II and the far blue wing of  Hα cuts shown in Figures 2 and 3 using the Morlet wavelet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In Figure 4 we show the results of the analysis with evident  4  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='(a) Hinode SOT Ca II 14−Feb−2012 12:28:55 UT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='845  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='850  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='855  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='860  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='865  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='870  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Solar−X (arcsec)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='485  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='490  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='495  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='505  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Solar−Y (arcsec)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='(b) Hinode SOT Ca II  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Time after 14-Feb-12 12:20:00 UT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='(minutes)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Distance (arcsec)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='(c) Ca II at D=5 arcsec  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Time after 14−Feb−12 12:20:00 UT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='450  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='550  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='600  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Ca II (DN)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='(d) Hinode SOT Ca II 14−Feb−2012 12:46:49 UT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='845  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='850  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='855  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='860  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='865  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='870  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Solar−X (arcsec)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='(e) Hinode SOT Ca II  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='Time after 14-Feb-12 12:36:00 UT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='Distance (arcsec)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Time after 14−Feb−12 12:36:00 UT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='550  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='600  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='650  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='700  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Ca II (DN)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) Image of the Ca II emission obtained with Hinode/SOT on 14-Feb-2012 12:28:56UT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The solid red line indicates  the data location for the time-distance diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Time-distance diagram showing the propagation of the features along the  solid red line in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) Plots of intensity as a function of time at the locations shown with the blue horizontal line in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (d)-(f) The same for a different set of pulses obtained along the solid green line in (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The slopes of the dashed red (b) and  green (e) lines indicate the propagation speed of the pulses in the plane of the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' A video showing the field of view in panels  (a) and (d) is included online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The video shows the Hinode SOT Ca II intensity observed on 14-Feb-2012 in the time interval  12:18:06 UT to 15:56:59 UT in an accelerated time of 4 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  highest confidence level for the wavelet magnitude greater than 85%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The cones of influence indicate the regions that  may be affected by the boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The results show the global wavelet power integrated inside the cone of influence,  indicating significant power in ∼ 1 − 3 min period oscillations, consistent with the temporal evolution at the indicated  temporal cuts, and in the animations of the observed oscillations included online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The wavelet analysis and the global  wavelets provide unbiased quantification of the observed oscillations and their statistical significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Thus, we observe multiple cases of a short series of oscillatory features propagating in a direction roughly away from  the limb in the plane of the sky, separated by ∼ 1 min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Each individual feature is slightly elongated perpendicular  to the direction of motion, hence is similar to features described previously by others (Schmieder et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Kucera et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Because the pillars are likely to be elongated structures along the line of sight, these  moving features may be related to motions observed in different (perpendicular) line of sight in extended prominence  structures as transverse oscillations combined with flows of cool material (Ofman & Wang 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Okamoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Ofman & Kucera 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' NUMERICAL 3D MHD MODEL, BOUNDARY CONDITIONS, AND PARAMETERS  In order to model the NFM waves in a prominence pillar we solve the resistive 3D MHD equations using our code  NLRAT described in detail in previous papers (Ofman & Thompson 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Provornikova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman & Liu  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman & Wang 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The normalized resistive MHD equations with gravity, using standard notation for the  Nonlinear Fast Waves in a Prominence Pillar  5  (a) Hinode SOT Hα far blue wing  14−Feb−2012 11:33:52 UT  850  855  860  865  870  875  Solar−X (arcsec)  465  470  475  480  485  490  495  Solar−Y (arcsec)  (b) Hinode SOT H-alpha far blue wing  0  2  4  6  8  10  Time after 14-Feb-12 11:30:00 UT  (minutes)  0  1  2  3  4  5  Distance (arcsec)  0  2  4  6  8  10  0  1  2  3  4  5  (c) Hα at D=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5 arcsec  2  4  6  8  Time after 14−Feb−12 11:30:00 UT  600  700  800  900  1000  1100  Hα far blue wing (DN)  (d) Hα at D=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5 arcsec  2  4  6  8  Time after 14−Feb−12 11:30:00 UT  500  600  700  800  900  1000  1100  Hα far blue wing (DN)  (e) Hα at D=2 arcsec  2  4  6  8  Time after 14−Feb−12 11:30:00 UT  500  600  700  800  900  1000  Hα far blue wing (DN)  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) Image in the far blue wing of Hα obtained with Hinode/SOT on 14-Feb-2012 at 11:33:52 UT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The solid purple  line shows the location of the data for the time-distance diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Time-distance diagram showing the propagation of the  pulses along the solid purple line indicated in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c)-(d) plots of intensity as a function of time at the locations shown with  the blue horizontal lines in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The slopes of the dashed purple lines in (b) indicate the propagation speed of the pulses in the  plane of the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' A video that corresponds to the field of view in panel (a) is included online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The observed Hinode SOT Hα  far blue wing field of view on 14-Feb-2021 in the time interval 11:25:17-11:42:26UT is shown in an accelerated time of 2 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  variables, are  ∂ρ  ∂t + ∇ · (ρV) = 0,  (1)  ∂(ρV)  ∂t  + ∇ ·  �  ρVV +  �  Eup + B · B  2  �  I − BB  �  = − 1  Fr  ρFg,  (2)  ∂B  ∂t − ∇ × (V × B) = 1  S ∇2B,  (3)  ∂(ρE)  ∂t  + ∇ ·  �  V  �  ρE + Eup + B · B  2  �  − B(B · V) + 1  S (∇ × B) × B  �  = − 1  Fr  ρFg · V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (4)  With our normalization Eu = β/2 is the magnetic Euler number (ratio of thermal pressure to Alfv´en-wave pressure),  Fr = V 2  ARs/(GMs) is the magnetic Froude number (ratio of magnetic force to gravitational force), where G is the  gravitational constant, Ms is the solar mass, Rs is the solar radius, and S is the Lundquist number (ratio of resistive  diffusion time to Alfv´en time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The details of the normalization of the variables can be found in Ofman & Liu (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The gravitational force,  Fg =  a2  0  (Rs + z − zmin)2ˆz,  (5)  is modeled with the assumption of small height of the prominence compared to the solar radius Rs, where a0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1Rs  about 70 Mm is the normalization length scale of the coordinates, and zmin is the height of the lower boundary in  the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We note that in the present model we have excluded radiative losses and thermal conduction, and the  prominence pillar structure is provided as an initial state, rather than produced self-consistently by the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  total energy density is given by  ρE =  Eup  (γ − 1) + ρV 2  2  + B2  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (6)  In the present model, we neglect radiative cooling and thermal conduction because these losses are small on the typical  time scales of the NFM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' For coronal temperature T = 1 × 106 K, density n = 109 cm−3, and magnetic field  magnitude B = 10 G we obtain the Alfv´en speed VA = 690 km s−1, the Alfv´en time τA = 101 s, the plasma β ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='07,  6  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (c)  (d)  (a)  (b)  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The results of the wavelet analysis of the oscillations shown in Figures (a) 2c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) 2f (c) 3d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (d) 3e;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  Morlet wavelet was used, and the 85% confidence level contour is indicated on the wavelet power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The cones of influence where  boundary effects may affect the results are indicated with the red curve on each wavelet panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The global wavelets in the cone  of influence for each case are shown in the corresponding right panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Nonlinear Fast Waves in a Prominence Pillar  7  the Froude number Fr = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='25, and the Euler number Eu = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='47 × 10−2 (for the case with B0 = 20 G, Eu is reduced  by a factor of four, to Eu = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='67 × 10−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Note that, for uniform magnetic field, the value of β is identical to the  coronal value all across the prominence pillar, due to the uniform thermal pressure along the magnetic field lines that  cross the pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' For computational stability purposes, the effect of gravity in the model is reduced by a factor of 10 by  correspondingly increasing Fr, in order to slow the gravitational settling of the cool material in the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The reduced gravity does not affect the results significantly, since the dominant restoring force of the oscillations is  the Lorentz force (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', magnetic field-line ‘tension’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In the above equations we have neglected viscosity, radiative  losses, and thermal conduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The resistive terms are used with the Lundquist number set to S = 105, which does  not affect the results significantly on the NFM time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' An empirical value of the nearly isothermal polytropic  index, γ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05, is used that accounts for coronal heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These modeling parameters improve the stability of the  background prominence pillar structure on the time scale of MHD wave propagation, without affecting significantly  the NFM wave dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1  1  10  100 n  , p , T  0    0    0  x  p0  n0  T0  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The x dependence (across the prominence pillar) of normalized initial temperature, T0 (red), density, n0 (blue), and  thermal pressure p0 (green) in the model prominence and surrounding corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The magnitudes of the variables are shown on  Log scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The initial x-dependent temperature T0 and density n0 structures are given by  T0(x) = Tmax − (Tmax − Tmin)e−[(x−x0)/w]2q,  (7)  n0(x) = p0/T(x),  (8)  where the coronal temperature is Tmax, the prominence temperature is Tmin, the exponent q = 2 defines the sharpness  of the temperature transition between the corona and the prominence pillar, w = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05 is the half-width of the  prominence pillar, and x0 = 0 is the center position of the pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The initial temperature and density dependencies  on the x coordinate across the model prominence pillar are shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The normalized thermal pressure,  p0 = n0T0 = 1, is uniform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In the present model we use Tmin/Tmax = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01, consistent with the typical ratios of the  prominence to corona temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' It is evident in Figure 5 that T0 decreases from its coronal value by two orders of  magnitude, while n0 increases correspondingly by the two orders of magnitude in the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Note, that the  fine-scale structuring of the background density in the direction of wave propagation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', with height, may introduce  dispersion, enhanced damping, and small deceleration of the fast magnetosonic waves (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Murawski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In  the present model the fast magnetosonic speed is lower by a factor of 10 in the pillar compared to the surrounding  corona, and the speed could be even lower in higher density cool prominence structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The prominence-corona  transition region (PCTR) (see the review, Parenti 2014) along the magnetic field is evident in the model, with the  length computed as the difference between the half width at half maximum (HWHM) of the prominence pillar and  the half width at 10% of peak density as ∼ 1 Mm in physical units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This value of PCTR thickness is consistent  with previous studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Chuideri Drago et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Gun´ar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In normalized units the mass density  is equal to the number density ρ0 = n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The initial state is in equilibrium when the magnetic field is uniform in  the x direction without gravity, which was first used to study prominence oscillations by Joarder & Roberts (1992)  and later in 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5D MHD models of NFM waves in prominences (Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman & Kucera 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Here we  adopt this initial state in the 3D MHD model, as well as study additional magnetic configuration that depart from  8  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Since we consider the effects of reduced solar gravity the initial state is not strictly in equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  initial nonequilibrium leads to formation of gradients in the initially uniform magnetic field that produce a Lorentz  force balancing gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' However, the departure from equilibrium is small in the low-β prominence model, as shown  below (see, Case 0 in Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' While the initial state of the density is uniform in the y and z directions, transverse  variability is introduced by the effects of the source of the waves (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', boundary conditions), in addition to the effects  of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Since the source of the waves at the lower boundary of the prominence pillar depends on x and y and on  time (see, Equation 12 below), the compressional fast magnetosonic wave pressure introduces structure primarily in  the density and magnetic field in x, y, and z directions inside the pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Realistic three-dimensional force-free extrapolations show that magnetic field of dips in quiescent prominences is  mostly horizontal (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Dud´ık et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Observed prominence structure shows evidence of magnetic shear and  flows (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Antiochos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (1994) and the recent review by Gibson (2018)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Our aim is to investigate the effects  of uniform as well as sheared magnetic field on the propagation of nonlinear fast magnetosonic waves in the prominence  pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' There are many past observations of flows in prominence pillars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Ofman & Kucera 2020, and references  within).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' While there could be several possible sources for the observed flows in prominences of jet-like or large-scale  flows, here, we model the effects of an unbalanced Lorentz force (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', non-force free magnetic configuration) with small  shear as the driver of the large-scale flows in the prominence foot, Cases 4-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' While in some observations of Polarity  Inversion Lines (PIL) in prominences the magnetic shear could be large and the magnetic field possibly force-free,  modeled with linear force-free field magnetic field (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Aulanier & Demoulin 1998), or nonlinear force-free field (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=',  Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2014), our model investigates for the first time the effect of non-force-free field on the formation of large-  scale flows and on the propagation of fast magnetosonic waves in the prominence pillar self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Our model  reproduces the main properties of such sheared magnetic configurations by introducing the x-dependent By component  that changes sign in the center of the prominence pillar at x=0, as modeled by Equation 9,  B0 = Bx0ˆx + By0tanh(x/w)ˆy,  (9)  where Bx0 and By0 are given in Table 1 for the eight cases studied, and w = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05 is the fixed half-width of the  prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' When By0 = 0, the magnetic field is potential, and the initial state given by Equations 7 and 8 is  in equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In order to study initial states that depart from equilibrium and contain currents (non-force-free), we  use small values of By0 ≪ Bx0 in the initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The corresponding current density j0 and Lorentz force L0 in the  x-y plane are given by  j0 = ∇ × B0 = By0  w sech2(x/w)ˆz,  (10)  L0 = j0 × B0 = jz0(−By0 tanh(x/w)ˆx + Bx0ˆy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (11)  The x dependence of j0 and L0 along with the corresponding magnetic field in the x-y plane are shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The present model produced the desired Lorentz force that points toward the center of the pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Note, that we have  also experimented with other forms of By, such as a centrally peaked profiles, and found similar results for the fast  magnetosonic waves, but with different forms of the Lorentz force and directions of the large-scale flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The location  of the prominence pillar is depicted by the yellow-shaded area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The adopted form of By is justified by the dynamics of the observed flows and allows exploring the fast magnetosonic  wave propagation effects in non-pontential and non-force-free magnetic field in a prominence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Moreover, this magnetic  configuration may correspond qualitatively to a section of a sigmoidal filament structure that is often unstable, leading  to eruption (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Yan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The vertical extent of the prominence pillar is evident in the observations in Figure 1 of about ∼ 40′′in the plane  of the sky (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', the lower limit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In the model we used ∆z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4 for the height of the pillar, with the coordinates  normalization of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1Rs the vertical extent of the model prominence pillar is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='04Rs = 28 Mm in agreement with  observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Clearly, the extent of the observed low temperature prominence pillar material of ∼ 28 Mm is much  longer than the scale height for the 104 K prominence material of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='6 Mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Thus, one does not expect to see the  cool material in gravitational equilibrium at these heights in a field-free or in purely vertically directed magnetic field  region, and the prominence material must supported by a horizontal magnetic field component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The boundary conditions at x = xmin and x = xmax are line tied, and the other boundary conditions are open  except for the lower boundary of the prominence pillar (z = zmin = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In order to launch the NFM waves at the  Nonlinear Fast Waves in a Prominence Pillar  9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  x  1  0  1  2  3  4  By0, Jz0, Lx0  Initial Magnetic Field Model  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  X  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  Y  Initial Magnetic Field Model  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  X  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  Y  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The initial magnetic field with By0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2 (see Case 7, below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) The x dependencies of the y component of the  magnetic field B0 (black), the corresponding z component of the current density j0 (blue), and the resultant x component of  the Lorentz force L0 (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) The initial magnetic field vectors in the x-y plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The shaded area indicates schematically the  location of the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Parameters of the numerical 3D MHD models of prominence pillars with waves and flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The velocity amplitude is  given in units of VA, the frequencies in τ −1  A , and the magnetic field strength in Gauss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Case #  Vd [VA]  ω [τ −1  A ]  Bx,0 [G]  By,0/B0  0  0 10  0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='28  10  0  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56  10  0  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56  10  0  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='28  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2  8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='28  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1  lower pillar boundary, the following time-dependent boundary conditions are applied on the Vz velocity component:  Vz(t, x, y, z = zmin) = Vd  2 [1 + cos(ωt)] e−[(x−x0)/sx]4−[(y−y0)/sy]2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (12)  Motivated by the observed wave propagation primarily inside the pillar as evident in Figure 2 and the related anima-  tions, the source of the wave flux is set to be maximal in the center of the prominence pillar by using the parameters  x0 = y0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='0, sx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10, and sy = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' the amplitude Vd controls the nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The density and magnetic field  perturbations are computed by zero-order interpolation from the interior of the computational domain, whereas the  transverse velocity components are set to zero at the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This results in periodic perturbations of the magnetic  field, density, and velocity Vz that inject NFM waves into the prominence pillar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In Table 1, we provide the  values of Vd, ω, Bx,0, and By,0 for the nine modeled cases in the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The results of Case 0 without waves  are provided for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' NUMERICAL RESULTS  10  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Here we present the results of the 3D MHD modeling of the NFM waves in the prominence pillar for the parameters  given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In order to explore the details of the waves, we first show in Figure 7 the results in the x-z plane cut  at y = 0 for Case 3 at t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This prominence pillar is embedded in a uniform horizontal (potential) magnetic  field modeled as described in Equation 9 with By0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The NFM waves are launched by the time-dependent velocity  source (Vz, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 12) at the lower boundary with amplitude Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1VA and frequency ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56 localized at the center  of the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The waves propagate inside the pillar with nonlinear effects evident in non-modal structure  of the oscillations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', asymmetric and sharp peaks in the variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The nonlinear wave pressure displaces the  magnetic field lines upwards, as is evident in this figure, affecting the temperature, magnetosonic speed, and plasma β  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The details of the perturbations due to the waves are particularly clear in the density contrast, ∆ρ/ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  prominence pillar acts as a leaky waveguide (Cally 1986) for the NFM waves, as the magnetosonic speed Vf is smaller  by an order of magnitude inside the prominence pillar compared to the outside (coronal) region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The small leakage  of the wave is most apparent in Figure 7e as the periodic density perturbations outside of the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  squared magnitude of the current density, j2, shows the regions of enhanced currents that lead to Ohmic dissipation  (j2/S in normalized units) associated with the NFM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The velocity components in the x-z plane are shown  Figure 7f, where the arrows indicate the local direction (not magnitude) of the velocity vectors and the magnitude V  is color-shaded as indicated by the color bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The corresponding magnetic field in the x-z plane is shown in Figure 7h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The dominant Bx component is evident, along with the perturbations in the magnetic field magnitude B due to the  fast magnetosonic waves and the nonlinear wave pressure effects within the base of the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (h)  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The variables in the x-z plane at y = 0, t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14 with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02, ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56 for Case 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) ρ with overlaid magnetic  field lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) The normalized fast magnetosonic speed Vf magnitude with several isocontours, (c) T, (d) β, (e) ∆ρ/ρ0, (f) V  magnitude with arrows indicating the local direction of the velocity vectors, (g) j2, (h) B magnitude with arrows indicating the  local magnetic field direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' An animation of panels (a) and (f) is available online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The video shows the density structure in  the x-z plane (left) with over-plotted field lines, and the corresponding velocity maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The duration of the animation is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='21 in  normalized time units in the 5 s video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  In Figure 8 we show the variables in a cut along the prominence pillar axis, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', in the y-z plane at x = 0 in the  high-density, low-temperature (relative to coronal values) region at time t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The effects of the NFM waves  generated by the time-dependent boundary conditions in Vz are evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In particular, the density perturbations are  in phase with the magnetic field perturbations, as seen by comparing the panels in Figure 8e and h, as expected for  the fast magnetosonic waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The magnitude of the waves is largest in the center of the pillar due to the form of the  wave source in Equation 12, as well as to the waveguide trapping of the wave flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The squared current magnitude j2  is shown in Figure 8g, where the larger currents are associated with the wave fronts and are regions of higher Ohmic  dissipation (therefore also affecting the temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The directions of the perturbations in V and B in the y-z plane  Nonlinear Fast Waves in a Prominence Pillar  11  are shown in Figure 8f and h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The waves propagate in the z direction since Vf is nearly uniform in the y-z plane, with  very small perturbations due to the waves (note the intensity range in the color bar of Figure 8b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (h)  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The variables in the y − z plane at x = 0, t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14 for Case 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) ρ, (b) Vf, (c) T, (d) β, (e) ∆ρ/ρ0, (f) V with  arrows showing the direction of the velocity, (g) j2, (h) B with arrows showing the direction of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The temporal evolution of the variables at a point in the center of the prominence pillar at x=0, y=0, z=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2 for  Cases 0-3 is shown in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The three components of the velocity and magnetic field perturbations (with respect to  B0) and the change in density and temperature are displayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The difference between Case 1 and Case 2 is the increase  of wave frequency by a factor of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4, while in Case 3 the amplitude of the velocity at the boundary is increased by a  factor of 2 with respect to Cases 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Evaluating the propagation speed of the NFM waves from the animations  for Cases 2 and 3, we find that they travel close and slightly above (5%-15%) the theoretical linear fast magnetosonic  speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The speedup is larger for the higher amplitude waves suggesting nonlinearity effect (see, Ofman & Davila 1997,  and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The nonlinearity of the fast magnetosonic waves is evident primarily in their non-sinusoidal  temporal structure, which shows evidence of steepening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This nonlinear effect is more evident in the low-frequency  waves and in the large-amplitude waves, where the wave peaks are sharper than the troughs due to steepening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  magnetic field perturbations show secular growth of the amplitude, an indication of nonlinear wave pressure effects  on the background magnetic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The density perturbations show an oscillatory increasing trend, whereas the  temperature perturbations are small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The case without without waves (Case 0) shows the evolution of the background state in the center of the pillar due  to the gravitational settling of the initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' One can estimate the magnetic field change expected for the given  density increase of ∼5% due to the gravitational settling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This corresponds to a magnetic pressure change that is  5% of β, or about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4%, which equals to the value of ∆B/(2B0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Therefore, the estimated ∆B/B0 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='8% = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='008  is consistent with the magnitude of the changes shown in Figure 9 in the field component plotted there for Case 0  (green curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' It is evident that the small velocity Vz readjustment exhibits an initial oscillatory evolution due to  the effect of gravity, followed by a nearly constant downward velocity Vz ≈ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='003VA corresponding in physical units  to about −2 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We investigated the effects of diffusion by repeating Case 0 with higher (S = 104) and lower  (S = 106) resistivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In the latter case the spatial resolution was doubled in each direction (5143) compared to other  runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We find that in the case with S = 104 the small down flow velocity increases by 30%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' However, in the reduced  resistivity, high resolution run with S = 106, the asymptotic down flow speed remains nearly the same as in the case  with S = 105, where the density structure shows slight compression and broadening of the lower part of the pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The diffusion of cold prominence material through the supporting magnetic field is expected in real prominences in  12  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  qualitative agreement with the present model for higher resistivity case, since the material is partially ionized (for  example, see Gilbert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Khomenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2014), and where the frozen in condition breaks down due to finite  resistivity (Low et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Low & Egan 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Jenkins & Keppens 2021), see the review by Gibson (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' While  in the MHD model the down flow velocity at lower resistivity is due to compressive effects, we find that this velocity is  small compared to the phase speed of the fast magnetosonic waves and therefore has no significant effect on the wave  propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (a)  0  1  2  3  4  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='015  Vx, Vy, Vz  (b)  0  1  2  3  4  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='20  DBx, DBy, DBz  (c)  0  1  2  3  4  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='15  Dr/r0, DT/T0  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Temporal evolution of the variables in the center of the prominence pillar for Case 1 (blue) with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01, ω = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='26,  Case 2 (red) with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01, ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56, and Case 3 (black) with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02, ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) Velocity components Vz (solid),  Vy (short dashes), Vx (long dashes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Magnetic field component perturbations ∆Bx (solid), ∆By (short dashes), ∆Bz (long  dashes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) Changes in density ∆ρ/ρ0 (solid) and temperature ∆T/T0 (long dashes) normalized by the respective initial values  ρ0 and T0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The case without waves (Case 0) is shown (green) for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Times are in units of τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The structure of the magnetic field and density perturbations due to the NFM waves for Case 2 is shown in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  In the present model the initial state was the result of Case 0 without waves, where slight dips form in the magnetic  configuration of the pillar due to the effects of reduced gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The figure and the animation show the magnetic field  lines and the density isocontours in the domain at t = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='8τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' A small lifting of the magnetic field lines by the wave  pressure is evident mostly in the lower region of the pillar, while the small gravitational dipping of the field lines is  most evident in the upper part of the domain in the initial state, reduced at later times due to the effects of wave  pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Isocontours of density indicate the locations of the propagating compressions due to the guided NFM waves,  while further details of the wave propagation are exhibited in the animations provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The effects of non-potential, non-force-free magnetic fields on the propagation of the fast magnetosonic waves in the  prominence pillar are explored in Cases 4-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The form of the background magnetic field is given by Equation 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  parameters of Cases 4-6 are the same as in Cases 1-3 except that By,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In Case 7 we consider By = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2, with  the other parameters as in Case 3, and in Case 8 we consider B0 = 20 G, with the rest of the parameters the same as  in Case 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' These results are discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  In Figure 11 we show the variables in the x-z plane at y = 0 for Case 6 with By0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1 at t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='03τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The NFM wave  structure is most evident inside the prominence pillar in the relative density compressions, ∆ρ/ρ0, but also is seen in  the variability in ρ, β, j2, and the velocity and magnetic field magnitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Comparing ∆ρ/ρ0 to Case 3 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 7e), we  find that the relative magnitude of the leakage in the x direction is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The effects of the x component of the  Lorentz force in compressing the prominence pillar density are seen by comparing the structure of ρ to the initial state  Nonlinear Fast Waves in a Prominence Pillar  13  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The results of the 3D MHD model in Case 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) Magnetic field lines and (b) density isocontours due to the  propagating NFM waves in the domain at t = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='8τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' An animation of this figure is available online.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The duration of the  animation is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='6 in normalized time units that shown in 2 s video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  in Figure 6 and to ρ in Case 3 shown in Figure 7a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The apparent half-width is reduced by about 30% in the present  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (a)  (b)  (c)  (d)  (a)  (b)  (c)  (d)  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The variables in the x-z plane cut at y = 0, t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='03τA for Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02, ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='56 (Case 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) ρ with field lines  indicated with white lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Vf magnitude with several isocontours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (d) β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (e) ∆ρ/ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (f) V magnitude with arrows  showing the local direction of the velocity vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (g) j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (h) B magnitude with arrows showing the local direction of the  magnetic field vectors (dominated by Bx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Figure 12 shows the variables in the y-z plane at x = 0 for the case with By0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1 (Case 6) at t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='03τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The  refraction of the wave fronts of the NFM waves due to the effect of the By0 magnetic field component is apparent  by comparison with Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The wave structure is evident in the density and magnetic field perturbations, as well  as in the corresponding current perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In this magnetic configuration, the waves leak significantly out of the  prominence pillar through the side boundary at y = ymax, decreasing the wave energy flux in the center of the pillar,  Time= 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='80e+00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2  0:10  1005  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00(b)14  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  whereas in the uniform magnetic field case, the main leakage takes place through the top of the prominence pillar  (z = zmax) with open boundary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (h)  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Variables in the y-z plane at x = 0, t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='03 for Case 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Vf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (d) β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (e) ∆ρ/ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (f) V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (g) j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (h)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The cut in the x-y plane (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', the solar ‘disk’ view) of the model shows the structure of the prominence pillar density,  temperature, fast magnetosonic speed, β, j2, B, and V at height z = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2 at t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='03τA for Case 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The effects of  the upward propagating NFM waves are evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In the x-y plane, the waves are most clear in ∆ρ/ρ0, j2, β, and the  magnitudes B and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The y dependence of the wave structure is affected by both the driving source and the wave  refraction due to the By0 component of the background magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' It is evident from ∆ρ/ρ0 that the leakage of the  wave is significant in the density compressions outside the prominence pillar region (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', |x| > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The Lorentz force  generates a compression of the density primarily in the x direction, with small magnetic field and density compression  in the y direction, as can be seen from the density and velocity structures in the x-y plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The temporal evolution of the variables for Cases 4-6 in the center of the prominence pillar at x=0, y=0, z=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2 are  shown in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Evidently, the non-force-free magnetic field introduces flows due to the Lorentz force that lead to  compression in the prominence pillar, and corresponding increases of magnetic field strength and density that disrupt  the initial gravitational equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In particular, it is evident that the Vy component has similar accelerated evolution  in Cases 4-6, with weak dependence on the properties of the fast magnetosonic waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Thus, the effects of the Lorentz  force in the non-force-free field in introducing mass flows self-consistently becomes evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The flow accelerates during  the simulated time, exceeding 10% of the Alfv´en speed (about 70 km s−1 with the present normalization) by the final  modeled time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The effect of increased Lorentz force on the structure of the prominence pillar and on the NFM waves is demonstrated  in Case 7 with By0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' As expected, the increased Lorentz force leads to more rapid and powerful compression of  the prominence pillar than in Cases 4-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This affects the properties of the background density structure of the pillar  and also the NFM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' In particular, the wave frequency has decreased due to the increased compression, mainly  due to the increase in density and corresponding decrease in Vf inside the prominence pillar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This also leads to the  decrease of the velocity amplitude associated with the NFM waves inside the pillar for the fixed wave source at the  boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  In Case 8 we investigate the effects of increased magnetic field strength on the NFM waves by doubling the assumed  magnitude of the magnetic field, B0 = 20 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' This change with respect to previous cases results in a doubling of VA  and a decrease of plasma β by a factor of four.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Since the velocity amplitude Vd is in units VA, the magnitude of the  nonlinearity of the fast magnetosonic wave in Case 8 is essentially the same as in Case 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Also, we note that τA is half  the value in Case 8 compared to other cases, and that the value of ω in Case 8 is equal to the value in Case 7 when  Nonlinear Fast Waves in a Prominence Pillar  15  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (h)  Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Variables in the x-y plane at z = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2, t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='03 for Case 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Vf with several isocontours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (d) β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (e)  ∆ρ/ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (f) V magnitude with direction arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (g) j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (h) B magnitude with direction arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  (a)  0  1  2  3  4  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='12  Vx, Vy, Vz  (b)  0  1  2  3  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='14  DBx, DBy, DBz  (c)  0  1  2  3  time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='4  Dr/r0, DT/T0  Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The temporal evolution of the variables in the center of the prominence pillar for Case 4 (red) with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01,  ω = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='28, Case 5 (blue) with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='01, ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='58, and Case 6 (black) with Vd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='02, ω = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (a) Velocity components  Vz (solid), Vy (short dashes), Vx (long dashes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (b) Magnetic field component perturbations ∆Bx (solid), ∆By (short dashes),  ∆Bz (long dashes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' (c) Changes in density ∆ρ/ρ0 (solid) and temperature ∆T/T0 (long dashes) normalized by the respective  initial values ρ0 and T0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Times are in units of τA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  converted to rad s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The main difference with respect to previous cases is the effect of the wave pressure, which is  now four times larger in Case 8 and leads to correspondingly stronger density compressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' DISCUSSION AND CONCLUSIONS  16  Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Recent high spatial and temporal resolution observations of a prominence pillar from Hinode/SOT in Hα and Ca II  and IRIS in Mg II show evidence of small-scale oscillations and propagating features associated with flows (Kucera  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Analysis of Doppler shifts from Hinode/SOT Hα and IRIS show red-wing/blue-wing contrasts that are  consistent with propagating waves and flows on extended magnetic field lines (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=', Ofman & Kucera 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Here,  we analyze additional observations of propagating small-scale oscillations in the Hinode/SOT Ca II line and the blue  wing of Hα in a prominence on 2012 February 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Using space-time plots and wavelet analysis, we find oscillations  with typical periods of order minutes and wavelengths of order 1000-2000 km with sharp peaks indicative of nonlinear  steepening, and we identify the propagating features as signatures of nonlinear fast magnetosonic (NFM) waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Motivated by past and recent observations of the small-scale oscillations, we developed an idealized 3D MHD model  of a prominence pillar that focuses on the generation and propagation of NFM waves guided by observed properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The advantage of the simplified 3D model is tractability of the wave features when the line-of-sight projection effects  inherent to single-point plane-of-the-sky observations are removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The 3D model reproduces the main physical  properties of the prominence cool material embedded in background magnetic field and of the observed propagating  small-scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The present model extends previous 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='5D MHD studies of the propagating NFM waves into more complex and  realistic prominence structures by allowing 3D wave propagation and couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' There is evidence of nonlinear coupling  of the NFM waves to other wave modes in the animation of the density structure, which shows secondary density  compressions due to slow magnetosonic mode that appear to follow the compressions associated with NFM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  There is also evidence of small amplitude Alfv´enic oscillation in the temporal signatures of the variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' However, we  find that the main effects of nonlinearity of the waves are the steepening and the coupling between the NFM waves  and the background pillar structure in the low-β plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  We modeled eight cases and varied the main parameters of the waves in two types of magnetic field configurations  (uniform potential and for the first time non-force-free) to provide insights on the effects of the various parameters  on the generation and propagation of NFM waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Evidence of velocity and magnetic shear is often observed in  pre-eruptive prominences configurations (Gibson 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Therefore, we modeled non-force-free field with magnetic  shear that introduces large-scale flows, corresponding (aperiodic) compressions of the prominence pillar, and dynamic  changes in wave propagation properties, all self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We find that the effects of the non-force-free sheared  magnetic field on the pillar structure and on the wave propagation are significant, even for relatively small magnitude  of the shear-produced Lorentz force, due to the low-β state of the prominence material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Thus, the effects of magnetic  field shear on the NFM waves may affect the application of coronal seismology in prominence pillars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The modeling results show qualitative agreement with the observed propagating oscillations with nonlinear steep-  ening in the prominence pillar, as demonstrated in previous studies (Ofman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Ofman & Kucera 2020) and  the present observational analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The 3D MHD results confirm further the interpretations of the observed propa-  gating small-scale features in terms of NFM waves that are wave-guided in the cool material (low fast magnetosonic  speed) of the prominence pillar region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' From the model we find that the wave nonlinearity leads to secular changes  in background magnetic field structure, density, and temperature due to the wave pressure, in addition to the wave  steeping effects that affect the small-scale compressive structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The low-frequency wave source leads to higher  amplitude guided NFM waves than the high-frequency waves, due to lower leakage and dissipation compared to the  high-frequency waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Our study demonstrates the potential applications to the observed small-scale waves together with modeling for  magnetic seismology of the prominence structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' One can apply coronal seismology by using the properties of the  observed waves, such as wavelengths and periods to determine the phase speed of the waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The relation between the  phase speed and the magnetic field can be obtained from linear theory for linear waves in simplified geometry (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=',  Nakariakov & Verwichte 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' For nonlinear waves in more complex geometry the phase speed can be obtained from  a 3D MHD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Finally, by comparing the theoretical/modeled phase speed with the observed phase speed and  with the density and temperature information, one can determine the magnetic field in the pillar (taking into account  possible plane of the sky (POS) projection effects).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The details of magnetic geometry structure could be deduced from  the observed direction of wave propagation where a 3D MHD model helps alleviate the POS observational ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  The present model considers the nonlinearity in various idealized magnetic field geometry scenarios, and in the future  more realistic 3D MHD wave models will include more detailed magnetic and density structure based on specific  observations, thus improving the accuracy of coronal seismology method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Nonlinear Fast Waves in a Prominence Pillar  17  LO acknowledges support by NASA Cooperative Agreement 80NSSC21M0180 to The Catholic University of America.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content='  Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA  Advanced Supercomputing (NAS) Division at Ames Research Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' TAK and CRD were supported by NASA’s H-  ISFM program at Goddard Space Flight Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' Hinode is a Japanese mission developed and launched by ISAS/JAXA,  with NAOJ as domestic partner and NASA and STFC (UK) as international partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' It is operated by these agencies  in co-operation with ESA and NSC (Norway).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' We are grateful to the late Ted Tarbell for helpful discussions concerning  the Hinode/SOT data during our past collaborations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
+page_content=' The Global Oscillation Network Group (GONG) Program,  managed by the NSO, is operated by AURA Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TdE3T4oBgHgl3EQfaArM/content/2301.04503v1.pdf'}
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diff --git a/UNE4T4oBgHgl3EQfMAxr/content/tmp_files/2301.04943v1.pdf.txt b/UNE4T4oBgHgl3EQfMAxr/content/tmp_files/2301.04943v1.pdf.txt
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@@ -0,0 +1,1436 @@
+1
+Robust Nonlinear Optimal Control
+via System Level Synthesis
+Antoine P. Leeman1, Johannes K¨ohler1, Andrea Zanelli1, Samir Bennani2, and Melanie N. Zeilinger1
+Abstract—This paper addresses the problem of finite horizon
+constrained robust optimal control for nonlinear systems subject
+to norm-bounded disturbances. To this end, the underlying
+uncertain nonlinear system is decomposed based on a first-
+order Taylor series expansion into a nominal system and an
+error (deviation) described as an uncertain linear time-varying
+system. This decomposition allows us to leverage system level
+synthesis to optimize an affine error feedback while planning the
+nominal trajectory and ensuring robust constraint satisfaction
+for the nonlinear system. The proposed approach thereby results
+in a less conservative planning compared with state-of-the-
+art techniques. A tailored sequential quadratic programming
+strategy is proposed to solve the resulting nonlinear program
+efficiently. We demonstrate the benefits of the proposed approach
+to control the rotational motion of a rigid body subject to state
+and input constraints.
+Index Terms—NL predictive control, Nonlinear systems, Opti-
+mal control, Robust control, System level synthesis
+I. INTRODUCTION
+Robust nonlinear optimal control represents one of the cen-
+tral problems in many safety-critical applications, involving,
+e.g., robotic systems, drones, spacecraft, and many others.
+While this problem has been extensively studied in the litera-
+ture [1], and rigorous constraint satisfaction properties can be
+derived in the presence of disturbances (see robust predictive
+control formulations, e.g., [2]–[4]), this is commonly achieved
+at the cost of introducing conservativeness.
+The robust control design task is traditionally divided into
+two main steps: the optimization of the nominal trajectory [5],
+[6] and the offline design of a stabilizing feedback [3] compen-
+sating for modeling errors or disturbances. To ensure robust
+satisfaction of safety-critical state constraints, the nominal tra-
+jectory optimization is coupled with the over-approximation of
+the error reachable set using, e.g., tubes or funnels [7]. There
+exists a wide range of techniques to construct corresponding
+over-approximations of the tubes/funnels (cf., e.g., [2]–[4],
+[7]–[10]), however, these methods can introduce significant
+conservatism, especially due to the choice of an offline fixed
+error feedback. We address this limitation by proposing a
+method to solve the robust trajectory optimization while jointly
+This work has been supported by the European Space Agency under
+OSIP 4000133352, the Swiss Space Center, and the Swiss National Science
+Foundation under NCCR Automation (grant agreement 51NF40 180545).
+1Antoine P. Leeman, Johannes K¨ohler, Andrea Zanelli, and Melanie N.
+Zeilinger are with the Institute for Dynamic Systems and Control, ETH
+Z¨urich, Z¨urich 8053, Switzerland (email: aleeman@ethz.ch; jkoehle@ethz.ch;
+zanellia@ethz.ch; mzeilinger@ethz.ch)
+2Samir Bennani is with the European Space Agency, Noordwijk 2201AZ,
+The Netherlands (email: samir.bennani@esa.int)
+Disturbance and linearization error
+dk = wk + r(xk, uk, zk, vk)
+Nominal dynamics
+zk+1 = f(zk, vk)
+SLS-based LTV error reachable set
+xk ∈ zk ⊕ Dk
+Theorem III.1
+(xk, uk) ∈ P
+∀wk ∈ W
+Fig. 1: Decomposition of the uncertain nonlinear dynamics
+into nominal nonlinear dynamics, an error term made up of
+the disturbance and linearization error (Section III-A), and an
+LTV error system used for the SLS-based error reachable sets
+(Section III-B). This decomposition enables optimization over
+affine error feedback with robust constraint satisfaction for the
+nonlinear uncertain system (Section III-C).
+optimizing over the error feedback and ensuring guaranteed
+robust constraint satisfaction.
+The conservativeness of an offline-determined error feed-
+back policy can be addressed for linear systems by directly
+predicting robust control invariant polytopes [11]. Compare
+also [12] for a recent approach for nonlinear systems. Another
+systematic approach to jointly optimize a linear feedback
+while considering constraints is presented in [13], [14], which
+extends approximate ellipsoidal disturbance propagation [10],
+[15] to include optimized feedback policies. Other methods
+to obtain feedback policies and (optimal) trajectories, which
+come without principled guarantees for robust constraint sat-
+isfaction (cf. [16]–[18]), are used in practice.
+However, all the above mentioned methods that jointly
+optimize over nominal trajectories and feedback policies result
+in an over- or under-approximation of the true reachable
+set, even for linear systems. We overcome this limitation by
+leveraging system level synthesis (SLS) [19]–[21], or equiva-
+lently affine disturbance feedback [22]–[24]. In particular, for
+linear systems, SLS allows to jointly optimize a linear error
+feedback policy and nominal trajectory and thereby provide
+a tight reachable set at least for linear systems. There exist
+conceptual extensions of the SLS framework to nonlinear
+systems [25]–[27], however these existing approaches do not
+consider (robust) constraint satisfaction.
+arXiv:2301.04943v1  [math.OC]  12 Jan 2023
+
+2
+Contribution: We propose a novel approach for optimal
+control of nonlinear systems with robust constraint satisfac-
+tion, using SLS. As shown in Fig. 1, the nonlinear system is
+decomposed into a nominal nonlinear system and a linear time-
+varying (LTV) error (deviation) system constructed around
+the online-optimized nominal trajectory, which includes an
+online-optimized error term corresponding to the linearization
+error (Section III-A). We apply a linear SLS formulation
+(Section III-B) to the LTV error system to jointly optimize the
+affine error feedback and the nominal trajectory and obtain
+an over-approximation of the reachable set (funnel) for the
+nonlinear system (Section III-C). The presented method has
+the following advantages when compared to the literature:
+• The nominal trajectory and the affine error feedback are
+optimized jointly to decrease conservativeness.
+• The reachable set used for robust constraint satisfaction
+is tight for linear systems, i.e., the only source of con-
+servativeness stems from the over-approximation of the
+linearization error.
+In addition, we provide an inexact sequential quadratic pro-
+gramming (SQP) algorithm to solve the corresponding nonlin-
+ear program (NLP), which can substantially reduce the compu-
+tation times compared to other SQP methods, or IPOPT [28],
+especially when the dynamics of the system are described by
+an expensive to integrate ordinary differential equation (Sec-
+tion IV). Furthermore, this inexact SQP algorithm ensures that
+the resulting QP sub-problems are comparable to linear SLS
+problems [20]. Overall, the proposed approach can be applied
+to any three times continuously differentiable nonlinear system
+and requires no complicated offline design.
+Finally, we demonstrate the benefits of the proposed method
+using a nonlinear numerical example and provide a comparison
+with open-loop (robust) trajectory optimization and optimal
+control based on the linearized dynamics to highlight the
+reduced conservativeness (Section V).
+Notation: We define the set NT := {0, . . . , T − 1} where
+T is a natural number. We denote stacked vectors or matrices
+by (a, b) = [a⊤ b⊤]⊤. For a vector r ∈ Rn, we denote its
+ith component by ri. Let R be the set of real numbers, and
+0p,q ∈ Rp,q be a matrix of zeros. Let LT,p×q denote the set of
+all block lower-triangular matrices with the following structure
+M =
+�
+����
+M 0,0
+0p,q
+. . .
+0p,q
+M 1,1
+M 1,0
+. . .
+0p,q
+...
+...
+...
+...
+M T −1,T −1
+M T −1,T −2
+. . .
+M T −1,0
+�
+���� ,
+(1)
+where M i,j ∈ Rp×q. The block diagonal matrix consisting
+of matrices A1, . . . , AT is denoted by blkdiag(A1, . . . , AT ).
+The matrix I denotes the identity with its dimensions ei-
+ther inferred from the context or indicated by the subscript,
+i.e., Inx ∈ Rnx×nx. Let Bm
+∞, be the unit ball defined by
+Bm
+∞ := {d ∈ Rm| ∥d∥∞ ≤ 1}. For a matrix M ∈ Rn×m,
+the ∞-norm is given by ∥M∥∞ := maxd∈Bm
+∞ ∥Md∥∞. For
+two sets W1, W2 ⊆ Rn, the Minkowski sum is defined as
+W1 ⊕ W2 := {w1 + w2| w1 ∈ W1, w2 ∈ W2}. We define
+Wk := W × · · · × W
+�
+��
+�
+k times
+. For a sequence of vectors wk ∈ Wk ⊆
+Rm and k ∈ N, we define w0:k := (w0, . . . , wk) ∈ W0:k :=
+W0 × · · · × Wk.
+II. PROBLEM FORMULATION
+We consider the following robust nonlinear optimal control
+problem:
+min
+π(·)
+JT (¯x, π(·)),
+(2a)
+s.t.
+xk+1 = f(xk, uk) + wk ∀k ∈ NT ,
+(2b)
+x0 = ¯x,
+(2c)
+uk = πk(x0:k) ∀k ∈ NT ,
+(2d)
+(xk, uk) ∈ P ∀k ∈ NT +1 ∀wk ∈ W.
+(2e)
+The dynamics are given by (2b), with the state xk ∈ Rnx, the
+input uk ∈ Rnu and the disturbance wk ∈ W ⊆ Rnx at time
+step k. The initial condition is given by ¯x ∈ Rnx in (2c). The
+control input is obtained by optimizing over general causal
+policies πk (2d), with π = (π0, . . . , πT ) : R(T +1)nx �→
+R(T +1)nu, and the last input uT is kept in the problem
+formulation for notational convenience. We primarily focus
+on the robust constraint satisfaction (2e) and, for simplicity,
+consider a general cost (2a) over the prediction horizon T
+which does not depend on w.
+Problem (2) is not computationally tractable because of the
+optimization over the general feedback policy π(·) and the
+robust constraint satisfaction required in (2e). Consequently,
+the goal is to find a feasible, but potentially sub-optimal,
+solution to this problem. To this end, we define a nominal
+trajectory as
+zk+1 = f(zk, vk) ∀k ∈ NT , z0 = ¯x,
+(3)
+and restrict the policy to a causal affine time-varying error
+feedback
+πk(x0:k) = vk +
+k−1
+�
+j=0
+Kk−1,j∆xk−j
+(4)
+with πk(x0:k) : R(k+1)nx �→ Rnu, vk ∈ Rnu, zk ∈ Rnx,
+Ki,j ∈ Rnu×nx, and the errors ∆xk := xk − zk, ∆uk :=
+uk −vk. We also consider the following standard assumptions.
+Assumption II.1. The nonlinear dynamics (2b) f : Rnx ×
+Rnu �→ Rnx are three times continuously differentiable.
+Assumption II.2. The constraint set P (2e) is a compact
+polytopic set with P := {(x, u)| c⊤
+i (x, u) + bi ≤ 0, ∀i ∈ NI},
+where ci ∈ Rnx+nu and bi ∈ R.
+Assumption II.3. The disturbance set is given by
+wk ∈ W = {Ed| d ∈ Bnw
+∞ } = EBnw
+∞ ⊆ Rnx,
+(5)
+with E ∈ Rnx×nw.
+III. ROBUST NONLINEAR OPTIMAL CONTROL VIA SLS
+In this section, we derive the main result of the paper using
+the steps depicted in Fig. 1, i.e., we propose a formulation to
+optimize over affine policies (4) that provide robust constraint
+satisfaction for the nonlinear system (2b). We decompose
+
+3
+the nonlinear system equivalently as the sum of a nominal
+nonlinear system and an LTV error system that accounts both
+for the local linearization error (Section III-A) and the additive
+disturbance. Using established SLS tools for LTV systems
+(Section III-B), we parameterize the closed-loop response for
+this LTV system. As a result, we obtain an optimization
+problem that jointly optimizes the nominal trajectory (3) and
+the error feedback (4), and that guarantees robust constraint
+satisfaction (Section III-C).
+A. Over-approximation of nonlinear reachable set
+The goal of this section is to decompose the uncertain
+nonlinear system into a nominal nonlinear system and an LTV
+error system subject to some disturbance. The linearization of
+the dynamics (3) around a nominal state and input (z, v) is
+characterized by the Jacobian matrices:
+A(z, v) := ∂f
+∂x
+����
+(x,u)=(z,v)
+, B(z, v) := ∂f
+∂u
+����
+(x,u)=(z,v)
+.(6)
+Using the Lagrange form of the remainder of the Taylor series
+expansion, we obtain
+f(x, u) + w
+(3)= f(z, v)
++ A(z, v)(x − z) + B(z, v)(u − v)
++ r(x, u, z, v) + w
+�
+��
+�
+=:d
+,
+(7)
+with the remainder r : Rnx×Rnu×Rnx×Rnu �→ Rnx and both
+the disturbance w and the remainder r(x, u, z, v) are lumped
+in the disturbance d := r(x, u, z, v) + w ∈ Rnx.
+To bound the remainder, we consider the (symmetric) Hes-
+sian Hi : Rnx+nu �→ R(nx+nu)×(nx+nu) of the ith component
+of f, i.e.,
+Hi(ξ) =
+�
+∂2fi
+∂x2
+∂2fi
+∂x∂u
+∗
+∂2fi
+∂u2
+������
+(x,u)=ξ
+,
+(8)
+where ξ ∈ Rnx+nu lies between the linearization point (z, v)
+and the evaluation point (x, u). We define the constant1 µ ∈
+Rnx×nx as
+µ := diag(µ1, . . . , µnx), µi := 1
+2
+max
+ξ∈P,∥h∥∞≤1 |h⊤Hi(ξ)h|,
+(9)
+and the error ek := (∆xk, ∆uk) ∈ Rnx+nu.
+Proposition III.1. Given Assumptions II.1 and II.2, the re-
+mainder in (7) satisfies
+|ri(x, u, z, v)| ≤ ∥e∥2
+∞µi,
+(10)
+for any (x, u) ∈ P, (z, v) ∈ P.
+1Note that max∥h∥∞≤1 |h⊤Hh| ≤ �
+i
+�
+j |Hij|, with Hij, the element
+on the ith row and jth column of the matrix H.
+Proof. Applying the definition of the Lagrange form of the
+remainder, for all (x, u, z, v) and for all i, there exists a ξ ∈ P
+(using convexity) such that
+|ri(x, u, z, v)| = 1
+2|e⊤Hi(ξ)e|
+≤ max
+ξ∈P
+1
+2|e⊤Hi(ξ)e|
+(11)
+(9)
+≤ ∥e∥2
+∞µi.
+The constants µi are computed offline, which is the only
+offline design required for the proposed method. Intuitively,
+the magnitude of µi quantifies the nonlinearity of the system,
+which will be incorporated in the disturbance propagation in
+the proposed formulation (Sec. III.C).
+Due to Proposition III.1 and Assumption II.3, the combined
+disturbance d from (7) satisfies
+d := w + r(x, u, z, v) ∈ EBnw
+∞ ⊕ ∥e∥2
+∞µBnx
+∞
+= [E, ∥e∥2
+∞µ]Bnw+nx
+∞
+.
+(12)
+Given a bound on ∥e∥∞, we can compute an outer approxi-
+mation of the reachable set of the nonlinear system, using the
+following LTV error system
+∆xk+1 = Ak∆xk + Bk∆uk + dk ∀k ∈ NT +1, ∆x0 = 0nx,
+(13)
+with Ak := A(zk, vk), Bk := B(zk, vk).
+Similar LTV error dynamics are used in [8]–[10], [12], [14]
+to over-approximate the reachable set. To optimize affine error
+feedback (4) while ensuring robust constraint satisfaction of
+the nonlinear system based on this LTV error dynamics, we
+next study the robust optimal control problem for the special
+case of LTV systems.
+B. Robust optimal control for LTV systems
+In this section, we study the parameterization of affine
+feedback policies for LTV systems, which will provide the
+basis for the employed parameterization of affine error feed-
+back for nonlinear systems. We show that by using SLS
+techniques [19] we can jointly optimize the error feedback
+and nominal trajectory of any LTV system. Consider an LTV
+system of the form
+˜xk+1 = ˜Ak˜xk + ˜Bk˜uk + ˜wk ∀k ∈ NT , ˜x0 = 0nx,
+(14)
+with ˜Ak ∈ Rnx×nx, ˜Bk ∈ Rnx×nu, and
+˜wk ∈ ˜Wk := ˜EkBn˜
+w
+∞ ,
+(15)
+with some ˜Ek ∈ Rnx×n˜
+w. The dynamics (14) are written
+compactly as
+˜x = Z ˜
+A˜x + Z ˜B˜u + ˜w,
+(16)
+with
+˜w
+:=
+( ˜w0, . . . , ˜wT −1)
+∈
+RT nx,
+˜x
+:=
+(˜x1, . . . , ˜xT )
+∈
+RT nx,
+˜u
+:=
+(˜u1, . . . , ˜uT )
+∈
+RT nu,
+˜
+A
+:=
+blkdiag( ˜A1, . . . , ˜AT −1, 0nx,nx)
+∈
+LT,nx×nx,
+
+4
+˜B
+:=
+blkdiag( ˜B1, . . . , ˜BT −1, 0nx,nu)
+∈
+LT,nx×nu
+and
+the block-lower shift matrix Z ∈ LT,nx×nx is given by
+Z :=
+�
+����
+0nx,nx
+0nx,nx
+. . .
+0nx,nx
+Inx
+0nx,nx
+. . .
+0nx,nx
+...
+...
+...
+...
+0nx,nx
+. . .
+Inx
+0nx,nx
+�
+���� .
+(17)
+We introduce the causal linear feedback ˜u =
+˜K˜x, ˜K ∈
+LT,nu×nx i.e., ˜uk = �k−1
+j=0 ˜Kk−1,j ˜xk−j, ˜Ki,j ∈ Rnu×nx.
+Using this feedback, we can write the closed-loop dynamics
+as
+˜x = Z( ˜
+A + ˜B ˜K)˜x + ˜w, ˜u = ˜K˜x, ˜x0 = 0nx,
+(18)
+or equivalently as
+�˜x
+˜u
+�
+=
+� (I − Z ˜
+A − Z ˜B ˜K)−1
+˜K(I − Z ˜
+A − Z ˜B ˜K)−1
+�
+˜w =:
+�˜Φx
+˜Φu
+�
+˜w,
+(19)
+with
+˜Φx =
+�
+��
+˜Φ0,0
+x
+...
+...
+˜ΦT −1,T −1
+x
+· · ·
+˜ΦT −1,0
+x
+�
+�� ∈ LT,nx×nx,
+˜Φu =
+�
+��
+˜Φ0,0
+u
+...
+...
+˜ΦT −1,T −1
+u
+· · ·
+˜ΦT −1,0
+u
+�
+�� ∈ LT,nu×nx.
+(20)
+The matrices ˜Φx and ˜Φu are called the system responses
+from the disturbance to the closed-loop state and input, re-
+spectively. The following proposition from the literature shows
+that the closed-loop response under arbitrary affine feedback
+is given by all system responses in a linear subspace.
+Proposition III.2.
+[19, adapted from Theorem 2.1] Let
+˜w ∈ ˜W0:T −1 be an arbitrary disturbance sequence. Any ˜x, ˜u
+satisfying (18), also satisfy (19) with some ˜Φx ∈ LT,nx×nx,
+˜Φu ∈ LT,nu×nx lying on the affine subspace
+�
+I − Z ˜
+A
+− Z ˜B
+� � ˜Φx
+˜Φu
+�
+= I.
+(21)
+Let ˜Φx and ˜Φu be arbitrary matrices satisfying (21). Then the
+corresponding ˜x and ˜u computed with (19) also satisfy (18)
+with ˜K = ˜Φu ˜Φ−1
+x
+∈ LT,nu×nx.
+Proof. The proof follows directly from [19, Theorem 2.1] for
+systems with zero initial conditions.
+Note that this proposition holds for any LTV system and in
+particular for (13), where the matrices ˜
+A and ˜B depend on the
+nominal trajectory (z, v).
+Next, we show how the parameterization (21) can be utilized
+to exactly solve Problem (2) with affine feedback in the case
+of LTV systems. To this end, we introduce a nominal LTV
+system
+˜zk+1 = ˜Ak˜zk + ˜Bk˜vk ∀k ∈ NT , ˜z0 = ˜x0.
+(22)
+The error dynamics are written as
+˜xk+1 − ˜zk+1 = ˜Ak(˜xk − ˜zk) + ˜Bk(˜uk − ˜vk) + ˜wk ∀k ∈ NT .
+(23)
+By considering a causal affine error feedback of the form
+˜u = ˜v + ˜K(˜x − ˜z), ˜u0 = ˜v0, ˜K ∈ LT,nu×nx,
+(24)
+we can apply Proposition III.2 to characterize the system
+response of the LTV error system (23). Note that the linear
+feedback on the error system corresponds to the affine feed-
+back in (24). The closed-loop error on the states and inputs
+is expressed using the definition of ˜Φx and ˜Φu in (19) for the
+LTV system (23), i.e.,
+˜ek = (˜xk, ˜uk) − (˜zk, ˜vk) =
+k−1
+�
+j=0
+˜Φk−1,j ˜wk−1−j ∀k ∈ NT +1,
+(25)
+where ˜Φk,j :=
+�
+˜Φk,j
+x , ˜Φk,j
+u
+�
+, ˜Φx ∈ LT,nx×nx and ˜Φu ∈
+LT,nu×nx. Given Proposition III.2, we can provide tight con-
+ditions for robust state and input constraint satisfaction for the
+LTV system.
+Proposition III.3. There exists a causal error feedback of the
+form (24) such that for any ˜w ∈ ˜WT
+c⊤
+i (˜xk, ˜uk) + bi ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI,
+(26)
+with (˜xk, ˜uk) according to (14) if and only if there exist
+matrices ˜Φx, ˜Φu and a nominal trajectory satisfying (21), (22),
+and
+c⊤
+i (˜zk, ˜vk) + bi
++
+k−1
+�
+j=0
+∥c⊤
+i ˜Φk−1,j ˜Ek−1−j∥1 ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI. (27)
+Proof. As per Proposition III.2, the LTV error system can be
+written with Equation (25), and we can apply directly [22,
+Example 8]. Namely, ∀k ∈ NT +1 ∀i ∈ NI, we have
+max
+˜w0:k−1∈ ˜W0:k−1 c⊤
+i (˜xk, ˜uk) + bi
+(28)
+(25)
+= c⊤
+i (˜zk, ˜vk) +
+max
+˜w0:k−1∈ ˜W0:k−1
+k−1
+�
+j=0
+c⊤
+i ˜Φk−1,j ˜wk−1−j + bi
+= c⊤
+i (˜zk, ˜vk) +
+k−1
+�
+j=0
+max
+˜
+wj∈ ˜Wk−1−j
+c⊤
+i ˜Φk−1,j ˜wk−1−j + bi
+(15)
+= c⊤
+i (˜zk, ˜vk) +
+k−1
+�
+j=0
+���c⊤
+i ˜Φk−1,j ˜Ek−1−j
+���
+1 + bi.
+Remark III.1. A similar reformulation for ellipsoidal distur-
+bances or more general polytopic disturbances can be found
+in [22, Example 7-8]. Likewise, the result can be naturally
+extended to time-varying constraints.
+We have presented conditions for affine error feedback with
+guaranteed constraint satisfaction for a given LTV system
+using the following three components in the SLS formula-
+tion: the nominal trajectory (22), the affine error feedback
+parameterization (21), and a description of the disturbance set
+˜W (15). In combination, Proposition III.2 characterizes the
+system response of the error dynamics, while Proposition III.3
+provides tight bounds on the nominal trajectory and system
+response to ensure robust constraint satisfaction. By combining
+
+5
+these two results, we can solve the robust optimal control prob-
+lem (2) for LTV dynamics (23), affine error feedback (24), and
+disturbances of the form (15) using the following optimization
+problem:
+min
+˜z,˜v0,˜v,˜Φ
+JT (¯x, ˜z, ˜v, ˜Φ),
+(29a)
+s.t.
+�
+I − Z ˜
+A
+− Z ˜B
+� � ˜Φx
+˜Φu
+�
+= I,
+(29b)
+˜zk+1 = ˜Ak˜zk + ˜Bk˜vk ∀k ∈ NT , z0 = ¯x,
+(29c)
+k−1
+�
+j=0
+∥c⊤
+i ˜Φk−1,j ˜Ek−1−j∥1
+(29d)
++ c⊤
+i (˜zk, ˜vk) + bi ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI,
+where we define ˜Φ := (˜Φx, ˜Φu). Specifically, the solution
+of (29) provides a jointly optimized nominal trajectory ˜z,
+˜v and linear error feedback ˜K = ˜Φu ˜Φ−1
+x
+which guarantee
+robust satisfaction of the constraints for the closed-loop state
+and input trajectories. Problem (29) is a reformulation of
+established results in the literature (see, e.g., [19], [29]). In
+the following, we address the nonlinear problem (29) by
+merging the robust optimal control for LTV systems with the
+linearization error bounds from Section III-B for nonlinear
+systems.
+C. Robust nonlinear finite-horizon optimal control problem
+In this section, given the parameterization of the affine
+error feedback for the LTV system (Section III-B) and the
+linearization error of the nonlinear system (Section III-A), we
+are in a position to introduce the main result of this paper
+(cf. Fig. 1). In particular, we will show in Theorem III.1 that
+the following NLP provides a feasible solution to the robust
+optimal control problem in (2):
+min
+z,v0,v,Φ,τJT (¯x, z, v, Φ),
+(30a)
+s.t. [I − ZA(z, v)
+− ZB(z, v)]
+�Φx
+Φu
+�
+= I,
+(30b)
+zk+1 = f(zk, vk) ∀k ∈ NT , z0 = ¯x,
+(30c)
+k−1
+�
+j=0
+∥c⊤
+i Φk−1,j[E, τ 2
+k−1−jµ]∥1
+(30d)
++ c⊤
+i (zk, vk) + bi ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI,
+k−1
+�
+j=0
+∥Φk−1,j[E, τ 2
+k−1−jµ]∥∞ ≤ τk ∀k ∈ NT ,(30e)
+where we denote a feasible solution as {z⋄, v⋄
+0, v⋄, Φ⋄, τ ⋄},
+with z := (z1, . . . , zT ) ∈ RT nx, v := (v1, . . . , vT ) ∈ RT nu,
+A(z, v)
+:=
+blkdiag(A1, . . . , AT −1, 0nx,nx)
+∈
+LT,nx×nx,
+B(z, v) := blkdiag(B1, . . . , BT −1, 0nx,nu) ∈ LT,nx×nu, τ =
+(τ0, . . . , τT −1) ∈ RT , Φx ∈ LT,nx×nx, Φu ∈ LT,nu×nx and
+µ according to (9). The nominal prediction is given by (30c).
+Equation (30b) computes the system response for the lineariza-
+tion around the nominal trajectory z, v (cf. Proposition III.2).
+The auxiliary variable τk is introduced to upper bound ∥ek∥∞,
+which is used to obtain a bound on the linearization error
+(cf. Proposition III.2), which depends on all previous τj,
+j = 0, . . . , k − 1, giving (30e). Using Proposition III.3, the
+constraints are tightened with respect to both the additive
+disturbance wk ∈ W and the linearization error ∥ek∥∞µ
+combined as in (12), i.e., the additive uncertainties on the
+LTV error lie in the set EBnw
+∞ ⊕ ∥e∥2
+∞µBnx
+∞ . As a result,
+the reachable set of the nonlinear system (2b) at time step k,
+in closed-loop with the affine error feedback computed as in
+Theorem III.1 satisfies
+xk ∈ z⋄
+k
+k−1
+�
+j=0
+Φ⋄k−1,j
+x
+[E, τ ⋄2
+k−1−jµ]Bnx+nw
+∞
+=: Dk ∀k ∈ NT +1.
+(31)
+The following theorem summarizes the properties of the
+proposed NLP (30).
+Theorem III.1. Given Assumptions II.1, II.2 and II.3, suppose
+the optimization problem (30) is feasible. Then, the affine error
+feedback u = v⋄ + K⋄(x − z⋄), K⋄ = Φ⋄
+uΦ⋄
+x
+−1, u0 = v⋄
+0
+provides a feasible solution to Problem (2), i.e., the closed-
+loop trajectories of system (2b) under this error feedback
+robustly satisfy the constraints (2e).
+Proof. First, the constraints (30c) ensure that the nominal tra-
+jectory satisfies the dynamics (3). Then, we use a Taylor series
+approximation with respect to the nominal trajectory (30c),
+resulting in the LTV error system (13). We apply Proposi-
+tion III.2 to the LTV error system (13) and the constraint (30b)
+implies that the closed-loop trajectories of the error system
+satisfy
+�
+x − z
+u − v
+�
+=
+�
+Φx
+Φu
+�
+d,
+(32)
+with d := (d0, . . . , dT −1) ∈ RT nx given by (12), x, u
+satisfying (2b) and z, v satisfying (3). In the following, we
+show by induction that the auxiliary variables τ ∈ RT satisfy
+∥ej∥∞ ≤ τj ∀j ∈ NT .
+(33)
+Inequality (33) holds for j = 0 since ∥e0∥∞ = 0 (cf. (30d))
+and τ0 ≥ 0 (cf. (30e)). Note that, as per Proposition III.1, the
+disturbance on the LTV error system dk satisfies (12). Then,
+assuming Inequality (33) holds ∀j ∈ Nk−1, we have
+dj ∈ [E, ∥ej∥2
+∞µ]Bnx+nw
+∞
+⊆ [E, τ 2
+j µ]Bnx+nw
+∞
+∀j ∈ Nk−1.
+(34)
+Hence, we obtain
+∥ek∥∞
+(32)
+=
+������
+k−1
+�
+j=0
+Φk−1,jdk−1−j
+������
+∞
+(35)
+(34)
+≤
+k−1
+�
+j=0
+∥Φk−1,j[E, τ 2
+k−1−jµ]∥∞
+(30e)
+≤ τk.
+Therefore, the constraints (30e) ensure that Inequality (33)
+holds for any realization of the disturbance. Finally, the
+constraint (30d) in combination with Equation (34) ensures
+that the constraints are robustly satisfied, analogously to
+Proposition III.3, which can be seen by substituting ˜Ek for
+[E, τ 2
+kµ] with n˜w = nx + nw.
+
+6
+Remark III.2. When the disturbance w is set to zero with E =
+0nx,nw, we recover a nominal trajectory optimization problem
+(cf., e.g., [5]) as the constraints (30d) reduce to a nominal
+constraint, with τ = 0T , independent of Φ. In case the system
+is linear (µ = 0nx,nx), we recover the linear SLS formulation
+(cf. [20, Eq.(26)]) since τ does not enter the constraints (30d).
+Remark III.3. The considered handling of the nonlinear
+system is based on a linearization along an online optimized
+nominal trajectory and is comparable to [8], [12]–[14],
+where the latter results also provide an affine feedback policy.
+However, the over-approximation of the reachable set in [13]
+is based on the ellipsoidal propagation in [10], where even
+the linear case is not tight. In contrast to [9], both the
+linearized system A, B and the bound on the remainder term
+τ are adjusted online based on the jointly optimized nominal
+trajectory z, v, which avoids conservativeness.
+In the next section, we present an inexact SQP variant to
+solve the NLP (30), with a reduced computational footprint
+with respect to standard SQP methods or IPOPT and results
+in QP sub-problems comparable to linear SLS problems [20].
+IV. INEXACT SQP FOR SLS-BASED ROBUST NONLINEAR
+OPTIMAL CONTROL
+Standard methods to solve the NLP (30) (nonlinear interior
+point methods [28], SQP) use the derivatives of the functions
+used in the constraints. In general, for a function in Rn �→ R,
+evaluating its Jacobian and Hessian has a runtime cost up
+to respectively 2n and 8n times the cost of evaluating the
+function alone [30]. This section discusses how to obtain a
+feasible solution to (30) via a tailored inexact SQP algorithm
+to speed up the computations. The proposed SQP avoids the
+derivatives of the constraint (30b), and hence the Hessian of
+the dynamics, and only uses the Jacobians of the dynamics.
+As evaluating the derivatives is often very expensive computa-
+tionally when solving an NLP, we can expect a speedup of up
+to 1+2n+8n
+1+2n
+when the evaluation of the dynamics dominates
+the computational complexity. To outline the algorithm and its
+properties, we utilize a compact formulation of Problem (30):
+min
+y
+JT (¯x, y),
+(36a)
+s.t.
+g(y) = 0, h(y) ≤ 0, s(y) ≤ 0,
+(36b)
+where y ∈ Rny collects Φ, z, v0, v, and τ in a vector, as well
+as the auxiliary variables needed to encode the 1- and ∞-
+norms. Here, g(y) = 0 and h(y) ≤ 0 correspond respectively
+to the nonconvex equality constraints (30b)-(30c) and the
+nonconvex inequality constraints (30d)-(30e), while s(y) ≤ 0
+corresponds to the additional linear inequality constraints on
+the auxiliary variables.
+A standard SQP implementation iteratively solves the fol-
+lowing QP sub-problems
+min
+∆y
+∂
+∂yJT (¯x, y)
+����
+y=ˆy
+∆y + 1
+2∆y⊤HJ∆y,
+(37a)
+s.t.
+g(ˆy) + ∂
+∂yg(y)
+����
+y=ˆy
+∆y = 0,
+(37b)
+h(ˆy) + ∂
+∂yh(y)
+����
+y=ˆy
+∆y ≤ 0,
+(37c)
+s(ˆy + ∆y) ≤ 0,
+(37d)
+where we denote the solution at the previous iteration with the
+symbol ˆ and define ∆y := y − ˆy. The matrix HJ ∈ Rny×ny
+is an approximation of the Hessian of the Lagrangian (see,
+e.g., [31] for practical approximations).
+In the following, we describe an inexact SQP algorithm [32]
+to improve the computational efficiency and highlight the
+numerical similarities with linear SLS [19], [20]. In particular,
+the linearization of (30b) is given by
+[I − ZA(ˆz, ˆv)
+−ZB(ˆz, ˆv)] Φ
+(38)
++
+T (nx+nu)
+�
+i=1
+∂
+∂ξi
+[−ZA − ZB]
+����
+(z,v)=(ˆz,ˆv)
+ˆΦ(ξi − ˆξi) = I,
+where ξi is the ith element of the vector (z, v). The proposed
+inexact SQP algorithm replaces the equality constraint (38) by
+[I − ZA(ˆz, ˆv)
+−ZB(ˆz, ˆv)] Φ = I,
+(39)
+within the QP (37), i.e., the Jacobians with respect to ξi in the
+constraint (38) are set to zero. Thus, the proposed inexact SQP
+avoids evaluating second-order derivatives of the dynamics (3),
+leading to improved computation times as shown in Section V.
+The numerical complexity of each QP sub-problem of the
+inexact SQP scheme is similar to a linear SLS problem (29),
+as each constraint of the resulting QPs, except (30e), has its
+analog in (29).
+Under
+several
+mild
+assumptions,
+inexact
+SQP
+us-
+ing (39) converges to a feasible, but suboptimal, solution
+{Φ⋄, z⋄, v⋄
+0, v⋄, τ ⋄} of the original NLP (30) (see, e.g., [33]
+for the proof).
+Remark IV.1. To decrease the number of decision variables
+and improve the numerical efficiency, one could consider K
+to be block-banded, as in [24]. It is important to note that
+the feedback K in (24) can be implemented without explicitly
+computing the inverse of Φx [19].
+Remark IV.2. Both SQP and inexact SQP are commonly
+combined with a globalization strategy such as trust-region
+or line search methods to ensure convergence when the initial
+guess is relatively far from a local optimum [31].
+V. CASE STUDY: SATELLITE ATTITUDE CONTROL
+The following example demonstrates the benefits of the
+proposed approach where we optimize jointly the error feed-
+back and the nominal trajectory for nonlinear systems with
+additive disturbances. Moreover, it demonstrates the numerical
+properties of the method. In particular, we study a nonlinear
+aerospace problem, the constrained attitude control of a satel-
+lite [6].
+
+7
+0
+2
+4
+6
+8
+10
+Step k
+-0.4
+-0.2
+0
+0.2
+0.4
+0.6
+0.8
+1
+Quaternion q
+-0.1
+0
+0.1
+Constraints
+Uncertain sys.
+LTV
+Nonlinear reach. set
+Nominal
+-0.1
+0
+0.1
+Angular speed !
+0
+2
+4
+6
+8
+10
+Step k
+-0.1
+0
+0.1
+0
+2
+4
+6
+8
+10
+Step k
+-0.1
+-0.05
+0
+0.05
+0.1
+Control input u
+0
+2
+4
+6
+8
+10
+Step k
+0
+2
+4
+6
+8
+10
+Step k
+Fig. 2: Robust nonlinear optimal control for the attitude control of a spacecraft computed with inexact SQP. For each state and
+input, the reachable set (see Equation (31)) around the nominal trajectory depicts the online-computed reachable sets (green)
+and its LTV approximation (blue). The reachable sets are designed to remain within the constraints (black), and the sample
+trajectory (red) is hence guaranteed to stay therein.
+A. System and constraints
+We consider the following Euler’s equation of the dynamics
+˙z =
+�
+Ω(ω)q
+I−1
+S (v − ω × (ISω))
+�
+,
+(40)
+with states z := (q, ω), attitude quaternion q ∈ R4, angular
+rotation rate ω ∈ R3, input torque v ∈ Rnu, nx = 7, nu = 3
+and × is the cross product. The symmetric inertia matrix of
+the satellite is IS = diag(5, 2, 1) ∈ R3×3 and
+Ω(ω) := 1
+2
+�
+���
+0
+−ω1
+−ω2
+−ω3
+ω1
+0
+ω3
+−ω2
+ω2
+−ω3
+0
+ω1
+ω3
+ω2
+−ω1
+0
+�
+��� ,
+(41)
+with Ω : R3 �→ R4×4. The dynamics are discretized using
+the 4th order Runge–Kutta method, using a time step of one,
+which results in a negligible discretization error. We consider
+a bounded disturbance applied to the system described by (5)
+with E = 5 · 10−3[03,4 I3]⊤ ∈ R7×nw with nw = 3,
+which could stem, e.g., from the solar radiation pressure, the
+flexible modes of the solar panels, the aerodynamic drag,
+or any unmodelled dynamics. Additionally, we consider the
+constraints −0.1 ≤ ωi ≤ 0.1 and −0.1 ≤ vi ≤ 0.1 for
+i = 1, 2, 3. We use the nominal cost function JT (¯x, z, v) =
+�T −1
+k=0 ℓ(zk, vk) + ℓT (zT ), with stage cost
+ℓ(z, v) = (z −zref)⊤Q(z −zref)+(v−vref)⊤R(v−vref), (42)
+and the terminal cost
+ℓT (z) = (z − zref)⊤Q(z − zref),
+(43)
+with Q = 0.7I ∈ R7×7, R = I ∈ R3×3, the reference
+zref = (1, 0, 0, 0, 0, 0, 0)⊤, vref = (0, 0, 0)⊤, and the horizon
+is T = 10. As often seen in numerical optimization, we
+consider an additional term to the cost function, i.e., we use
+JT + αy⊤y, with α = 10−2. We approximate the constant
+µ ≈ diag(3.699, 3.703, 3.717, 3.635, 0.649, 4.608, 5.635) ∈
+R7×7 from Equation (9) for the nonlinear dynamics (40) by
+using a Monte-Carlo method with 104 samples for a total
+offline computation time of 444 seconds. The initial condition
+is ¯x = (¯q, ¯ω), where ¯q is inferred from the Euler angles
+(180, 45, 45) ·
+π
+180 and ¯ω = (−1, −4.5, 4.5) ·
+π
+180.
+
+8
+B. Results
+!2
+This paper (a)
+!3
+!2
+Nominal (c)
+7x
+Linear (b)
+!3
+Open-loop (d)
+Fig. 3: Comparison between the proposed robust nonlinear
+optimal control (30) (a), the linear optimal control problem,
+based on the linearization around a reference point, applied to
+the nonlinear system (b), the nominal trajectory optimization
+without robustness guarantees (c), and the (reduced-horizon)
+open-loop robust nonlinear optimal control (d). The reachable
+set (31) around the nominal trajectory (blue) is plotted with a
+different color for each time step k, together with the trajectory
+with disturbance (red).
+The NLP (30) is solved using the inexact SQP (Sec. IV)
+formulated with Casadi [34] with the QPs solved with
+Gurobi [35]. In addition, a Gauss-Newton approximation of
+the Hessian (37a) is used, with a small regularization term,
+i.e., we use HJ + γIny instead of HJ in
+(37a), with
+γ
+= 10−2. We assume convergence when the condition
+∥(∆y, ∆ν)∥∞ ≤ 10−6 is fulfilled, where ∆ν is the decrease
+in the dual solution [31].
+1) Nonlinear system with affine error feedback: For the
+problem considered, Fig. 2 shows the solution of the NLP (30)
+computed with inexact SQP, which ensures that the trajectories
+of the nonlinear system remain robustly within the constraints.
+The shaded areas correspond to the reachable sets of the
+nonlinear system (Equation (31)) (green) and its LTV approx-
+imation (blue), i.e., µ = 0. Illustrative disturbance sequences
+have been applied and, as ensured by the proposed design, the
+resulting trajectory (red) remains within the reachable sets.
+The flexible error feedback parameterization allows the tubes
+to grow in some directions and shrink in others to meet the
+constraints, which illustrates the flexibility of this method. A
+phase plot of the states ω2 and ω3 is also depicted in Fig. 3(a)
+for comparison with other approaches.
+2) Comparison with open-loop counterpart: To highlight
+the benefits of the proposed method, we solve the NLP (30),
+with Φu = 0T nu,T nx, resulting in an open-loop robust formu-
+lation, i.e., K = 0T nu,T nx. For the open-loop case only, we
+consider a reduced horizon of T = 6, as a longer horizon
+leads to infeasibilities. Indeed, this open-loop robust method
+does not apply error feedback, making the reachable set effec-
+tively larger. The open-loop robust formulation maintains the
+guarantees of robust constraint satisfaction, as the reachable
+set or tube always stays within the constraints as depicted in
+Fig. 3(d). Because of the large size of the tube, the nominal
+trajectory is forced to move away from the constraints, leading
+to poor performance. Indeed, for the system considered, the
+tube cross-section keeps increasing, which limits both the size
+of the disturbance and the horizon that can be considered.
+Therefore, the affine error feedback is instrumental to ensure
+robust constraint satisfaction for large disturbances without
+acting overly conservatively.
+3) Comparison with nominal counterpart: The method is
+also compared with its nominal counterpart, i.e., where we do
+not optimize error feedback and neglect the disturbance (Φx =
+0T nx,T nx, Φu = 0T nu,T nx) and hence do not guarantee robust
+constraint satisfaction. The optimal nominal trajectory satisfies
+the constraints, but the trajectory with disturbance results in
+significant constraint violations (see Fig. 3(c)). Therefore, it
+is crucial to consider the disturbance in the optimal control
+problem.
+4) Comparison with linear counterpart: We design a con-
+troller based on a linearization of the nonlinear dynamics (40),
+i.e., we linearize the dynamics around the reference point
+(zref, vref) ∈ Rnx+nu, ignoring the nonlinearity (µ = 0nx,nx),
+and solve the resulting linear SLS problem. Subsequently, we
+apply the resulting controller to the nonlinear dynamics. When
+the linearization point is far from the operation point, or when
+the linear model is not a good approximation of the nonlinear
+system dynamics, the resulting controller leads to poor perfor-
+mance and large constraint violations (see Fig. 3(b)).
+5) Computation times: To assess the performance of the
+two SQP variants (cf. Section IV), we compare them with
+the well-established NLP solver, IPOPT [28] using just-in-
+time compilation (cf. jit [34]) and MUMPS as a linear solver.
+The problem was solved on an i9-7940X processor with
+32GB of RAM memory. Table I shows the comparison in the
+number of iterations required until the convergence condition
+is satisfied, the solve time, and the optimal cost for the three
+methods. The inexact SQP achieves the fastest convergence
+time with negligible difference in minimizer, highlighting the
+benefit of this SQP variant. Fig. 4 illustrates the convergence
+rate of both SQP variants. The speedup between inexact-
+SQP and SQP largely depends on the computational cost
+of evaluating the Hessians of the dynamics f. Hence, we
+expect a larger difference for a stiff system or other high-
+order integration methods. We observe linear convergence for
+both SQP variants, as predicted by the theory in [31], [32].
+VI. CONCLUSION
+We proposed a novel approach to solve finite horizon con-
+strained robust optimal control problems for nonlinear systems
+subject to additive disturbances, as commonly encountered in
+
+9
+0
+5
+10
+15
+20
+Iteration #
+10-6
+10-4
+10-2
+100
+102
+Primal-dual step size k("y; "8)k1
+inex. SQP
+SQP
+conv. threshold
+Fig. 4: Numerical convergence of SQP and inexact SQP in
+terms of primal-dual step size.
+Inexact SQP
+SQP
+IPOPT
+Iterations
+18
+18
+52
+Computation time [s]
+4.45
+5.79
+70.88
+JT (¯x, y⋄)
+12.27
+12.27
+12.27
+TABLE I: Numerical comparison between SQP, inexact SQP,
+and IPOPT for solving Problem (30) in terms of the number
+of iterations to reach convergence, the total computation time,
+and the optimal cost achieved. A just in time compiler was
+used for both SQP variants but not for IPOPT.
+trajectory optimization or MPC. One of the main novelties lies
+in the joint optimization of a nominal trajectory and an affine
+error feedback policy to compensate for disturbances with ro-
+bust constraint satisfaction. We also presented an inexact-SQP
+variant, which results in sub-problems comparable to linear
+SLS and reduces the computation times compared to state-
+of-the-art methods (SQP, IPOPT). We showcased the method
+for the control of a rigid body in rotation with constraints on
+the states and inputs. We showed that a robust formulation
+is needed for the constraints to be robustly satisfied, that a
+linearized model may not be sufficient, and that the optimized
+affine error feedback improves the overall performance.
+Considering a receding horizon implementation, as is typical
+in robust MPC, including a corresponding recursive feasibility
+and stability analysis is left for future work.
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+Antoine P. Leeman received a Master degree in
+aerospace engineering from the University of Li`ege,
+Belgium and a Diplˆome d’Ing´enieur (MSc) from
+ISAE-SUPAERO, France, both in 2018. After his
+research exchange in the Korea Advanced Institute
+of Science and Technology (KAIST), South Korea,
+he was working as a Young Graduate Trainee at
+the European Space Agency (ESA), the Netherlands,
+within the Guidance, Navigation and Control (GNC)
+section from 2018 to 2020. Since 2020, he is a Ph.D.
+candidate at the Institute for Dynamic Systems and
+Control (IDSC) at ETH Z¨urich, Switzerland. His research interests include
+model predictive control, and control of robotics and aerospace systems.
+Johannes K¨ohler received his Master degree in
+Engineering Cybernetics from the University of
+Stuttgart, Germany, in 2017. In 2021, he obtained
+a Ph.D. in mechanical engineering, also from the
+University of Stuttgart, Germany, for which he re-
+ceived the 2021 European Systems & Control Ph.D.
+award. He is currently a postdoctoral researcher
+at the Institute for Dynamic Systems and Control
+(IDSC) at ETH Z¨urich. His research interests are in
+the area of model predictive control and control and
+estimation for nonlinear uncertain systems.
+Andrea Zanelli received a BSc degree in Automa-
+tion Engineering from Politecnico di Milano and
+an MSc degree in Robotics, Systems and Control
+from ETH Zurich in 2012 and 2015, respectively.
+He pursued a Ph.D. at the Systems Control and Op-
+timization Laboratory at the University of Freiburg,
+Germany. Since 2021, he is a postdoctoral researcher
+at the Institute for Dynamic Systems and Control
+at ETH Zurich. His research focuses on the de-
+velopment and software implementation of efficient
+numerical methods for embedded optimization and
+nonlinear model predictive control with numerical and system theoretic
+guarantees.
+Samir Benanni has a Ph.D in aerospace engineering
+from Delft University, Faculty of Aerospace Engi-
+neering. He is specialized in the field of dynamical
+systems and robust control theory with application
+to space flight controls problem. He is at the Eu-
+ropean Space Agency (ESA) technology center as
+a Guidance Navigation and Control (GNC) Fellow
+and Senior Advisor to the GNC division. In the last
+two decades relevant efforts were made in infus-
+ing robust control technologies enabling challenging
+ESA missions. Among these were, LISA Pathfinder,
+Rosetta and VEGA launch vehicle family and many others. He is conducting
+various technology maturation programs in the domain of space transportation,
+exploration, science and new space missions. He is currently working on GNC
+validation and verification technologies, real-time optimized and data-driven
+guidance and control technologies for the next generation ESA technology
+demonstrator platforms. He is a member of various professional organisations
+such as IEEE, AIAA.
+Melanie N. Zeilinger is an Associate Professor at
+ETH Zurich, Switzerland. She received the Diploma
+degree in engineering cybernetics from the Uni-
+versity of Stuttgart, Germany, in 2006, and the
+Ph.D. degree with honors in electrical engineering
+from ETH Zurich, Switzerland, in 2011. From 2011
+to 2012 she was a Postdoctoral Fellow with the
+Ecole Polytechnique Federale de Lausanne (EPFL),
+Switzerland. She was a Marie Curie Fellow and
+Postdoctoral Researcher with the Max Planck In-
+stitute for Intelligent Systems, T¨ubingen, Germany
+until 2015 and with the Department of Electrical Engineering and Computer
+Sciences at the University of California at Berkeley, CA, USA, from 2012 to
+2014. From 2018 to 2019 she was a professor at the University of Freiburg,
+Germany. Her current research interests include safe learning-based control,
+as well as distributed control and optimization, with applications to robotics
+and human-in-the-loop control.
+
diff --git a/UNE4T4oBgHgl3EQfMAxr/content/tmp_files/load_file.txt b/UNE4T4oBgHgl3EQfMAxr/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,798 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf,len=797
+page_content='1  Robust Nonlinear Optimal Control  via System Level Synthesis  Antoine P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Leeman1, Johannes K¨ohler1, Andrea Zanelli1, Samir Bennani2, and Melanie N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Zeilinger1  Abstract—This paper addresses the problem of finite horizon  constrained robust optimal control for nonlinear systems subject  to norm-bounded disturbances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To this end, the underlying  uncertain nonlinear system is decomposed based on a first-  order Taylor series expansion into a nominal system and an  error (deviation) described as an uncertain linear time-varying  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' This decomposition allows us to leverage system level  synthesis to optimize an affine error feedback while planning the  nominal trajectory and ensuring robust constraint satisfaction  for the nonlinear system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The proposed approach thereby results  in a less conservative planning compared with state-of-the-  art techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' A tailored sequential quadratic programming  strategy is proposed to solve the resulting nonlinear program  efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We demonstrate the benefits of the proposed approach  to control the rotational motion of a rigid body subject to state  and input constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Index Terms—NL predictive control, Nonlinear systems, Opti-  mal control, Robust control, System level synthesis  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' INTRODUCTION  Robust nonlinear optimal control represents one of the cen-  tral problems in many safety-critical applications, involving,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', robotic systems, drones, spacecraft, and many others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  While this problem has been extensively studied in the litera-  ture [1], and rigorous constraint satisfaction properties can be  derived in the presence of disturbances (see robust predictive  control formulations, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', [2]–[4]), this is commonly achieved  at the cost of introducing conservativeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The robust control design task is traditionally divided into  two main steps: the optimization of the nominal trajectory [5],  [6] and the offline design of a stabilizing feedback [3] compen-  sating for modeling errors or disturbances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To ensure robust  satisfaction of safety-critical state constraints, the nominal tra-  jectory optimization is coupled with the over-approximation of  the error reachable set using, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', tubes or funnels [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' There  exists a wide range of techniques to construct corresponding  over-approximations of the tubes/funnels (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', [2]–[4],  [7]–[10]), however, these methods can introduce significant  conservatism, especially due to the choice of an offline fixed  error feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We address this limitation by proposing a  method to solve the robust trajectory optimization while jointly  This work has been supported by the European Space Agency under  OSIP 4000133352, the Swiss Space Center, and the Swiss National Science  Foundation under NCCR Automation (grant agreement 51NF40 180545).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  1Antoine P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Leeman, Johannes K¨ohler, Andrea Zanelli, and Melanie N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Zeilinger are with the Institute for Dynamic Systems and Control, ETH  Z¨urich, Z¨urich 8053, Switzerland (email: aleeman@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='ch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' jkoehle@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='ch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  zanellia@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='ch;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' mzeilinger@ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='ch)  2Samir Bennani is with the European Space Agency, Noordwijk 2201AZ,  The Netherlands (email: samir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='bennani@esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='int)  Disturbance and linearization error  dk = wk + r(xk, uk, zk, vk)  Nominal dynamics  zk+1 = f(zk, vk)  SLS-based LTV error reachable set  xk ∈ zk ⊕ Dk  Theorem III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  (xk, uk) ∈ P  ∀wk ∈ W  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 1: Decomposition of the uncertain nonlinear dynamics  into nominal nonlinear dynamics, an error term made up of  the disturbance and linearization error (Section III-A), and an  LTV error system used for the SLS-based error reachable sets  (Section III-B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' This decomposition enables optimization over  affine error feedback with robust constraint satisfaction for the  nonlinear uncertain system (Section III-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  optimizing over the error feedback and ensuring guaranteed  robust constraint satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The conservativeness of an offline-determined error feed-  back policy can be addressed for linear systems by directly  predicting robust control invariant polytopes [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Compare  also [12] for a recent approach for nonlinear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Another  systematic approach to jointly optimize a linear feedback  while considering constraints is presented in [13], [14], which  extends approximate ellipsoidal disturbance propagation [10],  [15] to include optimized feedback policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Other methods  to obtain feedback policies and (optimal) trajectories, which  come without principled guarantees for robust constraint sat-  isfaction (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' [16]–[18]), are used in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  However, all the above mentioned methods that jointly  optimize over nominal trajectories and feedback policies result  in an over- or under-approximation of the true reachable  set, even for linear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We overcome this limitation by  leveraging system level synthesis (SLS) [19]–[21], or equiva-  lently affine disturbance feedback [22]–[24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In particular, for  linear systems, SLS allows to jointly optimize a linear error  feedback policy and nominal trajectory and thereby provide  a tight reachable set at least for linear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' There exist  conceptual extensions of the SLS framework to nonlinear  systems [25]–[27], however these existing approaches do not  consider (robust) constraint satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='04943v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='OC]  12 Jan 2023  2  Contribution: We propose a novel approach for optimal  control of nonlinear systems with robust constraint satisfac-  tion, using SLS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 1, the nonlinear system is  decomposed into a nominal nonlinear system and a linear time-  varying (LTV) error (deviation) system constructed around  the online-optimized nominal trajectory, which includes an  online-optimized error term corresponding to the linearization  error (Section III-A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We apply a linear SLS formulation  (Section III-B) to the LTV error system to jointly optimize the  affine error feedback and the nominal trajectory and obtain  an over-approximation of the reachable set (funnel) for the  nonlinear system (Section III-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The presented method has  the following advantages when compared to the literature:  The nominal trajectory and the affine error feedback are  optimized jointly to decrease conservativeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The reachable set used for robust constraint satisfaction  is tight for linear systems, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', the only source of con-  servativeness stems from the over-approximation of the  linearization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  In addition, we provide an inexact sequential quadratic pro-  gramming (SQP) algorithm to solve the corresponding nonlin-  ear program (NLP), which can substantially reduce the compu-  tation times compared to other SQP methods, or IPOPT [28],  especially when the dynamics of the system are described by  an expensive to integrate ordinary differential equation (Sec-  tion IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Furthermore, this inexact SQP algorithm ensures that  the resulting QP sub-problems are comparable to linear SLS  problems [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Overall, the proposed approach can be applied  to any three times continuously differentiable nonlinear system  and requires no complicated offline design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Finally, we demonstrate the benefits of the proposed method  using a nonlinear numerical example and provide a comparison  with open-loop (robust) trajectory optimization and optimal  control based on the linearized dynamics to highlight the  reduced conservativeness (Section V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Notation: We define the set NT := {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , T − 1} where  T is a natural number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We denote stacked vectors or matrices  by (a, b) = [a⊤ b⊤]⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' For a vector r ∈ Rn, we denote its  ith component by ri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Let R be the set of real numbers, and  0p,q ∈ Rp,q be a matrix of zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Let LT,p×q denote the set of  all block lower-triangular matrices with the following structure  M =  �  ����  M 0,0  0p,q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  0p,q  M 1,1  M 1,0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  0p,q  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  M T −1,T −1  M T −1,T −2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  M T −1,0  �  ���� ,  (1)  where M i,j ∈ Rp×q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The block diagonal matrix consisting  of matrices A1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , AT is denoted by blkdiag(A1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , AT ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The matrix I denotes the identity with its dimensions ei-  ther inferred from the context or indicated by the subscript,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', Inx ∈ Rnx×nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Let Bm  ∞, be the unit ball defined by  Bm  ∞ := {d ∈ Rm| ∥d∥∞ ≤ 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' For a matrix M ∈ Rn×m,  the ∞-norm is given by ∥M∥∞ := maxd∈Bm  ∞ ∥Md∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' For  two sets W1, W2 ⊆ Rn, the Minkowski sum is defined as  W1 ⊕ W2 := {w1 + w2| w1 ∈ W1, w2 ∈ W2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We define  Wk := W × · · · × W  �  ��  �  k times  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' For a sequence of vectors wk ∈ Wk ⊆  Rm and k ∈ N, we define w0:k := (w0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , wk) ∈ W0:k :=  W0 × · · · × Wk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' PROBLEM FORMULATION  We consider the following robust nonlinear optimal control  problem:  min  π(·)  JT (¯x, π(·)),  (2a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  xk+1 = f(xk, uk) + wk ∀k ∈ NT ,  (2b)  x0 = ¯x,  (2c)  uk = πk(x0:k) ∀k ∈ NT ,  (2d)  (xk, uk) ∈ P ∀k ∈ NT +1 ∀wk ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (2e)  The dynamics are given by (2b), with the state xk ∈ Rnx, the  input uk ∈ Rnu and the disturbance wk ∈ W ⊆ Rnx at time  step k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The initial condition is given by ¯x ∈ Rnx in (2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The  control input is obtained by optimizing over general causal  policies πk (2d), with π = (π0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , πT ) : R(T +1)nx �→  R(T +1)nu, and the last input uT is kept in the problem  formulation for notational convenience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We primarily focus  on the robust constraint satisfaction (2e) and, for simplicity,  consider a general cost (2a) over the prediction horizon T  which does not depend on w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Problem (2) is not computationally tractable because of the  optimization over the general feedback policy π(·) and the  robust constraint satisfaction required in (2e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Consequently,  the goal is to find a feasible, but potentially sub-optimal,  solution to this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To this end, we define a nominal  trajectory as  zk+1 = f(zk, vk) ∀k ∈ NT , z0 = ¯x,  (3)  and restrict the policy to a causal affine time-varying error  feedback  πk(x0:k) = vk +  k−1  �  j=0  Kk−1,j∆xk−j  (4)  with πk(x0:k) : R(k+1)nx �→ Rnu, vk ∈ Rnu, zk ∈ Rnx,  Ki,j ∈ Rnu×nx, and the errors ∆xk := xk − zk, ∆uk :=  uk −vk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We also consider the following standard assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Assumption II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The nonlinear dynamics (2b) f : Rnx ×  Rnu �→ Rnx are three times continuously differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Assumption II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The constraint set P (2e) is a compact  polytopic set with P := {(x, u)| c⊤  i (x, u) + bi ≤ 0, ∀i ∈ NI},  where ci ∈ Rnx+nu and bi ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Assumption II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The disturbance set is given by  wk ∈ W = {Ed| d ∈ Bnw  ∞ } = EBnw  ∞ ⊆ Rnx,  (5)  with E ∈ Rnx×nw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' ROBUST NONLINEAR OPTIMAL CONTROL VIA SLS  In this section, we derive the main result of the paper using  the steps depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', we propose a formulation to  optimize over affine policies (4) that provide robust constraint  satisfaction for the nonlinear system (2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We decompose  3  the nonlinear system equivalently as the sum of a nominal  nonlinear system and an LTV error system that accounts both  for the local linearization error (Section III-A) and the additive  disturbance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Using established SLS tools for LTV systems  (Section III-B), we parameterize the closed-loop response for  this LTV system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' As a result, we obtain an optimization  problem that jointly optimizes the nominal trajectory (3) and  the error feedback (4), and that guarantees robust constraint  satisfaction (Section III-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Over-approximation of nonlinear reachable set  The goal of this section is to decompose the uncertain  nonlinear system into a nominal nonlinear system and an LTV  error system subject to some disturbance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The linearization of  the dynamics (3) around a nominal state and input (z, v) is  characterized by the Jacobian matrices:  A(z, v) := ∂f  ∂x  ����  (x,u)=(z,v)  , B(z, v) := ∂f  ∂u  ����  (x,u)=(z,v)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' (6)  Using the Lagrange form of the remainder of the Taylor series  expansion, we obtain  f(x, u) + w  (3)= f(z, v)  + A(z, v)(x − z) + B(z, v)(u − v)  + r(x, u, z, v) + w  �  ��  �  =:d  ,  (7)  with the remainder r : Rnx×Rnu×Rnx×Rnu �→ Rnx and both  the disturbance w and the remainder r(x, u, z, v) are lumped  in the disturbance d := r(x, u, z, v) + w ∈ Rnx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  To bound the remainder, we consider the (symmetric) Hes-  sian Hi : Rnx+nu �→ R(nx+nu)×(nx+nu) of the ith component  of f, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=',  Hi(ξ) =  �  ∂2fi  ∂x2  ∂2fi  ∂x∂u  ∗  ∂2fi  ∂u2  ������  (x,u)=ξ  ,  (8)  where ξ ∈ Rnx+nu lies between the linearization point (z, v)  and the evaluation point (x, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We define the constant1 µ ∈  Rnx×nx as  µ := diag(µ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , µnx), µi := 1  2  max  ξ∈P,∥h∥∞≤1 |h⊤Hi(ξ)h|,  (9)  and the error ek := (∆xk, ∆uk) ∈ Rnx+nu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Given Assumptions II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 and II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2, the re-  mainder in (7) satisfies  |ri(x, u, z, v)| ≤ ∥e∥2  ∞µi,  (10)  for any (x, u) ∈ P, (z, v) ∈ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  1Note that max∥h∥∞≤1 |h⊤Hh| ≤ �  i  �  j |Hij|, with Hij, the element  on the ith row and jth column of the matrix H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Applying the definition of the Lagrange form of the  remainder, for all (x, u, z, v) and for all i, there exists a ξ ∈ P  (using convexity) such that  |ri(x, u, z, v)| = 1  2|e⊤Hi(ξ)e|  ≤ max  ξ∈P  1  2|e⊤Hi(ξ)e|  (11)  (9)  ≤ ∥e∥2  ∞µi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The constants µi are computed offline, which is the only  offline design required for the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Intuitively,  the magnitude of µi quantifies the nonlinearity of the system,  which will be incorporated in the disturbance propagation in  the proposed formulation (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Due to Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 and Assumption II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3, the combined  disturbance d from (7) satisfies  d := w + r(x, u, z, v) ∈ EBnw  ∞ ⊕ ∥e∥2  ∞µBnx  ∞  = [E, ∥e∥2  ∞µ]Bnw+nx  ∞  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (12)  Given a bound on ∥e∥∞, we can compute an outer approxi-  mation of the reachable set of the nonlinear system, using the  following LTV error system  ∆xk+1 = Ak∆xk + Bk∆uk + dk ∀k ∈ NT +1, ∆x0 = 0nx,  (13)  with Ak := A(zk, vk), Bk := B(zk, vk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Similar LTV error dynamics are used in [8]–[10], [12], [14]  to over-approximate the reachable set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To optimize affine error  feedback (4) while ensuring robust constraint satisfaction of  the nonlinear system based on this LTV error dynamics, we  next study the robust optimal control problem for the special  case of LTV systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Robust optimal control for LTV systems  In this section, we study the parameterization of affine  feedback policies for LTV systems, which will provide the  basis for the employed parameterization of affine error feed-  back for nonlinear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We show that by using SLS  techniques [19] we can jointly optimize the error feedback  and nominal trajectory of any LTV system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Consider an LTV  system of the form  ˜xk+1 = ˜Ak˜xk + ˜Bk˜uk + ˜wk ∀k ∈ NT , ˜x0 = 0nx,  (14)  with ˜Ak ∈ Rnx×nx, ˜Bk ∈ Rnx×nu, and  ˜wk ∈ ˜Wk := ˜EkBn˜  w  ∞ ,  (15)  with some ˜Ek ∈ Rnx×n˜  w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The dynamics (14) are written  compactly as  ˜x = Z ˜  A˜x + Z ˜B˜u + ˜w,  (16)  with  ˜w  :=  ( ˜w0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , ˜wT −1)  ∈  RT nx,  ˜x  :=  (˜x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , ˜xT )  ∈  RT nx,  ˜u  :=  (˜u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , ˜uT )  ∈  RT nu,  ˜  A  :=  blkdiag( ˜A1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , ˜AT −1, 0nx,nx)  ∈  LT,nx×nx,  4  ˜B  :=  blkdiag( ˜B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , ˜BT −1, 0nx,nu)  ∈  LT,nx×nu  and  the block-lower shift matrix Z ∈ LT,nx×nx is given by  Z :=  �  ����  0nx,nx  0nx,nx  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  0nx,nx  Inx  0nx,nx  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  0nx,nx  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  0nx,nx  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Inx  0nx,nx  �  ���� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (17)  We introduce the causal linear feedback ˜u =  ˜K˜x, ˜K ∈  LT,nu×nx i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', ˜uk = �k−1  j=0 ˜Kk−1,j ˜xk−j, ˜Ki,j ∈ Rnu×nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Using this feedback, we can write the closed-loop dynamics  as  ˜x = Z( ˜  A + ˜B ˜K)˜x + ˜w, ˜u = ˜K˜x, ˜x0 = 0nx,  (18)  or equivalently as  �˜x  ˜u  �  =  � (I − Z ˜  A − Z ˜B ˜K)−1  ˜K(I − Z ˜  A − Z ˜B ˜K)−1  �  ˜w =:  �˜Φx  ˜Φu  �  ˜w,  (19)  with  ˜Φx =  �  ��  ˜Φ0,0  x  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  ˜ΦT −1,T −1  x  · ·  ˜ΦT −1,0  x  �  �� ∈ LT,nx×nx,  ˜Φu =  �  ��  ˜Φ0,0  u  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  ˜ΦT −1,T −1  u  · ·  ˜ΦT −1,0  u  �  �� ∈ LT,nu×nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (20)  The matrices ˜Φx and ˜Φu are called the system responses  from the disturbance to the closed-loop state and input, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The following proposition from the literature shows  that the closed-loop response under arbitrary affine feedback  is given by all system responses in a linear subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  [19, adapted from Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1] Let  ˜w ∈ ˜W0:T −1 be an arbitrary disturbance sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Any ˜x, ˜u  satisfying (18), also satisfy (19) with some ˜Φx ∈ LT,nx×nx,  ˜Φu ∈ LT,nu×nx lying on the affine subspace  �  I − Z ˜  A  − Z ˜B  � � ˜Φx  ˜Φu  �  = I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (21)  Let ˜Φx and ˜Φu be arbitrary matrices satisfying (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Then the  corresponding ˜x and ˜u computed with (19) also satisfy (18)  with ˜K = ˜Φu ˜Φ−1  x  ∈ LT,nu×nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The proof follows directly from [19, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1] for  systems with zero initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Note that this proposition holds for any LTV system and in  particular for (13), where the matrices ˜  A and ˜B depend on the  nominal trajectory (z, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Next, we show how the parameterization (21) can be utilized  to exactly solve Problem (2) with affine feedback in the case  of LTV systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To this end, we introduce a nominal LTV  system  ˜zk+1 = ˜Ak˜zk + ˜Bk˜vk ∀k ∈ NT , ˜z0 = ˜x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (22)  The error dynamics are written as  ˜xk+1 − ˜zk+1 = ˜Ak(˜xk − ˜zk) + ˜Bk(˜uk − ˜vk) + ˜wk ∀k ∈ NT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (23)  By considering a causal affine error feedback of the form  ˜u = ˜v + ˜K(˜x − ˜z), ˜u0 = ˜v0, ˜K ∈ LT,nu×nx,  (24)  we can apply Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2 to characterize the system  response of the LTV error system (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Note that the linear  feedback on the error system corresponds to the affine feed-  back in (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The closed-loop error on the states and inputs  is expressed using the definition of ˜Φx and ˜Φu in (19) for the  LTV system (23), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=',  ˜ek = (˜xk, ˜uk) − (˜zk, ˜vk) =  k−1  �  j=0  ˜Φk−1,j ˜wk−1−j ∀k ∈ NT +1,  (25)  where ˜Φk,j :=  �  ˜Φk,j  x , ˜Φk,j  u  �  , ˜Φx ∈ LT,nx×nx and ˜Φu ∈  LT,nu×nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Given Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2, we can provide tight con-  ditions for robust state and input constraint satisfaction for the  LTV system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' There exists a causal error feedback of the  form (24) such that for any ˜w ∈ ˜WT  c⊤  i (˜xk, ˜uk) + bi ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI,  (26)  with (˜xk, ˜uk) according to (14) if and only if there exist  matrices ˜Φx, ˜Φu and a nominal trajectory satisfying (21), (22),  and  c⊤  i (˜zk, ˜vk) + bi  +  k−1  �  j=0  ∥c⊤  i ˜Φk−1,j ˜Ek−1−j∥1 ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' (27)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' As per Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2, the LTV error system can be  written with Equation (25), and we can apply directly [22,  Example 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Namely, ∀k ∈ NT +1 ∀i ∈ NI, we have  max  ˜w0:k−1∈ ˜W0:k−1 c⊤  i (˜xk, ˜uk) + bi  (28)  (25)  = c⊤  i (˜zk, ˜vk) +  max  ˜w0:k−1∈ ˜W0:k−1  k−1  �  j=0  c⊤  i ˜Φk−1,j ˜wk−1−j + bi  = c⊤  i (˜zk, ˜vk) +  k−1  �  j=0  max  ˜  wj∈ ˜Wk−1−j  c⊤  i ˜Φk−1,j ˜wk−1−j + bi  (15)  = c⊤  i (˜zk, ˜vk) +  k−1  �  j=0  ���c⊤  i ˜Φk−1,j ˜Ek−1−j  ���  1 + bi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Remark III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' A similar reformulation for ellipsoidal distur-  bances or more general polytopic disturbances can be found  in [22, Example 7-8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Likewise, the result can be naturally  extended to time-varying constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  We have presented conditions for affine error feedback with  guaranteed constraint satisfaction for a given LTV system  using the following three components in the SLS formula-  tion: the nominal trajectory (22), the affine error feedback  parameterization (21), and a description of the disturbance set  ˜W (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In combination, Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2 characterizes the  system response of the error dynamics, while Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3  provides tight bounds on the nominal trajectory and system  response to ensure robust constraint satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' By combining  5  these two results, we can solve the robust optimal control prob-  lem (2) for LTV dynamics (23), affine error feedback (24), and  disturbances of the form (15) using the following optimization  problem:  min  ˜z,˜v0,˜v,˜Φ  JT (¯x, ˜z, ˜v, ˜Φ),  (29a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  �  I − Z ˜  A  − Z ˜B  � � ˜Φx  ˜Φu  �  = I,  (29b)  ˜zk+1 = ˜Ak˜zk + ˜Bk˜vk ∀k ∈ NT , z0 = ¯x,  (29c)  k−1  �  j=0  ∥c⊤  i ˜Φk−1,j ˜Ek−1−j∥1  (29d)  + c⊤  i (˜zk, ˜vk) + bi ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI,  where we define ˜Φ := (˜Φx, ˜Φu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Specifically, the solution  of (29) provides a jointly optimized nominal trajectory ˜z,  ˜v and linear error feedback ˜K = ˜Φu ˜Φ−1  x  which guarantee  robust satisfaction of the constraints for the closed-loop state  and input trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Problem (29) is a reformulation of  established results in the literature (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', [19], [29]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In  the following, we address the nonlinear problem (29) by  merging the robust optimal control for LTV systems with the  linearization error bounds from Section III-B for nonlinear  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Robust nonlinear finite-horizon optimal control problem  In this section, given the parameterization of the affine  error feedback for the LTV system (Section III-B) and the  linearization error of the nonlinear system (Section III-A), we  are in a position to introduce the main result of this paper  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In particular, we will show in Theorem III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 that  the following NLP provides a feasible solution to the robust  optimal control problem in (2):  min  z,v0,v,Φ,τJT (¯x, z, v, Φ),  (30a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' [I − ZA(z, v)  − ZB(z, v)]  �Φx  Φu  �  = I,  (30b)  zk+1 = f(zk, vk) ∀k ∈ NT , z0 = ¯x,  (30c)  k−1  �  j=0  ∥c⊤  i Φk−1,j[E, τ 2  k−1−jµ]∥1  (30d)  + c⊤  i (zk, vk) + bi ≤ 0 ∀k ∈ NT +1 ∀i ∈ NI,  k−1  �  j=0  ∥Φk−1,j[E, τ 2  k−1−jµ]∥∞ ≤ τk ∀k ∈ NT ,(30e)  where we denote a feasible solution as {z⋄, v⋄  0, v⋄, Φ⋄, τ ⋄},  with z := (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , zT ) ∈ RT nx, v := (v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , vT ) ∈ RT nu,  A(z, v)  :=  blkdiag(A1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , AT −1, 0nx,nx)  ∈  LT,nx×nx,  B(z, v) := blkdiag(B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , BT −1, 0nx,nu) ∈ LT,nx×nu, τ =  (τ0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , τT −1) ∈ RT , Φx ∈ LT,nx×nx, Φu ∈ LT,nu×nx and  µ according to (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The nominal prediction is given by (30c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Equation (30b) computes the system response for the lineariza-  tion around the nominal trajectory z, v (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The auxiliary variable τk is introduced to upper bound ∥ek∥∞,  which is used to obtain a bound on the linearization error  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2), which depends on all previous τj,  j = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , k − 1, giving (30e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Using Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3, the  constraints are tightened with respect to both the additive  disturbance wk ∈ W and the linearization error ∥ek∥∞µ  combined as in (12), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', the additive uncertainties on the  LTV error lie in the set EBnw  ∞ ⊕ ∥e∥2  ∞µBnx  ∞ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' As a result,  the reachable set of the nonlinear system (2b) at time step k,  in closed-loop with the affine error feedback computed as in  Theorem III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 satisfies  xk ∈ z⋄  k  k−1  �  j=0  Φ⋄k−1,j  x  [E, τ ⋄2  k−1−jµ]Bnx+nw  ∞  =: Dk ∀k ∈ NT +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (31)  The following theorem summarizes the properties of the  proposed NLP (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Theorem III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Given Assumptions II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1, II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2 and II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3, suppose  the optimization problem (30) is feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Then, the affine error  feedback u = v⋄ + K⋄(x − z⋄), K⋄ = Φ⋄  uΦ⋄  x  −1, u0 = v⋄  0  provides a feasible solution to Problem (2), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', the closed-  loop trajectories of system (2b) under this error feedback  robustly satisfy the constraints (2e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' First, the constraints (30c) ensure that the nominal tra-  jectory satisfies the dynamics (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Then, we use a Taylor series  approximation with respect to the nominal trajectory (30c),  resulting in the LTV error system (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We apply Proposi-  tion III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2 to the LTV error system (13) and the constraint (30b)  implies that the closed-loop trajectories of the error system  satisfy  �  x − z  u − v  �  =  �  Φx  Φu  �  d,  (32)  with d := (d0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' , dT −1) ∈ RT nx given by (12), x, u  satisfying (2b) and z, v satisfying (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In the following, we  show by induction that the auxiliary variables τ ∈ RT satisfy  ∥ej∥∞ ≤ τj ∀j ∈ NT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (33)  Inequality (33) holds for j = 0 since ∥e0∥∞ = 0 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' (30d))  and τ0 ≥ 0 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' (30e)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Note that, as per Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1, the  disturbance on the LTV error system dk satisfies (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Then,  assuming Inequality (33) holds ∀j ∈ Nk−1, we have  dj ∈ [E, ∥ej∥2  ∞µ]Bnx+nw  ∞  ⊆ [E, τ 2  j µ]Bnx+nw  ∞  ∀j ∈ Nk−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  (34)  Hence, we obtain  ∥ek∥∞  (32)  =  ������  k−1  �  j=0  Φk−1,jdk−1−j  ������  ∞  (35)  (34)  ≤  k−1  �  j=0  ∥Φk−1,j[E, τ 2  k−1−jµ]∥∞  (30e)  ≤ τk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Therefore, the constraints (30e) ensure that Inequality (33)  holds for any realization of the disturbance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Finally, the  constraint (30d) in combination with Equation (34) ensures  that the constraints are robustly satisfied, analogously to  Proposition III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3, which can be seen by substituting ˜Ek for  [E, τ 2  kµ] with n˜w = nx + nw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  6  Remark III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' When the disturbance w is set to zero with E =  0nx,nw, we recover a nominal trajectory optimization problem  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', [5]) as the constraints (30d) reduce to a nominal  constraint, with τ = 0T , independent of Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In case the system  is linear (µ = 0nx,nx), we recover the linear SLS formulation  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' [20, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' (26)]) since τ does not enter the constraints (30d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Remark III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The considered handling of the nonlinear  system is based on a linearization along an online optimized  nominal trajectory and is comparable to [8], [12]–[14],  where the latter results also provide an affine feedback policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  However, the over-approximation of the reachable set in [13]  is based on the ellipsoidal propagation in [10], where even  the linear case is not tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In contrast to [9], both the  linearized system A, B and the bound on the remainder term  τ are adjusted online based on the jointly optimized nominal  trajectory z, v, which avoids conservativeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  In the next section, we present an inexact SQP variant to  solve the NLP (30), with a reduced computational footprint  with respect to standard SQP methods or IPOPT and results  in QP sub-problems comparable to linear SLS problems [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' INEXACT SQP FOR SLS-BASED ROBUST NONLINEAR  OPTIMAL CONTROL  Standard methods to solve the NLP (30) (nonlinear interior  point methods [28], SQP) use the derivatives of the functions  used in the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In general, for a function in Rn �→ R,  evaluating its Jacobian and Hessian has a runtime cost up  to respectively 2n and 8n times the cost of evaluating the  function alone [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' This section discusses how to obtain a  feasible solution to (30) via a tailored inexact SQP algorithm  to speed up the computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The proposed SQP avoids the  derivatives of the constraint (30b), and hence the Hessian of  the dynamics, and only uses the Jacobians of the dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  As evaluating the derivatives is often very expensive computa-  tionally when solving an NLP, we can expect a speedup of up  to 1+2n+8n  1+2n  when the evaluation of the dynamics dominates  the computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To outline the algorithm and its  properties, we utilize a compact formulation of Problem (30):  min  y  JT (¯x, y),  (36a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  g(y) = 0, h(y) ≤ 0, s(y) ≤ 0,  (36b)  where y ∈ Rny collects Φ, z, v0, v, and τ in a vector, as well  as the auxiliary variables needed to encode the 1- and ∞-  norms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Here, g(y) = 0 and h(y) ≤ 0 correspond respectively  to the nonconvex equality constraints (30b)-(30c) and the  nonconvex inequality constraints (30d)-(30e), while s(y) ≤ 0  corresponds to the additional linear inequality constraints on  the auxiliary variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  A standard SQP implementation iteratively solves the fol-  lowing QP sub-problems  min  ∆y  ∂  ∂yJT (¯x, y)  ����  y=ˆy  ∆y + 1  2∆y⊤HJ∆y,  (37a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  g(ˆy) + ∂  ∂yg(y)  ����  y=ˆy  ∆y = 0,  (37b)  h(ˆy) + ∂  ∂yh(y)  ����  y=ˆy  ∆y ≤ 0,  (37c)  s(ˆy + ∆y) ≤ 0,  (37d)  where we denote the solution at the previous iteration with the  symbol ˆ and define ∆y := y − ˆy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The matrix HJ ∈ Rny×ny  is an approximation of the Hessian of the Lagrangian (see,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', [31] for practical approximations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  In the following, we describe an inexact SQP algorithm [32]  to improve the computational efficiency and highlight the  numerical similarities with linear SLS [19], [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In particular,  the linearization of (30b) is given by  [I − ZA(ˆz, ˆv)  −ZB(ˆz, ˆv)] Φ  (38)  +  T (nx+nu)  �  i=1  ∂  ∂ξi  [−ZA − ZB]  ����  (z,v)=(ˆz,ˆv)  ˆΦ(ξi − ˆξi) = I,  where ξi is the ith element of the vector (z, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The proposed  inexact SQP algorithm replaces the equality constraint (38) by  [I − ZA(ˆz, ˆv)  −ZB(ˆz, ˆv)] Φ = I,  (39)  within the QP (37), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', the Jacobians with respect to ξi in the  constraint (38) are set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Thus, the proposed inexact SQP  avoids evaluating second-order derivatives of the dynamics (3),  leading to improved computation times as shown in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The numerical complexity of each QP sub-problem of the  inexact SQP scheme is similar to a linear SLS problem (29),  as each constraint of the resulting QPs, except (30e), has its  analog in (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Under  several  mild  assumptions,  inexact  SQP  us-  ing (39) converges to a feasible, but suboptimal, solution  {Φ⋄, z⋄, v⋄  0, v⋄, τ ⋄} of the original NLP (30) (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', [33]  for the proof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Remark IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' To decrease the number of decision variables  and improve the numerical efficiency, one could consider K  to be block-banded, as in [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' It is important to note that  the feedback K in (24) can be implemented without explicitly  computing the inverse of Φx [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Remark IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Both SQP and inexact SQP are commonly  combined with a globalization strategy such as trust-region  or line search methods to ensure convergence when the initial  guess is relatively far from a local optimum [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' CASE STUDY: SATELLITE ATTITUDE CONTROL  The following example demonstrates the benefits of the  proposed approach where we optimize jointly the error feed-  back and the nominal trajectory for nonlinear systems with  additive disturbances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Moreover, it demonstrates the numerical  properties of the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In particular, we study a nonlinear  aerospace problem, the constrained attitude control of a satel-  lite [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  7  0  2  4  6  8  10  Step k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='8  1  Quaternion q  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  Constraints  Uncertain sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  LTV  Nonlinear reach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' set  Nominal  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  Angular speed !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  0  2  4  6  8  10  Step k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  0  2  4  6  8  10  Step k  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1  Control input u  0  2  4  6  8  10  Step k  0  2  4  6  8  10  Step k  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 2: Robust nonlinear optimal control for the attitude control of a spacecraft computed with inexact SQP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' For each state and  input, the reachable set (see Equation (31)) around the nominal trajectory depicts the online-computed reachable sets (green)  and its LTV approximation (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The reachable sets are designed to remain within the constraints (black), and the sample  trajectory (red) is hence guaranteed to stay therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' System and constraints  We consider the following Euler’s equation of the dynamics  ˙z =  �  Ω(ω)q  I−1  S (v − ω × (ISω))  �  ,  (40)  with states z := (q, ω), attitude quaternion q ∈ R4, angular  rotation rate ω ∈ R3, input torque v ∈ Rnu, nx = 7, nu = 3  and × is the cross product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The symmetric inertia matrix of  the satellite is IS = diag(5, 2, 1) ∈ R3×3 and  Ω(ω) := 1  2  �  ���  0  −ω1  −ω2  −ω3  ω1  0  ω3  −ω2  ω2  −ω3  0  ω1  ω3  ω2  −ω1  0  �  ��� ,  (41)  with Ω : R3 �→ R4×4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The dynamics are discretized using  the 4th order Runge–Kutta method, using a time step of one,  which results in a negligible discretization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We consider  a bounded disturbance applied to the system described by (5)  with E = 5 · 10−3[03,4 I3]⊤ ∈ R7×nw with nw = 3,  which could stem, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', from the solar radiation pressure, the  flexible modes of the solar panels, the aerodynamic drag,  or any unmodelled dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Additionally, we consider the  constraints −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 ≤ ωi ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 ≤ vi ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='1 for  i = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We use the nominal cost function JT (¯x, z, v) =  �T −1  k=0 ℓ(zk, vk) + ℓT (zT ), with stage cost  ℓ(z, v) = (z −zref)⊤Q(z −zref)+(v−vref)⊤R(v−vref), (42)  and the terminal cost  ℓT (z) = (z − zref)⊤Q(z − zref),  (43)  with Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='7I ∈ R7×7, R = I ∈ R3×3, the reference  zref = (1, 0, 0, 0, 0, 0, 0)⊤, vref = (0, 0, 0)⊤, and the horizon  is T = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' As often seen in numerical optimization, we  consider an additional term to the cost function, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', we use  JT + αy⊤y, with α = 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We approximate the constant  µ ≈ diag(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='699, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='703, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='717, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='635, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='649, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='608, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='635) ∈  R7×7 from Equation (9) for the nonlinear dynamics (40) by  using a Monte-Carlo method with 104 samples for a total  offline computation time of 444 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The initial condition  is ¯x = (¯q, ¯ω), where ¯q is inferred from the Euler angles  (180, 45, 45) ·  π  180 and ¯ω = (−1, −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='5) ·  π  180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  8  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Results  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2  This paper (a)  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='2  Nominal (c)  7x  Linear (b)  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='3  Open-loop (d)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 3: Comparison between the proposed robust nonlinear  optimal control (30) (a), the linear optimal control problem,  based on the linearization around a reference point, applied to  the nonlinear system (b), the nominal trajectory optimization  without robustness guarantees (c), and the (reduced-horizon)  open-loop robust nonlinear optimal control (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The reachable  set (31) around the nominal trajectory (blue) is plotted with a  different color for each time step k, together with the trajectory  with disturbance (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The NLP (30) is solved using the inexact SQP (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' IV)  formulated with Casadi [34] with the QPs solved with  Gurobi [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In addition, a Gauss-Newton approximation of  the Hessian (37a) is used, with a small regularization term,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', we use HJ + γIny instead of HJ in  (37a), with  γ  = 10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We assume convergence when the condition  ∥(∆y, ∆ν)∥∞ ≤ 10−6 is fulfilled, where ∆ν is the decrease  in the dual solution [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  1) Nonlinear system with affine error feedback: For the  problem considered, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 2 shows the solution of the NLP (30)  computed with inexact SQP, which ensures that the trajectories  of the nonlinear system remain robustly within the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The shaded areas correspond to the reachable sets of the  nonlinear system (Equation (31)) (green) and its LTV approx-  imation (blue), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Illustrative disturbance sequences  have been applied and, as ensured by the proposed design, the  resulting trajectory (red) remains within the reachable sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The flexible error feedback parameterization allows the tubes  to grow in some directions and shrink in others to meet the  constraints, which illustrates the flexibility of this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' A  phase plot of the states ω2 and ω3 is also depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 3(a)  for comparison with other approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  2) Comparison with open-loop counterpart: To highlight  the benefits of the proposed method, we solve the NLP (30),  with Φu = 0T nu,T nx, resulting in an open-loop robust formu-  lation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', K = 0T nu,T nx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' For the open-loop case only, we  consider a reduced horizon of T = 6, as a longer horizon  leads to infeasibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Indeed, this open-loop robust method  does not apply error feedback, making the reachable set effec-  tively larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The open-loop robust formulation maintains the  guarantees of robust constraint satisfaction, as the reachable  set or tube always stays within the constraints as depicted in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 3(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Because of the large size of the tube, the nominal  trajectory is forced to move away from the constraints, leading  to poor performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Indeed, for the system considered, the  tube cross-section keeps increasing, which limits both the size  of the disturbance and the horizon that can be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Therefore, the affine error feedback is instrumental to ensure  robust constraint satisfaction for large disturbances without  acting overly conservatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  3) Comparison with nominal counterpart: The method is  also compared with its nominal counterpart, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', where we do  not optimize error feedback and neglect the disturbance (Φx =  0T nx,T nx, Φu = 0T nu,T nx) and hence do not guarantee robust  constraint satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The optimal nominal trajectory satisfies  the constraints, but the trajectory with disturbance results in  significant constraint violations (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 3(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Therefore, it  is crucial to consider the disturbance in the optimal control  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  4) Comparison with linear counterpart: We design a con-  troller based on a linearization of the nonlinear dynamics (40),  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=', we linearize the dynamics around the reference point  (zref, vref) ∈ Rnx+nu, ignoring the nonlinearity (µ = 0nx,nx),  and solve the resulting linear SLS problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Subsequently, we  apply the resulting controller to the nonlinear dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' When  the linearization point is far from the operation point, or when  the linear model is not a good approximation of the nonlinear  system dynamics, the resulting controller leads to poor perfor-  mance and large constraint violations (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 3(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  5) Computation times: To assess the performance of the  two SQP variants (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Section IV), we compare them with  the well-established NLP solver, IPOPT [28] using just-in-  time compilation (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' jit [34]) and MUMPS as a linear solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  The problem was solved on an i9-7940X processor with  32GB of RAM memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Table I shows the comparison in the  number of iterations required until the convergence condition  is satisfied, the solve time, and the optimal cost for the three  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The inexact SQP achieves the fastest convergence  time with negligible difference in minimizer, highlighting the  benefit of this SQP variant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 4 illustrates the convergence  rate of both SQP variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' The speedup between inexact-  SQP and SQP largely depends on the computational cost  of evaluating the Hessians of the dynamics f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Hence, we  expect a larger difference for a stiff system or other high-  order integration methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We observe linear convergence for  both SQP variants, as predicted by the theory in [31], [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' CONCLUSION  We proposed a novel approach to solve finite horizon con-  strained robust optimal control problems for nonlinear systems  subject to additive disturbances, as commonly encountered in  9  0  5  10  15  20  Iteration #  10-6  10-4  10-2  100  102  Primal-dual step size k("y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' "8)k1  inex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' SQP  SQP  conv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' threshold  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' 4: Numerical convergence of SQP and inexact SQP in  terms of primal-dual step size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Inexact SQP  SQP  IPOPT  Iterations  18  18  52  Computation time [s]  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='45  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='79  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='88  JT (¯x, y⋄)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='27  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='27  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='27  TABLE I: Numerical comparison between SQP, inexact SQP,  and IPOPT for solving Problem (30) in terms of the number  of iterations to reach convergence, the total computation time,  and the optimal cost achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' A just in time compiler was  used for both SQP variants but not for IPOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  trajectory optimization or MPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' One of the main novelties lies  in the joint optimization of a nominal trajectory and an affine  error feedback policy to compensate for disturbances with ro-  bust constraint satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We also presented an inexact-SQP  variant, which results in sub-problems comparable to linear  SLS and reduces the computation times compared to state-  of-the-art methods (SQP, IPOPT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We showcased the method  for the control of a rigid body in rotation with constraints on  the states and inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' We showed that a robust formulation  is needed for the constraints to be robustly satisfied, that a  linearized model may not be sufficient, and that the optimized  affine error feedback improves the overall performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Considering a receding horizon implementation, as is typical  in robust MPC, including a corresponding recursive feasibility  and stability analysis is left for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
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+page_content='gurobi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='com  Antoine P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Leeman received a Master degree in  aerospace engineering from the University of Li`ege,  Belgium and a Diplˆome d’Ing´enieur (MSc) from  ISAE-SUPAERO, France, both in 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' After his  research exchange in the Korea Advanced Institute  of Science and Technology (KAIST), South Korea,  he was working as a Young Graduate Trainee at  the European Space Agency (ESA), the Netherlands,  within the Guidance, Navigation and Control (GNC)  section from 2018 to 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Since 2020, he is a Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  candidate at the Institute for Dynamic Systems and  Control (IDSC) at ETH Z¨urich, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' His research interests include  model predictive control, and control of robotics and aerospace systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Johannes K¨ohler received his Master degree in  Engineering Cybernetics from the University of  Stuttgart, Germany, in 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In 2021, he obtained  a Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' in mechanical engineering, also from the  University of Stuttgart, Germany, for which he re-  ceived the 2021 European Systems & Control Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' He is currently a postdoctoral researcher  at the Institute for Dynamic Systems and Control  (IDSC) at ETH Z¨urich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' His research interests are in  the area of model predictive control and control and  estimation for nonlinear uncertain systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Andrea Zanelli received a BSc degree in Automa-  tion Engineering from Politecnico di Milano and  an MSc degree in Robotics, Systems and Control  from ETH Zurich in 2012 and 2015, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  He pursued a Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' at the Systems Control and Op-  timization Laboratory at the University of Freiburg,  Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Since 2021, he is a postdoctoral researcher  at the Institute for Dynamic Systems and Control  at ETH Zurich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' His research focuses on the de-  velopment and software implementation of efficient  numerical methods for embedded optimization and  nonlinear model predictive control with numerical and system theoretic  guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Samir Benanni has a Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='D in aerospace engineering  from Delft University, Faculty of Aerospace Engi-  neering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' He is specialized in the field of dynamical  systems and robust control theory with application  to space flight controls problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' He is at the Eu-  ropean Space Agency (ESA) technology center as  a Guidance Navigation and Control (GNC) Fellow  and Senior Advisor to the GNC division.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' In the last  two decades relevant efforts were made in infus-  ing robust control technologies enabling challenging  ESA missions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Among these were, LISA Pathfinder,  Rosetta and VEGA launch vehicle family and many others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' He is conducting  various technology maturation programs in the domain of space transportation,  exploration, science and new space missions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' He is currently working on GNC  validation and verification technologies, real-time optimized and data-driven  guidance and control technologies for the next generation ESA technology  demonstrator platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' He is a member of various professional organisations  such as IEEE, AIAA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='  Melanie N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Zeilinger is an Associate Professor at  ETH Zurich, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' She received the Diploma  degree in engineering cybernetics from the Uni-  versity of Stuttgart, Germany, in 2006, and the  Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' degree with honors in electrical engineering  from ETH Zurich, Switzerland, in 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' From 2011  to 2012 she was a Postdoctoral Fellow with the  Ecole Polytechnique Federale de Lausanne (EPFL),  Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' She was a Marie Curie Fellow and  Postdoctoral Researcher with the Max Planck In-  stitute for Intelligent Systems, T¨ubingen, Germany  until 2015 and with the Department of Electrical Engineering and Computer  Sciences at the University of California at Berkeley, CA, USA, from 2012 to  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' From 2018 to 2019 she was a professor at the University of Freiburg,  Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
+page_content=' Her current research interests include safe learning-based control,  as well as distributed control and optimization, with applications to robotics  and human-in-the-loop control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE4T4oBgHgl3EQfMAxr/content/2301.04943v1.pdf'}
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+arXiv:2301.02717v1  [math.PR]  6 Jan 2023
+Thick trace at infinity
+for the Hyperbolic Radial Spanning Tree
+David Coupier∗,
+Lucas Flammant†,
+Viet Chi Tran‡
+January 10, 2023
+Abstract
+Since the works of Howard & Newman (2001), it is known that in straight radial
+rooted trees, with probability 1, infinite paths all have an asymptotic direction and
+each asymptotic direction is reached by (at least) an infinite path. Moreover, there
+exists a set of ’exceptionnal’ directions reached by (at least) two infinite paths which
+is random, dense and only countable in dimension 2. Howard & Newman’s method
+says nothing about (random) directions reached by more than two infinite paths and,
+in particular, if such ’very exceptionnal’ directions exist in dimension 2. In this pa-
+per, we prove that the answer is no for the hyperbolic Radial Spanning Tree (RST):
+in dimension 2, this tree does not contain 3 infinite paths with the same (random)
+asymptotic direction with probability one. Turned in another way, this means that
+there is no infinite but thin subtree in the hyperbolic RST, i.e. whose infinite paths
+would all have the same asymptotic direction. We actually prove a stronger result in
+dimension d + 1, d ≥ 1, stating that any infinite subtree of the hyperbolic RST a.s.
+generates a thick trace at infinity, i.e. the set of asymptotic directions reached by its
+infinite paths has a positive measure.
+Key words:
+hyperbolic space, stochastic geometry, random geometric tree, Radial
+Spanning Tree, continuum percolation, Poisson point processes.
+AMS 2010 Subject Classification: Primary 60D05, 60K35, 82B21.
+Acknowledgments. This work has been supported by the RT GeoSto 3477, the Labex
+Bézout (ANR-10-LABX-58), the ANR PPPP (ANR-16-CE40-0016) and the ANR GrHyDy
+(ANR-20-CE40-0002). V.C.T. thanks the CRM Montréal (IRL CNRS 3457) where part of
+this work was completed.
+1
+Introduction
+Unlike combinatorial random graphs whose Erdös-Rényi model is certainly the most famous
+specimen (see [15, 24]), the structure of a geometric random graph depends on the locations
+of its vertices (embedded in a metric space) and on some geometrical rules. This feature
+makes geometric random graphs suitable to model real phenomena (in biology, material
+science, image analysis or telecommunication networks) and this is the reason why they
+∗IMT Nord Europe, Institut Mines Télécom, Univ. Lille, david.coupier@imt-nord-europe.fr
+†LAMAV, Univ. Polytechnique Hauts-de-France, CNRS
+‡LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS; IRL 3457, CRM-CNRS, Université de
+Montréal, Canada. chi.tran@univ-eiffel.fr
+1
+
+have been intensively studied in the last decades. See the book of Penrose [21] for a general
+reference on the topic.
+For geometric random graphs, macroscopic properties trigger challenging questions,
+such as studying the number of the topological ends of these structures. Alexander solves
+this question in [2] for Minimal Spanning Forests on infinite graphs. In the case of Euclidean
+trees, i.e. trees whose vertices are points of Rd+1 with d ≥ 1, a fundamental step has been
+taken by Howard & Newman for straight rooted trees, i.e.
+whose subtrees are all the
+thinner as their roots are far away from that of the entire tree [18, Section 2.3]. They
+develop an efficient method [18, Proposition 2.8] ensuring that any straight tree T satisfies
+the two following properties almost surely (a.s.):
+(A) Every infinite path (zn)n≥0 of T– a sequence of different vertices (zn)n≥0 such that
+{zn, zn+1} is an edge of the tree for every n ≥ 0 –admits an asymptotic direction u in the
+unit sphere Sd of Rd+1, i.e.
+lim
+n→+∞
+zn
+|zn| = u .
+(1.1)
+(B) Every direction u ∈ Sd is asymptotically reached by (at least) one infinite path of the
+tree T.
+We will also say that the direction u satisfying (1.1) is asymptotically reached or targeted
+by the path (zn)n≥0. In the whole paper, the dimension of the ambiant space is denoted
+by d + 1.
+Howard and Newman applied their method to the case of first-passage percolation
+trees built on a Poisson Point Process (PPP). They also proved that, for any deterministic
+u ∈ Sd, the tree T a.s. contains exactly one infinite path with u as asymptotic direction.
+However there exists a.s. a set of random directions, thought as ’exceptional’, targeted by
+at least two infinite paths which is dense in Sd, and only countable in dimension 2. See
+Fig. 1 and Remark 3.7 for details about these ’exceptional’ directions.
+Howard & Newman’s method then motivated many works on geometric random trees
+(in particular in dimension 2). Various authors stated the straightness of their favorite
+tree so as to obtain Properties (A) and (B) for its infinite paths. Here are some examples.
+The Directed Last-Passage Percolation (LPP) Tree is obtained by a last-passage procedure
+from i.i.d. weights associated to the vertices of the grid Nd+1. In the case of exponential
+weights and d + 1 = 2, Ferrari & Pimentel [16] established the straightness of the directed
+LPP tree. From asymptotic directions of infinite paths of the LPP tree, they deduced
+the existence of an asymptotic direction for a competition interface. Other works focused
+on geometric trees directed towards a distinguished point 0, with edges defined by local
+geometric rules. A first example is the Radial Spanning Tree (RST) introduced by Baccelli
+& Bordenave in the Euclidean plane to model communication networks [4]. Each vertex
+of this tree has an outgoing edge towards the nearest vertex among those closer to 0. The
+hyperbolic RST studied in this paper is an extension of their RST. Using a directed forest
+(namely the Directed Spanning Forest) approximating locally, in distribution and far from
+the root the RST, they proved the straightness of the RST. A second example is the Nav-
+igation Tree defined by Bonichon & Marckert in [6]. Each vertex has also outdegree one
+and the corresponding edge links it to the closet vertex in a given cone directed towards
+0. To describe the asymptotic geometry of the navigations paths, the authors stated the
+straightness of the Navigation Tree.
+Since in dimension 2, only a countable number of random directions are targeted by at
+least two infinite paths, it is natural to ask whether some of them are ‘very exceptional’,
+i.e. targeted by more than two infinite paths. Assuming the non-crossing path property
+2
+
+(satisfied by all the previously mentioned trees), the existence of such a ’very exceptional’
+direction would mean that of an infinite subtree– containing the middle infinite path –
+which would be very thin because trapped between both extreme infinite paths having the
+same asymptotic direction. The existence of such a subtree is suspicious since it is involved
+in a spatial competition that it neither wins (it fails to occupy a macroscopic part of the
+space) nor loses (it is unbounded). This heuristic sustains the following refinement of the
+Howard & Newman’s results:
+Conjecture 1.1. For most of straight bi-dimensional geometric random trees having the
+non-crossing path property which are studied in the literature (including those cited above),
+there is no (random) direction targeted with more than two infinite paths with probability
+1.
+To our knowledge, this conjecture has been established in only one case: for the Directed
+LPP Tree with exponential weights in N2 by Coupier [10]. His proof is based on a surprising
+coupling– exhibited for the first time by Rost [23] –between the LPP model and the Totally
+Asymmetric Simple Exclusion Process (abbreviated in the literature to TASEP) and on
+results on some special particles (called second class particles) of this particle system [3].
+In this paper, we present a second example satisfying this conjecture, namely the
+hyperbolic Radial Spanning Tree introduced in [12]. See Fig. 1. Let us emphasize that
+the nature of this new example is completely different from the first one since it lies in a
+continuum hyperbolic space instead of N2.
+Figure 1: Simulation of the two-dimensional hyperbolic RST, with λ = 30, in the Poincaré
+disc model. The edges are represented by geodesics. The different connected components of
+the RST (apart from the root) are represented with different colors. This coloring allows
+to distinguish some random directions reached by two infinite paths, namely the three
+directions separating the three colored traces at infinity: see Remark 3.7 for details.
+The construction of the hyperbolic RST is the same as for the bi-dimensional Euclidean
+RST of Baccelli & Bordenave [4], whatever the dimension d + 1 ≥ 2. The set of vertices
+3
+
+>is given by a homogeneous Poisson Point Process (PPP) N of intensity λ > 0. The RST
+rooted at the origin 0 is the graph obtained by connecting each point z ∈ N to its parent
+A(z), defined as the closest point to z among all points z′ ∈ N ∪ {0} that are closer to the
+origin than z. This procedure defines a random radial tree rooted at 0 which is straight
+in Hd+1; see [12, Proposition 2.7] or Property 3.2 below. This key property is available
+here thanks to the fact that the hyperbolic metric guarantees that angular deviations of
+RST paths decay exponentially fast with the distance to the origin. This feature entails in
+fact much more than the straightness of the hyperbolic RST. It also implies that there is
+a positive proportion of RST edges at level r giving rise to infinite paths (Proposition 3.8
+below). This later statement does not occur in the Euclidean case, where the probability
+that a given edge at level r belongs to an infinite path tends to 0 as r → ∞ [5].
+Our main result (Theorem 3.5) holds in any dimension. Heuristically, we will show that
+the set of directions u ∈ Sd that are asymptotically reached by infinite paths stemming
+from an arbitrary Poisson point z, called the trace of z at infinity, is either empty or has
+positive measure. In the first case, the subtree rooted at z is finite while in the second case,
+it is infinite and generates a thick trace at infinity. In dimension 2, thanks to planarity
+and the non-crossing path property, it is easily deduced from Theorem 3.5 that a.s. there
+is no direction reached by more than two infinite paths, i.e. Conjecture 1.1. See Corollary
+3.6, Item (iii).
+The proof of Theorem 3.5 can be summarized by the geometric construction depicted
+in Fig. 2 and mainly relies on the fact that the probability with which a given Poisson
+point z at level r generates a thick trace at infinity (plus extra conditions as in partic-
+ular a stabilization criteria) is bounded away from 0 uniformly on r (Lemma 4.5). This
+technical result is specific to the hyperbolic metric: this explains why we are able to prove
+Conjecture 1.1 for the hyperbolic RST and not for its Euclidean counterpart (although
+the Euclidean RST contains in proportion fewer infinite paths than the hyperbolic RST).
+Lemma 4.5 also uses a control of path fluctuations developed in [12] (recalled Lemma 5.2).
+In Section 2, we recall shortly some results on the hyperbolic geometry that will be
+useful in the paper. In Section 3, we enounce our main result: Theorem 3.5 for the general
+dimension d + 1, d ≥ 1, and its Corollary 3.6 in dimension 2, that answers the Conjecture
+1.1 for the hyperbolic Radial Spanning Tree, providing the first example in continuum
+space where this question can be answered. Section 4 presents the proofs of Theorem 3.5
+and of the technical Lemma 4.5 introduced in the previous paragraph. Section 5 is devoted
+to the proof of this later result. Finally, in Section 6, we prove that there is a positive
+proportion of points of the tree at level r that generates thick tracks at infinity.
+2
+Hyperbolic geometry and notations
+Generalities on hyperbolic geometry. We refer to [7, 8, 20, 22] for a complete introduc-
+tion to hyperbolic geometry. For d ∈ N∗ = {1, 2, . . . }, the (d + 1)-dimensional hyperbolic
+space denoted by Hd+1 is a (d + 1)-dimensional Riemannian manifold of constant negative
+curvature −1 that can be defined by several isometric models. One of them is the open-ball
+model D (or Poincaré disc model in dimension 2) consisting in the unit open-ball
+D := {(x1, . . . , xd+1) ∈ Rd+1 : x2
+1 + . . . + x2
+d+1 < 1}
+4
+
+endowed with the metric:
+ds2
+D := 4
+dx2
+1 + . . . + dx2
+n+1
+(1 − x2
+1 − . . . − x2
+d+1)2 .
+The volume measure on (D, ds2
+D) is then given by 2d+1dx1 . . . dxd+1/(1−x2
+1−. . .−x2
+d+1)d+1.
+A convenient way to represent points in the open-ball model is to use polar coordinates
+(w.r.t. the origin 0). Any z ∈ D can be written as z = (r; u) where r = d(z, 0) is its
+distance to 0 and u ∈ Sd is its direction.
+Let σ be the spherical probability measure
+on Sd (in particular σ(Sd) = 1). In polar coordinates, the rescaled volume measure Vol,
+corresponding to the rescaled probability measure σ, becomes
+dVol(r; u) = sinh(r)d dr dσ(u) .
+(2.1)
+The choice of rescaling of the volume measure is adopted to avoid writing the constant
+2π(d+1)/2/Γ((d+1)/2) that would appear a lot in the paper otherwise (this constant is the
+non-rescaled measure of Sd, see [8, (III.3.10) p.125]).
+The hyperbolic space Hd+1 is also naturally equipped with a set of points at infinity
+denoted by ∂Hd+1.
+In the open-ball model, this set is identified with the unit sphere
+Sd. The distances are distorted in comparison with the Euclidean distance and become
+‘smaller’ when we approach the boundary ∂D = Sd, which is at infinite hyperbolic distance
+from the center 0. We also set Hd+1 := Hd+1 ∪ ∂Hd+1 endowed with the topology given
+by the closed ball.
+In (D, ds2
+D), geodesics are of two types: either diameters of D or arcs perpendicular
+to the boundary ∂D. Also, this model is conformal in the sense that the hyperbolic angle
+between two geodesics is equal to the Euclidean angle between them, in the open ball
+representation. Another important fact about hyperbolic geometry is that all points and
+all directions play the same role: Hd+1 is homogeneous and isotropic.
+Notations. We denote by d(·, ·) the hyperbolic distance in Hd+1. For z, z′ ∈ Hd+1, let
+[z, z′] be the geodesic between z and z′. We will denote by (z, z′) the geodesic without the
+extremities z and z′.
+For z ∈ Hd+1 and r > 0, we respectively denote by B(z, r) := {z′ ∈ Hd+1 : d(z, z′) < r}
+and S(z, r) := {z′ ∈ Hd+1 : d(z, z′) = r} the hyperbolic open ball and hyperbolic sphere
+centered at z with radius r > 0. We will write B(r) := B(0, r) and S(r) := S(0, r) for
+short. Writting Vol(B(r)) =
+� r
+0 sinhd(ρ)dρ (see e.g. [22, p.79]), it is easy to prove that
+there exists c = c(d) ∈ (0, 1) such that for any r ≥ 1,
+cedr ≤ Vol(B(r)) ≤ νedr .
+(2.2)
+Let us also denote by C(z, r, R) := {z′ ∈ Hd+1 : r < d(z, z′) < R} the annulus with radii
+r < R and C(r, R) := C(0, r, R).
+For z, z′, z′′ ∈ Hd+1, �
+zz′z′′ is the measure of the corresponding (non-oriented) hyperbolic
+angle. For any z ∈ Hd+1 and θ > 0, Cone(z, θ) := {z′ ∈ Hd+1 : �
+z0z′ ≤ θ} is defined as the
+cone of apex 0, axis z and aperture θ. In addition, for z ∈ Hd+1 and r > 0, we will use the
+spherical cap
+BS(r)(z, θ) := Cone(z, θ) ∩ S(r) .
+(2.3)
+For its surface, note that there exists a constant C = C(d) > 0 such that:
+σ
+�
+BS(r)(z, θ)
+�
+≤ Cθd .
+(2.4)
+5
+
+3
+Main results
+In the sequel, we pick some arbitrary origin point 0 ∈ Hd+1 (thought as the center of D in
+the open-ball representation) to be the root of the hyperbolic RST that we now define.
+The hyperbolic RST. Let N be a homogeneous PPP of intensity λ > 0 in Hd+1. The
+definition of the hyperbolic RST is similar to the Euclidean case. This is a directed graph
+whose vertex set is N ∪ {0} and in which each vertex z ∈ N is connected to the closest
+Poisson point among (N ∪ {0}) ∩ B(r), with r := d(0, z), for the hyperbolic distance.
+Definition 3.1 (Radial Spanning Tree in Hd+1). The ancestor of z ∈ N is defined as
+A(z) :=
+argmin
+z′∈(N ∪{0})∩B(d(0,z))
+d(z′, z) .
+(3.1)
+The Radial Spanning Tree (RST) in Hd+1 is the directed graph (V, ⃗E) where V := N ∪{0}
+and ⃗E := {(z, A(z)) : z ∈ N}.
+Since N ∪ {0} contains no isosceles triangles with probability 1, the ancestor A(z) of
+any Poisson point z is a.s. well-defined. In other words, any Poisson point admits only
+one outgoing edge, but possibly several ingoing edges. In any case, these ingoing edges are
+finitely many:
+Property 3.2 (Proposition 2.2 of [12]). A.s. the RST is a tree rooted at 0 where all vertices
+have finite degrees. In the bi-dimensional case (d = 1), the union of geodesics [z, A(z)],
+z ∈ N, is planar, i.e. whatever z ̸= z′ ∈ N, the geodesics [z, A(z)] and [z′, A(z′)] may only
+overlap on their endpoints.
+For z ∈ N and r > 0, we also define
+B+(z, r) := B(z, r) ∩ B(d(0, z))
+and
+B+(z) := B+(z, d(z, A(z))) .
+(3.2)
+By construction of the ancestor, the random set B+(z) avoids the PPP N. This fact is
+responsible for many difficulties when studying the RST. Indeed, when restarting from
+A(z) = (r′; u′) and constructing the path forward (towards 0), with probability 1, B(r′) ∩
+B+(z) is non-empty. This means that the geometric information used to determine A(z)
+is still involved for next steps of the process, generating statistical dependencies.
+A path of the RST is a sequence (finite or not) of different vertices (z0, z1, z2 . . .) in
+N ∪ {0} such that A(zn+1) = zn for any n ≥ 0. By (3.1), we have that for all z ∈ N,
+d(0, A(z)) < d(0, z). Applying this to z = zn, n ≥ 1, we obtain that d(0, zn) < d(0, zn+1).
+The path (z0, z1, z2 . . .) can thus be viewed as an exploration of the RST starting at z0
+and moving away from 0. We will say that the forward direction is towards 0 and the
+backward direction is towards infinity. Every path can be started at z0 = 0, but this is not
+an obligation.
+The set of descendants D(z) of a given vertex z is made up of all vertices that can be
+reached by a backward finite path starting at z (including z itself by convention). Because
+a vertex can be the ancestor of no other vertex, all sets of descendants are not infinite.
+As mentioned in the Introduction, a very important feature of the hyperbolic RST is
+its straightness:
+Property 3.3 (Proposition 2.7 of [12]). A.s. for any ε > 0 there exists some r0 > 0 such
+that, for any radius r ≥ r0 and for any vertex z of the hyperbolic RST with d(0, z) ≥ r,
+the set of descendants D(z) is contained in a cone of apex 0 and aperture e−(1−ε)r, i.e. for
+any z′, z′′ ∈ D(z), �
+z′0z′′ ≤ e−(1−ε)r.
+6
+
+Trace on the boundary ∂Hd+1. Let us consider a point z ∈ N and its set of descendants
+D(z). When it is infinite, it contains (at least) an infinite path (zn)n≥0 by the finite degree
+property (Property 3.2). Theorem 1.1 of [12] then asserts that the path (zn)n≥0 admits
+an asymptotic direction u ∈ ∂Hd+1. Thus, let us define by D∞(z) the set of asymptotic
+directions in ∂Hd+1 that can be reached by the infinite paths of D(z). Roughly speaking,
+D∞(z) is the trace left by the set of descendants D(z) on the boundary ∂Hd+1 (see the
+traces at infinity left by the children of 0 in Fig. 1). We just have proved that:
+Property 3.4. A.s. for any vertex z ∈ N,
+#D(z) = +∞ ⇐⇒ D∞(z) ̸= ∅ .
+(3.3)
+Our main result (Theorem 3.5) establishes a stronger statement: infinitely many de-
+scendants in D(z) actually implies that D(z) leaves a trace with positive volume at infinity,
+i.e. σ(D∞(z)) > 0. In this case, we will say that z generates a thick trace at infinity.
+Theorem 3.5. Consider the hyperbolic RST in Hd+1, for any dimension d ≥ 1. A.s. for
+any vertex z ∈ N, either z admits finitely many descendants or σ(D∞(z)) > 0.
+Consequence in H2. Theorem 3.5 holds in any dimension. In dimension 2 (i.e. with
+d = 1), combined to the non-crossing path property (Property 3.2), it leads to Conjecture
+1.1: a.s. the RST does not contain three infinite paths with the same (random) asymptotic
+direction. This statement– Item (iii) of Corollary 3.6 –completes the description of infinite
+paths and their asymptotic directions of the hyperbolic RST started in [12]. The first
+three items below are given by [12, Theorem 1.1]. Their proofs are based on the strategy
+developed by Howard and Newman in [18] and on the straightness of the hyperbolic RST.
+Corollary 3.6. The following properties concern the hyperbolic RST in H2.
+(o) A.s. any infinite path admits an asymptotic direction and, for any u ∈ ∂H2, the RST
+contains an infinite path with asymptotic direction u.
+(i) For any (deterministic) u ∈ ∂H2, the RST a.s. contains a unique infinite path with
+asymptotic direction u.
+(ii) A.s. the subset of ∂H2 of asymptotic directions reached by at least two infinite paths
+is dense and countable in ∂H2.
+(iii) A.s. no (random) asymptotic direction of ∂H2 is reached by more than two infinite
+paths.
+Item (o) says that any u in ∂H2 is reached by at least one infinite path and exactly
+one when u is deterministic (Item (i)). There exist by Item (ii) asymptotic directions
+which are reached by several infinite paths but these directions are random and few (only
+countable). Finally, Theorem 3.5 specifies that there is no random asymptotic direction
+reached by more than two infinite paths.
+Proof of Corollary 3.6, Item (iii). Let us assume that the hyperbolic RST contains three
+different infinite paths, say (xn)n≥0, (yn)n≥0 and (zn)n≥0 having the same asymptotic
+direction in ∂H2. Without loss of generality, we can also assume that these three paths
+have no vertices in common.
+By the non-crossing path property and planarity, one of
+these three infinite paths, say (yn)n≥0, is trapped between the two other paths which by
+hypothesis have the same asymptotic direction. This forces σ(D∞(y0)) = 0 while the set of
+descendants D(y0) is infinite. This occurs with null probability thanks to Theorem 3.5.
+7
+
+Remark 3.7. Let us show that the asymptotic direction separating the green and red traces
+at infinity on Fig. 1, is reached by two infinite paths (a green one and a red one). In the
+green (resp. red) infinite subtree, pick the leftmost (resp. rightmost) infinite path in the
+trigonometric sense. Such construction makes sense in dimension 2 thanks to the non-
+crossing path property. These two paths πgreen and πred admit asymptotic directions, say
+ugreen and ured in ∂H2 by Corollary 3.6, Item (o). If ugreen and ured were different, any
+asymptotic direction u′ located (strictly) between them shoud be reached by an infinite
+path π thanks to Corollary 3.6, Item (o). By construction of πgreen and πred, the path π
+could not be neither green or red, leading to a contradiction.
+Positive density with σ(D∞(·)) > 0. Although the previous results concern the combi-
+natorial structure of the RST, it will be useful in the proofs to represent the graph RST
+as a subset of Hd+1, denoted by RST, in which each edge (z, A(z)) is represented by the
+arc |[z, A(z)]| (defined in Appendix A) and not by the (hyperbolic) geodesic [z, A(z)]:
+RST :=
+�
+z∈N
+|[z, A(z)]| .
+(3.4)
+This choice (somewhat unnatural) is motivated by the fact that the (hyperbolic) distance
+to the origin 0 is monotonous along the arc |[z, A(z)]| which fails for the geodesic [z, A(z)]
+(or for the Euclidean segment between z and its ancestor A(z)). In particular each arc
+|[z, A(z)]| crosses any given sphere at most once. Thus, we define the RST at level r > 0
+as the following random set:
+Lr := RST ∩ S(r) .
+(3.5)
+Elements of Lr are a.s. not Poisson points on S(r) with probability 1. However we extend
+to elements of Lr the notations D(·) and D∞(·) as follows. For z ∈ Lr, we denote by z↓
+the Poisson point whose arc |[z↓, A(z↓)]| crosses S(r) at z: with a slight abuse of notations,
+z↓ can be defined without ambiguity (see Appendix).
+Then we set D(z) = D(z↓) and
+D∞(z) = D∞(z↓).
+This section ends with a density result.
+Proposition 3.8 heuristically says that in
+expectation a macroscopic proportion of elements of Lr generates a thick trace at infinity:
+Proposition 3.8. There exists c = c(d) > 0 such that for any r > 0,
+E
+�
+#{z ∈ Lr : σ(D∞(z)) > 0}
+�
+≥ c E
+�
+#Lr
+�
+.
+Proposition 3.8 contrasts with several Euclidean bi-dimensional trees [1, 11], including
+the Euclidean RST [5], where the proportion of edges at level r belonging to infinite paths
+is negligible.
+Proposition 3.8 is an immediate consequence of some intermediate results leading to
+Theorem 3.5, and its proof is done in Section 6. It could be improved in several directions
+(an almost sure result rather than in expectation, a positive limit of the ratio rather than
+a positive lim inf etc.) but this is not the goal of the current work.
+4
+Proof of Theorem 3.5
+4.1
+Global strategy
+Let r0 ∈ (0, 1), u0 ∈ Sd and select the closest Poisson point to (r0; u0) (with polar coordi-
+nates) denoted by
+z0 := argmin
+z∈N
+d(z, (r0; u0)) .
+8
+
+Consider the event E(r0; u0) on which the set of points at infinity D∞(z0) reached by
+descendants of z0 is nonempty but with null volume:
+E(r0; u0) :=
+�
+D∞(z0) ̸= ∅ and σ
+�
+D∞(z0)
+�
+= 0
+�
+.
+(4.1)
+Our purpose is to prove that P(E(r0; u0)) = 0.
+For δ > 0, let us consider the set G(δ) of descendants z of z0 whose ancestor A(z) is
+not too close to z:
+G(δ) :=
+�
+z ∈ D(z0) : d(z, A(z)) ≥ δ
+�
+.
+Let H(δ) be the set of corresponding radii:
+H(δ) :=
+�
+r > 0 : ∃u ∈ Sd, (r; u) ∈ G(δ)
+�
+.
+The next result states that, for δ small enough, if z0 admits infinitely many descendants
+(or in an equivalent way D∞(z0) ̸= ∅) then infinitely many of them are in G(δ):
+Lemma 4.1. For any δ > 0 small enough, D∞(z0) ̸= ∅ a.s. implies that H(δ) is un-
+bounded.
+For any radius r > 0, let NB(r) := N ∩ B(r) be the PPP N restricted to the ball
+B(r).
+The following Lemma 4.2 says that a.s.
+on D∞(z0) ̸= ∅ the random variable
+P(σ(D∞(z0)) > 0 | NB(r)) is bounded away from 0 for all radii r ∈ H(δ) and uniformly on
+those radii.
+Lemma 4.2. For any δ > 0 small enough, there exists ε > 0 such that, a.s. on D∞(z0) ̸= ∅,
+∀r ∈ H(δ), P
+�
+σ(D∞(z0)) > 0 | NB(r)
+�
+≥ ε .
+(4.2)
+As shown below, Lemmas 4.1 and 4.2 together imply P(E(r0; u0)) = 0 from which
+Theorem 3.5 immediatly follows.
+The proofs of Lemmas 4.1 and 4.2 are respectively
+postponed to Sections 4.2 and 4.3.
+Proof of Theorem 3.5. Choose parameters δ and ε such that both Lemmas 4.1 and 4.2 hold.
+The second lemma says that for this choice of δ and ε, we have a.s. on {D∞(z0) ̸= ∅} and
+for any r ∈ H(δ),
+P
+�
+E(r0; u0) | NB(r)
+�
+≤ P
+�
+σ(D∞(z0)) = 0 | NB(r)
+�
+≤ 1 − ε .
+Since ε is uniform on r ∈ H(δ) and since we work on {D∞(z0) ̸= ∅}, the set H(δ) is a.s.
+unbounded. We can take the lim inf: a.s. on {D∞(z0) ̸= ∅},
+lim inf
+r→∞ P
+�
+E(r0; u0) | NB(r)
+�
+≤ 1 − ε .
+(4.3)
+But the martingale convergence theorem asserts that:
+lim
+r→∞ P
+�
+E(r0; u0) | NB(r)
+�
+= 1E(r0;u0).
+(4.4)
+So, on E(r0; u0) ⊂ {D∞(z0) ̸= ∅}, the limit in (4.4) equals 1. Thus, both statements (4.3)
+and (4.4) are compatible only if P(E(r0; u0)) = 0.
+Hence, the union of the events E(r0; u0) with rational radius r0 and rational direction
+u0 has null probability too. Since any Poisson point is the closest one to some rational
+element (r0; u0) of Hd+1, we can conclude that with probability 1, any vertex z ∈ N
+satisfies either D∞(z) = ∅ (or D(z) is finite in an equivalent way) or σ(D∞(z)) is (strictly)
+positive.
+9
+
+4.2
+Proof of Lemma 4.1
+The proof of Lemma 4.1 is based on a percolation argument. To set it up, we first need a
+covering of the hyperbolic space Hd+1 (except in the vicinity of the origin) with a uniform
+control of overlappings.
+This will be done using the Covering Lemma (below).
+This
+classical result will be used several times in this paper and is stated in [12, Lemma 4.2].
+Lemma 4.3 (Covering Lemma). There exists a covering constant K = K(d) > 0 such
+that, for any r > 0, there exists a collection of N(r) points z1, ..., zN(r) ∈ S(r) such that:
+(a) �
+1≤i≤N(r) BS(r)(zi, e−r) = S(r),
+(b) ∀z ∈ S(r), #{1 ≤ i ≤ N(r) : z ∈ BS(r)(zi, e−r)} ≤ K.
+Moreover, there exists C = C(K, d) > 0 such that, for any r > 0, z ∈ S(r) and A ≥ 1, the
+number of caps overlapping BS(r)(z, Ae−r) is bounded by CAd:
+#
+�
+1 ≤ i ≤ N(r) : BS(r)(zi, e−r) ∩ BS(r)(z, Ae−r) ̸= ∅
+�
+≤ CAd .
+In particular (taking A := πer in the previous inequality), N(r) ≤ Cedr.
+For any integer radius r > 0 and any index 1 ≤ m ≤ N(r), let us set
+Br,m := C(r, r + 1) ∩ Cone(zr,m, e−r)
+where {zr,1, . . . , zr,N(r)} is the collection of points of the sphere S(r) given by Lemma 4.3
+(in this proof we stress the dependence on r of the zm’s by adding the index r in zr,m).
+Each block Br,m is based on the spherical cap BS(r)(zr,m, e−r) = S(r) ∩ Cone(zr,m, e−r)
+and has thickness 1. Two blocks Br,m and Br′,m′ are said to be adjacent, which is denoted
+by Br,m ∼ Br′,m′, if they are at distance less than δ from each other. Lemma 4.4 asserts
+that the volumes of Br,m’s are uniformly bounded and the degrees in the graph generated
+by the adjacency relation are bounded.
+Lemma 4.4. There exist two positive constants C1 and C2 only depending on d such that
+for all integer radius r > 0 and m ∈ {1, . . . , N(r)}, the following holds :
+Vol(Br,m) ≤ C1,
+and
+#
+�
+(r′, m′) : Br′,m′ ∼ Br,m
+�
+≤ C2 .
+(4.5)
+Proof. First, using (2.4),
+Vol(Br,m)
+=
+� r+1
+r
+sinhd(ρ) × σ
+�
+Cone(zρ,m, e−ρ) ∩ Sd�
+dρ
+≤
+C
+� r+1
+r
+edρ dρ × e−dr = C
+d (ed − 1) =: C1 .
+For the second inequality of (4.5), two blocks Br′,m′ and Br,m are adjacent whenever Br′,m′
+overlaps {z ∈ Hd+1 : d(z, Br,m) ≤ δ}. Since δ < 1 this forces r′ to be in {r − 1, r, r + 1}
+and Br′,m′ to overlap Cone(zr,m, (1 + δ)e−r). Now, Lemma 4.3 asserts that for each layer
+r′ ∈ {r − 1, r, r + 1}, there are at most CAd = C(1 + δ)ded(r′−r) ≤ C2ded blocks Br′,m′
+overlapping Cone(zr,m, (1+δ)e−r). Consequently, Br,m has at most C2 := 3C2ded adjacent
+blocks.
+10
+
+The block Br,m is said δ-bad if it contains a Poisson point z such that d(z, A(z)) < δ.
+Let us first prove that it is possible to choose δ > 0 small enough so that the set of δ-bad
+blocks denoted as Ψδ is a.s. subcritical w.r.t. the adjacency relation, i.e. Ψδ only admits
+finite connected components. To do it, we first use the Mecke’s formula [14, Prop. 13.1.IV]
+to bound the probability for a block to be δ-bad: for any (r, m),
+P
+�
+Br,m is δ-bad
+�
+≤
+E [#{z ∈ Br,m ∩ N : d(z, A(z)) < δ}]
+=
+E
+�
+#{z ∈ Br,m ∩ N : B+(z, δ) ∩ N ̸= ∅
+�
+=
+λ
+�
+Br,m
+P
+�
+B+(z, δ) ∩ N ̸= ∅
+�
+dz
+≤
+λVol(Br,m)
+�
+1 − e−λVol(B(δ))�
+≤
+λC1
+�
+1 − e−λVol(B(δ))�
+=: p(δ)
+(4.6)
+thanks to Lemma 4.4. Hence, P(Br,m is δ-bad) tends to 0 as δ → 0 uniformly on the couple
+(r, m).
+In a second step, we adapt the Peierls argument to our context to establish the sub-
+criticality of Ψδ for δ small enough. Given (r, m), let Pr,m(k) be the set of paths with
+length k of adjacent blocks starting at Br,m. By Lemma 4.4, #Pr,m(k) ≤ (C2)k. Such a
+path π = (B1, . . . , Bk) is said δ-bad if all the blocks Bi it contains are δ-bad. Henceforth
+the probability for Br,m to belong to an infinite connected component of δ-bad blocks is
+upperbounded by
+lim sup
+k→∞
+�
+π∈Pr,m(k)
+P
+�
+π is δ-bad
+�
+.
+For any path π = (B1, . . . , Bk) in Pr,m(k), we can choose a subset of blocks {Bi1, . . . , Biℓ}
+included in {B1, . . . , Bk} such that the Bij’s are two by two non adjacent and ℓ ≥ k/C2
+(here we use that each block has at most C2 adjacent blocks). Besides, the adjacency
+relation has been defined so that the events {Bij is δ-bad}’s are mutually independent. So
+P
+�
+π is δ-bad
+�
+≤ P
+�
+Bi1, . . . , Biℓ are δ-bad
+�
+≤ p(δ)k/C2 ,
+where p(δ) is defined in (4.6). It follows
+�
+π∈Pr,m(k)
+P
+�
+π is δ-bad
+�
+≤
+�
+C2p(δ)1/C2�k .
+Choosing δ small enough so that C2p(δ)1/C2 < 1, we then obtain that a.s. the block Br,m
+cannot belong to an unbounded connected component of δ-bad blocks. Consequently, for
+such parameter δ, the set Ψδ is subcritical with probability 1.
+To conclude the proof of Lemma 4.1, let us pick δ small enough such that the set of
+δ-bad blocks does not percolate. Assume also that D∞(z0) is non empty, i.e. the subtree
+of the RST rooted at z0 admits (at least) one infinite path (zn)n≥0 of Poisson points. The
+PPP N being locally finite, the path (zn)n≥0 cannot be stuck, from some index, inside a
+δ-bad connected component of blocks which is bounded by choice of δ. It eventually comes
+out of each δ-bad connected component. Two cases must be distinguished.
+Either (zn)n≥0 visits infinitely many δ-good blocks where of course a block is said δ-good if
+it is not δ-bad. Hence, infinitely many of the zn’s satisfy d(zn, A(zn)) ≥ δ. These vertices
+are in G(δ) which means that H(δ) is unbounded.
+11
+
+Or, the infinite path (zn)n≥0 jumps infinitely many times from a δ-bad connected compo-
+nent to another one. But, by construction, two different bad connected components are at
+distance at least δ from each other. So these jumps provide as many zn’s in G(δ): H(δ) is
+unbounded in this case too.
+4.3
+Proof of Lemma 4.2
+In what follows, we will modify configurations locally.
+This is why we emphasize the
+dependence of any random set A (think about D(z), D∞(z) or H(δ)) on the current
+configuration η, a realization of the PPP N, by writting A[η].
+Given r0 > 0 and u0 ∈ Sd, recall that z0 is the closest Poisson point to (r0; u0). For
+this section, let us consider a configuration η satisfying D∞(z0) ̸= ∅. Let δ > 0 and r > r0
+be an element of the set H(δ)[η]– by Lemma 4.1, this latter set is unbounded provided δ
+is small enough. Let us set z1 := (r; u) ∈ G(δ) for some u ∈ Sd (z1 is in N). In the sequel,
+we will work conditionally on NB(r) = ηB(r), the configuration of the PPP N restricted to
+the ball B(r).
+Let 0 < δ′ < δ and h > 0 (thought as large). Let also z2 := (r + h; u) (with the same
+direction as z1). The event Stab(r, h, δ′) encodes the fact that the set of descendants of
+any Poisson point in B(z2, δ′) is not sensitive to what happens inside B(r):
+Stab(r, h, δ′) :=
+�
+η′ : ∀z ∈ N ∩ B(z2, δ′), ∀η′′, D(z)[η′′
+B(r) ∪ η′
+B(r)∁] = D(z)[η′]
+�
+.
+(4.7)
+It will be proved in Lemma 5.4 that Stab(r, h, δ′) has a probability tending to 1 as h → ∞
+uniformly on r.
+Let us now introduce the event F(r, h, δ′) on which there exists z ∈ N ∩ B(z2, δ′) such
+that the four following items hold:
+(i) N ∩ B(z2, δ′) = {z},
+(ii) σ(D∞(z)) > 0,
+(iii) Stab(r, h, δ′) occurs
+(iv) and D(z) ⊂ B(r + h + δ′)∁.
+On the event F(r, h, δ′), there is a unique point of the PPP N in the ball B(z2, δ′) that
+has a thick trace at infinity. This subtree is outside the ball B(r + h + δ′) and does not
+depend on the points of N in the ball B(r). The distance h is the separation gap ensuring
+that the subtree rooted at z2 = (r + h; u) remains independent from the Poisson points
+inside the ball B(r).
+Lemma 4.5 states that the event F(r, h, δ′) has a probability larger than some positive ε
+which is uniform on r. Getting such uniformity of ε (or A) on r will significantly complicate
+the proof of Lemma 4.5, postponed to Section 5.
+Lemma 4.5. There exists A > 0 large enough such that, for any δ′ > 0 small enough,
+there exists ε = ε(A, d, λ, δ′) > 0 such that for any h0 > 0 large enough and r > 0, there
+exists h ∈ [h0, h0 + A] such that P(F(r, h, δ′)) ≥ ε. Note also that among the previous
+parameters, only h may depend on r.
+For θ > 0, let us consider the subset U = U(r, h, δ′, θ) of Hd+1 defined as
+U :=
+�
+B(r + h + δ′) \ (B(r) ∪ B(z2, δ′))
+�
+∩ Cone(0, θ) .
+(4.8)
+12
+
+See Figure 2. Let η′ ∈ F(r, h, δ′) such that η′
+B(r) = ηB(r). When all the Poisson points of
+the configuration η′ inside the set U are removed, the ancestor of z– the only Poisson point
+in B(z2, δ′) according to the event F(r, h, δ′) –becomes z1 which itself is a descendant of z0.
+This leads to σ(D∞(z0))[η′
+U∁] > 0. This construction requires the hypothesis r ∈ H(δ)[η],
+i.e. there is no Poisson points in B+(z1, δ), and this is the only place in the proof of Lemma
+4.2 where it is needed.
+Lemma 4.6. For any r ∈ H(δ) with r ≥ r0, for any h and δ′ < δ/3, there exists θ
+large enough such that the following statement holds. Almost every configuration η′ with
+η′
+B(r) = ηB(r) and η′ ∈ F(r, h, δ′) satisfies σ(D∞(z0))[η′
+U∁] > 0.
+PSfrag replacements
+0
+z0
+z1
+z
+B(z2, δ′)
+r
+r + h + δ′
+∞
+r0
+Figure 2: Illustration of Lemma 4.6. Black dots are Poisson points. This picture represents
+a configuration η′
+U∁ (i.e. Poisson points of η′
+U have been removed) where η′
+B(r) = ηB(r)
+and η′ ∈ F(r, h, δ′). The ball B(z2, δ′) whose (deterministic) center z2 is marked by a
+grey square, contains only one Poisson point, namely z. Its set of descendants D(z) is
+represented by the hatched region and satisfies σ(D∞(z))[η′] > 0 (the bold black curve on
+the unit sphere Sd). When the set U is emptying of Poisson points then A(z)[η′
+U∁] = z1
+which means that σ(D∞(z0))[η′
+U∁] > 0. Edges in dotted lines have been modified after
+deleting η′
+U.
+We are now ready to prove Lemma 4.2.
+Proof of Lemma 4.2. Parameters A, δ′, ε and h0 are chosen according to Lemma 4.5. Then
+for any r > 0 there exists h ∈ [h0, h0 + A] such that P(F(r, h, δ′)) ≥ ε. Because it requires
+Stab(r, h, δ′), the event F(r, h, δ′) does not depend on the configuration inside the ball
+B(r). So,
+P
+�
+F(r, h, δ′) | NB(r) = ηB(r)
+�
+= P
+�
+F(r, h, δ′)
+�
+≥ ε .
+Now r can be chosen in H(δ) with r > r0 and 0 < δ′ < δ/3 so that Lemma 4.6 applies:
+ε
+≤
+P
+�
+η′ ∈ F(r, h, δ′) | NB(r) = ηB(r)
+�
+≤
+P
+�
+σ(D∞(z0))[η′
+U∁] > 0 | NB(r) = ηB(r)
+�
+=
+P
+�
+σ(D∞(z0))[η′] > 0, η′
+U = ∅ | NB(r) = ηB(r)
+�
+≤
+P
+�
+σ(D∞(z0)) > 0 | NB(r) = ηB(r)
+�
+.
+Note that the lower bound ε = ε(A, d, λ, δ′) does not depend on the parameter r.
+13
+
+This section ends with the proof of Lemma 4.6.
+Proof of Lemma 4.6. Consider a configuration η′ equal to η inside the ball B(r) and be-
+longing to the event F(r, h, δ′). Let us first assume that, for the configuration η′
+U∁, the
+ancestor of the Poisson point z (whose existence is given by F(r, h, δ′)) is z1, i.e.
+A(z)[η′
+U∁] = z1 .
+(4.9)
+Let us prove Vol(D∞(z0))[η′
+U∁] > 0 from (4.9). Since η′ ∈ F(r, h, δ′), the set of descendants
+D(z)[η′] is included in B(r + h+ δ′)∁. So, removing Poisson points of η′
+U modifies no edges
+(z′, A(z′)) of the RST as long as A(z′) ∈ D(z).
+In fact, removing η′
+U may only add
+new descendants to the vertex z. Hence, D(z)[η′] is included in D(z)[η′
+U∁] which leads
+to σ(D∞(z))[η′
+U∁] ≥ σ(D∞(z))[η′] > 0. Finally, using A(z)[η′
+U∁] = z1 which is itself a
+descendant of z0, we get σ(D∞(z0))[η′
+U∁] > 0.
+It then remains to show (4.9). Let R be the hyperbolic distance between z and z1. It is
+sufficient to prove that B+(z, R) is included in U ∪B+(z1, δ) since, after removing Poisson
+points in U, z1 would become the closest Poisson point to z. Here we use that r ∈ H(δ),
+i.e. the ball B+(z1, δ) contains no other Poisson points except z1. Let us first remark that
+R = d(z, z1) ≤ d(z, z2) + d(z2, z1) ≤ δ′ + h ≤ h + 1
+with δ′ < 1. So, taking θ large enough such that B+(z, R) ⊂ Cone(0, θ), it then remains
+to prove that
+V := B+(z, R) ∩ B(r)
+⊂
+B+(z1, δ).
+(4.10)
+To do so, let us pick v1, v2, v3 on the geodesic γ between 0 and z as follows: v1, v2 and v3
+are the intersection points between γ and resp. the sphere S(0, r + h), S(0, r) and S(z, R).
+Let us denote by w the symmetric of z1 w.r.t. the line (0z). Henceforth, it is sufficient
+to show that w, z1 and v3 belong to B+(z1, δ). First, we have d(v2, z1) ≤ d(v1, z2) ≤ δ′.
+Thus, by symmetry, d(w, z1) ≤ d(w, v2) + d(v2, z1) = 2d(v2, z1) ≤ 2δ′. Since v3, v2 and z
+are on the same geodesic, we can write:
+d(v3, v2) = d(v3, z) − d(z, v2) ≤ R − h + δ′ .
+Since R ≤ h + δ′, we get d(v3, v2) ≤ 2δ′ and then d(v3, z1) ≤ d(v3, v2) + d(v2, z1) ≤ 3δ′.
+Whenever δ′ < δ/3, the three points w, z1 and v3 are inside B+(z1, δ). This proves (4.10)
+and concludes the proof.
+5
+Proof of Lemma 4.5: uniformity in r
+This section is devoted to the proof of Lemma 4.5, i.e. P(F(r, h, δ′)) ≥ ε where the lower
+bound ε does not depend on r, h. Recall the notation of Section 4.3 and of Figure 2. We
+first prove in Section 5.2 that a positive proportion of Poisson points of B(z2, δ′) satisfies
+σ(D∞(·)) > 0– Item (ii) in the definition of F(r, h, δ′) –where z2 = (r + h; u). Then we
+prove that the properties described by the other three items occur with high probability.
+In particular we state in Section 5.3 that Stab(r, h, δ′) has a probability tending to 1
+as h → ∞ uniformly on r.
+But first, in Section 5.1, we recall some properties of the
+Maximal Backward angular Deviations (MBD) which is the key tool here to control the
+path fluctuations in the hyperbolic RST.
+14
+
+5.1
+Maximal backward angular deviations
+A crucial ingredient in this work is the control of Maximal Backward angular Deviations
+(MBD) which has been done in [12] (see also [17] where these notions are introduced). Let
+us recall here the main definitions and results.
+Given r > 0 and z ∈ Lr, recall that z↓ denotes the Poisson point whose arc |[z↓, A(z↓)]|
+crosses S(r) at z and set z↑ := A(z↓). Let also A(k)(z) := A ◦ . . . ◦ A(z) (k times) be the
+k-th ancestor of z for any k ∈ N (by convention, we set A(0) := 0).
+Consider 0 < r ≤ r′ and z′ ∈ Lr′. Let us denote by z ∈ Lr the intersection point
+between the path of RST joining z′ to the origin and the sphere S(r).
+Let us define
+CFDr′
+r (z′) as the Cumulative Forward angular Deviations between levels r and r′ as
+CFDr′
+r (z′) :=
+
+
+
+
+
+
+
+�
+z′0z if z↓ = z′
+↓,
+�
+z′0z′
+↑ +
+n−1
+�
+k=0
+�
+A(k)(z′
+↑)0A(k+1)(z′
+↑) + �
+z↓0z else,
+where n is the unique non negative integer such that A(n)(z′
+↑) = z↓. We also set CFDr′
+r (z′) :=
+0 when z′ /∈ Lr′.
+Definition 5.1 (Maximal Backward angular Deviations). For 0 < r ≤ r′, let us define the
+Maximal Backward angular Deviations between levels r and r′ as
+MBDr′
+r (z) := sup
+ρ∈[r,r′]
+max
+y∈Dρ
+r(z) CFDρ
+r(y)
+(5.1)
+if z ∈ Lr and MBDr′
+r (z) := 0 if z /∈ Lr, where Dρ
+r(z) is the set of points y ∈ Lρ whose path
+of RST from y to 0 cuts S(r) at z (or, roughly speaking, the set of descendants of z at
+level ρ).
+Since r′ �→ MBDr′
+r (z) is non-decreasing, the MBD can be naturally extend to r′ = ∞
+by setting:
+MBD∞
+r (z) := lim
+r′→∞ MBDr′
+r (z) .
+The next lemma provides a control of the moments of MBD∞
+r (z), which is crucial for
+proving the positive density. The idea is that because the paths do not fluctuate too much,
+there is room for a positive number of points at a given level r to have a thick trace at
+infinity.
+Lemma 5.2 (Proposition 2.6 of [12]). For any p ≥ 3d/2, there exists a constant C =
+C(d) > 0 such that, for any r > 2, A > 0 and any direction u ∈ Sd,
+E
+�
+�
+z∈BS(r)(u,Ae−r)∩RST
+�
+MBD∞
+r (z)
+�p�
+≤ CAde−rp .
+(5.2)
+5.2
+Positive density of σ(D∞(·)) > 0
+Lemma 5.3. There exists A > 0 large and c0 = c0(A, d, λ) > 0 such that for any 0 < δ′ <
+1, h0 > 0 and r > 0, there exists h ∈ [h0, h0 + A] such that for any z2 = (r + h; u) (u ∈ Sd)
+E
+�
+#
+�
+z ∈ N ∩ B(z2, δ′) : σ(D∞(z)) > 0
+��
+≥ c0Vol
+�
+B(δ′)
+�
+.
+(5.3)
+Note also that among the previous parameters, only h = h(r) may depend on r.
+15
+
+Proof of Lemma 5.3. The proof is splitted into three steps. We first start with proving an
+estimate close to (5.3), but for z ∈ Lr (Step 1). Then, we extend the result to portion of
+annuli and to balls.
+Step 1. Let us first prove that there exists c = c(d) > 0 such that for any r > 0,
+E
+�
+#
+�
+z ∈ Lr : σ(D∞(z)) > 0
+��
+≥ cedr .
+(5.4)
+Let us first use the Cauchy-Schwarz inequality with the inner product ⟨X, Y ⟩ :=
+E[�
+i XiYi]:
+E
+� �
+z∈Lr
+σ(D∞(z))
+�2
+≤
+E
+� �
+z∈Lr
+1σ(D∞(z))>0
+�
+E
+� �
+z∈Lr
+σ(D∞(z))2�
+=
+E
+�
+#
+�
+z ∈ Lr : σ(D∞(z)) > 0
+��
+E
+� �
+z∈Lr
+σ(D∞(z))2�
+. (5.5)
+Thus, the left hand side of (5.4) is lower bounded by
+E
+�
+#
+�
+z ∈ Lr : σ(D∞(z)) > 0
+��
+≥
+E
+� �
+z∈Lr σ(D∞(z))
+�2
+E
+� �
+z∈Lr σ(D∞(z))2
+�.
+Recall that in the open-ball model, the set of points at infinity ∂Hd+1 is identified with
+the unit d-dimensional sphere Sd whose spherical probability measure σ(Sd) is (normalized
+to) 1. By [12, Theorem 1.1 (i)], with probability 1, any point at infinity is the asymptotic
+direction of (at least) one infinite path of the hyperbolic RST. So,
+a.s. 1 = σ(Sd) ≤
+�
+z∈Lr
+σ(D∞(z)) .
+(5.6)
+Given r > 0 and z ∈ Lr, let us denote by Ang(z) := sup{�
+z0I : I ∈ D∞(z)} if D∞(z) ̸=
+∅ and Ang(z) := 0 otherwise.
+Then, the set D∞(z) is included in the spherical cap
+Cone(z, Ang(z)) ∩ ∂Hd+1, which means σ(D∞(z)) ≤ CAng(z)d. Moreover, the quantity
+Ang(z) is bounded by the Maximal Backward angular Deviation MBD∞
+r (z): see Definition
+5.1. We then get
+E
+� �
+z∈Lr
+σ(D∞(z))2�
+≤ E
+� �
+z∈Lr
+MBD∞
+r (z)2d�
+≤ Ce−dr
+(5.7)
+by Lemma 5.2 (applied with A = πer and p = 2d), where the constant C = C(d) > 0 does
+not depend on r > 0.
+Finally, (5.4) follows from combining (5.5), (5.6) and (5.7).
+Inequality (5.4) refers to the elements of Lr while (5.3) concerns Poisson points. Pass-
+ing from ones to others while preserving the uniformity of A in r requires some technical
+considerations. We now extend (5.4) to annuli and then to balls.
+Step 2. For any A large enough there exists c0 = c0(d, A) > 0 such that for any r > 0
+and 0 < δ′ < 1,
+E
+�
+#
+�
+z ∈ N ∩ C(r, r + A − 2δ′) : σ(D∞(z)) > 0
+��
+≥ c0Vol
+�
+C(r, r + A − 2δ′)
+�
+,
+(5.8)
+16
+
+where we recall that C(r, R) has been defined in the notations of Section 2.
+For z ∈ Lr, recall that z↓ denotes the Poisson point whose arc |[z↓, A(z↓)]| crosses S(r)
+in z. In particular, σ(D∞(z)) and σ(D∞(z↓)) are equal. Henceforth,
+E
+�
+#
+�
+z ∈ N ∩ C(r, r + A − 2δ′) : σ(D∞(z)) > 0
+��
+≥ E
+�
+#
+�
+z ∈ Lr : z↓ ∈ B(r + A − 2δ′) and σ(D∞(z)) > 0
+��
+≥ c1E
+�
+#
+�
+z ∈ Lr : σ(D∞(z)) > 0
+��
+.
+(5.9)
+The inequality (5.9) makes the object of Lemma 5.5, and its proof is postponed to Section
+5.5. This choice is done as the proof uses arguments similar to the ones developed in the
+next Section in a more difficult case. The constants c1 = c1(d) > 0 and A above are chosen
+large enough according to Lemma 5.5. It then remains to use Step 1 and the inequalities
+Vol
+�
+C(r, r + A − 2δ′)
+�
+≤ Vol
+�
+B(r + A)
+�
+≤ Ced(r+A) ,
+to finally get
+E
+�
+#
+�
+z ∈ N ∩ C(r, r + A − 2δ′) : σ(D∞(z)) > 0
+��
+≥c1 c edr
+≥c1 × c × (CedA)−1Vol
+�
+C(r, r + A − 2δ′)
+�
+.
+Step 3. For short, let us set f(z′) := P(σ(D∞(z′)) > 0 | z′ ∈ N). The Mecke’s formula
+and Fubini’s theorem allow us to write:
+�
+C(r,r+A)
+E
+�
+#
+�
+z′ ∈ N ∩ B(z, δ′) : σ(D∞(z′)) > 0
+��
+dz
+= λ
+�
+z∈C(r,r+A)
+�
+z′∈B(z,δ′)
+f(z′) dz′ dz
+= λ
+�
+z′∈C(r−δ′,r+A+δ′)
+f(z′)Vol
+�
+B(z′, δ′) ∩ C(r, r + A)
+�
+dz′
+≥ λVol
+�
+B(δ′)
+� �
+z′∈C(r+δ′,r+A−δ′)
+f(z′) dz′
+≥ λVol
+�
+B(δ′)
+�
+E
+�
+#
+�
+z′ ∈ N ∩ C(r + δ′, r + A − δ′) : σ(D∞(z′)) > 0
+��
+≥ λVol
+�
+B(δ′)
+�
+c0Vol
+�
+C(r + δ′, r + A − δ′)
+�
+(5.10)
+by Step 2.
+Now, using Inequalities (2.2), it is not difficult to choose ˜c = ˜c(d) > 0 (small) and A =
+A(d) > 0 large enough and uniform on r > 0 and δ′ < 1 such that Vol(C(r +δ′, r +A−δ′))
+is bigger than ˜cVol(C(r, r + A)). Combining with (5.10), we get
+�
+C(r,r+A)
+E
+�
+#
+�
+z′ ∈ N ∩ B(z, δ′) : σ(D∞(z′)) > 0
+��
+dz ≥ c2Vol
+�
+B(δ′)
+�
+Vol
+�
+C(r, r + A)
+�
+.
+with c2 := λc0˜c. This forces the existence of some (r + h; u) ∈ C(r, r + A), with h ∈ [0, A]
+and u ∈ Sd, satisfying
+E
+�
+#
+�
+z′ ∈ N ∩ B((r + h; u), δ′) : σ(D∞(z′)) > 0
+��
+≥ c2Vol
+�
+B(δ′)
+�
+.
+(5.11)
+17
+
+To conclude, let us first specify that (5.11) holds for any direction u ∈ Sd by isotropy
+of the model. Moreover, for any given h0 > 0, the radius r + h with r > h0 can be written
+as r′ + h′ where r′ > 0 and h′ ∈ [h0, h0 + A]. Hence, we have proved that there exists A
+large and c2 = c2(A, d, λ) > 0 such that for any 0 < δ′ < 1, h0 > 0 and r > 0, there exists
+h ∈ [h0, h0 + A] such that (5.11) holds for any u ∈ Sd. This is Lemma 5.3.
+This last change on quantifiers, i.e. r > h0 and h ∈ [0, A] replaced with r > 0 and
+h ∈ [h0, h0 + A], will allow us to take simultaneously h in the good interval [h0, h0 + A]
+and also large enough. See Section 5.4.
+5.3
+A stabilization result for subtrees of the RST
+For 0 < δ′ < δ and r, h > 0, recall that z2 = (r + h; u) and recall the definition of
+Stab(r, h, δ′) in (4.7). In this section, we prove a stabilization result: subtrees of the RST
+rooted at Poisson points in B(z2, δ′) do not depend on what happens inside B(r) w.h.p.
+as h → ∞.
+Lemma 5.4. For any 0 < δ′ < δ,
+lim
+h→∞ sup
+r>0
+P(Stab(r, h, δ′)) = 1 .
+Proof. Let us denote by χ the union of descendant sets D(z) with z in N ∩ B(z2, δ′).
+So, for the configuration in B(r) to alter χ, it must exist a vertex z′ = (r′; u′) ∈ χ
+whose B+(z′, d(z′, A(z′))) overlaps B(r), which means d(z′, A(z′)) ≥ r′ − r.
+Roughly
+speaking, this would imply the occurrence of a large ball empty of Poisson points with
+radius r′ − r ≥ h − δ′ which is very unlikely as h → ∞. Hence, Stab(r, h, δ′)∁ is included
+in I ∪ II where, for a positive constant M > 0,
+I :=
+�
+χ ̸⊂ Cone(z2, Me−r−h)
+�
+and
+II :=
+�
+∃z′ = (r′; u′) ∈ N ∩ Cone(z2, Me−r−h) : d(z′, A(z′)) ≥ r′ − r
+�
+.
+We are going to prove that there exist c, C > 0 (not depending on r, h and M) such that
+∀r, h > 0, P(I) ≤
+C
+Md/2 + e−cM and
+lim
+h→∞ sup
+r>0
+P(II) = 0 .
+(5.12)
+The previous statement holding whatever the constant M > 0, Lemma 5.4 then follows.
+Let us deal with P(II). By Mecke’s formula and δ′ < 1,
+P(II)
+≤
+E
+�
+#
+�
+z′ = (r′; u′) ∈ N ∩ Cone(z2, Me−r−h) : d(z′, A(z′)) ≥ r′ − r
+��
+≤
+�
+n≥h−1
+λ
+�
+Vn
+P
+�
+d(z′, A(z′)) ≥ n | z′ ∈ N
+�
+dz′
+where Vn := Cone(z2, Me−r−h) ∩ C(r + n, r + n + 1). On the one hand, for z′ ∈ Vn,
+P
+�
+d(z′, A(z′)) ≥ n | z′ ∈ N
+�
+≤ P
+�
+N ∩ B+(z′, n) = ∅
+�
+= e−λVol(B+(z′,n)) .
+Here we need a lower bound of B+((r′; ·), ρ) and use the one obtained in [12, eq. (A1)]:
+there exists c = c(d) > 0 such that, for any radii r′, ρ ≥ 1,
+Vol
+�
+B+((r′; ·), ρ)
+�
+≥ ced(r′∧ρ)/2 .
+(5.13)
+18
+
+So we use (5.13) to get
+P(d(z′, A(z′)) ≥ n | z′ ∈ N) ≤ e−λcedn/2.
+On the other hand, we upperbound the volume of Vn:
+Vol(Vn)
+=
+� r+n+1
+r+n
+sinh(ρ)d dρ × σ
+�
+{u′ ∈ Sd : �
+u0u′ ≤ Me−r−h}
+�
+≤
+cded(r+n) × Mde−d(r+h)
+=
+cdMded(n−h) .
+Putting together the previous upperbounds, we get:
+P(II) ≤ λcdMde−dh �
+n≥h−1
+edn−λcedn/2,
+(5.14)
+which tends to 0 as h → ∞ uniformly on r.
+Let us now consider the term P(I). Let us denote by πz the path of RST starting from
+the Poisson point z until the origin. We define Rad(z2) as the maximal angular deviation
+generated by a path πz starting from some z ∈ B(z2, δ′) when it goes through the sphere
+S(r + h − δ′):
+Rad(z2) := max
+� �
+u0u′ : ∃z ∈ N ∩ B(z2, δ′) s.t. πz intersects S(r + h − δ′) at (·; u′)
+�
+.
+The maximal angular deviation cannot be too large.
+Precisely, setting with Rad :=
+{Rad(z2) ≤ Me−(r+h−δ′)}, Lemma 4.3 of [12] states that P(Rad∁) ≤ e−cM for c = c(d) > 0
+and M large enough. Besides,
+P(I ∩ Rad)
+=
+P
+��
+∃z′ = (r′; ·) ∈ N ∩ B(z2, δ′) : MBD∞
+r′ (z′) ≥ Me−(r+h)�
+∩ Rad
+�
+≤
+E
+�
+1Rad
+�
+z′∈N ∩B(z2,δ′)
+1{MBD∞
+r′ (z′)d≥Mde−d(r+h)}
+�
+≤
+M−ded(r+h)E
+�
+1Rad
+�
+z′∈N ∩B(z2,δ′)
+MBD∞
+r′ (z′)d�
+.
+Now, in order to apply Lemma 5.2, we have to turn the sum over elements of N ∩B(z2, δ′)
+into a sum over elements of Lr+h−δ′. Given z′ = (r′; ·), let us denote by Ar+h−δ′
+r′
+(z′) the
+intersection point between the path πz′ of RST and S(r + h − δ′). It is the ‘ancestor’ at
+radius r + h − δ′ < r′ of z′ in RST. A.s.
+1Rad
+�
+z′∈N ∩B(z2,δ′)
+MBD∞
+r′ (z′)d
+≤ 1Rad
+�
+z′∈N ∩B(z2,δ′)
+MBD∞
+r+h−δ′(Ar+h−δ′
+r′
+(z′))d
+≤
+�
+z′′∈BS(r+h−δ′)(z2,Me−(r+h−δ′))∩RST
+#
+�
+z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)
+�
+MBD∞
+r+h−δ′(z′′)d.
+19
+
+Thus, the Cauchy-Schwarz inequality gives:
+E
+�
+1Rad
+�
+z′∈N ∩B(z2,δ′)
+MBD∞
+r′ (z′)d�
+≤ E
+�
+�
+z′′∈Lr+h−δ′
+#
+�
+z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)
+�2�1/2
+×E
+�
+�
+z′′∈BS(r+h−δ′)(z2,Me−(r+h−δ′))∩RST
+MBD∞
+r+h−δ′(z′′)2d�1/2
+. (5.15)
+On the one hand, let us write
+�
+z′′∈Lr+h−δ′
+#
+�
+z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)
+�2
+≤
+�
+�
+z′′∈Lr+h−δ′
+#
+�
+z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)
+��2
+=
+�
+#N ∩ B(z2, δ′)
+�2
+which means that the first term of the upper bound in (5.15) is bounded by C1 := E[#(N ∩
+B(1))2]1/2. Finally we apply Lemma 5.2 to the second term of the upper bound in (5.15):
+it is bounded by the square root of CMde−2d(r+h−δ′). Combining the previous bounds, we
+get
+P(I ∩ Rad) ≤ CM−d/2.
+(5.16)
+Gathering (5.14) and (5.16) proves Lemma 5.4.
+5.4
+Conclusion
+Let us prove Lemma 4.5. We pay a special attention to dependencies between parameters.
+Let A > 0 and c0 = c0(A, d, λ) > 0 given by Lemma 5.3. It is well known that
+E
+�
+#N ∩ B(z2, δ′) 1#N ∩B(z2,δ′)≥2
+�
+(5.17)
+which does not depend on r, h by stationarity of the PPP, is negligible w.r.t. Vol(B(δ′))
+as δ′ → 0. Hence we choose δ′ > 0 small enough and uniformly on r, h > h1 = h1(d) so
+that the expectation (5.17) and
+P
+�
+∃z ∈ N ∩ B(z2, δ′), D(z)\{z} ̸⊂ B(r + h + δ′)∁�
+are both smaller than c0
+4 Vol(B(δ′)). This second upper-bound and the constant h1 = h1(d)
+are proved in Lemma 5.6, whose proof is postponed in Section 5.5. At this stage, parameters
+r > 0 and h > h1 are still free. Now we choose h0 ≥ h1 large enough so that for any h ≥ h0
+and uniformly on r > 0, the following holds by Lemma 5.4:
+P
+�
+Stab(r, h, δ′)∁�
+≤ c0
+4 Vol(B(δ′)) .
+Finally, for any given radius r > 0, we choose h (possibly depending on r) in [h0, h0 + A]
+such that
+E
+�
+#
+�
+z ∈ N ∩ B(z2, δ′) : σ(D∞(z)) > 0
+��
+≥ c0Vol
+�
+B(δ′)
+�
+by Lemma 5.3.
+20
+
+For these fixed parameters A, c0, δ′, h0, r and h,
+c0Vol(B(δ′))
+≤
+E
+�
+#
+�
+z ∈ N ∩ B(z2, δ′) : σ(D∞(z)) > 0
+��
+≤
+P
+�
+∃!z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0
+�
++E
+�
+#{N ∩ B(z2, δ′)} 1#N ∩B(z2,δ′)≥2
+�
+≤
+P
+�
+∃!z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0
+�
++ c0
+4 Vol(B(δ′))
+from which we get P(∃!z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0) ≥
+3c0
+4 Vol(B(δ′)).
+Thus we
+conclude with
+P
+�
+F(r, h, δ′)
+�
+≥
+P
+�
+∃!z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0
+�
+− P
+�
+Stab(r, h, δ′)∁�
+− P
+�
+∃z ∈ N ∩ B(z2, δ′), D(z)\{z} ̸⊂ B(r + h + δ′)∁�
+≥
+c0
+4 Vol(B(δ′)) .
+So ε := c0
+4 Vol(B(δ′)) depending on A, d, λ and δ′, is suitable, and Lemma 4.5 is proved.
+5.5
+Technical lemmas
+To complete the proof of Lemma 4.5, it remains to state the two following technical lemmas.
+Lemma 5.5. There exists c1 = c1(d) > 0 such that for any A large enough, r > 0 and
+0 < δ′ < 1,
+E
+�
+#
+�
+z ∈ Lr : z↓ ∈ B(r + A − 2δ′) and σ(D∞(z)) > 0
+��
+≥ c1E
+�
+#
+�
+z ∈ Lr : σ(D∞(z)) > 0
+��
+.
+Proof. For the proof, we will consider first a portion of the sphere of radius r, and then
+extend the result to the whole Lr using the (Covering) Lemma 4.3.
+Step 1: Given z0 ∈ S(r), let us consider the event
+L(A, r) :=
+�
+∃z ∈ BS(r)(z0, e−r) ∩ Lr : z↓ /∈ B(r + A − 2δ′)
+�
+.
+For short, let us set X0,r := #
+�
+z ∈ BS(r)(z0, e−r) ∩ Lr : σ(D∞(z)) > 0
+�
+. We will prove
+that
+E
+�
+X0,r1L(A,r)∁
+�
+≥ 1
+2E[X0,r] .
+(5.18)
+With
+X0,r1L(A,r)∁ = #
+�
+z ∈ BS(r)(z0, e−r) ∩ Lr : z↓ ∈ B(r + A − 2δ′) and σ(D∞(z)) > 0
+�
+.
+Lemma 5.5 then immediatly follows from the above inequality with c1 := 1/(2K) using
+the (Covering) Lemma 4.3, where the covering constant K = K(d) is given in that lemma.
+The proof of (5.18) relies on the two following inequalities (5.19) and (5.20) which will
+be proved in a second time.
+The first inequality states that the probability of L(A, r) tends to 0 when A → ∞, uniformly
+on r, δ′:
+lim
+A→∞
+sup
+r>0, δ′<1
+P(L(A, r)) = 0 .
+(5.19)
+21
+
+The second inequality ensures that there exists c = c(d) > 0 such that for any r > 0,
+E
+�
+X0,r
+�
+≥ c .
+(5.20)
+Then, the Cauchy-Schwarz inequality gives
+E
+�
+X0,r1L(A,r)
+�
+≤ C1/2P(L(A, r))1/2
+where C = C(d) > 0 upperbounds the expectation of #
+�
+BS(r)(z0, e−r) ∩ Lr
+�2 thanks to
+Lemma 6.1. Thus, combining (5.19) and (5.20), we can choose A large enough uniformly
+on r ≥ 2 and δ′ < 1 such that
+E
+�
+X0,r1L(A,r)
+�
+≤ 1
+2E
+�
+X0,r
+�
+.
+This proves (5.18).
+Step 2: proof of (5.19). The proof is very close to that of Lemma 5.4 with fewer technical
+difficulties. By analogy, we write L(A, r) ⊂ I ∪ II where
+I :=
+�
+∃z ∈ BS(r)(z0, e−r) ∩ Lr : D(z) ̸⊂ Cone(z0, Ae−r)
+�
+and
+II :=
+�
+∃z ∈ BS(r)(z0, e−r) ∩ Lr : z↓ ∈ Cone(z0, Ae−r) ∩ B(r + A − 2δ′)∁�
+.
+We upperbound P(I) more easily than in the proof of Lemma 5.4 since the points z con-
+cerned by the event I are already in Lr:
+P(I)
+≤
+P
+�
+∃z ∈ BS(r)(z0, e−r) ∩ Lr : MBD∞
+r (z) ≥ Ae−r�
+≤
+A−2de2dr E
+�
+�
+z∈BS(r)(z0,e−r)∩Lr
+�
+MBD∞
+r (z)
+�2d�
+≤ CA−2d
+(by Lemma 5.2) which tends to 0 uniformly on r, δ′. The same holds for P(II) as in the
+proof of Lemma 5.4. For this reason, we omit the details.
+Step 3: proof of (5.20).
+This inequality is a consequence of isotropy of the model,
+(Covering) Lemma 4.3 and Step 1 in the proof of Lemma 5.3:
+E
+�
+#
+�
+z ∈ BS(r)(z0, e−r) ∩ Lr : σ(D∞(z)) > 0
+��
+=
+1
+N(r)
+N(r)
+�
+i=1
+E
+�
+#
+�
+z ∈ BS(r)(zi, e−r) ∩ Lr : σ(D∞(z)) > 0
+��
+≥
+1
+N(r)E
+�
+#
+�
+z ∈ Lr : σ(D∞(z)) > 0
+��
+≥ c C−1
+with N(r) ≤ Cedr. This concludes the proof of the Lemma.
+Lemma 5.6. There exists h1 = h1(d) > 0 such that the following limit is uniform on r > 0
+and h > h1:
+lim
+δ′→0
+1
+Vol(B(δ′))P
+�
+∃z ∈ N ∩ B(z2, δ′), D(z)\{z} ̸⊂ B(r + h + δ′)∁�
+= 0 .
+22
+
+Proof. The Mecke’s formula allows to write:
+P
+�
+∃z ∈ N ∩ B(z2, δ′), D(z)\{z} ̸⊂ B(r + h + δ′)∁�
+≤ P
+�
+∃z ∈ N ∩ B(z2, δ′), ∃z′ ∈ N ∩ B(r + h + δ′) s.t. A(z′) = z
+�
+≤ E
+�
+#
+�
+z ∈ N ∩ B(z2, δ′) : ∃z′ ∈ N ∩ B(r + h + δ′) s.t. A(z′) = z
+��
+= λ
+�
+B(z2,δ′)
+P
+�
+∃z′ ∈ N ∩ B(r + h + δ′) s.t. A(z′) = z | z ∈ N
+�
+dz .
+(5.21)
+For z in B(z2, δ′),
+P
+�
+∃z′ ∈ N ∩ B(r + h + δ′) s.t. A(z′) = z | z ∈ N
+�
+≤
+�
+n≥0
+E
+�
+#
+�
+z′ ∈ N ∩ Vδ′,n : A(z′) = z
+�
+| z ∈ N
+�
+where we set
+Vδ′,n := C(r + h − δ′, r + h + δ′) ∩ Cone(u, ne−r−h, (n + 1)e−r−h)
+and Cone(u, ne−r−h, (n + 1)e−r−h) is the set of directions u′ ∈ Sd such that ne−r−h ≤
+�
+u0u′ ≤ (n + 1)e−r−h. A second use of the Mecke’s formula gives:
+E
+�
+#
+�
+z′ ∈ N ∩ Vδ′,n : A(z′) = z
+�
+| z ∈ N
+�
+= λ
+�
+Vδ′,n
+P
+�
+A(z′) = z | z, z′ ∈ N
+�
+dz′ .
+Given z′ ∈ Vδ′,n, we have
+P
+�
+A(z′) = z | z, z′ ∈ N
+�
+= P
+�
+B+(z′, d(z, z′)) ∩ N = ∅
+�
+= e−λVol(B+(z′,d(z,z′))) .
+Moreover
+Vol(B+(z′, d(z, z′)))
+≥
+ce
+d
+2 d(0,z′)∧d(z,z′)
+by (5.13)
+≥
+ce
+d
+4 d(z,z′)
+since d(z, z′) ≤ 2d(0, z′)
+≥
+ce
+d
+4 c′n
+because z′ ∈ Vδ′,n and r + h is larger than some h1 = h1(d) > 0.
+Let us now compute the volume of Vδ′,n:
+Vol(Vδ′,n) =
+� r+h+δ′
+r+h−δ′ sinh(ρ)d dρ×σ
+�
+{u′ ∈ Sd : ne−r−h ≤ �
+u0u′ ≤ (n+1)e−r−h}
+�
+. (5.22)
+The first term of the r.h.s. of (5.22) is bounded by c1δ′ed(r+h) while the second one is
+bounded by c2nde−d(r+h) using (2.2). The previous constants ci, i ∈ {1, 2}, are positive
+and only depend on d. Hence, the volume of Vδ′,n is smaller than c1c2ndδ′. Combining
+what precedees, we finally get for any r > 0 and h > h1
+P
+�
+∃z′ ∈ N ∩ B(r + h + δ′) s.t. A(z′) = z | z ∈ N
+�
+≤
+�
+n≥0
+λe−λce
+d
+4 c′nc1c2ndδ′
+whose upperbound can be expressed as Cδ′ with C = C(λ, d, h1) is a positive, finite
+constant. It then remains to plug this bound in (5.21) to conclude.
+23
+
+6
+Proof of Proposition 3.8
+Let us first recall an upperbound for the number of elements of Lr in a cap BS(r)(·, e−r).
+Lemma 6.1 (Lemma 4.4 of [12]). For any p ≥ 1, there exists a constant C = C(d, p) > 0
+such that, for any r ≥ 0 and any direction z ∈ S(r),
+E
+�
+#
+�
+RST ∩ BS(r)(z, e−r)
+�p�
+≤ C .
+Thanks to the Covering Lemma (Lemma 4.3), it is now easy to prove that Lr =
+RST ∩ S(r) admits in expectation about edr elements:
+E
+�
+#Lr
+�
+≤
+N(r)
+�
+i=1
+E
+�
+#(BS(r)(zi, e−r) ∩ Lr)
+�
+≤ Cedr .
+(6.1)
+Finally, combining the previous inequality and (5.4) proved in Step 1 of Lemma 5.3, we
+get Proposition 3.8.
+A
+Arcs of the RST as a subset of Hd+1
+Given z1, z2 ∈ Hd+1, the arc |[z1, z2]| is precisely defined in Section 2.2 of [12] but for
+convenience we recall the main lines. Let us write zi = (ri; ui) with polar cooordinates,
+i ∈ {1, 2}. Whenever u1 and u2 are not antipodal (and it will be a.s. the case when z2
+is the ancestor of z1), we consider the unique geodesic γu1,u2 : [0, 1] → Sd on the sphere
+connecting u1 to u2. Then, the arc |[z1, z2]| is the path
+t ∈ [0, 1] �→
+�
+(1 − t)r1 + tr2; γu1,u2(φz1,z2(t))
+�
+∈ Hd+1
+where φz1,z2 : [0, 1] → [0, 1] is defined as
+φz1,z2(t) :=
+1
+�
+u10u2
+arccos
+�(1 − t) sinh(r1) + t cos(�
+u10u2) sinh(r2)
+sinh((1 − t)r1 + tr2)
+�
+.
+This construction of the arc |[z1, z2]| ensures that the distance to the origin (as well as the
+distance to z1) are monotonous along the path |[z1, z2]|.
+By Property 3.2, we know that the geodesics [z, A(z)] and [z′, A(z′)], for z, z′ ∈ N,
+can overlap only at their extremities. This is not the case any more when we use the arcs
+|[z, A(z)]| and |[z′, A(z′)]|. For any r > 0, it may exist some points z ∈ Lr belonging to
+several arcs, say |[z1, A(z1)]|, . . . , |[zk, A(zk)]|. Hence, such a point z will be counted with
+multiplicity k in Lr. Also, to identify without ambiguity this point z, we should formally
+represent it as a couple made up with its location in Hd+1 and one of the arcs generating it,
+say |[zi, A(zi)]|. In this case the vertex z↓ ∈ N is defined as z↓ := zi. In this article, we will
+commit the following abuse of notations: we will count elements of Lr with multiplicity
+without specifying the arcs distinguishing them.
+References
+[1] D. Ahlberg, J. Hanson and C. Hoffman. The number of geodesics in planar first-passage percolation
+grows sublinearly. arXiv:2208.11576, 2022.
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+[2] K.S. Alexander. Percolation and Minimal Spanning Forests in Infinite Graphs. Annals of Probability,
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+[3] G. Amir, O. Angel and D. Valkó. The TASEP speed process. Annals of Probability, 39(4):1205–1242,
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+[4] F. Baccelli and C. Bordenave. The radial spanning tree of a Poisson point process. Annals of Applied
+Probability, 17(1):305–359, 2007.
+[5] F. Baccelli, D. Coupier, and V.C. Tran. Semi-infinite paths of the 2d-radial spanning tree. Advances
+in Applied Probability, 45(4):895–916, 2013.
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+
diff --git a/VdE0T4oBgHgl3EQf2wKz/content/tmp_files/load_file.txt b/VdE0T4oBgHgl3EQf2wKz/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..aceff7f61008136d54912ab2a9ce90480def0c46
--- /dev/null
+++ b/VdE0T4oBgHgl3EQf2wKz/content/tmp_files/load_file.txt
@@ -0,0 +1,1149 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf,len=1148
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='02717v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='PR]  6 Jan 2023  Thick trace at infinity  for the Hyperbolic Radial Spanning Tree  David Coupier∗,  Lucas Flammant†,  Viet Chi Tran‡  January 10, 2023  Abstract  Since the works of Howard & Newman (2001), it is known that in straight radial  rooted trees, with probability 1, infinite paths all have an asymptotic direction and  each asymptotic direction is reached by (at least) an infinite path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Moreover, there  exists a set of ’exceptionnal’ directions reached by (at least) two infinite paths which  is random, dense and only countable in dimension 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Howard & Newman’s method  says nothing about (random) directions reached by more than two infinite paths and,  in particular, if such ’very exceptionnal’ directions exist in dimension 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In this pa-  per, we prove that the answer is no for the hyperbolic Radial Spanning Tree (RST):  in dimension 2, this tree does not contain 3 infinite paths with the same (random)  asymptotic direction with probability one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Turned in another way, this means that  there is no infinite but thin subtree in the hyperbolic RST, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' whose infinite paths  would all have the same asymptotic direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We actually prove a stronger result in  dimension d + 1, d ≥ 1, stating that any infinite subtree of the hyperbolic RST a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  generates a thick trace at infinity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the set of asymptotic directions reached by its  infinite paths has a positive measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Key words:  hyperbolic space, stochastic geometry, random geometric tree, Radial  Spanning Tree, continuum percolation, Poisson point processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  AMS 2010 Subject Classification: Primary 60D05, 60K35, 82B21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This work has been supported by the RT GeoSto 3477, the Labex  Bézout (ANR-10-LABX-58), the ANR PPPP (ANR-16-CE40-0016) and the ANR GrHyDy  (ANR-20-CE40-0002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' thanks the CRM Montréal (IRL CNRS 3457) where part of  this work was completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  1  Introduction  Unlike combinatorial random graphs whose Erdös-Rényi model is certainly the most famous  specimen (see [15, 24]), the structure of a geometric random graph depends on the locations  of its vertices (embedded in a metric space) and on some geometrical rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This feature  makes geometric random graphs suitable to model real phenomena (in biology, material  science, image analysis or telecommunication networks) and this is the reason why they  ∗IMT Nord Europe, Institut Mines Télécom, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Lille, david.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='coupier@imt-nord-europe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='fr  †LAMAV, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Polytechnique Hauts-de-France, CNRS  ‡LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' IRL 3457, CRM-CNRS, Université de  Montréal, Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' chi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='tran@univ-eiffel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='fr  1  have been intensively studied in the last decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' See the book of Penrose [21] for a general  reference on the topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For geometric random graphs, macroscopic properties trigger challenging questions,  such as studying the number of the topological ends of these structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Alexander solves  this question in [2] for Minimal Spanning Forests on infinite graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the case of Euclidean  trees, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' trees whose vertices are points of Rd+1 with d ≥ 1, a fundamental step has been  taken by Howard & Newman for straight rooted trees, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  whose subtrees are all the  thinner as their roots are far away from that of the entire tree [18, Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' They  develop an efficient method [18, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8] ensuring that any straight tree T satisfies  the two following properties almost surely (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='):  (A) Every infinite path (zn)n≥0 of T– a sequence of different vertices (zn)n≥0 such that  {zn, zn+1} is an edge of the tree for every n ≥ 0 –admits an asymptotic direction u in the  unit sphere Sd of Rd+1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  lim  n→+∞  zn  |zn| = u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1)  (B) Every direction u ∈ Sd is asymptotically reached by (at least) one infinite path of the  tree T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  We will also say that the direction u satisfying (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1) is asymptotically reached or targeted  by the path (zn)n≥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the whole paper, the dimension of the ambiant space is denoted  by d + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Howard and Newman applied their method to the case of first-passage percolation  trees built on a Poisson Point Process (PPP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' They also proved that, for any deterministic  u ∈ Sd, the tree T a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' contains exactly one infinite path with u as asymptotic direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  However there exists a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' a set of random directions, thought as ’exceptional’, targeted by  at least two infinite paths which is dense in Sd, and only countable in dimension 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' See  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 1 and Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7 for details about these ’exceptional’ directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Howard & Newman’s method then motivated many works on geometric random trees  (in particular in dimension 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Various authors stated the straightness of their favorite  tree so as to obtain Properties (A) and (B) for its infinite paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Here are some examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The Directed Last-Passage Percolation (LPP) Tree is obtained by a last-passage procedure  from i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' weights associated to the vertices of the grid Nd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the case of exponential  weights and d + 1 = 2, Ferrari & Pimentel [16] established the straightness of the directed  LPP tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' From asymptotic directions of infinite paths of the LPP tree, they deduced  the existence of an asymptotic direction for a competition interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Other works focused  on geometric trees directed towards a distinguished point 0, with edges defined by local  geometric rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A first example is the Radial Spanning Tree (RST) introduced by Baccelli  & Bordenave in the Euclidean plane to model communication networks [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Each vertex  of this tree has an outgoing edge towards the nearest vertex among those closer to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The  hyperbolic RST studied in this paper is an extension of their RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Using a directed forest  (namely the Directed Spanning Forest) approximating locally, in distribution and far from  the root the RST, they proved the straightness of the RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A second example is the Nav-  igation Tree defined by Bonichon & Marckert in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Each vertex has also outdegree one  and the corresponding edge links it to the closet vertex in a given cone directed towards  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' To describe the asymptotic geometry of the navigations paths, the authors stated the  straightness of the Navigation Tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Since in dimension 2, only a countable number of random directions are targeted by at  least two infinite paths, it is natural to ask whether some of them are ‘very exceptional’,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' targeted by more than two infinite paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Assuming the non-crossing path property  2  (satisfied by all the previously mentioned trees), the existence of such a ’very exceptional’  direction would mean that of an infinite subtree– containing the middle infinite path –  which would be very thin because trapped between both extreme infinite paths having the  same asymptotic direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The existence of such a subtree is suspicious since it is involved  in a spatial competition that it neither wins (it fails to occupy a macroscopic part of the  space) nor loses (it is unbounded).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This heuristic sustains the following refinement of the  Howard & Newman’s results:  Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For most of straight bi-dimensional geometric random trees having the  non-crossing path property which are studied in the literature (including those cited above),  there is no (random) direction targeted with more than two infinite paths with probability  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  To our knowledge, this conjecture has been established in only one case: for the Directed  LPP Tree with exponential weights in N2 by Coupier [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' His proof is based on a surprising  coupling– exhibited for the first time by Rost [23] –between the LPP model and the Totally  Asymmetric Simple Exclusion Process (abbreviated in the literature to TASEP) and on  results on some special particles (called second class particles) of this particle system [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In this paper, we present a second example satisfying this conjecture, namely the  hyperbolic Radial Spanning Tree introduced in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us emphasize that  the nature of this new example is completely different from the first one since it lies in a  continuum hyperbolic space instead of N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Figure 1: Simulation of the two-dimensional hyperbolic RST, with λ = 30, in the Poincaré  disc model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The edges are represented by geodesics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The different connected components of  the RST (apart from the root) are represented with different colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This coloring allows  to distinguish some random directions reached by two infinite paths, namely the three  directions separating the three colored traces at infinity: see Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The construction of the hyperbolic RST is the same as for the bi-dimensional Euclidean  RST of Baccelli & Bordenave [4], whatever the dimension d + 1 ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The set of vertices  3  >is given by a homogeneous Poisson Point Process (PPP) N of intensity λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The RST  rooted at the origin 0 is the graph obtained by connecting each point z ∈ N to its parent  A(z), defined as the closest point to z among all points z′ ∈ N ∪ {0} that are closer to the  origin than z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This procedure defines a random radial tree rooted at 0 which is straight  in Hd+1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' see [12, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7] or Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This key property is available  here thanks to the fact that the hyperbolic metric guarantees that angular deviations of  RST paths decay exponentially fast with the distance to the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This feature entails in  fact much more than the straightness of the hyperbolic RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It also implies that there is  a positive proportion of RST edges at level r giving rise to infinite paths (Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8  below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This later statement does not occur in the Euclidean case, where the probability  that a given edge at level r belongs to an infinite path tends to 0 as r → ∞ [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Our main result (Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5) holds in any dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Heuristically, we will show that  the set of directions u ∈ Sd that are asymptotically reached by infinite paths stemming  from an arbitrary Poisson point z, called the trace of z at infinity, is either empty or has  positive measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the first case, the subtree rooted at z is finite while in the second case,  it is infinite and generates a thick trace at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In dimension 2, thanks to planarity  and the non-crossing path property, it is easily deduced from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 that a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' there  is no direction reached by more than two infinite paths, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' See Corollary  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6, Item (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 can be summarized by the geometric construction depicted  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 2 and mainly relies on the fact that the probability with which a given Poisson  point z at level r generates a thick trace at infinity (plus extra conditions as in partic-  ular a stabilization criteria) is bounded away from 0 uniformly on r (Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This  technical result is specific to the hyperbolic metric: this explains why we are able to prove  Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 for the hyperbolic RST and not for its Euclidean counterpart (although  the Euclidean RST contains in proportion fewer infinite paths than the hyperbolic RST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 also uses a control of path fluctuations developed in [12] (recalled Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In Section 2, we recall shortly some results on the hyperbolic geometry that will be  useful in the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In Section 3, we enounce our main result: Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 for the general  dimension d + 1, d ≥ 1, and its Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6 in dimension 2, that answers the Conjecture  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 for the hyperbolic Radial Spanning Tree, providing the first example in continuum  space where this question can be answered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Section 4 presents the proofs of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5  and of the technical Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 introduced in the previous paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Section 5 is devoted  to the proof of this later result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Finally, in Section 6, we prove that there is a positive  proportion of points of the tree at level r that generates thick tracks at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  2  Hyperbolic geometry and notations  Generalities on hyperbolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We refer to [7, 8, 20, 22] for a complete introduc-  tion to hyperbolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For d ∈ N∗ = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' }, the (d + 1)-dimensional hyperbolic  space denoted by Hd+1 is a (d + 1)-dimensional Riemannian manifold of constant negative  curvature −1 that can be defined by several isometric models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' One of them is the open-ball  model D (or Poincaré disc model in dimension 2) consisting in the unit open-ball  D := {(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , xd+1) ∈ Rd+1 : x2  1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' + x2  d+1 < 1}  4  endowed with the metric:  ds2  D := 4  dx2  1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' + dx2  n+1  (1 − x2  1 − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' − x2  d+1)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The volume measure on (D, ds2  D) is then given by 2d+1dx1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' dxd+1/(1−x2  1−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='−x2  d+1)d+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  A convenient way to represent points in the open-ball model is to use polar coordinates  (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the origin 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Any z ∈ D can be written as z = (r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) where r = d(z, 0) is its  distance to 0 and u ∈ Sd is its direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let σ be the spherical probability measure  on Sd (in particular σ(Sd) = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In polar coordinates, the rescaled volume measure Vol,  corresponding to the rescaled probability measure σ, becomes  dVol(r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) = sinh(r)d dr dσ(u) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1)  The choice of rescaling of the volume measure is adopted to avoid writing the constant  2π(d+1)/2/Γ((d+1)/2) that would appear a lot in the paper otherwise (this constant is the  non-rescaled measure of Sd, see [8, (III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='10) p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='125]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The hyperbolic space Hd+1 is also naturally equipped with a set of points at infinity  denoted by ∂Hd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In the open-ball model, this set is identified with the unit sphere  Sd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The distances are distorted in comparison with the Euclidean distance and become  ‘smaller’ when we approach the boundary ∂D = Sd, which is at infinite hyperbolic distance  from the center 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We also set Hd+1 := Hd+1 ∪ ∂Hd+1 endowed with the topology given  by the closed ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In (D, ds2  D), geodesics are of two types: either diameters of D or arcs perpendicular  to the boundary ∂D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Also, this model is conformal in the sense that the hyperbolic angle  between two geodesics is equal to the Euclidean angle between them, in the open ball  representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Another important fact about hyperbolic geometry is that all points and  all directions play the same role: Hd+1 is homogeneous and isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We denote by d(·, ·) the hyperbolic distance in Hd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For z, z′ ∈ Hd+1, let  [z, z′] be the geodesic between z and z′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We will denote by (z, z′) the geodesic without the  extremities z and z′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For z ∈ Hd+1 and r > 0, we respectively denote by B(z, r) := {z′ ∈ Hd+1 : d(z, z′) < r}  and S(z, r) := {z′ ∈ Hd+1 : d(z, z′) = r} the hyperbolic open ball and hyperbolic sphere  centered at z with radius r > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We will write B(r) := B(0, r) and S(r) := S(0, r) for  short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Writting Vol(B(r)) =  � r  0 sinhd(ρ)dρ (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' [22, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='79]), it is easy to prove that  there exists c = c(d) ∈ (0, 1) such that for any r ≥ 1,  cedr ≤ Vol(B(r)) ≤ νedr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2)  Let us also denote by C(z, r, R) := {z′ ∈ Hd+1 : r < d(z, z′) < R} the annulus with radii  r < R and C(r, R) := C(0, r, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For z, z′, z′′ ∈ Hd+1, �  zz′z′′ is the measure of the corresponding (non-oriented) hyperbolic  angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any z ∈ Hd+1 and θ > 0, Cone(z, θ) := {z′ ∈ Hd+1 : �  z0z′ ≤ θ} is defined as the  cone of apex 0, axis z and aperture θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In addition, for z ∈ Hd+1 and r > 0, we will use the  spherical cap  BS(r)(z, θ) := Cone(z, θ) ∩ S(r) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3)  For its surface, note that there exists a constant C = C(d) > 0 such that:  σ  �  BS(r)(z, θ)  �  ≤ Cθd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4)  5  3  Main results  In the sequel, we pick some arbitrary origin point 0 ∈ Hd+1 (thought as the center of D in  the open-ball representation) to be the root of the hyperbolic RST that we now define.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The hyperbolic RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let N be a homogeneous PPP of intensity λ > 0 in Hd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The  definition of the hyperbolic RST is similar to the Euclidean case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This is a directed graph  whose vertex set is N ∪ {0} and in which each vertex z ∈ N is connected to the closest  Poisson point among (N ∪ {0}) ∩ B(r), with r := d(0, z), for the hyperbolic distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 (Radial Spanning Tree in Hd+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The ancestor of z ∈ N is defined as  A(z) :=  argmin  z′∈(N ∪{0})∩B(d(0,z))  d(z′, z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1)  The Radial Spanning Tree (RST) in Hd+1 is the directed graph (V, ⃗E) where V := N ∪{0}  and ⃗E := {(z, A(z)) : z ∈ N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Since N ∪ {0} contains no isosceles triangles with probability 1, the ancestor A(z) of  any Poisson point z is a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In other words, any Poisson point admits only  one outgoing edge, but possibly several ingoing edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In any case, these ingoing edges are  finitely many:  Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 (Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 of [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the RST is a tree rooted at 0 where all vertices  have finite degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the bi-dimensional case (d = 1), the union of geodesics [z, A(z)],  z ∈ N, is planar, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' whatever z ̸= z′ ∈ N, the geodesics [z, A(z)] and [z′, A(z′)] may only  overlap on their endpoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For z ∈ N and r > 0, we also define  B+(z, r) := B(z, r) ∩ B(d(0, z))  and  B+(z) := B+(z, d(z, A(z))) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2)  By construction of the ancestor, the random set B+(z) avoids the PPP N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This fact is  responsible for many difficulties when studying the RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Indeed, when restarting from  A(z) = (r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u′) and constructing the path forward (towards 0), with probability 1, B(r′) ∩  B+(z) is non-empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This means that the geometric information used to determine A(z)  is still involved for next steps of the process, generating statistical dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  A path of the RST is a sequence (finite or not) of different vertices (z0, z1, z2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=') in  N ∪ {0} such that A(zn+1) = zn for any n ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1), we have that for all z ∈ N,  d(0, A(z)) < d(0, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Applying this to z = zn, n ≥ 1, we obtain that d(0, zn) < d(0, zn+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The path (z0, z1, z2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=') can thus be viewed as an exploration of the RST starting at z0  and moving away from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We will say that the forward direction is towards 0 and the  backward direction is towards infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Every path can be started at z0 = 0, but this is not  an obligation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The set of descendants D(z) of a given vertex z is made up of all vertices that can be  reached by a backward finite path starting at z (including z itself by convention).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Because  a vertex can be the ancestor of no other vertex, all sets of descendants are not infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  As mentioned in the Introduction, a very important feature of the hyperbolic RST is  its straightness:  Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 (Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7 of [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' for any ε > 0 there exists some r0 > 0 such  that, for any radius r ≥ r0 and for any vertex z of the hyperbolic RST with d(0, z) ≥ r,  the set of descendants D(z) is contained in a cone of apex 0 and aperture e−(1−ε)r, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' for  any z′, z′′ ∈ D(z), �  z′0z′′ ≤ e−(1−ε)r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  6  Trace on the boundary ∂Hd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us consider a point z ∈ N and its set of descendants  D(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' When it is infinite, it contains (at least) an infinite path (zn)n≥0 by the finite degree  property (Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 of [12] then asserts that the path (zn)n≥0 admits  an asymptotic direction u ∈ ∂Hd+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Thus, let us define by D∞(z) the set of asymptotic  directions in ∂Hd+1 that can be reached by the infinite paths of D(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Roughly speaking,  D∞(z) is the trace left by the set of descendants D(z) on the boundary ∂Hd+1 (see the  traces at infinity left by the children of 0 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We just have proved that:  Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' for any vertex z ∈ N,  #D(z) = +∞ ⇐⇒ D∞(z) ̸= ∅ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3)  Our main result (Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5) establishes a stronger statement: infinitely many de-  scendants in D(z) actually implies that D(z) leaves a trace with positive volume at infinity,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' σ(D∞(z)) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In this case, we will say that z generates a thick trace at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Consider the hyperbolic RST in Hd+1, for any dimension d ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' for  any vertex z ∈ N, either z admits finitely many descendants or σ(D∞(z)) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Consequence in H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 holds in any dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In dimension 2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' with  d = 1), combined to the non-crossing path property (Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2), it leads to Conjecture  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1: a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the RST does not contain three infinite paths with the same (random) asymptotic  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This statement– Item (iii) of Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6 –completes the description of infinite  paths and their asymptotic directions of the hyperbolic RST started in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The first  three items below are given by [12, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Their proofs are based on the strategy  developed by Howard and Newman in [18] and on the straightness of the hyperbolic RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The following properties concern the hyperbolic RST in H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (o) A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' any infinite path admits an asymptotic direction and, for any u ∈ ∂H2, the RST  contains an infinite path with asymptotic direction u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (i) For any (deterministic) u ∈ ∂H2, the RST a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' contains a unique infinite path with  asymptotic direction u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (ii) A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the subset of ∂H2 of asymptotic directions reached by at least two infinite paths  is dense and countable in ∂H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (iii) A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' no (random) asymptotic direction of ∂H2 is reached by more than two infinite  paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Item (o) says that any u in ∂H2 is reached by at least one infinite path and exactly  one when u is deterministic (Item (i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exist by Item (ii) asymptotic directions  which are reached by several infinite paths but these directions are random and few (only  countable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Finally, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 specifies that there is no random asymptotic direction  reached by more than two infinite paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proof of Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6, Item (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us assume that the hyperbolic RST contains three  different infinite paths, say (xn)n≥0, (yn)n≥0 and (zn)n≥0 having the same asymptotic  direction in ∂H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Without loss of generality, we can also assume that these three paths  have no vertices in common.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  By the non-crossing path property and planarity, one of  these three infinite paths, say (yn)n≥0, is trapped between the two other paths which by  hypothesis have the same asymptotic direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This forces σ(D∞(y0)) = 0 while the set of  descendants D(y0) is infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This occurs with null probability thanks to Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  7  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us show that the asymptotic direction separating the green and red traces  at infinity on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 1, is reached by two infinite paths (a green one and a red one).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the  green (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' red) infinite subtree, pick the leftmost (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' rightmost) infinite path in the  trigonometric sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Such construction makes sense in dimension 2 thanks to the non-  crossing path property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' These two paths πgreen and πred admit asymptotic directions, say  ugreen and ured in ∂H2 by Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6, Item (o).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' If ugreen and ured were different, any  asymptotic direction u′ located (strictly) between them shoud be reached by an infinite  path π thanks to Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6, Item (o).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' By construction of πgreen and πred, the path π  could not be neither green or red, leading to a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Positive density with σ(D∞(·)) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Although the previous results concern the combi-  natorial structure of the RST, it will be useful in the proofs to represent the graph RST  as a subset of Hd+1, denoted by RST, in which each edge (z, A(z)) is represented by the  arc |[z, A(z)]| (defined in Appendix A) and not by the (hyperbolic) geodesic [z, A(z)]:  RST :=  �  z∈N  |[z, A(z)]| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4)  This choice (somewhat unnatural) is motivated by the fact that the (hyperbolic) distance  to the origin 0 is monotonous along the arc |[z, A(z)]| which fails for the geodesic [z, A(z)]  (or for the Euclidean segment between z and its ancestor A(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In particular each arc  |[z, A(z)]| crosses any given sphere at most once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Thus, we define the RST at level r > 0  as the following random set:  Lr := RST ∩ S(r) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5)  Elements of Lr are a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' not Poisson points on S(r) with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' However we extend  to elements of Lr the notations D(·) and D∞(·) as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For z ∈ Lr, we denote by z↓  the Poisson point whose arc |[z↓, A(z↓)]| crosses S(r) at z: with a slight abuse of notations,  z↓ can be defined without ambiguity (see Appendix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Then we set D(z) = D(z↓) and  D∞(z) = D∞(z↓).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This section ends with a density result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8 heuristically says that in  expectation a macroscopic proportion of elements of Lr generates a thick trace at infinity:  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exists c = c(d) > 0 such that for any r > 0,  E  �  #{z ∈ Lr : σ(D∞(z)) > 0}  �  ≥ c E  �  #Lr  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8 contrasts with several Euclidean bi-dimensional trees [1, 11], including  the Euclidean RST [5], where the proportion of edges at level r belonging to infinite paths  is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8 is an immediate consequence of some intermediate results leading to  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5, and its proof is done in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It could be improved in several directions  (an almost sure result rather than in expectation, a positive limit of the ratio rather than  a positive lim inf etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=') but this is not the goal of the current work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  4  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1  Global strategy  Let r0 ∈ (0, 1), u0 ∈ Sd and select the closest Poisson point to (r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) (with polar coordi-  nates) denoted by  z0 := argmin  z∈N  d(z, (r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  8  Consider the event E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) on which the set of points at infinity D∞(z0) reached by  descendants of z0 is nonempty but with null volume:  E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) :=  �  D∞(z0) ̸= ∅ and σ  �  D∞(z0)  �  = 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1)  Our purpose is to prove that P(E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For δ > 0, let us consider the set G(δ) of descendants z of z0 whose ancestor A(z) is  not too close to z:  G(δ) :=  �  z ∈ D(z0) : d(z, A(z)) ≥ δ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let H(δ) be the set of corresponding radii:  H(δ) :=  �  r > 0 : ∃u ∈ Sd, (r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) ∈ G(δ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The next result states that, for δ small enough, if z0 admits infinitely many descendants  (or in an equivalent way D∞(z0) ̸= ∅) then infinitely many of them are in G(δ):  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any δ > 0 small enough, D∞(z0) ̸= ∅ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' implies that H(δ) is un-  bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For any radius r > 0, let NB(r) := N ∩ B(r) be the PPP N restricted to the ball  B(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The following Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 says that a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  on D∞(z0) ̸= ∅ the random variable  P(σ(D∞(z0)) > 0 | NB(r)) is bounded away from 0 for all radii r ∈ H(δ) and uniformly on  those radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any δ > 0 small enough, there exists ε > 0 such that, a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' on D∞(z0) ̸= ∅,  ∀r ∈ H(δ), P  �  σ(D∞(z0)) > 0 | NB(r)  �  ≥ ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2)  As shown below, Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 together imply P(E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0)) = 0 from which  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 immediatly follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The proofs of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 are respectively  postponed to Sections 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Choose parameters δ and ε such that both Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The second lemma says that for this choice of δ and ε, we have a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' on {D∞(z0) ̸= ∅} and  for any r ∈ H(δ),  P  �  E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) | NB(r)  �  ≤ P  �  σ(D∞(z0)) = 0 | NB(r)  �  ≤ 1 − ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Since ε is uniform on r ∈ H(δ) and since we work on {D∞(z0) ̸= ∅}, the set H(δ) is a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  unbounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We can take the lim inf: a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' on {D∞(z0) ̸= ∅},  lim inf  r→∞ P  �  E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) | NB(r)  �  ≤ 1 − ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3)  But the martingale convergence theorem asserts that:  lim  r→∞ P  �  E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) | NB(r)  �  = 1E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='u0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4)  So, on E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) ⊂ {D∞(z0) ̸= ∅}, the limit in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) equals 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Thus, both statements (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3)  and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) are compatible only if P(E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Hence, the union of the events E(r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) with rational radius r0 and rational direction  u0 has null probability too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Since any Poisson point is the closest one to some rational  element (r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0) of Hd+1, we can conclude that with probability 1, any vertex z ∈ N  satisfies either D∞(z) = ∅ (or D(z) is finite in an equivalent way) or σ(D∞(z)) is (strictly)  positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1  The proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 is based on a percolation argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' To set it up, we first need a  covering of the hyperbolic space Hd+1 (except in the vicinity of the origin) with a uniform  control of overlappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This will be done using the Covering Lemma (below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This  classical result will be used several times in this paper and is stated in [12, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 (Covering Lemma).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exists a covering constant K = K(d) > 0 such  that, for any r > 0, there exists a collection of N(r) points z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=', zN(r) ∈ S(r) such that:  (a) �  1≤i≤N(r) BS(r)(zi, e−r) = S(r),  (b) ∀z ∈ S(r), #{1 ≤ i ≤ N(r) : z ∈ BS(r)(zi, e−r)} ≤ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Moreover, there exists C = C(K, d) > 0 such that, for any r > 0, z ∈ S(r) and A ≥ 1, the  number of caps overlapping BS(r)(z, Ae−r) is bounded by CAd:  #  �  1 ≤ i ≤ N(r) : BS(r)(zi, e−r) ∩ BS(r)(z, Ae−r) ̸= ∅  �  ≤ CAd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In particular (taking A := πer in the previous inequality), N(r) ≤ Cedr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For any integer radius r > 0 and any index 1 ≤ m ≤ N(r), let us set  Br,m := C(r, r + 1) ∩ Cone(zr,m, e−r)  where {zr,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , zr,N(r)} is the collection of points of the sphere S(r) given by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3  (in this proof we stress the dependence on r of the zm’s by adding the index r in zr,m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Each block Br,m is based on the spherical cap BS(r)(zr,m, e−r) = S(r) ∩ Cone(zr,m, e−r)  and has thickness 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Two blocks Br,m and Br′,m′ are said to be adjacent, which is denoted  by Br,m ∼ Br′,m′, if they are at distance less than δ from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4 asserts  that the volumes of Br,m’s are uniformly bounded and the degrees in the graph generated  by the adjacency relation are bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exist two positive constants C1 and C2 only depending on d such that  for all integer radius r > 0 and m ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , N(r)}, the following holds :  Vol(Br,m) ≤ C1,  and  #  �  (r′, m′) : Br′,m′ ∼ Br,m  �  ≤ C2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' First, using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4),  Vol(Br,m)  =  � r+1  r  sinhd(ρ) × σ  �  Cone(zρ,m, e−ρ) ∩ Sd�  dρ  ≤  C  � r+1  r  edρ dρ × e−dr = C  d (ed − 1) =: C1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For the second inequality of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5), two blocks Br′,m′ and Br,m are adjacent whenever Br′,m′  overlaps {z ∈ Hd+1 : d(z, Br,m) ≤ δ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Since δ < 1 this forces r′ to be in {r − 1, r, r + 1}  and Br′,m′ to overlap Cone(zr,m, (1 + δ)e−r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Now, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 asserts that for each layer  r′ ∈ {r − 1, r, r + 1}, there are at most CAd = C(1 + δ)ded(r′−r) ≤ C2ded blocks Br′,m′  overlapping Cone(zr,m, (1+δ)e−r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Consequently, Br,m has at most C2 := 3C2ded adjacent  blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  10  The block Br,m is said δ-bad if it contains a Poisson point z such that d(z, A(z)) < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us first prove that it is possible to choose δ > 0 small enough so that the set of δ-bad  blocks denoted as Ψδ is a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' subcritical w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the adjacency relation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Ψδ only admits  finite connected components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' To do it, we first use the Mecke’s formula [14, Prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='IV]  to bound the probability for a block to be δ-bad: for any (r, m),  P  �  Br,m is δ-bad  �  ≤  E [#{z ∈ Br,m ∩ N : d(z, A(z)) < δ}]  =  E  �  #{z ∈ Br,m ∩ N : B+(z, δ) ∩ N ̸= ∅  �  =  λ  �  Br,m  P  �  B+(z, δ) ∩ N ̸= ∅  �  dz  ≤  λVol(Br,m)  �  1 − e−λVol(B(δ))�  ≤  λC1  �  1 − e−λVol(B(δ))�  =: p(δ)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6)  thanks to Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, P(Br,m is δ-bad) tends to 0 as δ → 0 uniformly on the couple  (r, m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In a second step, we adapt the Peierls argument to our context to establish the sub-  criticality of Ψδ for δ small enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Given (r, m), let Pr,m(k) be the set of paths with  length k of adjacent blocks starting at Br,m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4, #Pr,m(k) ≤ (C2)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Such a  path π = (B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , Bk) is said δ-bad if all the blocks Bi it contains are δ-bad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Henceforth  the probability for Br,m to belong to an infinite connected component of δ-bad blocks is  upperbounded by  lim sup  k→∞  �  π∈Pr,m(k)  P  �  π is δ-bad  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For any path π = (B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , Bk) in Pr,m(k), we can choose a subset of blocks {Bi1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , Biℓ}  included in {B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , Bk} such that the Bij’s are two by two non adjacent and ℓ ≥ k/C2  (here we use that each block has at most C2 adjacent blocks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Besides, the adjacency  relation has been defined so that the events {Bij is δ-bad}’s are mutually independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' So  P  �  π is δ-bad  �  ≤ P  �  Bi1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , Biℓ are δ-bad  �  ≤ p(δ)k/C2 ,  where p(δ) is defined in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It follows  �  π∈Pr,m(k)  P  �  π is δ-bad  �  ≤  �  C2p(δ)1/C2�k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Choosing δ small enough so that C2p(δ)1/C2 < 1, we then obtain that a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the block Br,m  cannot belong to an unbounded connected component of δ-bad blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Consequently, for  such parameter δ, the set Ψδ is subcritical with probability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  To conclude the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1, let us pick δ small enough such that the set of  δ-bad blocks does not percolate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Assume also that D∞(z0) is non empty, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the subtree  of the RST rooted at z0 admits (at least) one infinite path (zn)n≥0 of Poisson points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The  PPP N being locally finite, the path (zn)n≥0 cannot be stuck, from some index, inside a  δ-bad connected component of blocks which is bounded by choice of δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It eventually comes  out of each δ-bad connected component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Two cases must be distinguished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Either (zn)n≥0 visits infinitely many δ-good blocks where of course a block is said δ-good if  it is not δ-bad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, infinitely many of the zn’s satisfy d(zn, A(zn)) ≥ δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' These vertices  are in G(δ) which means that H(δ) is unbounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  11  Or, the infinite path (zn)n≥0 jumps infinitely many times from a δ-bad connected compo-  nent to another one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' But, by construction, two different bad connected components are at  distance at least δ from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' So these jumps provide as many zn’s in G(δ): H(δ) is  unbounded in this case too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2  In what follows, we will modify configurations locally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This is why we emphasize the  dependence of any random set A (think about D(z), D∞(z) or H(δ)) on the current  configuration η, a realization of the PPP N, by writting A[η].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Given r0 > 0 and u0 ∈ Sd, recall that z0 is the closest Poisson point to (r0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For  this section, let us consider a configuration η satisfying D∞(z0) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let δ > 0 and r > r0  be an element of the set H(δ)[η]– by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1, this latter set is unbounded provided δ  is small enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us set z1 := (r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) ∈ G(δ) for some u ∈ Sd (z1 is in N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In the sequel,  we will work conditionally on NB(r) = ηB(r), the configuration of the PPP N restricted to  the ball B(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let 0 < δ′ < δ and h > 0 (thought as large).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let also z2 := (r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) (with the same  direction as z1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The event Stab(r, h, δ′) encodes the fact that the set of descendants of  any Poisson point in B(z2, δ′) is not sensitive to what happens inside B(r):  Stab(r, h, δ′) :=  �  η′ : ∀z ∈ N ∩ B(z2, δ′), ∀η′′, D(z)[η′′  B(r) ∪ η′  B(r)∁] = D(z)[η′]  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7)  It will be proved in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4 that Stab(r, h, δ′) has a probability tending to 1 as h → ∞  uniformly on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us now introduce the event F(r, h, δ′) on which there exists z ∈ N ∩ B(z2, δ′) such  that the four following items hold:  (i) N ∩ B(z2, δ′) = {z},  (ii) σ(D∞(z)) > 0,  (iii) Stab(r, h, δ′) occurs  (iv) and D(z) ⊂ B(r + h + δ′)∁.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  On the event F(r, h, δ′), there is a unique point of the PPP N in the ball B(z2, δ′) that  has a thick trace at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This subtree is outside the ball B(r + h + δ′) and does not  depend on the points of N in the ball B(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The distance h is the separation gap ensuring  that the subtree rooted at z2 = (r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) remains independent from the Poisson points  inside the ball B(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 states that the event F(r, h, δ′) has a probability larger than some positive ε  which is uniform on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Getting such uniformity of ε (or A) on r will significantly complicate  the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5, postponed to Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exists A > 0 large enough such that, for any δ′ > 0 small enough,  there exists ε = ε(A, d, λ, δ′) > 0 such that for any h0 > 0 large enough and r > 0, there  exists h ∈ [h0, h0 + A] such that P(F(r, h, δ′)) ≥ ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Note also that among the previous  parameters, only h may depend on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For θ > 0, let us consider the subset U = U(r, h, δ′, θ) of Hd+1 defined as  U :=  �  B(r + h + δ′) \\ (B(r) ∪ B(z2, δ′))  �  ∩ Cone(0, θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8)  12  See Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let η′ ∈ F(r, h, δ′) such that η′  B(r) = ηB(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' When all the Poisson points of  the configuration η′ inside the set U are removed, the ancestor of z– the only Poisson point  in B(z2, δ′) according to the event F(r, h, δ′) –becomes z1 which itself is a descendant of z0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This leads to σ(D∞(z0))[η′  U∁] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This construction requires the hypothesis r ∈ H(δ)[η],  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' there is no Poisson points in B+(z1, δ), and this is the only place in the proof of Lemma  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 where it is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any r ∈ H(δ) with r ≥ r0, for any h and δ′ < δ/3, there exists θ  large enough such that the following statement holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Almost every configuration η′ with  η′  B(r) = ηB(r) and η′ ∈ F(r, h, δ′) satisfies σ(D∞(z0))[η′  U∁] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  PSfrag replacements  0  z0  z1  z  B(z2, δ′)  r  r + h + δ′  ∞  r0  Figure 2: Illustration of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Black dots are Poisson points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This picture represents  a configuration η′  U∁ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Poisson points of η′  U have been removed) where η′  B(r) = ηB(r)  and η′ ∈ F(r, h, δ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The ball B(z2, δ′) whose (deterministic) center z2 is marked by a  grey square, contains only one Poisson point, namely z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Its set of descendants D(z) is  represented by the hatched region and satisfies σ(D∞(z))[η′] > 0 (the bold black curve on  the unit sphere Sd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' When the set U is emptying of Poisson points then A(z)[η′  U∁] = z1  which means that σ(D∞(z0))[η′  U∁] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Edges in dotted lines have been modified after  deleting η′  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  We are now ready to prove Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Parameters A, δ′, ε and h0 are chosen according to Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Then  for any r > 0 there exists h ∈ [h0, h0 + A] such that P(F(r, h, δ′)) ≥ ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Because it requires  Stab(r, h, δ′), the event F(r, h, δ′) does not depend on the configuration inside the ball  B(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' So,  P  �  F(r, h, δ′) | NB(r) = ηB(r)  �  = P  �  F(r, h, δ′)  �  ≥ ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Now r can be chosen in H(δ) with r > r0 and 0 < δ′ < δ/3 so that Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6 applies:  ε  ≤  P  �  η′ ∈ F(r, h, δ′) | NB(r) = ηB(r)  �  ≤  P  �  σ(D∞(z0))[η′  U∁] > 0 | NB(r) = ηB(r)  �  =  P  �  σ(D∞(z0))[η′] > 0, η′  U = ∅ | NB(r) = ηB(r)  �  ≤  P  �  σ(D∞(z0)) > 0 | NB(r) = ηB(r)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Note that the lower bound ε = ε(A, d, λ, δ′) does not depend on the parameter r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  13  This section ends with the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Consider a configuration η′ equal to η inside the ball B(r) and be-  longing to the event F(r, h, δ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us first assume that, for the configuration η′  U∁, the  ancestor of the Poisson point z (whose existence is given by F(r, h, δ′)) is z1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  A(z)[η′  U∁] = z1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='9)  Let us prove Vol(D∞(z0))[η′  U∁] > 0 from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Since η′ ∈ F(r, h, δ′), the set of descendants  D(z)[η′] is included in B(r + h+ δ′)∁.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' So, removing Poisson points of η′  U modifies no edges  (z′, A(z′)) of the RST as long as A(z′) ∈ D(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In fact, removing η′  U may only add  new descendants to the vertex z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, D(z)[η′] is included in D(z)[η′  U∁] which leads  to σ(D∞(z))[η′  U∁] ≥ σ(D∞(z))[η′] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Finally, using A(z)[η′  U∁] = z1 which is itself a  descendant of z0, we get σ(D∞(z0))[η′  U∁] > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  It then remains to show (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let R be the hyperbolic distance between z and z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It is  sufficient to prove that B+(z, R) is included in U ∪B+(z1, δ) since, after removing Poisson  points in U, z1 would become the closest Poisson point to z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Here we use that r ∈ H(δ),  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the ball B+(z1, δ) contains no other Poisson points except z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us first remark that  R = d(z, z1) ≤ d(z, z2) + d(z2, z1) ≤ δ′ + h ≤ h + 1  with δ′ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' So, taking θ large enough such that B+(z, R) ⊂ Cone(0, θ), it then remains  to prove that  V := B+(z, R) ∩ B(r)  ⊂  B+(z1, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='10)  To do so, let us pick v1, v2, v3 on the geodesic γ between 0 and z as follows: v1, v2 and v3  are the intersection points between γ and resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the sphere S(0, r + h), S(0, r) and S(z, R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us denote by w the symmetric of z1 w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the line (0z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Henceforth, it is sufficient  to show that w, z1 and v3 belong to B+(z1, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' First, we have d(v2, z1) ≤ d(v1, z2) ≤ δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Thus, by symmetry, d(w, z1) ≤ d(w, v2) + d(v2, z1) = 2d(v2, z1) ≤ 2δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Since v3, v2 and z  are on the same geodesic, we can write:  d(v3, v2) = d(v3, z) − d(z, v2) ≤ R − h + δ′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Since R ≤ h + δ′, we get d(v3, v2) ≤ 2δ′ and then d(v3, z1) ≤ d(v3, v2) + d(v2, z1) ≤ 3δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Whenever δ′ < δ/3, the three points w, z1 and v3 are inside B+(z1, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This proves (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='10)  and concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  5  Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5: uniformity in r  This section is devoted to the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' P(F(r, h, δ′)) ≥ ε where the lower  bound ε does not depend on r, h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Recall the notation of Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 and of Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We  first prove in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 that a positive proportion of Poisson points of B(z2, δ′) satisfies  σ(D∞(·)) > 0– Item (ii) in the definition of F(r, h, δ′) –where z2 = (r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Then we  prove that the properties described by the other three items occur with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  In particular we state in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 that Stab(r, h, δ′) has a probability tending to 1  as h → ∞ uniformly on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  But first, in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1, we recall some properties of the  Maximal Backward angular Deviations (MBD) which is the key tool here to control the  path fluctuations in the hyperbolic RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  14  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1  Maximal backward angular deviations  A crucial ingredient in this work is the control of Maximal Backward angular Deviations  (MBD) which has been done in [12] (see also [17] where these notions are introduced).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let  us recall here the main definitions and results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Given r > 0 and z ∈ Lr, recall that z↓ denotes the Poisson point whose arc |[z↓, A(z↓)]|  crosses S(r) at z and set z↑ := A(z↓).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let also A(k)(z) := A ◦ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' ◦ A(z) (k times) be the  k-th ancestor of z for any k ∈ N (by convention, we set A(0) := 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Consider 0 < r ≤ r′ and z′ ∈ Lr′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us denote by z ∈ Lr the intersection point  between the path of RST joining z′ to the origin and the sphere S(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us define  CFDr′  r (z′) as the Cumulative Forward angular Deviations between levels r and r′ as  CFDr′  r (z′) :=  \uf8f1  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f3  �  z′0z if z↓ = z′  ↓,  �  z′0z′  ↑ +  n−1  �  k=0  �  A(k)(z′  ↑)0A(k+1)(z′  ↑) + �  z↓0z else,  where n is the unique non negative integer such that A(n)(z′  ↑) = z↓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We also set CFDr′  r (z′) :=  0 when z′ /∈ Lr′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 (Maximal Backward angular Deviations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For 0 < r ≤ r′, let us define the  Maximal Backward angular Deviations between levels r and r′ as  MBDr′  r (z) := sup  ρ∈[r,r′]  max  y∈Dρ  r(z) CFDρ  r(y)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1)  if z ∈ Lr and MBDr′  r (z) := 0 if z /∈ Lr, where Dρ  r(z) is the set of points y ∈ Lρ whose path  of RST from y to 0 cuts S(r) at z (or, roughly speaking, the set of descendants of z at  level ρ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Since r′ �→ MBDr′  r (z) is non-decreasing, the MBD can be naturally extend to r′ = ∞  by setting:  MBD∞  r (z) := lim  r′→∞ MBDr′  r (z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The next lemma provides a control of the moments of MBD∞  r (z), which is crucial for  proving the positive density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The idea is that because the paths do not fluctuate too much,  there is room for a positive number of points at a given level r to have a thick trace at  infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 (Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6 of [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any p ≥ 3d/2, there exists a constant C =  C(d) > 0 such that, for any r > 2, A > 0 and any direction u ∈ Sd,  E  �  �  z∈BS(r)(u,Ae−r)∩RST  �  MBD∞  r (z)  �p�  ≤ CAde−rp .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2  Positive density of σ(D∞(·)) > 0  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exists A > 0 large and c0 = c0(A, d, λ) > 0 such that for any 0 < δ′ <  1, h0 > 0 and r > 0, there exists h ∈ [h0, h0 + A] such that for any z2 = (r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) (u ∈ Sd)  E  �  #  �  z ∈ N ∩ B(z2, δ′) : σ(D∞(z)) > 0  ��  ≥ c0Vol  �  B(δ′)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3)  Note also that among the previous parameters, only h = h(r) may depend on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  15  Proof of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The proof is splitted into three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We first start with proving an  estimate close to (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3), but for z ∈ Lr (Step 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Then, we extend the result to portion of  annuli and to balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us first prove that there exists c = c(d) > 0 such that for any r > 0,  E  �  #  �  z ∈ Lr : σ(D∞(z)) > 0  ��  ≥ cedr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4)  Let us first use the Cauchy-Schwarz inequality with the inner product ⟨X, Y ⟩ :=  E[�  i XiYi]:  E  � �  z∈Lr  σ(D∞(z))  �2  ≤  E  � �  z∈Lr  1σ(D∞(z))>0  �  E  � �  z∈Lr  σ(D∞(z))2�  =  E  �  #  �  z ∈ Lr : σ(D∞(z)) > 0  ��  E  � �  z∈Lr  σ(D∞(z))2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5)  Thus, the left hand side of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) is lower bounded by  E  �  #  �  z ∈ Lr : σ(D∞(z)) > 0  ��  ≥  E  � �  z∈Lr σ(D∞(z))  �2  E  � �  z∈Lr σ(D∞(z))2  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Recall that in the open-ball model, the set of points at infinity ∂Hd+1 is identified with  the unit d-dimensional sphere Sd whose spherical probability measure σ(Sd) is (normalized  to) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' By [12, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 (i)], with probability 1, any point at infinity is the asymptotic  direction of (at least) one infinite path of the hyperbolic RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' So,  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 1 = σ(Sd) ≤  �  z∈Lr  σ(D∞(z)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6)  Given r > 0 and z ∈ Lr, let us denote by Ang(z) := sup{�  z0I : I ∈ D∞(z)} if D∞(z) ̸=  ∅ and Ang(z) := 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Then, the set D∞(z) is included in the spherical cap  Cone(z, Ang(z)) ∩ ∂Hd+1, which means σ(D∞(z)) ≤ CAng(z)d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Moreover, the quantity  Ang(z) is bounded by the Maximal Backward angular Deviation MBD∞  r (z): see Definition  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We then get  E  � �  z∈Lr  σ(D∞(z))2�  ≤ E  � �  z∈Lr  MBD∞  r (z)2d�  ≤ Ce−dr  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7)  by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 (applied with A = πer and p = 2d), where the constant C = C(d) > 0 does  not depend on r > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Finally, (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) follows from combining (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5), (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Inequality (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) refers to the elements of Lr while (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3) concerns Poisson points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Pass-  ing from ones to others while preserving the uniformity of A in r requires some technical  considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We now extend (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) to annuli and then to balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any A large enough there exists c0 = c0(d, A) > 0 such that for any r > 0  and 0 < δ′ < 1,  E  �  #  �  z ∈ N ∩ C(r, r + A − 2δ′) : σ(D∞(z)) > 0  ��  ≥ c0Vol  �  C(r, r + A − 2δ′)  �  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8)  16  where we recall that C(r, R) has been defined in the notations of Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For z ∈ Lr, recall that z↓ denotes the Poisson point whose arc |[z↓, A(z↓)]| crosses S(r)  in z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In particular, σ(D∞(z)) and σ(D∞(z↓)) are equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Henceforth,  E  �  #  �  z ∈ N ∩ C(r, r + A − 2δ′) : σ(D∞(z)) > 0  ��  ≥ E  �  #  �  z ∈ Lr : z↓ ∈ B(r + A − 2δ′) and σ(D∞(z)) > 0  ��  ≥ c1E  �  #  �  z ∈ Lr : σ(D∞(z)) > 0  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='9)  The inequality (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='9) makes the object of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5, and its proof is postponed to Section  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This choice is done as the proof uses arguments similar to the ones developed in the  next Section in a more difficult case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The constants c1 = c1(d) > 0 and A above are chosen  large enough according to Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It then remains to use Step 1 and the inequalities  Vol  �  C(r, r + A − 2δ′)  �  ≤ Vol  �  B(r + A)  �  ≤ Ced(r+A) ,  to finally get  E  �  #  �  z ∈ N ∩ C(r, r + A − 2δ′) : σ(D∞(z)) > 0  ��  ≥c1 c edr  ≥c1 × c × (CedA)−1Vol  �  C(r, r + A − 2δ′)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Step 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For short, let us set f(z′) := P(σ(D∞(z′)) > 0 | z′ ∈ N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The Mecke’s formula  and Fubini’s theorem allow us to write:  �  C(r,r+A)  E  �  #  �  z′ ∈ N ∩ B(z, δ′) : σ(D∞(z′)) > 0  ��  dz  = λ  �  z∈C(r,r+A)  �  z′∈B(z,δ′)  f(z′) dz′ dz  = λ  �  z′∈C(r−δ′,r+A+δ′)  f(z′)Vol  �  B(z′, δ′) ∩ C(r, r + A)  �  dz′  ≥ λVol  �  B(δ′)  � �  z′∈C(r+δ′,r+A−δ′)  f(z′) dz′  ≥ λVol  �  B(δ′)  �  E  �  #  �  z′ ∈ N ∩ C(r + δ′, r + A − δ′) : σ(D∞(z′)) > 0  ��  ≥ λVol  �  B(δ′)  �  c0Vol  �  C(r + δ′, r + A − δ′)  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='10)  by Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Now, using Inequalities (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2), it is not difficult to choose ˜c = ˜c(d) > 0 (small) and A =  A(d) > 0 large enough and uniform on r > 0 and δ′ < 1 such that Vol(C(r +δ′, r +A−δ′))  is bigger than ˜cVol(C(r, r + A)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Combining with (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='10), we get  �  C(r,r+A)  E  �  #  �  z′ ∈ N ∩ B(z, δ′) : σ(D∞(z′)) > 0  ��  dz ≥ c2Vol  �  B(δ′)  �  Vol  �  C(r, r + A)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  with c2 := λc0˜c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This forces the existence of some (r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) ∈ C(r, r + A), with h ∈ [0, A]  and u ∈ Sd, satisfying  E  �  #  �  z′ ∈ N ∩ B((r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u), δ′) : σ(D∞(z′)) > 0  ��  ≥ c2Vol  �  B(δ′)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='11)  17  To conclude, let us first specify that (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='11) holds for any direction u ∈ Sd by isotropy  of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Moreover, for any given h0 > 0, the radius r + h with r > h0 can be written  as r′ + h′ where r′ > 0 and h′ ∈ [h0, h0 + A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, we have proved that there exists A  large and c2 = c2(A, d, λ) > 0 such that for any 0 < δ′ < 1, h0 > 0 and r > 0, there exists  h ∈ [h0, h0 + A] such that (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='11) holds for any u ∈ Sd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This is Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This last change on quantifiers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' r > h0 and h ∈ [0, A] replaced with r > 0 and  h ∈ [h0, h0 + A], will allow us to take simultaneously h in the good interval [h0, h0 + A]  and also large enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' See Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3  A stabilization result for subtrees of the RST  For 0 < δ′ < δ and r, h > 0, recall that z2 = (r + h;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u) and recall the definition of  Stab(r, h, δ′) in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In this section, we prove a stabilization result: subtrees of the RST  rooted at Poisson points in B(z2, δ′) do not depend on what happens inside B(r) w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  as h → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any 0 < δ′ < δ,  lim  h→∞ sup  r>0  P(Stab(r, h, δ′)) = 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us denote by χ the union of descendant sets D(z) with z in N ∩ B(z2, δ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  So, for the configuration in B(r) to alter χ, it must exist a vertex z′ = (r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u′) ∈ χ  whose B+(z′, d(z′, A(z′))) overlaps B(r), which means d(z′, A(z′)) ≥ r′ − r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Roughly  speaking, this would imply the occurrence of a large ball empty of Poisson points with  radius r′ − r ≥ h − δ′ which is very unlikely as h → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, Stab(r, h, δ′)∁ is included  in I ∪ II where, for a positive constant M > 0,  I :=  �  χ ̸⊂ Cone(z2, Me−r−h)  �  and  II :=  �  ∃z′ = (r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u′) ∈ N ∩ Cone(z2, Me−r−h) : d(z′, A(z′)) ≥ r′ − r  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  We are going to prove that there exist c, C > 0 (not depending on r, h and M) such that  ∀r, h > 0, P(I) ≤  C  Md/2 + e−cM and  lim  h→∞ sup  r>0  P(II) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='12)  The previous statement holding whatever the constant M > 0, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4 then follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us deal with P(II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' By Mecke’s formula and δ′ < 1,  P(II)  ≤  E  �  #  �  z′ = (r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u′) ∈ N ∩ Cone(z2, Me−r−h) : d(z′, A(z′)) ≥ r′ − r  ��  ≤  �  n≥h−1  λ  �  Vn  P  �  d(z′, A(z′)) ≥ n | z′ ∈ N  �  dz′  where Vn := Cone(z2, Me−r−h) ∩ C(r + n, r + n + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' On the one hand, for z′ ∈ Vn,  P  �  d(z′, A(z′)) ≥ n | z′ ∈ N  �  ≤ P  �  N ∩ B+(z′, n) = ∅  �  = e−λVol(B+(z′,n)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Here we need a lower bound of B+((r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' ·), ρ) and use the one obtained in [12, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' (A1)]:  there exists c = c(d) > 0 such that, for any radii r′, ρ ≥ 1,  Vol  �  B+((r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' ·), ρ)  �  ≥ ced(r′∧ρ)/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='13)  18  So we use (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='13) to get  P(d(z′, A(z′)) ≥ n | z′ ∈ N) ≤ e−λcedn/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  On the other hand, we upperbound the volume of Vn:  Vol(Vn)  =  � r+n+1  r+n  sinh(ρ)d dρ × σ  �  {u′ ∈ Sd : �  u0u′ ≤ Me−r−h}  �  ≤  cded(r+n) × Mde−d(r+h)  =  cdMded(n−h) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Putting together the previous upperbounds, we get:  P(II) ≤ λcdMde−dh �  n≥h−1  edn−λcedn/2,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='14)  which tends to 0 as h → ∞ uniformly on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us now consider the term P(I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us denote by πz the path of RST starting from  the Poisson point z until the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We define Rad(z2) as the maximal angular deviation  generated by a path πz starting from some z ∈ B(z2, δ′) when it goes through the sphere  S(r + h − δ′):  Rad(z2) := max  � �  u0u′ : ∃z ∈ N ∩ B(z2, δ′) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' πz intersects S(r + h − δ′) at (·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' u′)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The maximal angular deviation cannot be too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Precisely, setting with Rad :=  {Rad(z2) ≤ Me−(r+h−δ′)}, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 of [12] states that P(Rad∁) ≤ e−cM for c = c(d) > 0  and M large enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Besides,  P(I ∩ Rad)  =  P  ��  ∃z′ = (r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' ·) ∈ N ∩ B(z2, δ′) : MBD∞  r′ (z′) ≥ Me−(r+h)�  ∩ Rad  �  ≤  E  �  1Rad  �  z′∈N ∩B(z2,δ′)  1{MBD∞  r′ (z′)d≥Mde−d(r+h)}  �  ≤  M−ded(r+h)E  �  1Rad  �  z′∈N ∩B(z2,δ′)  MBD∞  r′ (z′)d�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Now, in order to apply Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2, we have to turn the sum over elements of N ∩B(z2, δ′)  into a sum over elements of Lr+h−δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Given z′ = (r′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' ·), let us denote by Ar+h−δ′  r′  (z′) the  intersection point between the path πz′ of RST and S(r + h − δ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It is the ‘ancestor’ at  radius r + h − δ′ < r′ of z′ in RST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  1Rad  �  z′∈N ∩B(z2,δ′)  MBD∞  r′ (z′)d  ≤ 1Rad  �  z′∈N ∩B(z2,δ′)  MBD∞  r+h−δ′(Ar+h−δ′  r′  (z′))d  ≤  �  z′′∈BS(r+h−δ′)(z2,Me−(r+h−δ′))∩RST  #  �  z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)  �  MBD∞  r+h−δ′(z′′)d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  19  Thus, the Cauchy-Schwarz inequality gives:  E  �  1Rad  �  z′∈N ∩B(z2,δ′)  MBD∞  r′ (z′)d�  ≤ E  �  �  z′′∈Lr+h−δ′  #  �  z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)  �2�1/2  ×E  �  �  z′′∈BS(r+h−δ′)(z2,Me−(r+h−δ′))∩RST  MBD∞  r+h−δ′(z′′)2d�1/2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='15)  On the one hand, let us write  �  z′′∈Lr+h−δ′  #  �  z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)  �2  ≤  �  �  z′′∈Lr+h−δ′  #  �  z′ ∈ N ∩ B(z2, δ′) : z′ ∈ D(z′′)  ��2  =  �  #N ∩ B(z2, δ′)  �2  which means that the first term of the upper bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='15) is bounded by C1 := E[#(N ∩  B(1))2]1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Finally we apply Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 to the second term of the upper bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='15):  it is bounded by the square root of CMde−2d(r+h−δ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Combining the previous bounds, we  get  P(I ∩ Rad) ≤ CM−d/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='16)  Gathering (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='14) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='16) proves Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4  Conclusion  Let us prove Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We pay a special attention to dependencies between parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let A > 0 and c0 = c0(A, d, λ) > 0 given by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It is well known that  E  �  #N ∩ B(z2, δ′) 1#N ∩B(z2,δ′)≥2  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='17)  which does not depend on r, h by stationarity of the PPP, is negligible w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Vol(B(δ′))  as δ′ → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence we choose δ′ > 0 small enough and uniformly on r, h > h1 = h1(d) so  that the expectation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='17) and  P  �  ∃z ∈ N ∩ B(z2, δ′), D(z)\\{z} ̸⊂ B(r + h + δ′)∁�  are both smaller than c0  4 Vol(B(δ′)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This second upper-bound and the constant h1 = h1(d)  are proved in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6, whose proof is postponed in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' At this stage, parameters  r > 0 and h > h1 are still free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Now we choose h0 ≥ h1 large enough so that for any h ≥ h0  and uniformly on r > 0, the following holds by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4:  P  �  Stab(r, h, δ′)∁�  ≤ c0  4 Vol(B(δ′)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Finally, for any given radius r > 0, we choose h (possibly depending on r) in [h0, h0 + A]  such that  E  �  #  �  z ∈ N ∩ B(z2, δ′) : σ(D∞(z)) > 0  ��  ≥ c0Vol  �  B(δ′)  �  by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  20  For these fixed parameters A, c0, δ′, h0, r and h,  c0Vol(B(δ′))  ≤  E  �  #  �  z ∈ N ∩ B(z2, δ′) : σ(D∞(z)) > 0  ��  ≤  P  �  ∃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0  �  +E  �  #{N ∩ B(z2, δ′)} 1#N ∩B(z2,δ′)≥2  �  ≤  P  �  ∃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0  �  + c0  4 Vol(B(δ′))  from which we get P(∃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0) ≥  3c0  4 Vol(B(δ′)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Thus we  conclude with  P  �  F(r, h, δ′)  �  ≥  P  �  ∃!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='z ∈ N ∩ B(z2, δ′), σ(D∞(z)) > 0  �  − P  �  Stab(r, h, δ′)∁�  − P  �  ∃z ∈ N ∩ B(z2, δ′), D(z)\\{z} ̸⊂ B(r + h + δ′)∁�  ≥  c0  4 Vol(B(δ′)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  So ε := c0  4 Vol(B(δ′)) depending on A, d, λ and δ′, is suitable, and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5  Technical lemmas  To complete the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5, it remains to state the two following technical lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exists c1 = c1(d) > 0 such that for any A large enough, r > 0 and  0 < δ′ < 1,  E  �  #  �  z ∈ Lr : z↓ ∈ B(r + A − 2δ′) and σ(D∞(z)) > 0  ��  ≥ c1E  �  #  �  z ∈ Lr : σ(D∞(z)) > 0  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For the proof, we will consider first a portion of the sphere of radius r, and then  extend the result to the whole Lr using the (Covering) Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Step 1: Given z0 ∈ S(r), let us consider the event  L(A, r) :=  �  ∃z ∈ BS(r)(z0, e−r) ∩ Lr : z↓ /∈ B(r + A − 2δ′)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  For short, let us set X0,r := #  �  z ∈ BS(r)(z0, e−r) ∩ Lr : σ(D∞(z)) > 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' We will prove  that  E  �  X0,r1L(A,r)∁  �  ≥ 1  2E[X0,r] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='18)  With  X0,r1L(A,r)∁ = #  �  z ∈ BS(r)(z0, e−r) ∩ Lr : z↓ ∈ B(r + A − 2δ′) and σ(D∞(z)) > 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='5 then immediatly follows from the above inequality with c1 := 1/(2K) using  the (Covering) Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3, where the covering constant K = K(d) is given in that lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The proof of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='18) relies on the two following inequalities (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='19) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='20) which will  be proved in a second time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  The first inequality states that the probability of L(A, r) tends to 0 when A → ∞, uniformly  on r, δ′:  lim  A→∞  sup  r>0, δ′<1  P(L(A, r)) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='19)  21  The second inequality ensures that there exists c = c(d) > 0 such that for any r > 0,  E  �  X0,r  �  ≥ c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='20)  Then, the Cauchy-Schwarz inequality gives  E  �  X0,r1L(A,r)  �  ≤ C1/2P(L(A, r))1/2  where C = C(d) > 0 upperbounds the expectation of #  �  BS(r)(z0, e−r) ∩ Lr  �2 thanks to  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Thus, combining (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='19) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='20), we can choose A large enough uniformly  on r ≥ 2 and δ′ < 1 such that  E  �  X0,r1L(A,r)  �  ≤ 1  2E  �  X0,r  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This proves (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Step 2: proof of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The proof is very close to that of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4 with fewer technical  difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' By analogy, we write L(A, r) ⊂ I ∪ II where  I :=  �  ∃z ∈ BS(r)(z0, e−r) ∩ Lr : D(z) ̸⊂ Cone(z0, Ae−r)  �  and  II :=  �  ∃z ∈ BS(r)(z0, e−r) ∩ Lr : z↓ ∈ Cone(z0, Ae−r) ∩ B(r + A − 2δ′)∁�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  We upperbound P(I) more easily than in the proof of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4 since the points z con-  cerned by the event I are already in Lr:  P(I)  ≤  P  �  ∃z ∈ BS(r)(z0, e−r) ∩ Lr : MBD∞  r (z) ≥ Ae−r�  ≤  A−2de2dr E  �  �  z∈BS(r)(z0,e−r)∩Lr  �  MBD∞  r (z)  �2d�  ≤ CA−2d  (by Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2) which tends to 0 uniformly on r, δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The same holds for P(II) as in the  proof of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For this reason, we omit the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Step 3: proof of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This inequality is a consequence of isotropy of the model,  (Covering) Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3 and Step 1 in the proof of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3:  E  �  #  �  z ∈ BS(r)(z0, e−r) ∩ Lr : σ(D∞(z)) > 0  ��  =  1  N(r)  N(r)  �  i=1  E  �  #  �  z ∈ BS(r)(zi, e−r) ∩ Lr : σ(D∞(z)) > 0  ��  ≥  1  N(r)E  �  #  �  z ∈ Lr : σ(D∞(z)) > 0  ��  ≥ c C−1  with N(r) ≤ Cedr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This concludes the proof of the Lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' There exists h1 = h1(d) > 0 such that the following limit is uniform on r > 0  and h > h1:  lim  δ′→0  1  Vol(B(δ′))P  �  ∃z ∈ N ∩ B(z2, δ′), D(z)\\{z} ̸⊂ B(r + h + δ′)∁�  = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  22  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The Mecke’s formula allows to write:  P  �  ∃z ∈ N ∩ B(z2, δ′), D(z)\\{z} ̸⊂ B(r + h + δ′)∁�  ≤ P  �  ∃z ∈ N ∩ B(z2, δ′), ∃z′ ∈ N ∩ B(r + h + δ′) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A(z′) = z  �  ≤ E  �  #  �  z ∈ N ∩ B(z2, δ′) : ∃z′ ∈ N ∩ B(r + h + δ′) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A(z′) = z  ��  = λ  �  B(z2,δ′)  P  �  ∃z′ ∈ N ∩ B(r + h + δ′) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A(z′) = z | z ∈ N  �  dz .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='21)  For z in B(z2, δ′),  P  �  ∃z′ ∈ N ∩ B(r + h + δ′) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A(z′) = z | z ∈ N  �  ≤  �  n≥0  E  �  #  �  z′ ∈ N ∩ Vδ′,n : A(z′) = z  �  | z ∈ N  �  where we set  Vδ′,n := C(r + h − δ′, r + h + δ′) ∩ Cone(u, ne−r−h, (n + 1)e−r−h)  and Cone(u, ne−r−h, (n + 1)e−r−h) is the set of directions u′ ∈ Sd such that ne−r−h ≤  �  u0u′ ≤ (n + 1)e−r−h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A second use of the Mecke’s formula gives:  E  �  #  �  z′ ∈ N ∩ Vδ′,n : A(z′) = z  �  | z ∈ N  �  = λ  �  Vδ′,n  P  �  A(z′) = z | z, z′ ∈ N  �  dz′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Given z′ ∈ Vδ′,n, we have  P  �  A(z′) = z | z, z′ ∈ N  �  = P  �  B+(z′, d(z, z′)) ∩ N = ∅  �  = e−λVol(B+(z′,d(z,z′))) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Moreover  Vol(B+(z′, d(z, z′)))  ≥  ce  d  2 d(0,z′)∧d(z,z′)  by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='13)  ≥  ce  d  4 d(z,z′)  since d(z, z′) ≤ 2d(0, z′)  ≥  ce  d  4 c′n  because z′ ∈ Vδ′,n and r + h is larger than some h1 = h1(d) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Let us now compute the volume of Vδ′,n:  Vol(Vδ′,n) =  � r+h+δ′  r+h−δ′ sinh(ρ)d dρ×σ  �  {u′ ∈ Sd : ne−r−h ≤ �  u0u′ ≤ (n+1)e−r−h}  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='22)  The first term of the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='22) is bounded by c1δ′ed(r+h) while the second one is  bounded by c2nde−d(r+h) using (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The previous constants ci, i ∈ {1, 2}, are positive  and only depend on d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, the volume of Vδ′,n is smaller than c1c2ndδ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Combining  what precedees, we finally get for any r > 0 and h > h1  P  �  ∃z′ ∈ N ∩ B(r + h + δ′) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' A(z′) = z | z ∈ N  �  ≤  �  n≥0  λe−λce  d  4 c′nc1c2ndδ′  whose upperbound can be expressed as Cδ′ with C = C(λ, d, h1) is a positive, finite  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' It then remains to plug this bound in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='21) to conclude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  23  6  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8  Let us first recall an upperbound for the number of elements of Lr in a cap BS(r)(·, e−r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1 (Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4 of [12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any p ≥ 1, there exists a constant C = C(d, p) > 0  such that, for any r ≥ 0 and any direction z ∈ S(r),  E  �  #  �  RST ∩ BS(r)(z, e−r)  �p�  ≤ C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Thanks to the Covering Lemma (Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3), it is now easy to prove that Lr =  RST ∩ S(r) admits in expectation about edr elements:  E  �  #Lr  �  ≤  N(r)  �  i=1  E  �  #(BS(r)(zi, e−r) ∩ Lr)  �  ≤ Cedr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='1)  Finally, combining the previous inequality and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='4) proved in Step 1 of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='3, we  get Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  A  Arcs of the RST as a subset of Hd+1  Given z1, z2 ∈ Hd+1, the arc |[z1, z2]| is precisely defined in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2 of [12] but for  convenience we recall the main lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Let us write zi = (ri;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' ui) with polar cooordinates,  i ∈ {1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Whenever u1 and u2 are not antipodal (and it will be a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' the case when z2  is the ancestor of z1), we consider the unique geodesic γu1,u2 : [0, 1] → Sd on the sphere  connecting u1 to u2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Then, the arc |[z1, z2]| is the path  t ∈ [0, 1] �→  �  (1 − t)r1 + tr2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' γu1,u2(φz1,z2(t))  �  ∈ Hd+1  where φz1,z2 : [0, 1] → [0, 1] is defined as  φz1,z2(t) :=  1  �  u10u2  arccos  �(1 − t) sinh(r1) + t cos(�  u10u2) sinh(r2)  sinh((1 − t)r1 + tr2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  This construction of the arc |[z1, z2]| ensures that the distance to the origin (as well as the  distance to z1) are monotonous along the path |[z1, z2]|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  By Property 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='2, we know that the geodesics [z, A(z)] and [z′, A(z′)], for z, z′ ∈ N,  can overlap only at their extremities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' This is not the case any more when we use the arcs  |[z, A(z)]| and |[z′, A(z′)]|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' For any r > 0, it may exist some points z ∈ Lr belonging to  several arcs, say |[z1, A(z1)]|, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' , |[zk, A(zk)]|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hence, such a point z will be counted with  multiplicity k in Lr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Also, to identify without ambiguity this point z, we should formally  represent it as a couple made up with its location in Hd+1 and one of the arcs generating it,  say |[zi, A(zi)]|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In this case the vertex z↓ ∈ N is defined as z↓ := zi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' In this article, we will  commit the following abuse of notations: we will count elements of Lr with multiplicity  without specifying the arcs distinguishing them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  References  [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Ahlberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hanson and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hoffman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The number of geodesics in planar first-passage percolation  grows sublinearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='11576, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  24  [2] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Percolation and Minimal Spanning Forests in Infinite Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Annals of Probability,  23(1):87–104, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Amir, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Angel and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Valkó.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The TASEP speed process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Annals of Probability, 39(4):1205–1242,  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Baccelli and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Bordenave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The radial spanning tree of a Poisson point process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Annals of Applied  Probability, 17(1):305–359, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [5] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Baccelli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Coupier, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Tran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Semi-infinite paths of the 2d-radial spanning tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Advances  in Applied Probability, 45(4):895–916, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [6] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Bonichon and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Marckert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Asymptotics of geometrical navigation on a random set of points in  the plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Advances in Applied Probability, 43(4):899–942, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Cannon, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Floyd, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Kenyon, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Parry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Hyperbolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Flavors of geometry,  31:59–115, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [8] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Chavel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Riemannian Geometry: A Modern Introduction, Second Edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Cambridge studies in  advanced mathematics 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Cambridge University Press, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Coletti and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Valencia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Scaling limit for a family of coalescing radial random paths absorbed  at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=', 63:033303, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Coupier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Multiple geodesics with the same direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Electronic Communications in Probability,  16:517–527, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Coupier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Sublinearity of the number of semi-infinite branches for geometric random trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Probab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=', 23:Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' 37, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Coupier, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Flammant and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Tran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Hyperbolic radial spanning tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  arXiv preprint  arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='03467, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Coupier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Marckert, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Tran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Directed, cylindric and radial brownian webs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Electronic  Journal of Probability, 24(20):1-48, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [14] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Daley and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Vere-Jones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' An introduction to the theory of point processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' II, Second  edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Springer, New York, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Rényi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Közl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=', 5:17–60, 1960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Ferrari and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Pimentel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Competition interfaces and second class particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Annals of  Probability, 33(4):1235–1254, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Flammant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The directed spanning forest in the hyperbolic space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='13731,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [18] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Howard and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Newman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Geodesics and spanning trees for Euclidean first-passage percola-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Probab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Liggett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Schonmann, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Stacey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Domination by product measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' The Annals of  Probability, 25(1):71–95, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Paupert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Introduction to hyperbolic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Arizona State University Lecture Notes, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Penrose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Random geometric graphs, volume 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Oxford university press, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Ratcliffe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Foundations of Hyperbolic Manifolds, Second edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Graduate texts in  Mathematics 149, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' Rost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Nonequilibrium behaviour of a many particle process: density profile and local equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content='  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Wahrsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Verw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Gebiete, 58(1):41–53, 1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+page_content=' van der Hofstad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Random Graphs and Complex Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Volume 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
+page_content=' Cambridge Series in Statis-  tical and Probabilistic Mathematics, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VdE0T4oBgHgl3EQf2wKz/content/2301.02717v1.pdf'}
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+42
+The Messenger 189 | 2022
+Pascale Hibon 1
+Jesús Corral-Santana 1
+Itziar de Gregorio-Monsalvo 1
+Leopoldo Infante 2
+Elizabeth Humphreys 3
+John Blakeslee 4
+1 ESO
+2 Las Campanas Observatory, Chile
+3 Joint ALMA Observatory, Chile
+4 NOIRLab, USA
+The Joint Observatories Kavli Science 
+Forum in Chile was organised in hybrid 
+mode with the aim of encouraging col-
+laborations, not only with the Chilean 
+institutions, but also between the differ-
+ent observing facilities based in Chile. 
+The meeting featured scientific talks 
+showing results obtained with the astro-
+nomical facilities based in Chile, but 
+significant time was also dedicated to 
+round-table discussions on Life Balance, 
+Diversity-Equity-Inclusion, and the 
+Road Ahead (i.e., the future of those 
+Chile-based facilities).
+Chile-based observatories have been 
+leading scientific research in several astro-
+nomical areas. The forum was organised 
+around the highest-impact scientific 
+results provided by those facilities over the 
+last few years. The aim was to show how 
+these different observatories have contrib-
+uted to those advances in astrophysics 
+and, with that goal in mind, the organising 
+committee placed particular emphasis on 
+the scientific involvement of the astrono-
+mers working at those observatories  
+to achieve cutting-edge results. The 
+intention was to organise a meeting to 
+gather together both observatory staff 
+(astronomers, scientists, fellows, stu-
+dents, engineers, operators etc.) and 
+Chilean institute researchers (postdocs, 
+students etc.) to present their research. 
+This would also reinforce the scientific 
+collaboration between observatories and 
+Chilean research institutes, to examine 
+common experiences and concerns, and 
+to discuss different points of view on how 
+to cope with similar challenges. 
+Each half-day of the meeting was dedi-
+cated to a specific field of astronomy that 
+had seen major advances thanks to the 
+observing facilities based in Chile, fol-
+lowed by dedicated time for discussion. 
+After an introductory speech that 
+included a report from the Director of the 
+Chilean Astronomical Society (SOCHIAS), 
+Monday was dedicated to the transient 
+sky with talks focusing on cataclysmic 
+variables, multi-messenger follow-up, and 
+supernovae. It was reported that new 
+observing systems are being developed, 
+focused on the management of time-do-
+main observations. We would like to high-
+light the sharing of the different points of 
+view, concerns and strategies between 
+several observatories during this session. 
+Representatives of all the observatories 
+agreed that although there will be an 
+enormous number of alerts/triggers at 
+the beginning of the Legacy Survey of 
+Space and Time, the rate of triggering will 
+slow down and the tools will adapt, as 
+will the observatories and the community.
+Tuesday morning’s talks focused on 
+exoplanets and star formation. A great 
+example was presented of successful 
+ALMA+VLT science and how a Chile-
+an-led research team is making great use 
+of all the Chile-based facilities. During the 
+afternoon we had our first round-table 
+discussion, on Life Balance, chaired by 
+Itziar de Gregorio-Monsalvo and with 
+several invited panellists (see de Gregorio- 
+Monsalvo, Hibon & Alcalde Pampliega on 
+p. 44 of this issue for more details). The 
+three key words in the discussion were 
+flexibility, tolerance and empathy, and the 
+conclusion can be summarised as: “Don’t 
+live to work but work to live!”. Participants 
+spontaneously rearranged the chairs to 
+form a big circle so as to facilitate discus-
+sion and be able to see everyone, an 
+arrangement that was then reproduced for 
+each round table. 
+Wednesday morning’s talks targeted the 
+cosmic distance scale and stellar popula-
+tions. Again we saw great scientific 
+results thanks to the synergy between 
+different organisations and facilities. The 
+afternoon was dedicated to a round-table 
+discussion on Diversity-Equity-Inclusion, 
+chaired by Belén Alcalde and with several 
+panellists (see Alcalde Pampliega, Hibon 
+& de Gregorio Monsalvo on p. 46 of this 
+issue for more details). Everyone showed 
+genuine concern for this topic and 
+agreed it should not be a side-issue. We 
+must educate ourselves in this area to 
+ensure progress. 
+Thursday’s presentations concentrated 
+on extragalactic astronomy: the high-red-
+shift Universe, active galactic nuclei, and 
+large-scale structure. We learned about 
+impressive results from programmes at 
+many different observatories, including 
+some Large Programmes, and the power 
+of combining ALMA and other observa-
+tions (ground- or space-based) for mak-
+ing progress on important problems in 
+Report on the Workshop
+Joint Observatories Kavli Science Forum
+held at ESO Vitacura, Santiago, Chile, 25–29 April 2022
+Figure 1. Round table photo. This room configuration 
+optimised the discussions.
+Astronomical News
+DOI: 10.18727/0722-6691/5289
+
+43
+The Messenger 189 | 2022
+the area galaxy formation and evolution. 
+Through these efforts, the high-redshift 
+Universe is revealing itself more and more. 
+On Friday morning the talks were centred 
+on technical developments and some 
+issues that we all face at observatories, 
+including the latest astronomical technol-
+ogies developed in Chile (Polymer 
+Reinforced Carbon Fiber mirrors, adap-
+tive optics) and the impact of low-Earth-
+orbit satellites on nighttime observations. 
+The afternoon was dedicated to a round- 
+table discussion, chaired by Franz Bauer, 
+with the directors of the Chile-based 
+observatories: Andreas Kaufer (ESO-LPO 
+Director), Leopoldo Infante (LCO Director), 
+Elizabeth Humphreys (ALMA Head of 
+Science Operations), Robert Blum 
+(Director for Operations at Vera C. Rubin 
+Observatory), and the chair of the Chilean 
+Telescope Allocation Committee, Patricio 
+Rojo. Discussions were focused on the 
+road ahead. Panellists and participants 
+engaged in lively discussion of the new 
+projects, observatory sustainability, 
+remote working and the several opportu-
+nities to link the different observatories 
+and the Chilean institutes. We all agreed 
+on the efforts and actions that needed to 
+be undertaken to involve the Chilean 
+community and to retain minorities. 
+Although the weather during the week 
+was highly variable, the quality of the 
+food at each coffee break and lunch, pro-
+vided by new catering companies that 
+are all managed by Chilean women, 
+spoiled us. The feedback from speakers, 
+panellists, and participants was extremely 
+positive and most of the audience asked 
+for a repeat of the forum. This will allow 
+continued discussion of the progress 
+made, not only from the scientific per-
+spective, but especially on the topics 
+from the different round tables. Everyone 
+left the meeting with a big smile.
+Demographics
+ 
+As with many workshops, the Science 
+Organising Committee sought fair rep-
+resentation from the community. To this 
+end, we voted on 16 invited speakers, 
+using the sole criterion of who would give 
+the best review of each topic. The end 
+result was a 50:50 ratio of male to female 
+invited speakers, with four PhD students 
+delivering invited talks. The Diversity 
+panel had a 50:50 ratio of male to female 
+panellists, The Life Balance panel had a 
+20:80 ratio of male to female panellists, 
+and The Road Ahead panel an 80:20 ratio 
+of male to female panellists. This last does 
+reflect the actual ratio of males to females 
+in observatory senior management. 
+Attendees came from all Chile-based 
+astronomical observatories and institu-
+tions with the following percentages:
+–  58% from observatories (ESO, ALMA, 
+NOIRLab, LCO, Carnegie, GMT);
+–  42% from Chilean astronomical 
+universities/institutions.
+Of the abstract submissions, 35% were 
+from women, which matched the 35 % of 
+talk allocations to women. The talk selec-
+tion was made blind (the SOC chair 
+removed first names and identifying infor-
+mation about the authors), so we con-
+clude that the method likely worked to 
+address gender biases. We also had a 
+decent level of participation from young 
+researchers, within the following break-
+down according to seniority: ~ 14% stu-
+dents, ~ 18% postdoctoral researchers, 
+15% engineers and operators, and 48% 
+tenure-track or tenured astronomers and 
+5% outreach or HR professionals. Each 
+of these groups was well represented in 
+the talks, including the invited talks.
+The workshop had a high level of partici-
+pation, with approximately 110 partici-
+pants. We attribute this to both the com-
+pelling nature of the subject matter, which 
+draws researchers at all career stages, 
+and to the generous support that ensured 
+attendance was completely free.
+Acknowledgements
+We would like to acknowledge and sincerely thank 
+Christopher Martin and the Kavli Foundation who 
+provided the funding for this forum and without 
+whom this meeting would not have been possible. 
+We also would like to acknowledge the forum pro-
+posal Co-Is, the SOC, the LOC and the ESO logistics 
+team. We also would like to thank the ESO Chile 
+Office for Science and Logistics for their support 
+with the organisation of this forum. 
+Figure 2. Conference photo.
+
diff --git a/a9FAT4oBgHgl3EQf4x7K/content/tmp_files/load_file.txt b/a9FAT4oBgHgl3EQf4x7K/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf,len=64
+page_content='42  The Messenger 189 | 2022  Pascale Hibon 1  Jesús Corral-Santana 1  Itziar de Gregorio-Monsalvo 1  Leopoldo Infante 2  Elizabeth Humphreys 3  John Blakeslee 4  1 ESO  2 Las Campanas Observatory, Chile  3 Joint ALMA Observatory, Chile  4 NOIRLab, USA  The Joint Observatories Kavli Science  Forum in Chile was organised in hybrid  mode with the aim of encouraging col-  laborations, not only with the Chilean  institutions, but also between the differ-  ent observing facilities based in Chile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  The meeting featured scientific talks  showing results obtained with the astro-  nomical facilities based in Chile, but  significant time was also dedicated to  round-table discussions on Life Balance,  Diversity-Equity-Inclusion, and the  Road Ahead (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=', the future of those  Chile-based facilities).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Chile-based observatories have been  leading scientific research in several astro-  nomical areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The forum was organised  around the highest-impact scientific  results provided by those facilities over the  last few years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The aim was to show how  these different observatories have contrib-  uted to those advances in astrophysics  and, with that goal in mind, the organising  committee placed particular emphasis on  the scientific involvement of the astrono-  mers working at those observatories  to achieve cutting-edge results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The  intention was to organise a meeting to  gather together both observatory staff  (astronomers, scientists, fellows, stu-  dents, engineers, operators etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=') and  Chilean institute researchers (postdocs,  students etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=') to present their research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  This would also reinforce the scientific  collaboration between observatories and  Chilean research institutes, to examine  common experiences and concerns, and  to discuss different points of view on how  to cope with similar challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Each half-day of the meeting was dedi-  cated to a specific field of astronomy that  had seen major advances thanks to the  observing facilities based in Chile, fol-  lowed by dedicated time for discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  After an introductory speech that  included a report from the Director of the  Chilean Astronomical Society (SOCHIAS),  Monday was dedicated to the transient  sky with talks focusing on cataclysmic  variables, multi-messenger follow-up, and  supernovae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' It was reported that new  observing systems are being developed,  focused on the management of time-do-  main observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We would like to high-  light the sharing of the different points of  view, concerns and strategies between  several observatories during this session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Representatives of all the observatories  agreed that although there will be an  enormous number of alerts/triggers at  the beginning of the Legacy Survey of  Space and Time, the rate of triggering will  slow down and the tools will adapt, as  will the observatories and the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Tuesday morning’s talks focused on  exoplanets and star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' A great  example was presented of successful  ALMA+VLT science and how a Chile-  an-led research team is making great use  of all the Chile-based facilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' During the  afternoon we had our first round-table  discussion, on Life Balance, chaired by  Itziar de Gregorio-Monsalvo and with  several invited panellists (see de Gregorio-  Monsalvo, Hibon & Alcalde Pampliega on  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' 44 of this issue for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The  three key words in the discussion were  flexibility, tolerance and empathy, and the  conclusion can be summarised as: “Don’t  live to work but work to live!”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Participants  spontaneously rearranged the chairs to  form a big circle so as to facilitate discus-  sion and be able to see everyone, an  arrangement that was then reproduced for  each round table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Wednesday morning’s talks targeted the  cosmic distance scale and stellar popula-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Again we saw great scientific  results thanks to the synergy between  different organisations and facilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The  afternoon was dedicated to a round-table  discussion on Diversity-Equity-Inclusion,  chaired by Belén Alcalde and with several  panellists (see Alcalde Pampliega, Hibon  & de Gregorio Monsalvo on p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' 46 of this  issue for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Everyone showed  genuine concern for this topic and  agreed it should not be a side-issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We  must educate ourselves in this area to  ensure progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Thursday’s presentations concentrated  on extragalactic astronomy: the high-red-  shift Universe, active galactic nuclei, and  large-scale structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We learned about  impressive results from programmes at  many different observatories, including  some Large Programmes, and the power  of combining ALMA and other observa-  tions (ground- or space-based) for mak-  ing progress on important problems in  Report on the Workshop  Joint Observatories Kavli Science Forum  held at ESO Vitacura, Santiago, Chile, 25–29 April 2022  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Round table photo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' This room configuration  optimised the discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Astronomical News  DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='18727/0722-6691/5289  43  The Messenger 189 | 2022  the area galaxy formation and evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Through these efforts, the high-redshift  Universe is revealing itself more and more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  On Friday morning the talks were centred  on technical developments and some  issues that we all face at observatories,  including the latest astronomical technol-  ogies developed in Chile (Polymer  Reinforced Carbon Fiber mirrors, adap-  tive optics) and the impact of low-Earth-  orbit satellites on nighttime observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  The afternoon was dedicated to a round-  table discussion, chaired by Franz Bauer,  with the directors of the Chile-based  observatories: Andreas Kaufer (ESO-LPO  Director), Leopoldo Infante (LCO Director),  Elizabeth Humphreys (ALMA Head of  Science Operations), Robert Blum  (Director for Operations at Vera C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Rubin  Observatory), and the chair of the Chilean  Telescope Allocation Committee, Patricio  Rojo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Discussions were focused on the  road ahead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Panellists and participants  engaged in lively discussion of the new  projects, observatory sustainability,  remote working and the several opportu-  nities to link the different observatories  and the Chilean institutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We all agreed  on the efforts and actions that needed to  be undertaken to involve the Chilean  community and to retain minorities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Although the weather during the week  was highly variable, the quality of the  food at each coffee break and lunch, pro-  vided by new catering companies that  are all managed by Chilean women,  spoiled us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The feedback from speakers,  panellists, and participants was extremely  positive and most of the audience asked  for a repeat of the forum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' This will allow  continued discussion of the progress  made, not only from the scientific per-  spective, but especially on the topics  from the different round tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Everyone  left the meeting with a big smile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Demographics  As with many workshops, the Science  Organising Committee sought fair rep-  resentation from the community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' To this  end, we voted on 16 invited speakers,  using the sole criterion of who would give  the best review of each topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The end  result was a 50:50 ratio of male to female  invited speakers, with four PhD students  delivering invited talks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The Diversity  panel had a 50:50 ratio of male to female  panellists, The Life Balance panel had a  20:80 ratio of male to female panellists,  and The Road Ahead panel an 80:20 ratio  of male to female panellists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' This last does  reflect the actual ratio of males to females  in observatory senior management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Attendees came from all Chile-based  astronomical observatories and institu-  tions with the following percentages:  –  58% from observatories (ESO, ALMA,  NOIRLab, LCO, Carnegie, GMT);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  –  42% from Chilean astronomical  universities/institutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Of the abstract submissions, 35% were  from women, which matched the 35 % of  talk allocations to women.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' The talk selec-  tion was made blind (the SOC chair  removed first names and identifying infor-  mation about the authors), so we con-  clude that the method likely worked to  address gender biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We also had a  decent level of participation from young  researchers, within the following break-  down according to seniority: ~ 14% stu-  dents, ~ 18% postdoctoral researchers,  15% engineers and operators, and 48%  tenure-track or tenured astronomers and  5% outreach or HR professionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Each  of these groups was well represented in  the talks, including the invited talks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  The workshop had a high level of partici-  pation, with approximately 110 partici-  pants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We attribute this to both the com-  pelling nature of the subject matter, which  draws researchers at all career stages,  and to the generous support that ensured  attendance was completely free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Acknowledgements  We would like to acknowledge and sincerely thank  Christopher Martin and the Kavli Foundation who  provided the funding for this forum and without  whom this meeting would not have been possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  We also would like to acknowledge the forum pro-  posal Co-Is, the SOC, the LOC and the ESO logistics  team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' We also would like to thank the ESO Chile  Office for Science and Logistics for their support  with the organisation of this forum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
+page_content=' Conference photo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9FAT4oBgHgl3EQf4x7K/content/2301.08729v1.pdf'}
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+SPECTRAL PROPERTIES OF THE LAPLACIAN OF TEMPORAL
+NETWORKS FOLLOWING A CONSTANT BLOCK JACOBI MODEL
+A PREPRINT
+Zhana Kuncheva
+Data Science and Engineering
+Optima Partners
+London, UK
+zhana.kuncheva@optimapartners.co.uk
+Ognyan Kounchev
+Department of Mathematics and Computer Science
+Bulgarian Academy of Sciences
+Sofia, Bulgaria
+kounchev@math.bas.bg
+January 31, 2023
+ABSTRACT
+We study the behavior of the eigenvectors associated with the smallest eigenvalues of the Laplacian
+matrix of temporal networks. We consider the multilayer representation of temporal networks, i.e. a
+set of networks linked through ordinal interconnected layers. We analyze the Laplacian matrix, known
+as supra-Laplacian, constructed through the supra-adjacency matrix associated with the multilayer
+formulation of temporal networks, using a constant block Jacobi model which has closed-form
+solution. To do this, we assume that the inter-layer weights are perturbations of the Kronecker sum of
+the separate adjacency matrices forming the temporal network. Thus we investigate the properties
+of the eigenvectors associated with the smallest eigenvalues (close to zero) of the supra-Laplacian
+matrix. Using arguments of perturbation theory, we show that these eigenvectors can be approximated
+by linear combinations of the zero eigenvectors of the individual time layers. This finding is crucial
+in reconsidering and generalizing the role of the Fielder vector in supra-Laplacian matrices.
+1
+Introduction
+In recent years, one of the major lines of research in complex network analysis is the topological changes that occur
+in a network over time. A sequence of networks with such a time-varying nature can be formalized as a temporal
+network Holme and Saram¨aki [2012]. The multilayer formulation of temporal networks Kivel¨a et al. [2014] is one
+way to consider the interconnected topological structure changing over time: ordinal interconnections between layers
+determine how a given node in one layer and its given counterparts in the previous and next time point layers are
+linked and influence each other. The network analysis community has strong traditions in using the spectral properties
+Moreno and Arenas [2013], Sol et al. [2013] of multilayer networks for various purposes such as centrality measures
+De Domenico et al. [2016] or investigating diffusion processes Sol et al. [2013].
+One challenge associated with understanding the spectral properties of the temporal networks is the lack of available
+tools that respect the fundamental distinction between within-layer and inter-layer edges Kivel¨a et al. [2014], Taylor
+et al. [2015], De Domenico et al. [2013] when studying the spectral properties of the Laplacian matrix L of temporal
+networks, known as supra-Laplacian. A number of investigations were undertaken to show that the inter-layer couplings
+in multilayer networks distort those spectral properties and to explain the effect of different inter-layer weights over the
+eigenvalues of the supra-Laplacian Moreno and Arenas [2013], Sol et al. [2013]. Up to our knowledge, there is no work
+related to the understanding of the information carried by the eigenvectors corresponding to the smallest eignevalues of
+the supra-Laplacian.
+The spectral analysis on a network is nowadays understood as studying the spectral properties of the various Laplacian
+matrices defined on the network. In particular, for the so-called normalized Laplacian the most interesting are usually
+the smallest eigenvalues and their eigenvectors.
+arXiv:2301.13159v1  [math.NA]  12 Jan 2023
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+For a Laplacian matrix, the eigenvector corresponding to the smallest eigenvalue, λ1 = 0, is constant or weighted by
+the node degrees if the Laplacian is normalized Chung [1996]. The eigenvector corresponding to the smallest non-zero
+eigenvalue, known as the algebraic connectivity, is in practice used for partitioning purposes Luo et al. [2002], Luxburg
+[2007] and is known as the Fiedler vector. In this article, we consider slowly-changing temporal networks which means
+that the adjacency matrices forming the different time layers change relatively slowly Enright and Kao [2018]. The
+main objective of the present paper is to draw a maximal profit of this important property for the majority of temporal
+networks. In particular, for every temporal network, for a sufficiently small interval, we have this effect.
+Further, we add inter-layer weights to the temporal network which may be considered as perturbations of the Kronecker
+sum of the separate adjacency matrices forming the different time layers, and we consider the Laplacian of the resulting
+matrix which is usually called supra-Laplacian Kivel¨a et al. [2014]. This point of view on the temporal networks,
+allows us to find an approximate closed form solution of the eigenvectors corresponding to the smallest eigenvalues
+of the supra-Laplacian. In particular, by applying arguments from perturbation theory, we are able to show that the
+eigenvectors corresponding to the smallest eigenvalues (of the supra-Laplacian) are well approximated by the space
+of the perturbed eigenvectors corresponding to all zero eigenvalues of the Laplacian matrices corresponding to the
+networks of the separate time layers.
+The paper is organised as follows: in Sec. 2, we present the construction of the temporal network following a constant
+block Jacobi model. This model appears in a natural way as a first order approximation to the slowly-changing temporal
+network, and enjoys a closed-form solution of the eigenvectors of the supra-Laplacian matrix; in Sec. 3 we investigate
+the spectral properties of the supra-Laplacian and obtain an eigenvector solution of the reduced system; Sec. 4 is devoted
+to identifying the smallest eigenvectors, which are obtained by perturbation of the zero eigenvectors of the separate
+time layers, and discussing the influence of density and number of layers on these eigenvectors; finally we state the
+conclusions.
+2
+Temporal network following constant block Jacobi model: notations and definitions
+A temporal network is a set of networks in which edges and nodes vary in time. In this work, we make the assumption
+that each node i is present in all layers. We use the notation Gt for a layer in an ordered sequence of T networks
+T =
+�
+G1, G2, ..., GT �
+with Gt = (V, At) where t ∈ {1, 2, ..., T} and the number of nodes is N, i.e. N = |V | . Here
+At is a binary undirected and connected adjacency matrix. In order to use the multilayer framework for representing a
+temporal network, we consider the diagonal ordinal coupling of layers Kivel¨a et al. [2014], Bassett et al. [2011], Mucha
+et al. [2010], to define a new supra-network �T . We define the coupling edges: we denote by ωt,p
+i
+∈ R the value of the
+inter-layer edge weight between node i in different time layers t and p. Our main assumption is that only neighbouring
+layers may be connected, i.e. ωt,p
+i
+= 0 for all layers Gt and Gp, with p ̸= t − 1 and p ̸= t + 1. No other edges between
+Gt and Gp exist for indices t ̸= p.
+As a result, the multilayer framework of the temporal network is expressed in an NT-node single adjacency matrix
+A of size NT × NT which is simply the adjacency matrix of the network �T , referred to as supra-adjacency matrix.
+Clearly, the diagonal blocks of A are the adjacency matrices At, and the off-diagonal blocks are the inter-layer weight
+matrices W t,p = diag(ωt,p
+1 , ωt,p
+2 , ..., ωt,p
+N ) if p = t − 1 or p = t + 1.
+The usual within-layer degree of node i in layer Gt is defined as dt
+i
+:=
+�N
+j=1At
+ij while the multilayer
+node degree of node i in layer Gt is dt
+i := dt
+i + ωt,t−1
+i
++ ωt,t+1
+i
+.
+Define the degree matrix D as D :=
+diag
+�
+d1
+1, d1
+2, ..., d1
+N, d2
+1, ..., d2
+N, ..., dT
+N
+�
+. The normalized supra-Laplacian L is defined as L : =D− 1
+2 (D − A) D− 1
+2
+Chung [1996].
+The supra-adjacency matrix A0 with 0 inter-layer weights and its corresponding Laplacian matrix L0 are directly
+expressed as a Kronecker sum:
+A0 := ⊕T
+t=1At −→ L0 = ⊕T
+t=1Lt
+(1)
+where Lt is the normalized Laplacian of network Gt.
+From spectral graph theory Chung [1996], we know that due to the connectedness of At, for every time point t the
+solution to Ltvt
+1 = 0 corresponds to the first eigenvalue λt
+1 = 0 which has multiplicity one and the corresponding
+eigenvector v1 is the eigenvector (Dt)
+1
+2 1, where 1 is the constant one vector and Dt is the degree matrix for the
+adjacency matrix At.
+Hence, the equation L0v = 0 has a T−dimensional subspace of solutions and we find its basis explicitly: namely, for
+every t we define the column vector V t ∈ RNT , as a zero-padded vector with vt
+1 at the position of the tth block. Thus,
+all solutions to L0v = 0 are given by v = �T
+t=1 αtV t for arbitrary constants αt.
+2
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+The main objective of the present paper is to consider an ideal case of a temporal network which is slowly-changing in
+time, hence, is well approximated by a temporal network following a constant block Jacobi model: Let us consider the
+case where At = A for all t and W t,p = W for all t, p. An important step in our construction is to ”periodize” the
+temporal network, which will provide the existence of a nice closed-form solution of the resulting network. This is not
+a very artificial approach since the ”slowly-changing” of the network assumes that the network does not vary too much
+from the initial to the final layer: Namely, we construct a ”periodic” supra-adjacency matrix A and its corresponding
+supra-Laplacian matrix L for temporal networks, by including non-zero diagonal blocks on the upper-right and lower-
+left corner blocks. In other words, we include inter-layer weights between the first time layer A1 and the last time layer
+AT . The resulting matrix A is a periodic constant block Jacobi matrix which gives the name of the model. In view
+of the slowly-changing nature of the temporal network Gt, the matrix A is a perturbation of the matrix A0 and L is a
+perturbation of the matrix L0.
+Furtheron, the resulting supra-Laplacian matrix L is given by the following T × T block matrix, which may be easily
+proved to be an infinite periodic block Jacobi matrix Sahbani [2015]:
+L :=
+�
+�
+�
+�
+�
+�
+�
+�L
+�LW
+�LW
+�LW
+�L
+�LW
+�LW
+�L
+· · ·
+�LW
+�LW
+�LW
+�L
+�
+�
+�
+�
+�
+�
+�
+�
+��
+�
+T
+(2)
+We have to note that if we have the same ω for all matrices W, then the blocks of the block-diagonal matrix D
+contain the matrices Dt + 2ωI. Since for every t holds equation Lt = I − D−1/2AD−1/2, and since the ma-
+trix D−1/2AD−1/2 has entries d−1/2
+i
+d−1/2
+j
+aij, we see that �L is a perturbation of L which has just the elements
+− (di + 2ω)−1/2 (dj + 2ω)−1/2 aij and not −d−1/2
+i
+d−1/2
+j
+aij. Hence, written formally, we have the equality
+�L = I − (D + 2ωI)−1/2 A (D + 2ωI)−1/2
+On the other hand, the matrix �LW is equal to −ω (D + 2ωI)−1 , in equation (2).
+The big advantage of the constant block Jacobi model is that we can find ”explicitly” its spectrum which we discuss in
+the next sections.
+3
+Smallest eigenvalues and paired eigenvectors of the supra-Laplacian L of temporal
+networks following constant block Jacobi model
+As we know from spectral graph theory Chung [1996], the eigenvalues of the Laplacian Lt and of the supra-Laplacian
+L are non-negative, and the minimal eigenvalue is 0, as mentioned above. As usual, in the applications the small
+eigenvalues and the corresponding eigenvectors are of particular importance. By perturbation theory, some of those
+eigenvalues which are very close to 0 are obtained as a direct perturbation of the 0 eigenvalues of all separate time layer
+Laplacian matrices Lt, and the same holds about their paired eigenvectors. On the other hand, the eigenvectors paired
+to the bigger eigenvalues are obtained as perturbations not only of the 0 eigenvectors of the separate matrices Lt but
+also of the Fielder (and the higher) eigenvectors of the separate matrices Lt.
+The solution for the Laplacian L in equation (2) is defined by:
+Lψ = λψ
+(3)
+and for finding it we apply a classical technique based on discrete Fourier transforms (DFTs), see e.g. Sahbani [2015].
+To do this we represent each vector ψ ∈ RNT as the sequence of vectors [ψ1, ψ2, ..., ψT ] where each vector ψj is the
+portion of eigenvector ψ corresponding to the jth time block. Then equation (3) splits into the equations
+�LW ψj−1 + �Lψj + �LW ψj+1 = λψj
+for j = 1, 2, ..., T
+(4)
+where for the sake of notation simplicity we have put
+ψ0 = ψT ,
+ψT +1 = ψ1.
+For k = 0, 1, 2, ..., T − 1, we denote the DFT of vector ψ at value k by �ψ(k) ∈ RN, and put
+�ψ(k) :=
+T −1
+�
+j=0
+e−ijk 2π
+T ψj+1.
+(5)
+3
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+It is important that from the set of DFT vectors { �ψ (k)}T −1
+k=0 we may recover the whole vector ψ ∈ RNT using the
+Fourier inversion formula:
+ψj = 1
+T
+T −1
+�
+k=0
+�ψ(k)eijk 2π
+T .
+(6)
+Now by applying the DFT (5) to equations (4) (i.e. by multiplying by exponents and summing up the equations), we
+obtain the fundamental equations satisfied by the DFT of the vector ψ defined in formula (5):
+�
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW
+�
+�ψ (k) = λ �ψ (k)
+(7)
+for
+k = 0, 1, ..., T − 1.
+The following theorem justifies the application of the DFTs for solving the system (3):
+Theorem 1 The spectrum (with multiplicities) of the supra-Laplacian L in equation (2) of a temporal network following
+a periodic constant block Jacobi model coincides with the union of the spectra of the matrices �L + 2 cos
+�
+k 2π
+T
+� �LW , i.e.
+spec (L) = ∪T −1
+k=0 spec
+�
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW
+�
+(8)
+Proof 2 First, we prove the inclusion
+spec (L) ⊆ ∪T −1
+k=0 spec
+�
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW
+�
+.
+Indeed, by the above arguments, if we have an eigenvalue λ with eigenvector ψ solving system (4), then for every k with
+0 ≤ k ≤ T − 1 we have equation (7), i.e.
+�
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW
+�
+�ψ (k) = λ �ψ (k) .
+Hence, λ is an eigenvalue for all matrices �L + 2 cos
+�
+k 2π
+T
+� �LW with eigenvector �ψ (k) . Now, we prove the opposite
+inclusion:
+∪T −1
+k=0 spec
+�
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW
+�
+⊆ spec (L) .
+Assume that λ∗ is an eigenvalue with eigenvector v∗ for the matrix �L + 2 cos
+�
+k 2π
+T
+� �LW , i.e.
+�
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW
+�
+v∗ = λ∗v∗.
+We define the vector ϕ ∈ RNT by putting
+ϕk+1 = v∗
+ϕm = 0
+for m ̸= k + 1, m = 1, 2, ..., T.
+By the inversion formula (6) we define the vector
+ψj := ϕk+1eijk 2π
+T
+for j = 1, 2, ..., T.
+We show that it satisfies the eigenvalue equation (4) since
+�LW ψj−1 + �Lψj + �LW ψj+1 = λ∗ψj
+i.e.
+ei(j−1)k 2π
+T �LW v∗ + eijk 2π
+T �Lv∗ + ei(j+1)k 2π
+T �LW v∗ = λ∗eijk 2π
+T v∗
+But the last is equivalent to equation
+e−ik 2π
+T �LW v∗ + �Lv∗ + eik 2π
+T �LW v∗ = λ∗v∗
+hence, to equation �Lv∗ + 2 cos
+�
+k 2π
+T
+� �LW v∗ = λ∗v∗; which was our assumption. This completes the proof.
+4
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+0
+20
+40
+60
+80
+100
+120
+ Index
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+1.4
+ Value
+k=14,15
+k=13,16
+k=12,17
+k=11,18
+k=10,19
+k=9,20
+k=8,21
+k=7,22
+k=6,23
+k=5,24
+k=4,25
+k=3,26
+k=2,27
+k=1,28
+k=0,29
+0
+10
+20
+k
+-1
+0
+1
+Figure 1: The 100
+100
+100 smallest eigenvalues of matrices ˜L + 2 cos
+�
+k 2π
+T
+� ˜LW
+˜L + 2 cos
+�
+k 2π
+T
+� ˜LW
+˜L + 2 cos
+�
+k 2π
+T
+� ˜LW for each k = 0, 1, 2, ..., 29.
+k = 0, 1, 2, ..., 29.
+k = 0, 1, 2, ..., 29. The matrices
+˜L and ˜LW are obtained from a temporal benchmark network composed of T = 30 Erdos-Renyi random graphs each
+with N = 100 nodes and edge probability p = 0.3 (such dense consecutive ER networks are slowly-changing). The
+inter-layer weights ω are fixed at 1. We include the additional plot of cos
+�
+k 2π
+T
+�
+which determines the monotonically
+increasing behavior of eigenvalues corresponding to 0 ≤ k ≤ 14 and monotonically decreasing behaviour of eigenvalues
+corresponding to 15 ≤ k ≤ 29.
+In Figure 1 we have displayed the first 100 eigenvalues of the matrix L = �L+2 cos
+�
+k 2π
+T
+� �LW from equation (7), where
+we see that for every j ≥ 1, the jth eigenvalue λ(k)
+j
+of all matrices �L + 2 cos
+�
+k 2π
+T
+� �LW is monotonically increasing
+with k for
+0 ≤ k ≤ T − 1
+2
+− 1 if T is odd
+and
+0 ≤ k ≤ T
+2 − 1 if T is even.
+The following proposition explains the behavior of the eigenvalues.
+Proposition 3 Without loss of generality assume that T is odd.
+Then the jth eigenvalues of the matrices
+�L + 2 cos
+�
+k 2π
+T
+� �LW satisfy
+λ(0)
+j
+≤ λ(1)
+j
+≤ · · · ≤ λ( T −1
+2
+−1)
+j
+.
+Proof 4 The proof of this proposition is direct consequence of Theorem 8.1.5. in Golub and Van Loan [1996] which
+states that for symmetric matrices V and E of size N × N, and for all eigenvalues λj, for j = 1, 2, ..., N, hold the
+inequalities:
+λj (V ) + λmin (E) ≤ λj (V + E) ≤ λj (V ) + λmax (E) .
+(9)
+5
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+We take into account the fact that the eigenvalues of the diagonal matrix �LW are non-negative since they coincide with
+all non-negative weights ωt,p
+j . In particular, if all they are equal to a constant ω, then we see that
+λk
+j = λj(�L) + 2 cos
+�
+k 2π
+T
+�
+ω.
+This completes the proof.
+Now, by means of Theorem 1, we show how to construct a solution to eigenvalue equation (3) by using equality (7): Fix
+a k = ˆk and consider an eigenvector v with eigenvalue ˆλ solving the eigenvalue problem (7) for k = ˆk. We assume that
+ˆλ is among the smallest eigenvalues, close to 0. We are seeking for a block-vector Ψ = (ψ1, ψ2, ..., ψT ) ∈ RNT for
+which �Ψ (k) = ϕk, where the block-vector Φ = (ϕ1, ..., ϕT ) ∈ RNT is defined as
+ϕk :=
+�
+v
+for k = ˆk
+0
+for k ̸= ˆk
+Now we apply the inversion formula (6) to the vector Φ, and obtain the block-vector Ψ ∈ CNT with components
+ψj = e
+2π
+T ijˆkv
+for j = 0, 1, ..., T − 1.
+(10)
+Thus we have ϕk = 0 for k ̸= ˆk, and Ψ is a solution to the eigenvalue equation (3) with the same ˆλ. Since the vector
+Ψ is complex valued, we obtain two real-valued vectors (∈ RNT ), by taking the real and imaginary parts of e
+2π
+T ijˆk,
+namely:
+ψR
+j := cos
+�2π
+T jˆk
+�
+× v
+for j = 0, 1, ..., T − 1
+(11)
+ψI
+j := sin
+�2π
+T jˆk
+�
+× v
+for j = 0, 1, ..., T − 1
+In Figure 2 we visualise solutions (11) for ˆk = 1, 2, 3, accompanied by the corresponding plots of cos( 2π
+T jˆk) and
+sin( 2π
+T jˆk) for j = 0, 1, ..., T − 1.
+Every eigenvalue in equation (7) has even multiplicity due to the equality of the two matrices as indicated below:
+�L + 2 cos
+�
+k 2π
+T
+�
+�LW =�L + 2 cos
+�
+(T − k) 2π
+T
+�
+�LW
+for 0 ≤ k ≤ T − 1
+2
+− 1;
+the double multiplicity of the eigenvalues is clearly observed in Figure 1. In the case of odd T there are unique
+eigenvalues just for k = T −1
+2
+− 1; for even T all eigenvalues have even multiplicity. For ˆk = 0 we have one solution Ψ
+with ψj = v corresponding to the zero eigenvalue, ˆλ = 0.
+By using the results of perturbation theory for invariant subspaces Golub and Van Loan [1996], Luxburg [2007] we see
+that for every eigenvalue with even multiplicity, we may estimate the perturbation of its eigenspace, i.e. the space of
+its eigenvectors. Thus we obtain the solutions which look like “block sinusoids” of cos and sin type, Figure 2. The
+perturbation of the two-dimensional space spanned by cos and sin type solutions, results in a two-dimensional space
+corresponding to the perturbed eigenvalue of the matrix L. These eigenvectors may differ from cos or sin type solutions.
+The above theoretical results have a direct impact on the eigenvectors of the supra-Laplacian L, Figure 3. We show
+that the eigenvectors corresponding to the eigenvalues of the supra-Laplacian L, which are close to 0, are obtained by
+perturbation of the eigenvectors corresponding to the 0 eigenvalues of the separate layers Lt, derived as (Dt)
+1
+2 1. Thus
+they do not carry any information about the finer description of that layer as does the Fiedler vector. These eigenvectors
+of L give us only information about all T time layers being separate from each other. The bigger eigenvalues of L have
+eigenvectors which are perturbations of mixtures of higher eigenvectors for networks Lt, i.e. they contain information
+from the Fiedler eigenvectors for the separate networks Lt. We can conclude that only after the block nature of the
+constant block Jacobi model in the temporal network is captured the eigenvectors start capturing variability introduced
+by some certain within-layer patterns, which is clearly seen from Figure 3.
+6
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.15
+-0.1
+-0.05
+0
+0.05
+0.1
+0.15
+Eigenvector estimation
+0
+10
+20
+j
+-1
+0
+1
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.15
+-0.1
+-0.05
+0
+0.05
+0.1
+0.15
+Eigenvector estimation
+0
+10
+20
+j
+-1
+0
+1
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.15
+-0.1
+-0.05
+0
+0.05
+0.1
+0.15
+Eigenvector estimation
+0
+10
+20
+j
+-1
+0
+1
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.15
+-0.1
+-0.05
+0
+0.05
+0.1
+0.15
+Eigenvector estimation
+0
+10
+20
+j
+-1
+0
+1
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.15
+-0.1
+-0.05
+0
+0.05
+0.1
+0.15
+Eigenvector estimation
+0
+10
+20
+j
+-1
+0
+1
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.15
+-0.1
+-0.05
+0
+0.05
+0.1
+0.15
+Eigenvector estimation
+0
+10
+20
+j
+-1
+0
+1
+Figure 2: Eigenvector estimations for supra-Laplacian matrix LLL. This figure visualizes eigenvectors from equation
+(11) for ˆk = 1, 2, 3, each accompanied by the corresponding graph of the cos and sin functions. The eigenvector
+v corresponds to the eigenvalue λ = 0 which is a solution to the eigenvalue problem (7). The matrices ˜L and ˜LW
+are obtained from a temporal network following the constant block Jacobi model composed of T = 30 Erdos-Renyi
+random graphs each with N = 100 nodes and edge probability p = 0.3. The inter-layer weights ω are fixed at 1.
+7
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+20
+40
+60
+80
+100
+0
+0.1
+0.2
+Eigenvalues
+Eigenvalues
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time layers
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 1
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time layers
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 2
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time layers
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 3
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time layers
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 4
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time layers
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 5
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time layers
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 6
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
+23
+24
+25
+26
+27
+28
+29
+30
+Time points
+represented by nodes
+-0.04
+-0.02
+0
+0.02
+0.04
+Eigenvector
+Eigenvector 35
+...
+Figure 3:
+Eigenvalues and eigenvectors for an Erdos-Renyi benchmark temporal network. The Erdos-Renyi
+temporal benchmark network is composed of T = 30 random Erdos-Renyi graphs with N = 100 nodes and p = 0.1
+edge probability. The inter-layer weights are set to ω = 0.01. We plot the 100 smallest eigenvalues of the corresponding
+supra-Laplacian matrix, the 6 eigenvectors corresponding to the 6 smallest eigenvalues and the 35th eigenvector. The
+jump of the eigenvalue graph indicates precisely the position of λ∗ for index 31 and all following eigenvectors look
+as the 35th eigenvector plotted which captures local variability. Colouring of each eigenvector is consistent with the
+components that belong to different time points.
+4
+Properties of the eigenvectors corresponding to small eigenvalues of the supra-Laplacian
+L
+In this section we empirically showcase the theoretical results that eigenvectors corresponding to the small eigenvalues
+of L are well-approximated by linear combinations of the eigenvectors (paired to the zero eigenvalue) of the separate
+layers. We investigate their behavior with respect to the edge density of the layers and the inter-layer weights.
+4.1
+Evaluating the approximation of the eigenvectors of L using the eigenvectors of the separate time layers
+Let Λ be the set of smallest eigenvalues with paired eigenvectors well-approximated by the subspace of eigenvectors
+corresponding to the 0 eigenvalues for the separate layers. The theoretical results from Sec. 3 guarantee that the
+eigenvectors v corresponding to λ ∈ Λ satisfy (see Sec. 2 for V t def.)
+min
+{αt}
+�����v −
+T
+�
+t=1
+αtV t
+����� ≤ ε
+(12)
+8
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+20
+40
+60
+80
+100
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+p=0.03
+p=0.04
+p=0.05
+p=0.08
+p=0.1
+p=0.3
+20
+40
+60
+80
+100
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+p=0.03
+p=0.04
+p=0.05
+p=0.08
+p=0.1
+p=0.3
+20
+40
+60
+80
+100
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+p=0.03
+p=0.04
+p=0.05
+p=0.08
+p=0.1
+p=0.3
+20
+40
+60
+80
+100
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+p=0.03
+p=0.04
+p=0.05
+p=0.08
+p=0.1
+p=0.3
+Figure 4:
+Error ϵi of approximating supra-Laplacian eigenvectors (corresponding to eigenvalue λi
+λi
+λi for
+i = 1, 2, 3, ...., TN)
+i = 1, 2, 3, ...., TN)
+i = 1, 2, 3, ...., TN) by their separate time layers eigenvectors for the benchmark temporal network. All of
+the benchmark temporal networks were simulated using T = 30 random Erdos-Renyi graphs with N = 100 nodes
+and varying edge probabilities p = 0.03, 0.04, 0.05, 0.08, 0.1, 0.3 edge probabilities. Each of the four plots captures the
+results for different inter-layer weights set to ω = 0.01, 0.05, 1, 5. For each parameter combination (p, ω) we simulate
+100 networks and show their average error ϵi with 1 st.dev. intervals. The obtained approximation average errors and
+st.dev. intervals are visualized for the first 100 eigenvectors although at most T + 1 regressions are needed to capture
+all T layers as separate layers.
+for a small ε > 0, not true for the rest of the eigenvalues.
+We evaluate the approximation of each L’s eigenvector v using the eigenvectors of each time layer corresponding to the
+zero eigenvalue, V t, by solving a regression problem where εi is the NT × 1 vector of residuals, and we denote the
+error at i to be ϵi := ∥εi∥. Denote by λ∗ the first eigenvalue λi for which ϵi >> ϵi−1.
+4.2
+Discussion on the relation between edge density, inter-layer weights and eigenvectors corresponding to
+the smallest eigenvalues
+The present experimental results, in accordance with the developed theory, show that for a small eigenvalue of the
+supra-Laplacian L, the eigenvectors ψR and ψI are approximations to the corresponding eigenvectors of the supra-
+Laplacian L. In Figure 3 we observe the eigenvectors of the supra-Laplacian of a temporal network composed of
+random Erdos-Renyi graphs, Erdos and Renyi [1959]. The first few eigenvectors follow the same sin and cos functions
+as seen in Figure 2, and thus can be used to identify the first order approximation by the constant block Jacobi model
+structure of the temporal network.
+We investigate how the approximation of these eigenvectors is affected by the inter-layer weights and the density of the
+edge weights within each time layer. To showcase this, we simulate various benchmark temporal networks composed
+9
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+0
+20
+40
+60
+80
+100
+120
+ Index
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+1.1
+ Value
+k=16
+k=15,17
+k=14,18
+k=13,19
+k=12,20
+k=11,21
+k=10,22
+k=9,23
+k=8,24
+k=7,25
+k=6,26
+k=5,27
+k=4,28
+k=3,29
+k=2,30
+k=1,31
+k=0,32
+0
+10
+20
+30
+k
+-1
+0
+1
+Figure 5: The 100
+100
+100 smallest eigenvalues of matrices ˜L + 2 cos
+�
+k 2π
+T
+� ˜LW
+˜L + 2 cos
+�
+k 2π
+T
+� ˜LW
+˜L + 2 cos
+�
+k 2π
+T
+� ˜LW for each k = 0, 1, 2, ..., 32
+k = 0, 1, 2, ..., 32
+k = 0, 1, 2, ..., 32. The matrices ˜L
+and ˜LW are obtained from a temporal network composed of T = 33 Sales-Pardo graphs each with N = 640 nodes. The
+inter-layer weights ω are fixed at 1. We include the additional plot of cos
+�
+k 2π
+T
+�
+which determines the monotonically
+increasing behaviour for eigenvalues for 0 ≤ k ≤ 15 and monotonically decreasing behaviour for eigenvalues for
+17 ≤ k ≤ 32.
+of random Erdos-Renyi networks with a varying degree of edge probability p = 0.03, 0.04, 0.05, 0.08, 0.1, 0.3 and
+inter-layer weights ω = 0.01, 0.05, 1, 5, which are two factors that affect the approximation of the eigenvectors of the
+investigated supra-Laplacians L, Figure 4.
+Recall that we have denoted by λ∗ the smallest non-zero eigenvalue sensitive to within-layer connectivity patterns, i.e.
+breaking (12). Then for all benchmark networks types it is true that the value λ∗ is increasing with a decreasing ω
+value: Smaller inter-layer weights ω lead to greater separation between time layers, thus more eigenvectors behave as
+predicted by perturbation theory. More eigenvectors are needed to explain each layer as separate. Higher inter-layer
+weights influence more the resulting eigenvectors and fewer behave in a way as predicted by perturbation theory. Lower
+inter-layer weights interfere less and the behaviour of the eigenvectors resembles closely the behaviour of eigenvectors
+as predicted by perturbation theory.
+When the probability p increases, the density within layers At increases. Since ω is fixed it cannot reflect on the
+increasing density of At and the perturbation effect resulting from inter-layer matrices W t,t+1 is smaller. Thus for
+increasing p, i.e. for increasing density, the behaviour of more eigenvectors resembles closely the behaviour of the
+eigenvectors as predicted by perturbation theory.
+When p is decreasing, the eigenvalue λ∗ indicates that more eigenvectors resemble closely the behaviour of eigenvectors
+as predicted by perturbation theory. This is a result of the sparseness of the time layers and the corresponding lower
+inter-layer weights ωt,t+1
+i
+. The above observations need further rigorous theoretical justification.
+4.3
+Relation between the multi-scale community structure of the layers of a supra-Laplacian network and its
+eigenvalues.
+It is important to note that in Figure 1 the first few eigenvalues capture the block structure of the temporal network
+following the constant block Jacobi model, thus close to 0, however after they start monotonically increasing without
+any clear cuts. From spectral graph partitioning Ding et al. [2001] we know that this is indicative of the lack of structure
+within the networks, which is the case in here where each layer is a densely connected Erdos-Renyi random graphs
+10
+
+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
+A PREPRINT
+with no community structure. In Figure 5, we demonstrate the behavior of the supra-Laplacian eigenvalues when each
+of the layers has multi-scale community structure simulated using the Sales-Pardo model, Sales-Pardo et al. [2007].
+Again the smallest eigenvalues capture the block structure of the temporal network, however, there are clear eigenvalue
+cuts where a new multi-scale community structure within the layers is captured.
+5
+Conclusions
+The above results are crucial in interpreting spectral clustering properties of the supra-Laplacian matrix of all slowly-
+changing temporal networks that can be represented using a constant block Jacobi model. We have provided experimental
+results with Erdos-Renyi (unstructured) networks and Sales-Pardo hierarchical networks. Further investigation in these
+theoretical results will lead into more insights of the spectral properties of supra-Laplacian matrices for more general
+temporal networks. As presented in the paper, the above findings provide a fundamental understanding of the spectral
+properties of temporal networks on time periods where they are slowly changing which can significantly improve
+all spectral-based methods applied on temporal networks such as partitioning, node ranking, community detection,
+clustering, etc. The above results were successfully used to extend a multiscale community detection method, Tremblay
+and Borgnat [2014], based on a spectral graph wavelets approach, Hammond et al. [2011], to temporal networks. The
+extended method, Kuncheva and Montana [2017], takes advantage of the developed theory to automatically detect
+the different scales at which communities exist across layers, which is an advantage over the multilayer modularity
+maximization approach, Mucha et al. [2010], used for similar purposes. The above experimental results have been also
+replicated on temporal Sales-Pardo hierarchical benchmark networks, which are suitable for multi-scale community
+detection. There is also a detailed investigation of using inter-layer weights that account for the sparsity and similarity
+across layers, Kuncheva [2017], including a real life application example to social networks data.
+6
+Acknowledgements
+The author OK acknowledges the project KP-06-N52-1 with Bulgarian NSF. The author ZK acknowledges the project
+KP-06-N32-8 with Bulgarian NSF and EPSRC scholarship (2012-2016) at Imperial College London.
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+Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model
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+12
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf,len=675
+page_content='SPECTRAL PROPERTIES OF THE LAPLACIAN OF TEMPORAL  NETWORKS FOLLOWING A CONSTANT BLOCK JACOBI MODEL  A PREPRINT  Zhana Kuncheva  Data Science and Engineering  Optima Partners  London, UK  zhana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='uk  Ognyan Kounchev  Department of Mathematics and Computer Science  Bulgarian Academy of Sciences  Sofia, Bulgaria  kounchev@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='bas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='bg  January 31, 2023  ABSTRACT  We study the behavior of the eigenvectors associated with the smallest eigenvalues of the Laplacian  matrix of temporal networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We consider the multilayer representation of temporal networks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' a  set of networks linked through ordinal interconnected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We analyze the Laplacian matrix, known  as supra-Laplacian, constructed through the supra-adjacency matrix associated with the multilayer  formulation of temporal networks, using a constant block Jacobi model which has closed-form  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' To do this, we assume that the inter-layer weights are perturbations of the Kronecker sum of  the separate adjacency matrices forming the temporal network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Thus we investigate the properties  of the eigenvectors associated with the smallest eigenvalues (close to zero) of the supra-Laplacian  matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Using arguments of perturbation theory, we show that these eigenvectors can be approximated  by linear combinations of the zero eigenvectors of the individual time layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This finding is crucial  in reconsidering and generalizing the role of the Fielder vector in supra-Laplacian matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  1  Introduction  In recent years, one of the major lines of research in complex network analysis is the topological changes that occur  in a network over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' A sequence of networks with such a time-varying nature can be formalized as a temporal  network Holme and Saram¨aki [2012].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The multilayer formulation of temporal networks Kivel¨a et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2014] is one  way to consider the interconnected topological structure changing over time: ordinal interconnections between layers  determine how a given node in one layer and its given counterparts in the previous and next time point layers are  linked and influence each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The network analysis community has strong traditions in using the spectral properties  Moreno and Arenas [2013], Sol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2013] of multilayer networks for various purposes such as centrality measures  De Domenico et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2016] or investigating diffusion processes Sol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2013].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  One challenge associated with understanding the spectral properties of the temporal networks is the lack of available  tools that respect the fundamental distinction between within-layer and inter-layer edges Kivel¨a et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2014], Taylor  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2015], De Domenico et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2013] when studying the spectral properties of the Laplacian matrix L of temporal  networks, known as supra-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' A number of investigations were undertaken to show that the inter-layer couplings  in multilayer networks distort those spectral properties and to explain the effect of different inter-layer weights over the  eigenvalues of the supra-Laplacian Moreno and Arenas [2013], Sol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2013].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Up to our knowledge, there is no work  related to the understanding of the information carried by the eigenvectors corresponding to the smallest eignevalues of  the supra-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The spectral analysis on a network is nowadays understood as studying the spectral properties of the various Laplacian  matrices defined on the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In particular, for the so-called normalized Laplacian the most interesting are usually  the smallest eigenvalues and their eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='13159v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='NA]  12 Jan 2023  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  For a Laplacian matrix, the eigenvector corresponding to the smallest eigenvalue, λ1 = 0, is constant or weighted by  the node degrees if the Laplacian is normalized Chung [1996].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The eigenvector corresponding to the smallest non-zero  eigenvalue, known as the algebraic connectivity, is in practice used for partitioning purposes Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2002], Luxburg  [2007] and is known as the Fiedler vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In this article, we consider slowly-changing temporal networks which means  that the adjacency matrices forming the different time layers change relatively slowly Enright and Kao [2018].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The  main objective of the present paper is to draw a maximal profit of this important property for the majority of temporal  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In particular, for every temporal network, for a sufficiently small interval, we have this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Further, we add inter-layer weights to the temporal network which may be considered as perturbations of the Kronecker  sum of the separate adjacency matrices forming the different time layers, and we consider the Laplacian of the resulting  matrix which is usually called supra-Laplacian Kivel¨a et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2014].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This point of view on the temporal networks,  allows us to find an approximate closed form solution of the eigenvectors corresponding to the smallest eigenvalues  of the supra-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In particular, by applying arguments from perturbation theory, we are able to show that the  eigenvectors corresponding to the smallest eigenvalues (of the supra-Laplacian) are well approximated by the space  of the perturbed eigenvectors corresponding to all zero eigenvalues of the Laplacian matrices corresponding to the  networks of the separate time layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The paper is organised as follows: in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' 2, we present the construction of the temporal network following a constant  block Jacobi model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This model appears in a natural way as a first order approximation to the slowly-changing temporal  network, and enjoys a closed-form solution of the eigenvectors of the supra-Laplacian matrix;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' 3 we investigate  the spectral properties of the supra-Laplacian and obtain an eigenvector solution of the reduced system;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' 4 is devoted  to identifying the smallest eigenvectors, which are obtained by perturbation of the zero eigenvectors of the separate  time layers, and discussing the influence of density and number of layers on these eigenvectors;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' finally we state the  conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  2  Temporal network following constant block Jacobi model: notations and definitions  A temporal network is a set of networks in which edges and nodes vary in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In this work, we make the assumption  that each node i is present in all layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We use the notation Gt for a layer in an ordered sequence of T networks  T =  �  G1, G2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', GT �  with Gt = (V, At) where t ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T} and the number of nodes is N, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' N = |V | .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Here  At is a binary undirected and connected adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In order to use the multilayer framework for representing a  temporal network, we consider the diagonal ordinal coupling of layers Kivel¨a et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2014], Bassett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2011], Mucha  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2010], to define a new supra-network �T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We define the coupling edges: we denote by ωt,p  i  ∈ R the value of the  inter-layer edge weight between node i in different time layers t and p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Our main assumption is that only neighbouring  layers may be connected, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' ωt,p  i  = 0 for all layers Gt and Gp, with p ̸= t − 1 and p ̸= t + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' No other edges between  Gt and Gp exist for indices t ̸= p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  As a result, the multilayer framework of the temporal network is expressed in an NT-node single adjacency matrix  A of size NT × NT which is simply the adjacency matrix of the network �T , referred to as supra-adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Clearly, the diagonal blocks of A are the adjacency matrices At, and the off-diagonal blocks are the inter-layer weight  matrices W t,p = diag(ωt,p  1 , ωt,p  2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', ωt,p  N ) if p = t − 1 or p = t + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The usual within-layer degree of node i in layer Gt is defined as dt  i  :=  �N  j=1At  ij while the multilayer  node degree of node i in layer Gt is dt  i := dt  i + ωt,t−1  i  + ωt,t+1  i  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Define the degree matrix D as D :=  diag  �  d1  1, d1  2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', d1  N, d2  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', d2  N, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', dT  N  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The normalized supra-Laplacian L is defined as L : =D− 1  2 (D − A) D− 1  2  Chung [1996].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The supra-adjacency matrix A0 with 0 inter-layer weights and its corresponding Laplacian matrix L0 are directly  expressed as a Kronecker sum:  A0 := ⊕T  t=1At −→ L0 = ⊕T  t=1Lt  (1)  where Lt is the normalized Laplacian of network Gt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  From spectral graph theory Chung [1996], we know that due to the connectedness of At, for every time point t the  solution to Ltvt  1 = 0 corresponds to the first eigenvalue λt  1 = 0 which has multiplicity one and the corresponding  eigenvector v1 is the eigenvector (Dt)  1  2 1, where 1 is the constant one vector and Dt is the degree matrix for the  adjacency matrix At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Hence, the equation L0v = 0 has a T−dimensional subspace of solutions and we find its basis explicitly: namely, for  every t we define the column vector V t ∈ RNT , as a zero-padded vector with vt  1 at the position of the tth block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Thus,  all solutions to L0v = 0 are given by v = �T  t=1 αtV t for arbitrary constants αt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  2  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  The main objective of the present paper is to consider an ideal case of a temporal network which is slowly-changing in  time, hence, is well approximated by a temporal network following a constant block Jacobi model: Let us consider the  case where At = A for all t and W t,p = W for all t, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' An important step in our construction is to ”periodize” the  temporal network, which will provide the existence of a nice closed-form solution of the resulting network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This is not  a very artificial approach since the ”slowly-changing” of the network assumes that the network does not vary too much  from the initial to the final layer: Namely, we construct a ”periodic” supra-adjacency matrix A and its corresponding  supra-Laplacian matrix L for temporal networks, by including non-zero diagonal blocks on the upper-right and lower-  left corner blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In other words, we include inter-layer weights between the first time layer A1 and the last time layer  AT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The resulting matrix A is a periodic constant block Jacobi matrix which gives the name of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In view  of the slowly-changing nature of the temporal network Gt, the matrix A is a perturbation of the matrix A0 and L is a  perturbation of the matrix L0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Furtheron, the resulting supra-Laplacian matrix L is given by the following T × T block matrix, which may be easily  proved to be an infinite periodic block Jacobi matrix Sahbani [2015]:  L :=  �  �  �  �  �  �  �  �L  �LW  �LW  �LW  �L  �LW  �LW  �L  · ·  �LW  �LW  �LW  �L  �  �  �  �  �  �  �  �  ��  �  T  (2)  We have to note that if we have the same ω for all matrices W, then the blocks of the block-diagonal matrix D  contain the matrices Dt + 2ωI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Since for every t holds equation Lt = I − D−1/2AD−1/2, and since the ma-  trix D−1/2AD−1/2 has entries d−1/2  i  d−1/2  j  aij, we see that �L is a perturbation of L which has just the elements  − (di + 2ω)−1/2 (dj + 2ω)−1/2 aij and not −d−1/2  i  d−1/2  j  aij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Hence, written formally, we have the equality  �L = I − (D + 2ωI)−1/2 A (D + 2ωI)−1/2  On the other hand, the matrix �LW is equal to −ω (D + 2ωI)−1 , in equation (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The big advantage of the constant block Jacobi model is that we can find ”explicitly” its spectrum which we discuss in  the next sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  3  Smallest eigenvalues and paired eigenvectors of the supra-Laplacian L of temporal  networks following constant block Jacobi model  As we know from spectral graph theory Chung [1996], the eigenvalues of the Laplacian Lt and of the supra-Laplacian  L are non-negative, and the minimal eigenvalue is 0, as mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' As usual, in the applications the small  eigenvalues and the corresponding eigenvectors are of particular importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' By perturbation theory, some of those  eigenvalues which are very close to 0 are obtained as a direct perturbation of the 0 eigenvalues of all separate time layer  Laplacian matrices Lt, and the same holds about their paired eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' On the other hand, the eigenvectors paired  to the bigger eigenvalues are obtained as perturbations not only of the 0 eigenvectors of the separate matrices Lt but  also of the Fielder (and the higher) eigenvectors of the separate matrices Lt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The solution for the Laplacian L in equation (2) is defined by:  Lψ = λψ  (3)  and for finding it we apply a classical technique based on discrete Fourier transforms (DFTs), see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Sahbani [2015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  To do this we represent each vector ψ ∈ RNT as the sequence of vectors [ψ1, ψ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', ψT ] where each vector ψj is the  portion of eigenvector ψ corresponding to the jth time block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Then equation (3) splits into the equations  �LW ψj−1 + �Lψj + �LW ψj+1 = λψj  for j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T  (4)  where for the sake of notation simplicity we have put  ψ0 = ψT ,  ψT +1 = ψ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  For k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T − 1, we denote the DFT of vector ψ at value k by �ψ(k) ∈ RN, and put  �ψ(k) :=  T −1  �  j=0  e−ijk 2π  T ψj+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  (5)  3  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  It is important that from the set of DFT vectors { �ψ (k)}T −1  k=0 we may recover the whole vector ψ ∈ RNT using the  Fourier inversion formula:  ψj = 1  T  T −1  �  k=0  �ψ(k)eijk 2π  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  (6)  Now by applying the DFT (5) to equations (4) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' by multiplying by exponents and summing up the equations), we  obtain the fundamental equations satisfied by the DFT of the vector ψ defined in formula (5):  �  �L + 2 cos  �  k 2π  T  �  �LW  �  �ψ (k) = λ �ψ (k)  (7)  for  k = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The following theorem justifies the application of the DFTs for solving the system (3):  Theorem 1 The spectrum (with multiplicities) of the supra-Laplacian L in equation (2) of a temporal network following  a periodic constant block Jacobi model coincides with the union of the spectra of the matrices �L + 2 cos  �  k 2π  T  � �LW , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  spec (L) = ∪T −1  k=0 spec  �  �L + 2 cos  �  k 2π  T  �  �LW  �  (8)  Proof 2 First, we prove the inclusion  spec (L) ⊆ ∪T −1  k=0 spec  �  �L + 2 cos  �  k 2π  T  �  �LW  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Indeed, by the above arguments, if we have an eigenvalue λ with eigenvector ψ solving system (4), then for every k with  0 ≤ k ≤ T − 1 we have equation (7), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  �  �L + 2 cos  �  k 2π  T  �  �LW  �  �ψ (k) = λ �ψ (k) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Hence, λ is an eigenvalue for all matrices �L + 2 cos  �  k 2π  T  � �LW with eigenvector �ψ (k) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Now, we prove the opposite  inclusion:  ∪T −1  k=0 spec  �  �L + 2 cos  �  k 2π  T  �  �LW  �  ⊆ spec (L) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Assume that λ∗ is an eigenvalue with eigenvector v∗ for the matrix �L + 2 cos  �  k 2π  T  � �LW , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  �  �L + 2 cos  �  k 2π  T  �  �LW  �  v∗ = λ∗v∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  We define the vector ϕ ∈ RNT by putting  ϕk+1 = v∗  ϕm = 0  for m ̸= k + 1, m = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  By the inversion formula (6) we define the vector  ψj := ϕk+1eijk 2π  T  for j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  We show that it satisfies the eigenvalue equation (4) since  �LW ψj−1 + �Lψj + �LW ψj+1 = λ∗ψj  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  ei(j−1)k 2π  T �LW v∗ + eijk 2π  T �Lv∗ + ei(j+1)k 2π  T �LW v∗ = λ∗eijk 2π  T v∗  But the last is equivalent to equation  e−ik 2π  T �LW v∗ + �Lv∗ + eik 2π  T �LW v∗ = λ∗v∗  hence, to equation �Lv∗ + 2 cos  �  k 2π  T  � �LW v∗ = λ∗v∗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' which was our assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  4  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  0  20  40  60  80  100  120  Index  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='4  Value  k=14,15  k=13,16  k=12,17  k=11,18  k=10,19  k=9,20  k=8,21  k=7,22  k=6,23  k=5,24  k=4,25  k=3,26  k=2,27  k=1,28  k=0,29  0  10  20  k  1  0  1  Figure 1: The 100  100  100 smallest eigenvalues of matrices ˜L + 2 cos  �  k 2π  T  � ˜LW  ˜L + 2 cos  �  k 2π  T  � ˜LW  ˜L + 2 cos  �  k 2π  T  � ˜LW for each k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The matrices  ˜L and ˜LW are obtained from a temporal benchmark network composed of T = 30 Erdos-Renyi random graphs each  with N = 100 nodes and edge probability p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='3 (such dense consecutive ER networks are slowly-changing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The  inter-layer weights ω are fixed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We include the additional plot of cos  �  k 2π  T  �  which determines the monotonically  increasing behavior of eigenvalues corresponding to 0 ≤ k ≤ 14 and monotonically decreasing behaviour of eigenvalues  corresponding to 15 ≤ k ≤ 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  In Figure 1 we have displayed the first 100 eigenvalues of the matrix L = �L+2 cos  �  k 2π  T  � �LW from equation (7), where  we see that for every j ≥ 1, the jth eigenvalue λ(k)  j  of all matrices �L + 2 cos  �  k 2π  T  � �LW is monotonically increasing  with k for  0 ≤ k ≤ T − 1  2  − 1 if T is odd  and  0 ≤ k ≤ T  2 − 1 if T is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The following proposition explains the behavior of the eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Proposition 3 Without loss of generality assume that T is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Then the jth eigenvalues of the matrices  �L + 2 cos  �  k 2π  T  � �LW satisfy  λ(0)  j  ≤ λ(1)  j  ≤ · · · ≤ λ( T −1  2  −1)  j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Proof 4 The proof of this proposition is direct consequence of Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' in Golub and Van Loan [1996] which  states that for symmetric matrices V and E of size N × N, and for all eigenvalues λj, for j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', N, hold the  inequalities:  λj (V ) + λmin (E) ≤ λj (V + E) ≤ λj (V ) + λmax (E) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  (9)  5  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  We take into account the fact that the eigenvalues of the diagonal matrix �LW are non-negative since they coincide with  all non-negative weights ωt,p  j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In particular, if all they are equal to a constant ω, then we see that  λk  j = λj(�L) + 2 cos  �  k 2π  T  �  ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Now, by means of Theorem 1, we show how to construct a solution to eigenvalue equation (3) by using equality (7): Fix  a k = ˆk and consider an eigenvector v with eigenvalue ˆλ solving the eigenvalue problem (7) for k = ˆk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We assume that  ˆλ is among the smallest eigenvalues, close to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We are seeking for a block-vector Ψ = (ψ1, ψ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', ψT ) ∈ RNT for  which �Ψ (k) = ϕk, where the block-vector Φ = (ϕ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', ϕT ) ∈ RNT is defined as  ϕk :=  �  v  for k = ˆk  0  for k ̸= ˆk  Now we apply the inversion formula (6) to the vector Φ, and obtain the block-vector Ψ ∈ CNT with components  ψj = e  2π  T ijˆkv  for j = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  (10)  Thus we have ϕk = 0 for k ̸= ˆk, and Ψ is a solution to the eigenvalue equation (3) with the same ˆλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Since the vector  Ψ is complex valued, we obtain two real-valued vectors (∈ RNT ), by taking the real and imaginary parts of e  2π  T ijˆk,  namely:  ψR  j := cos  �2π  T jˆk  �  × v  for j = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T − 1  (11)  ψI  j := sin  �2π  T jˆk  �  × v  for j = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T − 1  In Figure 2 we visualise solutions (11) for ˆk = 1, 2, 3, accompanied by the corresponding plots of cos( 2π  T jˆk) and  sin( 2π  T jˆk) for j = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', T − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Every eigenvalue in equation (7) has even multiplicity due to the equality of the two matrices as indicated below:  �L + 2 cos  �  k 2π  T  �  �LW =�L + 2 cos  �  (T − k) 2π  T  �  �LW  for 0 ≤ k ≤ T − 1  2  − 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  the double multiplicity of the eigenvalues is clearly observed in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In the case of odd T there are unique  eigenvalues just for k = T −1  2  − 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' for even T all eigenvalues have even multiplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' For ˆk = 0 we have one solution Ψ  with ψj = v corresponding to the zero eigenvalue, ˆλ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  By using the results of perturbation theory for invariant subspaces Golub and Van Loan [1996], Luxburg [2007] we see  that for every eigenvalue with even multiplicity, we may estimate the perturbation of its eigenspace, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' the space of  its eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Thus we obtain the solutions which look like “block sinusoids” of cos and sin type, Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The  perturbation of the two-dimensional space spanned by cos and sin type solutions, results in a two-dimensional space  corresponding to the perturbed eigenvalue of the matrix L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' These eigenvectors may differ from cos or sin type solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  The above theoretical results have a direct impact on the eigenvectors of the supra-Laplacian L, Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We show  that the eigenvectors corresponding to the eigenvalues of the supra-Laplacian L, which are close to 0, are obtained by  perturbation of the eigenvectors corresponding to the 0 eigenvalues of the separate layers Lt, derived as (Dt)  1  2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Thus  they do not carry any information about the finer description of that layer as does the Fiedler vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' These eigenvectors  of L give us only information about all T time layers being separate from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The bigger eigenvalues of L have  eigenvectors which are perturbations of mixtures of higher eigenvectors for networks Lt, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' they contain information  from the Fiedler eigenvectors for the separate networks Lt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We can conclude that only after the block nature of the  constant block Jacobi model in the temporal network is captured the eigenvectors start capturing variability introduced  by some certain within-layer patterns, which is clearly seen from Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  6  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  Eigenvector estimation  0  10  20  j  1  0  1  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  Eigenvector estimation  0  10  20  j  1  0  1  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  Eigenvector estimation  0  10  20  j  1  0  1  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  Eigenvector estimation  0  10  20  j  1  0  1  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  Eigenvector estimation  0  10  20  j  1  0  1  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='15  Eigenvector estimation  0  10  20  j  1  0  1  Figure 2: Eigenvector estimations for supra-Laplacian matrix LLL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This figure visualizes eigenvectors from equation  (11) for ˆk = 1, 2, 3, each accompanied by the corresponding graph of the cos and sin functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The eigenvector  v corresponds to the eigenvalue λ = 0 which is a solution to the eigenvalue problem (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The matrices ˜L and ˜LW  are obtained from a temporal network following the constant block Jacobi model composed of T = 30 Erdos-Renyi  random graphs each with N = 100 nodes and edge probability p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The inter-layer weights ω are fixed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  7  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  20  40  60  80  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2  Eigenvalues  Eigenvalues  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time layers  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 1  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time layers  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 2  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time layers  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 3  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time layers  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 4  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time layers  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 5  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time layers  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 6  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  Time points  represented by nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04  Eigenvector  Eigenvector 35  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Figure 3:  Eigenvalues and eigenvectors for an Erdos-Renyi benchmark temporal network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The Erdos-Renyi  temporal benchmark network is composed of T = 30 random Erdos-Renyi graphs with N = 100 nodes and p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  edge probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The inter-layer weights are set to ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We plot the 100 smallest eigenvalues of the corresponding  supra-Laplacian matrix, the 6 eigenvectors corresponding to the 6 smallest eigenvalues and the 35th eigenvector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The  jump of the eigenvalue graph indicates precisely the position of λ∗ for index 31 and all following eigenvectors look  as the 35th eigenvector plotted which captures local variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Colouring of each eigenvector is consistent with the  components that belong to different time points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  4  Properties of the eigenvectors corresponding to small eigenvalues of the supra-Laplacian  L  In this section we empirically showcase the theoretical results that eigenvectors corresponding to the small eigenvalues  of L are well-approximated by linear combinations of the eigenvectors (paired to the zero eigenvalue) of the separate  layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We investigate their behavior with respect to the edge density of the layers and the inter-layer weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  Evaluating the approximation of the eigenvectors of L using the eigenvectors of the separate time layers  Let Λ be the set of smallest eigenvalues with paired eigenvectors well-approximated by the subspace of eigenvectors  corresponding to the 0 eigenvalues for the separate layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The theoretical results from Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' 3 guarantee that the  eigenvectors v corresponding to λ ∈ Λ satisfy (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' 2 for V t def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=')  min  {αt}  �����v −  T  �  t=1  αtV t  ����� ≤ ε  (12)  8  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  20  40  60  80  100  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='3  Figure 4:  Error ϵi of approximating supra-Laplacian eigenvectors (corresponding to eigenvalue λi  λi  λi for  i = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='., TN)  i = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='., TN)  i = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='., TN) by their separate time layers eigenvectors for the benchmark temporal network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' All of  the benchmark temporal networks were simulated using T = 30 random Erdos-Renyi graphs with N = 100 nodes  and varying edge probabilities p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='08, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='3 edge probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Each of the four plots captures the  results for different inter-layer weights set to ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05, 1, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' For each parameter combination (p, ω) we simulate  100 networks and show their average error ϵi with 1 st.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The obtained approximation average errors and  st.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' intervals are visualized for the first 100 eigenvectors although at most T + 1 regressions are needed to capture  all T layers as separate layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  for a small ε > 0, not true for the rest of the eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  We evaluate the approximation of each L’s eigenvector v using the eigenvectors of each time layer corresponding to the  zero eigenvalue, V t, by solving a regression problem where εi is the NT × 1 vector of residuals, and we denote the  error at i to be ϵi := ∥εi∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Denote by λ∗ the first eigenvalue λi for which ϵi >> ϵi−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2  Discussion on the relation between edge density, inter-layer weights and eigenvectors corresponding to  the smallest eigenvalues  The present experimental results, in accordance with the developed theory, show that for a small eigenvalue of the  supra-Laplacian L, the eigenvectors ψR and ψI are approximations to the corresponding eigenvectors of the supra-  Laplacian L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In Figure 3 we observe the eigenvectors of the supra-Laplacian of a temporal network composed of  random Erdos-Renyi graphs, Erdos and Renyi [1959].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The first few eigenvectors follow the same sin and cos functions  as seen in Figure 2, and thus can be used to identify the first order approximation by the constant block Jacobi model  structure of the temporal network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  We investigate how the approximation of these eigenvectors is affected by the inter-layer weights and the density of the  edge weights within each time layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' To showcase this, we simulate various benchmark temporal networks composed  9  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  0  20  40  60  80  100  120  Index  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='9  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1  Value  k=16  k=15,17  k=14,18  k=13,19  k=12,20  k=11,21  k=10,22  k=9,23  k=8,24  k=7,25  k=6,26  k=5,27  k=4,28  k=3,29  k=2,30  k=1,31  k=0,32  0  10  20  30  k  1  0  1  Figure 5: The 100  100  100 smallest eigenvalues of matrices ˜L + 2 cos  �  k 2π  T  � ˜LW  ˜L + 2 cos  �  k 2π  T  � ˜LW  ˜L + 2 cos  �  k 2π  T  � ˜LW for each k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 32  k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 32  k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The matrices ˜L  and ˜LW are obtained from a temporal network composed of T = 33 Sales-Pardo graphs each with N = 640 nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The  inter-layer weights ω are fixed at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We include the additional plot of cos  �  k 2π  T  �  which determines the monotonically  increasing behaviour for eigenvalues for 0 ≤ k ≤ 15 and monotonically decreasing behaviour for eigenvalues for  17 ≤ k ≤ 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  of random Erdos-Renyi networks with a varying degree of edge probability p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='08, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='3 and  inter-layer weights ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='05, 1, 5, which are two factors that affect the approximation of the eigenvectors of the  investigated supra-Laplacians L, Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Recall that we have denoted by λ∗ the smallest non-zero eigenvalue sensitive to within-layer connectivity patterns, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  breaking (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Then for all benchmark networks types it is true that the value λ∗ is increasing with a decreasing ω  value: Smaller inter-layer weights ω lead to greater separation between time layers, thus more eigenvectors behave as  predicted by perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' More eigenvectors are needed to explain each layer as separate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Higher inter-layer  weights influence more the resulting eigenvectors and fewer behave in a way as predicted by perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Lower  inter-layer weights interfere less and the behaviour of the eigenvectors resembles closely the behaviour of eigenvectors  as predicted by perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  When the probability p increases, the density within layers At increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Since ω is fixed it cannot reflect on the  increasing density of At and the perturbation effect resulting from inter-layer matrices W t,t+1 is smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Thus for  increasing p, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' for increasing density, the behaviour of more eigenvectors resembles closely the behaviour of the  eigenvectors as predicted by perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  When p is decreasing, the eigenvalue λ∗ indicates that more eigenvectors resemble closely the behaviour of eigenvectors  as predicted by perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' This is a result of the sparseness of the time layers and the corresponding lower  inter-layer weights ωt,t+1  i  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The above observations need further rigorous theoretical justification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='3  Relation between the multi-scale community structure of the layers of a supra-Laplacian network and its  eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  It is important to note that in Figure 1 the first few eigenvalues capture the block structure of the temporal network  following the constant block Jacobi model, thus close to 0, however after they start monotonically increasing without  any clear cuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' From spectral graph partitioning Ding et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2001] we know that this is indicative of the lack of structure  within the networks, which is the case in here where each layer is a densely connected Erdos-Renyi random graphs  10  Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model  A PREPRINT  with no community structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' In Figure 5, we demonstrate the behavior of the supra-Laplacian eigenvalues when each  of the layers has multi-scale community structure simulated using the Sales-Pardo model, Sales-Pardo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2007].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Again the smallest eigenvalues capture the block structure of the temporal network, however, there are clear eigenvalue  cuts where a new multi-scale community structure within the layers is captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  5  Conclusions  The above results are crucial in interpreting spectral clustering properties of the supra-Laplacian matrix of all slowly-  changing temporal networks that can be represented using a constant block Jacobi model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' We have provided experimental  results with Erdos-Renyi (unstructured) networks and Sales-Pardo hierarchical networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Further investigation in these  theoretical results will lead into more insights of the spectral properties of supra-Laplacian matrices for more general  temporal networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' As presented in the paper, the above findings provide a fundamental understanding of the spectral  properties of temporal networks on time periods where they are slowly changing which can significantly improve  all spectral-based methods applied on temporal networks such as partitioning, node ranking, community detection,  clustering, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The above results were successfully used to extend a multiscale community detection method, Tremblay  and Borgnat [2014], based on a spectral graph wavelets approach, Hammond et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2011], to temporal networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The  extended method, Kuncheva and Montana [2017], takes advantage of the developed theory to automatically detect  the different scales at which communities exist across layers, which is an advantage over the multilayer modularity  maximization approach, Mucha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' [2010], used for similar purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The above experimental results have been also  replicated on temporal Sales-Pardo hierarchical benchmark networks, which are suitable for multi-scale community  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' There is also a detailed investigation of using inter-layer weights that account for the sparsity and similarity  across layers, Kuncheva [2017], including a real life application example to social networks data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  6  Acknowledgements  The author OK acknowledges the project KP-06-N52-1 with Bulgarian NSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' The author ZK acknowledges the project  KP-06-N32-8 with Bulgarian NSF and EPSRC scholarship (2012-2016) at Imperial College London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content=' Temporal Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='physrep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='  Mikko Kivel¨a, Alexandre Arenas, Marc Barthelemy, James P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Gleeson, Yamir Moreno, and Mason A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content=' Multilayer  Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Multilayer Networks, 2(3):203–271, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='org/pdf/1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='7233v4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='  A Sol, M De Domenico, and N E Kouvaris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content=' Random Walk Centrality  in Interconnected Multilayer Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='2906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Dane Taylor, Sean A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Myers, Aaron Clauset, Mason A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Porter, and Peter J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Mucha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Eigenvector-Based Centrality  Measures for Temporal Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' arxiv Prepr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content=' URL http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='org/abs/1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='01266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Manlio De Domenico, Albert Sol´e-Ribalta, Emanuele Cozzo, Mikko Kivel¨a, Yamir Moreno, Mason A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Porter, Sergio  G´omez, and Alex Arenas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Mathematical Formulation of Multilayer Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Nicolas Tremblay and Pierre Borgnat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Graph Wavelets for Multiscale Community Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Signal Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=',  62(20):5227–5239, oct 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' ISSN 1053-587X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1109/TSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2345355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' URL http://ieeexplore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='  org/lpdocs/epic03/wrapper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+page_content='  David K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Hammond, Pierre Vandergheynst, and R´emi Gribonval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Wavelets on Graphs via Spectral Graph Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Harmon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=', 30(2):129–150, mar 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' ISSN 10635203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='acha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' URL  http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='com/science/article/pii/S1063520310000552.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Zhana Kuncheva and Giovanni Montana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Multi-scale community detection in temporal networks using spectral graph  wavelets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' International Workshop on Personal Analytics and Privacy, 10708:139–154, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  Zhana Kuncheva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' Modelling Populations of Complex Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content=' PhD thesis, Department of Mathematics, Imperial  College London, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
+page_content='  12' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNFPT4oBgHgl3EQfvTWR/content/2301.13159v1.pdf'}
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+Astronomy & Astrophysics manuscript no. main
+©ESO 2023
+February 1, 2023
+Extended neutral hydrogen filamentary network in NGC 2403
+Simone Veronese1, 2, W. J. G. de Blok1, 2, 3, and F. Walter4, 5
+1 Netherlands Institute for Radio Astronomy (ASTRON), Postbus 2, 7990 AA Dwingeloo, The Netherlands, e-mail:
+veronese@astron.nl
+2 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
+3 Department of Astronomy, University of Cape Town, Private Bag X3, 7701 Rondebosch, South Africa
+4 Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
+5 National Radio Astronomy Observatory, Pete V. Domenici Array Science Center, P.O. Box O, Socorro, NM 87801, USA
+Received <date> / Accepted <date>
+ABSTRACT
+We present new neutral hydrogen (H i) observations of the nearby galaxy NGC 2403 to determine the nature of a low-column density
+cloud that was detected earlier by the Green Bank Telescope.
+We find that this cloud is the tip of a complex of filaments of extraplanar gas that is coincident with the thin disk. The total H i mass of
+the complex is 2×107 M⊙ or 0.6% of the total H i mass of the galaxy. The main structure, previously referred to as the 8-kpc filament,
+is now seen to be even more extended, along a 20 kpc stream.
+The kinematics and morphological properties of the filaments are unlikely to be the result of outflows related to galactic fountains. It
+is more likely that the 20 kpc filament is related to a recent galaxy interaction. In this context, a ∼ 50 kpc long stellar stream has been
+recently detected connecting NGC 2403 with the nearby dwarf satellite DDO 44. Intriguingly, the southern tip of this stream overlaps
+with that of 20 kpc H i filament.
+We conclude that the H i anomalies in NGC 2403 are the result of a recent (∼ 2 Gyr) interaction with DDO 44 leading to the observed
+filamentary complex.
+Key words. Galaxies: evolution - Galaxies: interactions - Radio lines: galaxies - Techniques: interferometric
+1. Introduction
+Galaxies form stars through the collapsing of giant molecular
+(mainly molecular hydrogen, H ii) clouds on timescales of ∼ 107
+yr (Meidt et al. 2015; Schinnerer et al. 2019; Walter et al. 2020)
+and over the cosmic time (Madau & Dickinson 2014) galaxies
+progressively deplete their molecular gas content. In a perfect
+steady state, the H ii reservoir is replenished by the cooling of
+the atomic hydrogen (H i) in the interstellar medium (Clark et al.
+2012; Walch et al. 2015), which will cause a reduction in the
+content of the atomic gas. However, both simulations and obser-
+vations reveal that the H i content in galaxies is almost constant
+from z ∼ 1 (Davé et al. 2017; Chen et al. 2021). Consequently, in
+order to maintain star formation over cosmic time, galaxies must
+accrete H i.
+Previous studies of H i interaction features and dwarf galaxies
+have shown that they do not provide enough cold gas to replen-
+ish the material reservoir for star formation (Sancisi et al. 2008;
+Putman et al. 2012; de Blok et al. 2020). Other extraplanar gas
+observed closer to the galaxy disks is usually related to galac-
+tic fountains (Putman et al. 2012; Li et al. 2021; Marasco et al.
+2022): star formation and supernova explosions eject interstellar
+medium from the disk to scale-heights of ∼ kpc. The gas catches
+material from the circum-galactic medium and falls back onto
+the galaxy carrying new gas to fuel the star formation. How-
+ever, the amount of material accreted with this process is again
+not enough to replenish the atomic gas reservoir (Putman et al.
+2012; Afruni et al. 2021).
+A hypothesis that could explain the constancy of the H i con-
+tent is that galaxies accrete gas from the Inter-Galactic Medium
+(IGM) (Somerville & Davé 2015; Danovich et al. 2015). The
+mode of this accretion, i.e., cold clouds and streams or hot dif-
+fuse gas (Dekel & Birnboim 2006; Danovich et al. 2015), is un-
+certain as well as the accretion rate. Nevertheless, this model
+could indicate a possible way to solve the problem of how to
+sustain the star formation activities over cosmic time.
+It has, however, one major limitation: the directly detectable
+component of this gas, namely the warm H i at ∼ 104 K, forms
+only a small fraction (< 1%) of the total amount of accreting ma-
+terial which mostly consists of warm-hot 105 K gas. This leads to
+low H i column densities of ∼ 1017 cm−2 (Popping et al. 2009).
+This value is at least one order of magnitude lower than the de-
+tection limits of the current radio interferometer observations.
+Single-dish telescopes can reach these column densities but only
+at low resolutions that usually do not resolve the relevant scales.
+So far, surveys that could potentially detect accreting H i clouds
+have not found any direct evidence of them (Barnes et al. 2001;
+de Blok et al. 2002; Pisano et al. 2004; Giovanelli et al. 2007;
+Walter et al. 2008; Heald et al. 2011).
+In this paper, we concentrate on one potential low-column den-
+sity cloud found with the Green Bank Telescope (GBT) near the
+well-studied spiral galaxy NGC 2403 (de Blok et al. 2014). The
+cloud is located ∼ 16 kpc (∼ 2R25) to the NW of the centre of the
+galaxy but the low spatial resolution of the data does not allow
+to properly distinguish it from the disk emission and to robustly
+constrain its properties. The motivation behind this study is to
+confirm its detection with high spatial resolution radio interfero-
+metric data and to understand its nature, especially, if it is indeed
+the signature of IGM accretion that previous studies have tried
+to find. With high-resolution data we can also test other scenar-
+Article number, page 1 of 9
+arXiv:2301.13526v1  [astro-ph.GA]  31 Jan 2023
+
+A&A proofs: manuscript no. main
+ios, for example whether it could be a result of strong outflow,
+or perhaps the remnant of a galactic interaction, and how it is
+linked to the kinematically anomalous H i features first detected
+by Fraternali et al. (2001) (see also Fraternali et al. 2002; Frater-
+nali & Binney 2006; Walter et al. 2008; de Blok et al. 2014).
+NGC 2403 is a member of the M81 group, located at a dis-
+tance of 3.18 Mpc(Madore & Freedman 1991) (1′ = 0.93 kpc,
+1′′ = 0.015 kpc) with a systemic velocity of 133.2 km s−1 (Fra-
+ternali et al. 2002). The main H i disk is inclined by 63° (Fra-
+ternali et al. 2002) and has a mass of 3.24 × 109 M⊙ (Fraternali
+et al. 2002). A list of the main optical and radio parameters can
+be found in Fraternali et al. (2002).
+We obtained new H i radio observations of NGC 2403 and the
+GBT cloud in order to determine the nature of this cloud and ex-
+plore its connection with the previously reported 8-kpc anoma-
+lous velocity filament (Fraternali et al. 2002).
+In Sec. 2.1 we describe the data reduction and the creation of the
+data products that were analysed following the methods illus-
+trated in Sec. 3. The main results and interpretation of our study
+are given in Sec. 4 and are summarised in Sec. 5.
+2. Observations
+The new Very Large Array (VLA) observations discussed in this
+paper were taken between December 5th 2019 and December
+9th 2019 with the Expanded VLA in D-configuration1 (hereafter
+referred to as the ‘2019 data’). The L-band bandwidth of 5.3
+MHz comprised 2700 1.9 kHz (0.4 km s−1) channels with a cen-
+tral frequency of 1.41701 GHz. Two pointings were observed:
+3-hours centred on the galaxy (α = 7h36m44s, δ = 65◦35′35′′)
+and another 3-hours centred on the GBT cloud (α = 7h35m00s,
+δ = 65◦44′4′′).
+In addition to these new data we also used archival VLA H i data
+of NGC 2403 centred on the galaxy. The archival data comprise
+The H i Nearby Galaxy Survey (THINGS) observations2 (Walter
+et al. 2008) and those discussed in Fraternali et al. (2001). Both
+data sets have a velocity resolution of 5.2 km s−1.
+2.1. Data Reduction
+Here we give a brief description of the procedure used to reduce
+the new 2019 dataset. The data reduction was carried out with
+the software CASA v5.8.0 (McMullin et al. 2007). A preliminary
+data flagging was performed on the primary and secondary cali-
+brator data (to correct for shadowing, correlator glitches, misbe-
+having antennas, bandwidth cut-offs, Radio Frequency Interfer-
+ence (RFI), Milky Way emission and absorption) as well as on
+NGC 2403 (to take into account shadowing, correlator glitches,
+misbehaving antennas) with the CASA task flagdata. The RFI
+was manually removed in CASA plotms. A calibration model
+was then built with the following corrections: target elevation,
+delay, bandpass, complex gain and flux scale using the CASA
+tasks gencal, gaincal and fluxscale. A set of weights for the
+data was constructed based on the variance of the data with the
+CASA task statwt and a Hanning-smoothing in frequency was
+applied to remove Gibbs ringing artefacts with the CASA task
+hanningsmooth. Finally, the continuum was estimated with a
+simple linear fit, justified by the narrow bandwidth, to the am-
+plitudes and phases in the line free channels and subtracted from
+the data with the CASA task uvcontsub.
+1 Project ID: 19B-081.
+2 We included the data from the C- and D-array configurations only.
+The THINGS and the 1999 data were re-reduced using similar
+standard procedures.
+2.2. Cube creation
+We used the CASA task tclean to create a combined mosaicked
+H i cube of the two pointings of the 2019 data. We applied a ro-
+bustness parameter of 0.5 and a tapering of 48′′ to the data in
+order to balance spatial resolution and sensitivity. Choosing a
+pixel size of 9′′ to properly sample the beam, and accounting for
+the primary beam size then yielded channel maps with the extent
+of 400 × 400 pixels. As our aim is to combine the new observa-
+tions with the archival data, we chose the channel width to be
+5.3 km s−1, leading to 209 channels covering the range −377.8
+to 724.6 km s−1.
+tclean was run in the auto-multithresh masking mode: for each
+iteration of the cleaning process and for each channel of the cube
+a mask that enclosed the emission above 4 × σ in the channel is
+created. Inside the masked region tclean smooths the data by a
+factor of 1.5 and cleans until it reaches the stopping threshold of
+0.5σ, where the noise is now the one of the smoothed channel.
+This results in a cube based on only the new data.
+In addition, we use tclean to combine all the available obser-
+vations including the archival data into a single H i cube and use
+the same imaging parameters as the mosaicked 2019 cube above.
+As the different uv distributions in the two pointings would lead
+to different resolutions over the mosaic, we applied a 48′′ taper
+which resulted in a common beam size for the entire mosaic. Fur-
+thermore, the noise is different for the two pointings, but at every
+position the mosaic has the highest signal to noise possible given
+the data. We will return to this below. The more limited velocity
+range of the archival data resulted in a cube with 102 channels
+of 5.3 km s−1.
+3. Data analysis
+3.1. Cube statistics
+Throughout this paper, the given noise values are referring to the
+non-primary beam corrected cubes, while all the flux density and
+H i mass measurements have been performed on primary beam
+corrected data.
+The 2019 H i cube has a beam size of 62 × 55 arcsec
+(1.24 × 1.1 kpc) and the single-channel median noise is σ =
+0.53 mJy beam−1. This can be converted into an H i column den-
+sity with the equation
+NHI = 1.25 × 1024 F∆v
+A
+cm−2
+(1)
+where F is the flux density in Jy beam−1, ∆v is the velocity width
+in km s−1, and A is the beam area in arcsec2 calculated assum-
+ing a Gaussian beam: A = 1.13ab, where a and b are the beam
+major and minor axis in arcsec, respectively. The resulting 3σ
+1-channel column density is 2.7 × 1018 cm−2.
+The H i cube which also includes the archival data has a beam
+size of 52×49 arcsec (1.04×0.98 kpc). The noise in this cube is
+not spatially constant due to the combination of different point-
+ings with different integration times. The median σ in the NW
+pointing is 0.31 mJy beam−1, while in the central pointing it is
+0.23 mJy beam−1. However, this difference is not relevant, be-
+cause in the analysis we opt to use the global noise value of
+σ = 0.295 mJy beam−1, giving a 3σ 1-channel H i column den-
+sity of 2×1018 cm−2, as an indicative sensitivity for the combined
+cube.
+Article number, page 2 of 9
+
+Simone Veronese et al.: Extended neutral hydrogen filamentary network in NGC 2403
+7h40m
+38m
+36m
+34m
+65°50'
+40'
+30'
+20'
+RA
+DEC
+Detection limit: 2.0e+18 cm
+2
+10 kpc
+5
+75
+200
+500
+1000
+2000
+HI column density [1018 cm
+2]
+7h40m
+38m
+36m
+34m
+RA
+Systemic velocity: 133.2 km/s
+10 kpc
+105
+70
+35
+0
+35
+70
+105
+Radial velocity [km/s]
+7h40m
+38m
+36m
+34m
+RA
+Median dispersion: 10.4 km/s
+10 kpc
+10.4
+16.6
+22.8
+29.0
+35.2
+Velocity dispersion [km/s]
+Fig. 1. Left panel: primary beam corrected H i column density map of NGC 2403 with reversed grey-scale colormap from faint (grey) to bright
+(black) emission. The sharp cut-off in the bottom left is due to the 20% cut-off threshold of the primary beam response, which is illustrated with
+the light grey curve. Contours levels are from 5 × 1018 cm-2 to 2 × 1021 cm-2. The column density limit 3 × σ × dv = 2 × 1018 cm-2, where dv = 5.3
+km s−1 is the spectral resolution, is reported at the bottom. In the bottom-right is shown the 52′′×49′′ beam. Central panel: intensity-weighted mean
+velocity field of NGC 2403 with respect to the systemic velocity of 133.2 km s−1, given at the bottom. Dashed contours (−105, −70, −35) km s−1
+refer to the approaching side, while solid lines correspond to radial velocities of (35, 70, 105) km s−1. The thick grey line is the kinematical minor
+axis, where the line-of-sight velocity is 0 km s−1. Right panel: second moment map, where the signature of the filaments with their anomalous
+velocities is visible in the increased second-moment values.
+3.2. H i detections
+Since the cube resulting from the combination of the new and
+archival data has a lower noise, we use it to create the detection
+mask by running the H i Source Finding Application (SoFiA2)
+v2.4.0 (Serra et al. 2015; Westmeier et al. 2021). SoFiA2 inter-
+nally takes care of the uneven noise, because it uses the global
+noise as the flux threshold for detecting emission. We blanked
+the channels from −55 km s−1 to 5 km s−1 since they contain
+strong Milky Way contamination, and used SoFiA2 to identify
+the emission in the data cube using the S+C method. We used a
+spatial kernel equal to 0, 1 and 2 times the beam size (i.e., a ker-
+nel of 0 × 0, 3.1 × 3.1 and 6.2 × 6.2 pixels) and a spectral kernel
+equal to 0, 3 and 7 channels, a detection threshold of 3σ and a
+reliability threshold of 0.95.
+We produced also the moment 0, 1 and 2 maps by setting the
+linker in SoFiA2 to be a 1×1×1 box (1×1 pixel and 1 channel)
+and by rejecting all the sources whose size is less than 6 × 6 × 3
+(6 × 6 pixel and 3 channels). The moment maps are given in Fig.
+1. We calculated an H i mass for the galaxy of 3.2 × 109 M⊙,
+which agrees with previous radio interferometric measurements
+(Fraternali et al. 2002; Walter et al. 2008).
+In Fig. 2 we show the channel maps covering the velocity range
+over which H i emission is found. From now on, all the velocities
+are referred to the systemic velocity of 133.2 km s−1. Apart from
+the well-known 8-kpc filament (Fraternali et al. 2002; de Blok
+et al. 2014), we indicate three additional filamentary structures,
+pointed out in Fig. 2 with the arrows:
+– between −59 km s−1 and −27 km s−1 on the east side (red
+arrow in Fig. 2);
+– from −27 km s−1 to 15 km s−1 on the west side of the galaxy
+(blue arrow in Fig. 2) next to the 8-kpc filament;
+– from 15 km s−1 to 47 km s−1 on the west side of the galaxy
+(green arrow in Fig. 2) above the 8-kpc filament.
+The 8-kpc filament found in previous work may be part of a more
+extended H i stream as clearly shown in the 15 km s−1 channel,
+whose total extent is at least 20 kpc. We will denote this as the
+‘20 kpc filament’ or ‘main filament’. The high column density
+parts of the other two structures were detected already in Fra-
+ternali et al. (2001), but the increased column density sensitivity
+of the new data presented here highlights their filamentary shape
+and extent.
+The location of those features in velocity space implies that they
+are not co-rotating with the thin disk. It is thus possible to kine-
+matically isolate them from the thin disk emission for a detailed
+study.
+3.3. Extraction of the H i filaments
+As a first step, we isolate the thin disk following the method pre-
+sented in Fraternali et al. (2002). We fit a single Gaussian to the
+line profile for each position in the sky resulting in a ‘Gaussian
+cube’ that we subtracted from the data cube.
+We then used the velocities of the peak values of these fitted pro-
+files to line up all H i emission profiles for each position on the
+sky at their peak velocities. This method is called ‘shuffle’ and
+was applied to both the cube and the SoFiA2 detection mask pro-
+duced before. It is a powerful tool to easily isolate the anomalous
+velocity gas, for example as a function of the deviation from the
+thin disk rotation as shown in Fig. 3. Here, the gas rotating with
+the disk occupies the central channels of the shuffled cube, while
+H i that is not rotating with the disk will be placed at higher/lower
+channels. Hence, the non-co-rotating gas can be easily identified,
+as we show in Fig. 3.
+We isolated the channels of the shuffled cube where the fila-
+mentary emission is present by blanking the channels between
+± 65 km s−1 (or equivalently ± 14 times the full width at half
+maximum of the disk profiles). This selection is conservative by
+design. Our purpose is to isolate the filaments with the highest
+Article number, page 3 of 9
+
+A&A proofs: manuscript no. main
+Fig. 2. Channel maps of the data cube with both new and archival observations where we show only every second channel. The colour-scale
+contours correspond to 2 × (1, 4, 16, 64) × 1018 cm-2, where 2 × 1018 cm-2 is the 3σ 1-channel column density limit. The thick contour levels
+indicate the significant emission identified by the SoFiA source finder. Most of the low-level structures shown in thin contours are noise or
+mosaicking artefacts. The dashed grey contours denote the column density of −2 × 1018 cm-2. The egg-shape borders are due to the 20% cut-off
+threshold of the primary beam response. At the bottom we report the line-of-sight velocity (w.r.t. the systemic velocity 133.2 km s−1) in each
+channel. The filamentary detections, labelled with coloured arrows, are evident between −59 km s−1 and 47 km s−1.
+velocities that are most likely not associated with the thin disk
+or the thicker and lagging disk as identified in Fraternali et al.
+(2002). A narrower velocity cut than used here would include a
+significant amount of gas from this lagging, thick disk. We cal-
+culated the moment maps of the anomalous-velocity gas using
+the shuffled detection mask. The result is given in Fig. 4, where
+we show the overlay between the galaxy emission and the GBT
+detection (left panel), the filamentary complex (central panel)
+and the selection effect introduced by the shuffle procedure (right
+panel), which we will discuss in the next section.
+Article number, page 4 of 9
+
+10 kpc
+65°45'
+DEC
+30'
+15'
+Vrad: -123.7 km/s
+Vrad: -113.1 km/s
+Vrad: -102.5 km/s
+Vrad: -91.9 km/s
+Vrad: -81.3 km/s
+回
+回
+10 kpc
+65°45'
+DEC
+30'
+15'
+Vrad: -70.7 km/s
+Vrad: -60.1 km/s
+Vrad: -38.9 km/s
+Vrad: -28.3 km/s
+回L
+回
+10 kpc
+65°45'
+.
+DEC
+30'
+15'
+Vrad: -17.7 km/s
+Vrad: -7.1 km/s
+Vrad: 3.5 km/s
+Vrad: 14.1 km/s
+Vrad: 24.7 km/s
+回
+回L
+10 kpc
+65°45'
+DEC
+30'
+15'
+Vrad: 35.3 km/s
+Vrad: 45.9 km/s
+Vrad: 56.5 km/s
+Vrad: 67.1 km/s
+Vrad: 77.7 km/s
+回
+10 kpc
+65°45'
+DEC
+30'
+15'
+Vrad: 109'5 km/s
+Vrad: 120.1'km/s
+Vrad: 88.3 km/s
+Vrad: 98.9 km/s
+Vrad: 130.7 km/s
+回
+36m
+34m
+38m
+36m
+7h40m
+36m
+34m
+38m
+36m
+34m
+7h40m
+38m
+36m
+7h40m
+38m
+7h40m
+34m
+38m
+7h40m
+34m
+RA
+RA
+RA
+RA
+RASimone Veronese et al.: Extended neutral hydrogen filamentary network in NGC 2403
+-20.0
+-10.0
+0.0
+10.0
+20.0
+200
+100
+0
+-100
+-200
+Offset from center [arcmin]
+Velocity [km/s]
+10 kpc
+Major axis
+-10.00
+-5.00
+0.00
+5.00
+10.00
+15.00
+Offset from center [arcmin]
+10 kpc
+Minor axis
+Fig. 3. Position-velocity diagram along the major axis (left panel) and minor axis (right panel) through a beam-wide slice of the shuffled data cube
+without the thin disk removal. The emission is mapped with a reversed grey-scale and we overlaid the 2 × (1, 3, 9) ×1018 cm-2 levels with grey-
+scale contours. The blanked area in the top-left and blanked stripe in the bottom are the result of the Milky Way filtering. The grey dashed lines
+denote the column density of −3σ. The channels between ± 65 km s−1 with the residual thin disk and diffuse extraplanar emission are highlighted
+with the hatched area. They were not used for the computation of the moment map shown in the central panel of Fig. 4.
+4. Discussion
+The H i filaments have a total mass of at least 2.0 × 107 M⊙,
+about 0.6% of the total H i mass of the galaxy. This is a lower
+limit, firstly because of the chosen channel cut at ± 65 km s−1,
+and secondly because close to the kinematical minor axis of
+the galaxy, any anomalous velocity gas co-rotating or counter-
+rotating with the disk will not be distinguishable. In other words,
+as we look close to the kinematical minor axis, the line profile of
+the thin disk and of the extraplanar gas overlap more and more,
+and we are not able to distinguish between thin disk and co-
+rotating or counter-rotating anomalous velocity gas.
+We used the following simple model to estimate the importance
+of this effect: we built a mock galaxy with a thin (dispersion of
+10 km s−1) thin disk and a thick (dispersion of 35 km s−1) disk
+which rotates 30 km s−1 slower and has a column density equal
+to 10% of the thin disk. These parameters are modelled on the
+properties of NGC 2403 as described in Fraternali et al. (2002).
+We repeated the same steps applied to the observed data (Gaus-
+sian fit, thin disk removal, shuffle and blanking of all the chan-
+nels between ± 65 km s−1) in order to check how our ability to
+extract the anomalous H i varies as a function of the position an-
+gle along the disk. We do indeed find that the ability to separate
+the anomalous velocity gas from the thin disk changes with po-
+sition angle. In the right panel of Fig. 4 we illustrate the effect.
+The projected extent of the filaments varies from ∼ 10 kpc up
+to ∼ 20 kpc, and they are almost aligned with the galactic major
+axis. This is not purely a result of selection effects, as the distri-
+bution of the observed anomalous H i in the right panel of Fig. 4
+clearly shows.
+The GBT cloud found by de Blok et al. (2014) is at the location
+of the tip of the 20 kpc filament and can possibly be identified
+with it, resembling a cloud in the GBT data only due to the very
+low spatial resolution of these data and the limited velocity range
+over which this feature could be identified.
+The larger extension of the main filament as visible in the new
+data due to the increased sensitivity is shown in Fig. 5, where we
+show the position-velocity diagram along the main filament and
+the cloud compared to the same position velocity slice presented
+in Fig. 6 in de Blok et al. (2014).
+In the following we discuss further the possible origins of this
+filamentary complex.
+4.1. Is the GBT cloud confirmed?
+The motivation of this study was to confirm the GBT detection
+of an H i cloud near NGC 2403 (de Blok et al. 2014) and to un-
+derstand its origin. The left panel of Fig. 4 shows that the GBT
+cloud overlaps with the northern part of the 20 kpc filament. In-
+deed, the column density of the gas in the northern region of the
+filament is > 1018 cm-2 at the spatial resolution of ∼ 50 arcsec
+and de Blok et al. (2014) estimates an average column density
+of 2.4 × 1018 cm-2 for the cloud. Therefore, the tip of the 20 kpc
+filament could have been seen by the GBT.
+The H i mass of the cloud as measured with the GBT is 6.3 × 106
+M⊙, while the H i content within the GBT contours in our data
+is 1.2 × 106 M⊙. Given the inherent difficulties of separating the
+cloud and disk emission in the GBT data and the conservative
+blanking criteria used to extract the filamentary emission in our
+shuffle cube, this must be regarded as reasonable agreement and
+thus further supports the identification of the GBT cloud with the
+northern tip of the filament detected by the VLA.
+Article number, page 5 of 9
+
+A&A proofs: manuscript no. main
+7h40m
+38m
+36m
+34m
+66°00'
+65°45'
+30'
+15'
+RA
+DEC
+Detection limit: 2.0e+18 cm
+2
+10 kpc
+Galaxy (-22 km s
+1 to 20 km s
+1)
+GBT cloud
+5
+25
+80
+200
+500
+1000
+HI column density [1018 cm
+2]
+7h40m
+38m
+36m
+34m
+RA
+Detection limit: 2.0e+18 cm
+2
+10 kpc
+Filamentary complex
+3
+10
+25
+50
+100
+HI column density [1018 cm
+2]
+7h40m
+38m
+36m
+34m
+RA
+10 kpc
+Mock extraplanar gas
+10
+15
+20
+25
+% of original flux
+Fig. 4. Left panel: primary beam corrected H i column density map of NGC 2403 (in reversed grey-scale colormap) overlaid with the GBT cloud
+candidate (green) from de Blok et al. (2014). The map was produced by integrating over the channels from −22 km s−1 to 20 km s−1 w.r.t. the
+systemic velocity. This range corresponds to the one used by de Blok et al. (2014) to compute the candidate GBT cloud moment 0 map. Grey-
+scale contour levels are from 5 × 1018 cm-2 to 1 × 1021 cm-2. The 3σ 1-channel column density limit is reported at the bottom. The beam of the
+interferometric data for both the GBT and our VLA observations is shown in the bottom right. The green contours, instead, define the (6.25, 12.5,
+25, 62.5) × 1017 cm-2 column density in the GBT data. The light-grey line denotes the 20% cut-off threshold of the primary beam response. Central
+panel: primary beam corrected H i column density map of the anomalous-velocity gas. Grey-scale contour levels are (3, 10, 25, 50, 100) × 1018
+cm-2 column density. The spatial scale is the same as in the left panel, as well as the definition of the light grey line. We indicate the galaxy edge
+with the dashed-black contour. The light blue dashed line represents the path along which the position-velocity slice has been extracted (see Fig.
+5). Right panel: Illustrative example of the selection effect introduced by the shuffle procedure (see discussion in section 4). The map shows the
+fraction of the original extraplanar flux density of a mock galaxy we were able to recover and the red contour encloses the region where we are
+severely affected by selection effect, i.e., where more than 90% of the original flux density is lost. The blanked bits in the centre denote the region
+where the result is unreliable because of the steep gradient in velocity. The dashed white contours are, instead, the region occupied by the observed
+filamentary complex.
+4.2. The nature of the 20 kpc filament
+One of the questions we try to answer is whether the GBT cloud,
+and by implication the filaments described in this paper, are
+formed due to a gas accretion event. There are however other
+possible explanations for these features, some of which we have
+already briefly alluded to. For example, the structures we observe
+could be the result of a galactic fountain process that ejects gas
+from the disk. This is certainly a likely scenario for the anoma-
+lous velocity gas closer to the disk (i.e. below our ± 65 km s−1
+cut-off), but it is less obvious for the filaments.
+It is difficult to form a straight 20 kpc long filament in an out-
+flow scenario. Indeed, in a pure galactic fountain model the gas
+ejecta reaches distances of at most 10 kpc even with extremely
+high kick velocities (Fraternali & Binney 2006, 2008).
+Is the origin of the filamentary complex a galactic interaction?
+In the event of a merging or disrupting dwarf, one might expect
+to see a disturbed stellar population from the dwarf, most likely
+coinciding with or near the filaments. Barker et al. (2012) per-
+formed an in-depth study of the stellar properties in NGC 2403
+but did not identify any peculiarities in the distribution of the
+stars and concluded that the galaxy has evolved in isolation with
+no significant recent merging event.
+However, their Fig. 10 shows some evidence for a slightly dis-
+turbed stellar component in the NW part of the disk. They also
+reported an extended low-metallicity Red Giant Branch (RGB)
+component at radii between 18 and 40 kpc. Their interpretation
+includes the presence of a stellar halo, or a thick stellar disk in
+NGC 2403, but it is not clear whether this component is associ-
+ated with an accretion or interaction event.
+In de Blok et al. (2014) it was shown that a line passing through
+the major axis of the 8-kpc filament and the GBT cloud intersects
+with nearby dwarf galaxies DDO 44 and NGC 2366, hinting at
+a possible interaction scenario with either of these galaxies. Re-
+cent deep optical wide-field data presented in Carlin et al. (2019)
+supports this idea. They observed a ∼ 50 kpc long stellar stream
+originating from the dwarf galaxy DDO 44 and connecting with
+the NW part of the stellar disk of NGC 2403. This dwarf is likely
+a satellite of NGC 2403 located about 70 kpc from it. A higher
+quality re-reduction of the data from Carlin et al. (2019) is given
+in Fig. 6 (J. Carlin, priv. comm) and this shows the stellar stream
+and the connection between DDO 44 and NGC 2403 even more
+clearly.
+This image is a 1.5◦ wide field composite mosaic of seven point-
+ings taken with the Hyper Suprime-Cam of the 8.2 m Subaru
+Telescope and converted into a density map of candidate RGB
+stars. Overlaid on that map, we show the filamentary H i. There
+is a remarkable coincidence between the position of the tip of the
+20 kpc filament and the region where the DDO 44 stellar stream
+connects with NGC 2403 stellar disk. This is therefore a strong
+indication that the dwarf interaction scenario can be responsible
+for the H i filaments in NGC 2403.
+This is also suggested by the star formation histories of the
+galaxies: NGC 2403 had an increase in its star formation rate
+about 2 Gyr ago (Williams et al. 2013), in particular, at radii >
+20 kpc; while DDO 44 had a burst of star formation from 1 to
+Article number, page 6 of 9
+
+Simone Veronese et al.: Extended neutral hydrogen filamentary network in NGC 2403
+-20.0
+-10.0
+0.0
+10.0
+20.0
+0
+50
+100
+150
+200
+250
+Offset from center [arcmin]
+Velocity [km/s]
+10 kpc
+This work
+-20.0
+-10.0
+0.0
+10.0
+20.0
+Offset from center [arcmin]
+de Blok et al. (2014)
+Fig. 5. Comparison between the position-velocity diagram through the centres of the cloud candidate and the 20 kpc filament along a 100”-thick
+slice as taken through our data (left panel) and as shown in Fig. 6 in de Blok et al. (2014) (right panel). The emission is mapped with a reversed
+grey-scale and we overlaid the 2.5 × (1, 9, 81) × 1018 cm-2 column density levels with colour-scale contours (black, red and white, respectively).
+The blue contour denotes a level of 1.2 × 1018 cm-2 and highlights the detection of the 20 kpc filament tip with the combination of the new and
+archival VLA data. The red circles highlight the tip of the 20 kpc filament which was not detected in the Fraternali et al. (2002) and de Blok et al.
+(2014) analysis.
+3 Gyr ago (Girardi et al. 2010; Weisz et al. 2011). Also, Carlin
+et al. (2019) calculated from the estimated trajectory of DDO 44
+that the interaction with NGC 2403 occurred ∼ 1 Gyr ago. These
+various estimates thus give very similar timescales for the inter-
+action.
+The most likely explanation is therefore that the H i filaments in
+NGC 2403 are the result of the interaction with DDO 44. This
+does, of course, not preclude a galactic fountain scenario as a
+potential origin for a part of the extraplanar gas in NGC 2403
+especially so for the gas at less extreme velocities than the fil-
+aments. It is interesting to note that for two of the most well-
+known nearby galaxies where extraplanar filaments are promi-
+nent, NGC 2403 and NGC 891, an interaction scenario is now
+the most likely cause (see Oosterloo et al. 2007 for the NGC 891
+analysis).
+5. Conclusion
+Using new and archival VLA observations, we have presented a
+study of NGC 2403, focusing on the nature of the GBT cloud (de
+Blok et al. 2014). These data show a filamentary complex around
+the galaxy with an H i mass of 2.0 × 107 M⊙. It comprises at least
+three filaments with extents of 10-20 kpc. The GBT cloud can
+now be shown to be the tip of the longest structure.
+Even though at first sight the stellar distribution in NGC 2403
+seems undisturbed, it is now likely that these filaments are the
+result of an interaction with a nearby dwarf galaxy. Hints of a
+disturbance in the stellar component were already visible in the
+data presented in Barker et al. (2012), but they were dramati-
+cally confirmed in the recent study by Carlin et al. (2019), who
+discovered a ∼ 50 kpc long stellar stream connecting DDO 44
+and NGC 2403. The intersection of that stream with NGC 2403
+coincides with the positions of the tip of the H i filaments. The
+star formation history of the two galaxies and the estimated tra-
+jectory of DDO 44 seems to suggest that the interaction occurred
+about 1 Gyr ago.
+These observations highlight the importance of minor interac-
+tions in shaping the H i disks of galaxies. Moreover, they point
+out the difficulties of unambiguously identifying the effects of
+direct cold gas accretion from the IGM, and distinguishing them
+from those of minor interactions with a satellite. In this regard,
+the multiwavelength approach is fundamental: optical observa-
+tions are crucial to move the needle toward accretion or inter-
+action as the most plausible explanation of anomalous H i struc-
+tures like the filaments.
+Future observations with the SKA and its precursors at higher
+resolution and higher sensitivity will undoubtedly uncover many
+more of these features in nearby galaxies and help us to better
+understand how the balance between accretion and interaction
+impacts the evolution of galaxies.
+Acknowledgements. We would like to thank A. Fergusson for providing us with
+the stellar catalogue from Barker et al. 2012. We thank F. Fraternali for the useful
+discussions about the interpretation of our results and F. Maccagni for the initial
+discussions on the DDO 44 optical data. A. Marasco’s help in the modelling of
+our data is gratefully acknowledged. Also, we thank J. Carlin for kindly sharing
+with us the new re-reduced optical data of DDO 44. We thank the anonymous
+referee for the constructive comments and the suggested improvements for the
+quality and clarity of this paper.
+This work has received funding from the European Research Council (ERC)
+under the European Union’s Horizon 2020 research and innovation programme
+(grant agreement No 882793 ‘MeerGas’).
+Article number, page 7 of 9
+
+A&A proofs: manuscript no. main
+7h50m
+40m
+30m
+20m
+67°
+66°
+65°
+64°
+RA
+DEC
+7h33m
+34m
+35m
+36m
+37m
+38m
+39m
+65°30'
+40'
+50'
+RA
+DEC
+Fig. 6. Overlay between the re-reduced density map of candidate RGB stars presented in Carlin et al. (2019) and the H i filaments observed in our
+data (white contours). Bins in the density map are completeness-corrected and have a resolution of 0.75 arcmin. The hole in the centre is due to
+extreme crowding. The colours denote the number of stars per 0.75’ bin. The stellar stream is connecting DDO 44 and NGC 2403 with the tip of
+the H i filaments, strongly suggesting that DDO 44 and NGC 2403 underwent a recent interaction.
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+
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' de Blok1, 2, 3, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Walter4, 5  1 Netherlands Institute for Radio Astronomy (ASTRON), Postbus 2, 7990 AA Dwingeloo, The Netherlands, e-mail:  veronese@astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='nl  2 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands  3 Department of Astronomy, University of Cape Town, Private Bag X3, 7701 Rondebosch, South Africa  4 Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany  5 National Radio Astronomy Observatory, Pete V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Domenici Array Science Center, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Box O, Socorro, NM 87801, USA  Received <date> / Accepted <date>  ABSTRACT  We present new neutral hydrogen (H i) observations of the nearby galaxy NGC 2403 to determine the nature of a low-column density  cloud that was detected earlier by the Green Bank Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We find that this cloud is the tip of a complex of filaments of extraplanar gas that is coincident with the thin disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The total H i mass of  the complex is 2×107 M⊙ or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='6% of the total H i mass of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The main structure, previously referred to as the 8-kpc filament,  is now seen to be even more extended, along a 20 kpc stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The kinematics and morphological properties of the filaments are unlikely to be the result of outflows related to galactic fountains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' It  is more likely that the 20 kpc filament is related to a recent galaxy interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In this context, a ∼ 50 kpc long stellar stream has been  recently detected connecting NGC 2403 with the nearby dwarf satellite DDO 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Intriguingly, the southern tip of this stream overlaps  with that of 20 kpc H i filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We conclude that the H i anomalies in NGC 2403 are the result of a recent (∼ 2 Gyr) interaction with DDO 44 leading to the observed  filamentary complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Galaxies: evolution - Galaxies: interactions - Radio lines: galaxies - Techniques: interferometric  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Introduction  Galaxies form stars through the collapsing of giant molecular  (mainly molecular hydrogen, H ii) clouds on timescales of ∼ 107  yr (Meidt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Schinnerer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2020)  and over the cosmic time (Madau & Dickinson 2014) galaxies  progressively deplete their molecular gas content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In a perfect  steady state, the H ii reservoir is replenished by the cooling of  the atomic hydrogen (H i) in the interstellar medium (Clark et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Walch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2015), which will cause a reduction in the  content of the atomic gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' However, both simulations and obser-  vations reveal that the H i content in galaxies is almost constant  from z ∼ 1 (Davé et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Consequently, in  order to maintain star formation over cosmic time, galaxies must  accrete H i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Previous studies of H i interaction features and dwarf galaxies  have shown that they do not provide enough cold gas to replen-  ish the material reservoir for star formation (Sancisi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Putman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Other extraplanar gas  observed closer to the galaxy disks is usually related to galac-  tic fountains (Putman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Marasco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2022): star formation and supernova explosions eject interstellar  medium from the disk to scale-heights of ∼ kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The gas catches  material from the circum-galactic medium and falls back onto  the galaxy carrying new gas to fuel the star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' How-  ever, the amount of material accreted with this process is again  not enough to replenish the atomic gas reservoir (Putman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Afruni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  A hypothesis that could explain the constancy of the H i con-  tent is that galaxies accrete gas from the Inter-Galactic Medium  (IGM) (Somerville & Davé 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Danovich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The  mode of this accretion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', cold clouds and streams or hot dif-  fuse gas (Dekel & Birnboim 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Danovich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2015), is un-  certain as well as the accretion rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Nevertheless, this model  could indicate a possible way to solve the problem of how to  sustain the star formation activities over cosmic time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  It has, however, one major limitation: the directly detectable  component of this gas, namely the warm H i at ∼ 104 K, forms  only a small fraction (< 1%) of the total amount of accreting ma-  terial which mostly consists of warm-hot 105 K gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This leads to  low H i column densities of ∼ 1017 cm−2 (Popping et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  This value is at least one order of magnitude lower than the de-  tection limits of the current radio interferometer observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Single-dish telescopes can reach these column densities but only  at low resolutions that usually do not resolve the relevant scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  So far, surveys that could potentially detect accreting H i clouds  have not found any direct evidence of them (Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Pisano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Giovanelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Heald et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In this paper, we concentrate on one potential low-column den-  sity cloud found with the Green Bank Telescope (GBT) near the  well-studied spiral galaxy NGC 2403 (de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The  cloud is located ∼ 16 kpc (∼ 2R25) to the NW of the centre of the  galaxy but the low spatial resolution of the data does not allow  to properly distinguish it from the disk emission and to robustly  constrain its properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The motivation behind this study is to  confirm its detection with high spatial resolution radio interfero-  metric data and to understand its nature, especially, if it is indeed  the signature of IGM accretion that previous studies have tried  to find.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' With high-resolution data we can also test other scenar-  Article number, page 1 of 9  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='13526v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='GA]  31 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' main  ios, for example whether it could be a result of strong outflow,  or perhaps the remnant of a galactic interaction, and how it is  linked to the kinematically anomalous H i features first detected  by Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2001) (see also Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Frater-  nali & Binney 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  NGC 2403 is a member of the M81 group, located at a dis-  tance of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='18 Mpc(Madore & Freedman 1991) (1′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='93 kpc,  1′′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='015 kpc) with a systemic velocity of 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 km s−1 (Fra-  ternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The main H i disk is inclined by 63° (Fra-  ternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002) and has a mass of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='24 × 109 M⊙ (Fraternali  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A list of the main optical and radio parameters can  be found in Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We obtained new H i radio observations of NGC 2403 and the  GBT cloud in order to determine the nature of this cloud and ex-  plore its connection with the previously reported 8-kpc anoma-  lous velocity filament (Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 we describe the data reduction and the creation of the  data products that were analysed following the methods illus-  trated in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The main results and interpretation of our study  are given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4 and are summarised in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Observations  The new Very Large Array (VLA) observations discussed in this  paper were taken between December 5th 2019 and December  9th 2019 with the Expanded VLA in D-configuration1 (hereafter  referred to as the ‘2019 data’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The L-band bandwidth of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3  MHz comprised 2700 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='9 kHz (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='4 km s−1) channels with a cen-  tral frequency of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='41701 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Two pointings were observed:  3-hours centred on the galaxy (α = 7h36m44s, δ = 65◦35′35′′)  and another 3-hours centred on the GBT cloud (α = 7h35m00s,  δ = 65◦44′4′′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In addition to these new data we also used archival VLA H i data  of NGC 2403 centred on the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The archival data comprise  The H i Nearby Galaxy Survey (THINGS) observations2 (Walter  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2008) and those discussed in Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Both  data sets have a velocity resolution of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Data Reduction  Here we give a brief description of the procedure used to reduce  the new 2019 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The data reduction was carried out with  the software CASA v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0 (McMullin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A preliminary  data flagging was performed on the primary and secondary cali-  brator data (to correct for shadowing, correlator glitches, misbe-  having antennas, bandwidth cut-offs, Radio Frequency Interfer-  ence (RFI), Milky Way emission and absorption) as well as on  NGC 2403 (to take into account shadowing, correlator glitches,  misbehaving antennas) with the CASA task flagdata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The RFI  was manually removed in CASA plotms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A calibration model  was then built with the following corrections: target elevation,  delay, bandpass, complex gain and flux scale using the CASA  tasks gencal, gaincal and fluxscale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A set of weights for the  data was constructed based on the variance of the data with the  CASA task statwt and a Hanning-smoothing in frequency was  applied to remove Gibbs ringing artefacts with the CASA task  hanningsmooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Finally, the continuum was estimated with a  simple linear fit, justified by the narrow bandwidth, to the am-  plitudes and phases in the line free channels and subtracted from  the data with the CASA task uvcontsub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  1 Project ID: 19B-081.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2 We included the data from the C- and D-array configurations only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The THINGS and the 1999 data were re-reduced using similar  standard procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Cube creation  We used the CASA task tclean to create a combined mosaicked  H i cube of the two pointings of the 2019 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We applied a ro-  bustness parameter of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5 and a tapering of 48′′ to the data in  order to balance spatial resolution and sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Choosing a  pixel size of 9′′ to properly sample the beam, and accounting for  the primary beam size then yielded channel maps with the extent  of 400 × 400 pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' As our aim is to combine the new observa-  tions with the archival data, we chose the channel width to be  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3 km s−1, leading to 209 channels covering the range −377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='8  to 724.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='6 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  tclean was run in the auto-multithresh masking mode: for each  iteration of the cleaning process and for each channel of the cube  a mask that enclosed the emission above 4 × σ in the channel is  created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Inside the masked region tclean smooths the data by a  factor of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5 and cleans until it reaches the stopping threshold of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5σ, where the noise is now the one of the smoothed channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  This results in a cube based on only the new data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In addition, we use tclean to combine all the available obser-  vations including the archival data into a single H i cube and use  the same imaging parameters as the mosaicked 2019 cube above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  As the different uv distributions in the two pointings would lead  to different resolutions over the mosaic, we applied a 48′′ taper  which resulted in a common beam size for the entire mosaic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Fur-  thermore, the noise is different for the two pointings, but at every  position the mosaic has the highest signal to noise possible given  the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We will return to this below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The more limited velocity  range of the archival data resulted in a cube with 102 channels  of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Data analysis  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Cube statistics  Throughout this paper, the given noise values are referring to the  non-primary beam corrected cubes, while all the flux density and  H i mass measurements have been performed on primary beam  corrected data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The 2019 H i cube has a beam size of 62 × 55 arcsec  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='24 × 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 kpc) and the single-channel median noise is σ =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='53 mJy beam−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This can be converted into an H i column den-  sity with the equation  NHI = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='25 × 1024 F∆v  A  cm−2  (1)  where F is the flux density in Jy beam−1, ∆v is the velocity width  in km s−1, and A is the beam area in arcsec2 calculated assum-  ing a Gaussian beam: A = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='13ab, where a and b are the beam  major and minor axis in arcsec, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The resulting 3σ  1-channel column density is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='7 × 1018 cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The H i cube which also includes the archival data has a beam  size of 52×49 arcsec (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='04×0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='98 kpc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The noise in this cube is  not spatially constant due to the combination of different point-  ings with different integration times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The median σ in the NW  pointing is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='31 mJy beam−1, while in the central pointing it is  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='23 mJy beam−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' However, this difference is not relevant, be-  cause in the analysis we opt to use the global noise value of  σ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='295 mJy beam−1, giving a 3σ 1-channel H i column den-  sity of 2×1018 cm−2, as an indicative sensitivity for the combined  cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Article number, page 2 of 9  Simone Veronese et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=" : Extended neutral hydrogen filamentary network in NGC 2403  7h40m  38m  36m  34m  65°50'  40'  30'  20'  RA  DEC  Detection limit: 2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0e+18 cm  2  10 kpc  5  75  200  500  1000  2000  HI column density [1018 cm  2]  7h40m  38m  36m  34m  RA  Systemic velocity: 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 km/s  10 kpc  105  70  35  0  35  70  105  Radial velocity [km/s]  7h40m  38m  36m  34m  RA  Median dispersion: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='4 km/s  10 kpc  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='6  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='8  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2  Velocity dispersion [km/s]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Left panel: primary beam corrected H i column density map of NGC 2403 with reversed grey-scale colormap from faint (grey) to bright  (black) emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The sharp cut-off in the bottom left is due to the 20% cut-off threshold of the primary beam response, which is illustrated with  the light grey curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Contours levels are from 5 × 1018 cm-2 to 2 × 1021 cm-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The column density limit 3 × σ × dv = 2 × 1018 cm-2, where dv = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3  km s−1 is the spectral resolution, is reported at the bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In the bottom-right is shown the 52′′×49′′ beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Central panel: intensity-weighted mean  velocity field of NGC 2403 with respect to the systemic velocity of 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 km s−1, given at the bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Dashed contours (−105, −70, −35) km s−1  refer to the approaching side, while solid lines correspond to radial velocities of (35, 70, 105) km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The thick grey line is the kinematical minor  axis, where the line-of-sight velocity is 0 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Right panel: second moment map, where the signature of the filaments with their anomalous  velocities is visible in the increased second-moment values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' H i detections  Since the cube resulting from the combination of the new and  archival data has a lower noise, we use it to create the detection  mask by running the H i Source Finding Application (SoFiA2)  v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0 (Serra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Westmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' SoFiA2 inter-  nally takes care of the uneven noise, because it uses the global  noise as the flux threshold for detecting emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We blanked  the channels from −55 km s−1 to 5 km s−1 since they contain  strong Milky Way contamination, and used SoFiA2 to identify  the emission in the data cube using the S+C method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We used a  spatial kernel equal to 0, 1 and 2 times the beam size (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', a ker-  nel of 0 × 0, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 × 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 × 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 pixels) and a spectral kernel  equal to 0, 3 and 7 channels, a detection threshold of 3σ and a  reliability threshold of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We produced also the moment 0, 1 and 2 maps by setting the  linker in SoFiA2 to be a 1×1×1 box (1×1 pixel and 1 channel)  and by rejecting all the sources whose size is less than 6 × 6 × 3  (6 × 6 pixel and 3 channels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The moment maps are given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We calculated an H i mass for the galaxy of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 × 109 M⊙,  which agrees with previous radio interferometric measurements  (Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Walter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2 we show the channel maps covering the velocity range  over which H i emission is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' From now on, all the velocities  are referred to the systemic velocity of 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Apart from  the well-known 8-kpc filament (Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' de Blok  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2014), we indicate three additional filamentary structures,  pointed out in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2 with the arrows:  – between −59 km s−1 and −27 km s−1 on the east side (red  arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  – from −27 km s−1 to 15 km s−1 on the west side of the galaxy  (blue arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2) next to the 8-kpc filament;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  – from 15 km s−1 to 47 km s−1 on the west side of the galaxy  (green arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2) above the 8-kpc filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The 8-kpc filament found in previous work may be part of a more  extended H i stream as clearly shown in the 15 km s−1 channel,  whose total extent is at least 20 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We will denote this as the  ‘20 kpc filament’ or ‘main filament’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The high column density  parts of the other two structures were detected already in Fra-  ternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2001), but the increased column density sensitivity  of the new data presented here highlights their filamentary shape  and extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The location of those features in velocity space implies that they  are not co-rotating with the thin disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' It is thus possible to kine-  matically isolate them from the thin disk emission for a detailed  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Extraction of the H i filaments  As a first step, we isolate the thin disk following the method pre-  sented in Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We fit a single Gaussian to the  line profile for each position in the sky resulting in a ‘Gaussian  cube’ that we subtracted from the data cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We then used the velocities of the peak values of these fitted pro-  files to line up all H i emission profiles for each position on the  sky at their peak velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This method is called ‘shuffle’ and  was applied to both the cube and the SoFiA2 detection mask pro-  duced before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' It is a powerful tool to easily isolate the anomalous  velocity gas, for example as a function of the deviation from the  thin disk rotation as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Here, the gas rotating with  the disk occupies the central channels of the shuffled cube, while  H i that is not rotating with the disk will be placed at higher/lower  channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Hence, the non-co-rotating gas can be easily identified,  as we show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We isolated the channels of the shuffled cube where the fila-  mentary emission is present by blanking the channels between  ± 65 km s−1 (or equivalently ± 14 times the full width at half  maximum of the disk profiles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This selection is conservative by  design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Our purpose is to isolate the filaments with the highest  Article number, page 3 of 9  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' main  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Channel maps of the data cube with both new and archival observations where we show only every second channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The colour-scale  contours correspond to 2 × (1, 4, 16, 64) × 1018 cm-2, where 2 × 1018 cm-2 is the 3σ 1-channel column density limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The thick contour levels  indicate the significant emission identified by the SoFiA source finder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Most of the low-level structures shown in thin contours are noise or  mosaicking artefacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The dashed grey contours denote the column density of −2 × 1018 cm-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The egg-shape borders are due to the 20% cut-off  threshold of the primary beam response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' At the bottom we report the line-of-sight velocity (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' the systemic velocity 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 km s−1) in each  channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The filamentary detections, labelled with coloured arrows, are evident between −59 km s−1 and 47 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  velocities that are most likely not associated with the thin disk  or the thicker and lagging disk as identified in Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A narrower velocity cut than used here would include a  significant amount of gas from this lagging, thick disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We cal-  culated the moment maps of the anomalous-velocity gas using  the shuffled detection mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The result is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4, where  we show the overlay between the galaxy emission and the GBT  detection (left panel), the filamentary complex (central panel)  and the selection effect introduced by the shuffle procedure (right  panel), which we will discuss in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="  Article number, page 4 of 9  10 kpc  65°45'  DEC  30'  15'  Vrad: -123." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='7 km/s  Vrad: -113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 km/s  Vrad: -102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5 km/s  Vrad: -91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='9 km/s  Vrad: -81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="3 km/s  回  回  10 kpc  65°45'  DEC  30'  15'  Vrad: -70." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='7 km/s  Vrad: -60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 km/s  Vrad: -38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='9 km/s  Vrad: -28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="3 km/s  回L  回  10 kpc  65°45'  ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="  DEC  30'  15'  Vrad: -17." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='7 km/s  Vrad: -7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 km/s  Vrad: 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5 km/s  Vrad: 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 km/s  Vrad: 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="7 km/s  回  回L  10 kpc  65°45'  DEC  30'  15'  Vrad: 35." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3 km/s  Vrad: 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='9 km/s  Vrad: 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5 km/s  Vrad: 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1 km/s  Vrad: 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="7 km/s  回  10 kpc  65°45'  DEC  30'  15'  Vrad: 109'5 km/s  Vrad: 120." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content="1'km/s  Vrad: 88." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3 km/s  Vrad: 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='9 km/s  Vrad: 130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='7 km/s  回  36m  34m  38m  36m  7h40m  36m  34m  38m  36m  34m  7h40m  38m  36m  7h40m  38m  7h40m  34m  38m  7h40m  34m  RA  RA  RA  RA  RASimone Veronese et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' : Extended neutral hydrogen filamentary network in NGC 2403  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  200  100  0  100  200  Offset from center [arcmin]  Velocity [km/s]  10 kpc  Major axis  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='00  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='00  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='00  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='00  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='00  Offset from center [arcmin]  10 kpc  Minor axis  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Position-velocity diagram along the major axis (left panel) and minor axis (right panel) through a beam-wide slice of the shuffled data cube  without the thin disk removal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The emission is mapped with a reversed grey-scale and we overlaid the 2 × (1, 3, 9) ×1018 cm-2 levels with grey-  scale contours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The blanked area in the top-left and blanked stripe in the bottom are the result of the Milky Way filtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The grey dashed lines  denote the column density of −3σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The channels between ± 65 km s−1 with the residual thin disk and diffuse extraplanar emission are highlighted  with the hatched area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' They were not used for the computation of the moment map shown in the central panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Discussion  The H i filaments have a total mass of at least 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0 × 107 M⊙,  about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='6% of the total H i mass of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This is a lower  limit, firstly because of the chosen channel cut at ± 65 km s−1,  and secondly because close to the kinematical minor axis of  the galaxy, any anomalous velocity gas co-rotating or counter-  rotating with the disk will not be distinguishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In other words,  as we look close to the kinematical minor axis, the line profile of  the thin disk and of the extraplanar gas overlap more and more,  and we are not able to distinguish between thin disk and co-  rotating or counter-rotating anomalous velocity gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We used the following simple model to estimate the importance  of this effect: we built a mock galaxy with a thin (dispersion of  10 km s−1) thin disk and a thick (dispersion of 35 km s−1) disk  which rotates 30 km s−1 slower and has a column density equal  to 10% of the thin disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' These parameters are modelled on the  properties of NGC 2403 as described in Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  We repeated the same steps applied to the observed data (Gaus-  sian fit, thin disk removal, shuffle and blanking of all the chan-  nels between ± 65 km s−1) in order to check how our ability to  extract the anomalous H i varies as a function of the position an-  gle along the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We do indeed find that the ability to separate  the anomalous velocity gas from the thin disk changes with po-  sition angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4 we illustrate the effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The projected extent of the filaments varies from ∼ 10 kpc up  to ∼ 20 kpc, and they are almost aligned with the galactic major  axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This is not purely a result of selection effects, as the distri-  bution of the observed anomalous H i in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4  clearly shows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The GBT cloud found by de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014) is at the location  of the tip of the 20 kpc filament and can possibly be identified  with it, resembling a cloud in the GBT data only due to the very  low spatial resolution of these data and the limited velocity range  over which this feature could be identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The larger extension of the main filament as visible in the new  data due to the increased sensitivity is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 5, where we  show the position-velocity diagram along the main filament and  the cloud compared to the same position velocity slice presented  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 6 in de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In the following we discuss further the possible origins of this  filamentary complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Is the GBT cloud confirmed?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The motivation of this study was to confirm the GBT detection  of an H i cloud near NGC 2403 (de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2014) and to un-  derstand its origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4 shows that the GBT  cloud overlaps with the northern part of the 20 kpc filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In-  deed, the column density of the gas in the northern region of the  filament is > 1018 cm-2 at the spatial resolution of ∼ 50 arcsec  and de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014) estimates an average column density  of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='4 × 1018 cm-2 for the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Therefore, the tip of the 20 kpc  filament could have been seen by the GBT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The H i mass of the cloud as measured with the GBT is 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='3 × 106  M⊙, while the H i content within the GBT contours in our data  is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 × 106 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Given the inherent difficulties of separating the  cloud and disk emission in the GBT data and the conservative  blanking criteria used to extract the filamentary emission in our  shuffle cube, this must be regarded as reasonable agreement and  thus further supports the identification of the GBT cloud with the  northern tip of the filament detected by the VLA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Article number, page 5 of 9  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=" main  7h40m  38m  36m  34m  66°00'  65°45'  30'  15'  RA  DEC  Detection limit: 2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0e+18 cm  2  10 kpc  Galaxy (-22 km s  1 to 20 km s  1)  GBT cloud  5  25  80  200  500  1000  HI column density [1018 cm  2]  7h40m  38m  36m  34m  RA  Detection limit: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0e+18 cm  2  10 kpc  Filamentary complex  3  10  25  50  100  HI column density [1018 cm  2]  7h40m  38m  36m  34m  RA  10 kpc  Mock extraplanar gas  10  15  20  25  % of original flux  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Left panel: primary beam corrected H i column density map of NGC 2403 (in reversed grey-scale colormap) overlaid with the GBT cloud  candidate (green) from de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The map was produced by integrating over the channels from −22 km s−1 to 20 km s−1 w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' the  systemic velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This range corresponds to the one used by de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014) to compute the candidate GBT cloud moment 0 map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Grey-  scale contour levels are from 5 × 1018 cm-2 to 1 × 1021 cm-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The 3σ 1-channel column density limit is reported at the bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The beam of the  interferometric data for both the GBT and our VLA observations is shown in the bottom right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The green contours, instead, define the (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='25, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5,  25, 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5) × 1017 cm-2 column density in the GBT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The light-grey line denotes the 20% cut-off threshold of the primary beam response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Central  panel: primary beam corrected H i column density map of the anomalous-velocity gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Grey-scale contour levels are (3, 10, 25, 50, 100) × 1018  cm-2 column density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The spatial scale is the same as in the left panel, as well as the definition of the light grey line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We indicate the galaxy edge  with the dashed-black contour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The light blue dashed line represents the path along which the position-velocity slice has been extracted (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Right panel: Illustrative example of the selection effect introduced by the shuffle procedure (see discussion in section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The map shows the  fraction of the original extraplanar flux density of a mock galaxy we were able to recover and the red contour encloses the region where we are  severely affected by selection effect, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', where more than 90% of the original flux density is lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The blanked bits in the centre denote the region  where the result is unreliable because of the steep gradient in velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The dashed white contours are, instead, the region occupied by the observed  filamentary complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The nature of the 20 kpc filament  One of the questions we try to answer is whether the GBT cloud,  and by implication the filaments described in this paper, are  formed due to a gas accretion event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' There are however other  possible explanations for these features, some of which we have  already briefly alluded to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' For example, the structures we observe  could be the result of a galactic fountain process that ejects gas  from the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This is certainly a likely scenario for the anoma-  lous velocity gas closer to the disk (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' below our ± 65 km s−1  cut-off), but it is less obvious for the filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  It is difficult to form a straight 20 kpc long filament in an out-  flow scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Indeed, in a pure galactic fountain model the gas  ejecta reaches distances of at most 10 kpc even with extremely  high kick velocities (Fraternali & Binney 2006, 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Is the origin of the filamentary complex a galactic interaction?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In the event of a merging or disrupting dwarf, one might expect  to see a disturbed stellar population from the dwarf, most likely  coinciding with or near the filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Barker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2012) per-  formed an in-depth study of the stellar properties in NGC 2403  but did not identify any peculiarities in the distribution of the  stars and concluded that the galaxy has evolved in isolation with  no significant recent merging event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  However, their Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 10 shows some evidence for a slightly dis-  turbed stellar component in the NW part of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' They also  reported an extended low-metallicity Red Giant Branch (RGB)  component at radii between 18 and 40 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Their interpretation  includes the presence of a stellar halo, or a thick stellar disk in  NGC 2403, but it is not clear whether this component is associ-  ated with an accretion or interaction event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  In de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014) it was shown that a line passing through  the major axis of the 8-kpc filament and the GBT cloud intersects  with nearby dwarf galaxies DDO 44 and NGC 2366, hinting at  a possible interaction scenario with either of these galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Re-  cent deep optical wide-field data presented in Carlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2019)  supports this idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' They observed a ∼ 50 kpc long stellar stream  originating from the dwarf galaxy DDO 44 and connecting with  the NW part of the stellar disk of NGC 2403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This dwarf is likely  a satellite of NGC 2403 located about 70 kpc from it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A higher  quality re-reduction of the data from Carlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2019) is given  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 6 (J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Carlin, priv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' comm) and this shows the stellar stream  and the connection between DDO 44 and NGC 2403 even more  clearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  This image is a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5◦ wide field composite mosaic of seven point-  ings taken with the Hyper Suprime-Cam of the 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 m Subaru  Telescope and converted into a density map of candidate RGB  stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Overlaid on that map, we show the filamentary H i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' There  is a remarkable coincidence between the position of the tip of the  20 kpc filament and the region where the DDO 44 stellar stream  connects with NGC 2403 stellar disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This is therefore a strong  indication that the dwarf interaction scenario can be responsible  for the H i filaments in NGC 2403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  This is also suggested by the star formation histories of the  galaxies: NGC 2403 had an increase in its star formation rate  about 2 Gyr ago (Williams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2013), in particular, at radii >  20 kpc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' while DDO 44 had a burst of star formation from 1 to  Article number, page 6 of 9  Simone Veronese et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' : Extended neutral hydrogen filamentary network in NGC 2403  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  0  50  100  150  200  250  Offset from center [arcmin]  Velocity [km/s]  10 kpc  This work  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0  Offset from center [arcmin]  de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Comparison between the position-velocity diagram through the centres of the cloud candidate and the 20 kpc filament along a 100”-thick  slice as taken through our data (left panel) and as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 6 in de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2014) (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The emission is mapped with a reversed  grey-scale and we overlaid the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='5 × (1, 9, 81) × 1018 cm-2 column density levels with colour-scale contours (black, red and white, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The blue contour denotes a level of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='2 × 1018 cm-2 and highlights the detection of the 20 kpc filament tip with the combination of the new and  archival VLA data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The red circles highlight the tip of the 20 kpc filament which was not detected in the Fraternali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2002) and de Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  (2014) analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  3 Gyr ago (Girardi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Weisz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Also, Carlin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2019) calculated from the estimated trajectory of DDO 44  that the interaction with NGC 2403 occurred ∼ 1 Gyr ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' These  various estimates thus give very similar timescales for the inter-  action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  The most likely explanation is therefore that the H i filaments in  NGC 2403 are the result of the interaction with DDO 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' This  does, of course, not preclude a galactic fountain scenario as a  potential origin for a part of the extraplanar gas in NGC 2403  especially so for the gas at less extreme velocities than the fil-  aments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' It is interesting to note that for two of the most well-  known nearby galaxies where extraplanar filaments are promi-  nent, NGC 2403 and NGC 891, an interaction scenario is now  the most likely cause (see Oosterloo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2007 for the NGC 891  analysis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Conclusion  Using new and archival VLA observations, we have presented a  study of NGC 2403, focusing on the nature of the GBT cloud (de  Blok et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' These data show a filamentary complex around  the galaxy with an H i mass of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='0 × 107 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' It comprises at least  three filaments with extents of 10-20 kpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The GBT cloud can  now be shown to be the tip of the longest structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Even though at first sight the stellar distribution in NGC 2403  seems undisturbed, it is now likely that these filaments are the  result of an interaction with a nearby dwarf galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Hints of a  disturbance in the stellar component were already visible in the  data presented in Barker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2012), but they were dramati-  cally confirmed in the recent study by Carlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2019), who  discovered a ∼ 50 kpc long stellar stream connecting DDO 44  and NGC 2403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The intersection of that stream with NGC 2403  coincides with the positions of the tip of the H i filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The  star formation history of the two galaxies and the estimated tra-  jectory of DDO 44 seems to suggest that the interaction occurred  about 1 Gyr ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  These observations highlight the importance of minor interac-  tions in shaping the H i disks of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Moreover, they point  out the difficulties of unambiguously identifying the effects of  direct cold gas accretion from the IGM, and distinguishing them  from those of minor interactions with a satellite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' In this regard,  the multiwavelength approach is fundamental: optical observa-  tions are crucial to move the needle toward accretion or inter-  action as the most plausible explanation of anomalous H i struc-  tures like the filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Future observations with the SKA and its precursors at higher  resolution and higher sensitivity will undoubtedly uncover many  more of these features in nearby galaxies and help us to better  understand how the balance between accretion and interaction  impacts the evolution of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We would like to thank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Fergusson for providing us with  the stellar catalogue from Barker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We thank F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Fraternali for the useful  discussions about the interpretation of our results and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Maccagni for the initial  discussions on the DDO 44 optical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Marasco’s help in the modelling of  our data is gratefully acknowledged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Also, we thank J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Carlin for kindly sharing  with us the new re-reduced optical data of DDO 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' We thank the anonymous  referee for the constructive comments and the suggested improvements for the  quality and clarity of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  This work has received funding from the European Research Council (ERC)  under the European Union’s Horizon 2020 research and innovation programme  (grant agreement No 882793 ‘MeerGas’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  Article number, page 7 of 9  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=" main  7h50m  40m  30m  20m  67°  66°  65°  64°  RA  DEC  7h33m  34m  35m  36m  37m  38m  39m  65°30'  40'  50'  RA  DEC  Fig." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Overlay between the re-reduced density map of candidate RGB stars presented in Carlin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' (2019) and the H i filaments observed in our  data (white contours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' Bins in the density map are completeness-corrected and have a resolution of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='75 arcmin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The hole in the centre is due to  extreme crowding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The colours denote the number of stars per 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='75’ bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' The stellar stream is connecting DDO 44 and NGC 2403 with the tip of  the H i filaments, strongly suggesting that DDO 44 and NGC 2403 underwent a recent interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content='  References  Afruni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', Fraternali, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', & Pezzulli, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' 2021, MNRAS, 501, 5575  Barker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', Ferguson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
+page_content=', Irwin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFRT4oBgHgl3EQfRzcI/content/2301.13526v1.pdf'}
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diff --git a/btFLT4oBgHgl3EQfYS80/content/tmp_files/2301.12064v1.pdf.txt b/btFLT4oBgHgl3EQfYS80/content/tmp_files/2301.12064v1.pdf.txt
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+arXiv:2301.12064v1  [q-bio.QM]  28 Jan 2023
+Springer Nature 2021 LATEX template
+Optimizing a Bayesian method for estimating
+the Hurst exponent in behavioral sciences
+Madhur Mangalam1*, Taylor Wilson1, Joel Sommerfeld1
+and Aaron D. Likens1*
+1Division of Biomechanics and Research Development,
+Department of Biomechanics, and Center for Research in Human
+Movement Variability, University of Nebraska at Omaha,
+University Dr S, Omaha, 68182, NE, USA.
+*Corresponding author(s). E-mail(s):
+mmangalam@unomaha.edu; alikens@unomaha.edu;
+Abstract
+The Bayesian Hurst-Kolmogorov (HK) method estimates the Hurst
+exponent of a time series more accurately than the age-old detrended
+fluctuation analysis (DFA), especially when the time series is short.
+However, this advantage comes at the cost of computation time. The
+computation time increases exponentially with N, easily exceeding sev-
+eral hours for N = 1024, limiting the utility of the HK method in
+real-time paradigms, such as biofeedback and brain-computer interfaces.
+To address this issue, we have provided data on the estimation accu-
+racy of H for synthetic time series as a function of a priori known
+values of H, the time series length, and the simulated sample size
+from the posterior distribution—a critical step in the Bayesian esti-
+mation method. The simulated sample from the posterior distribution
+as small as n = 25 suffices to estimate H with reasonable accuracy
+for a time series as short as 256 measurements. Using a larger simu-
+lated sample from the posterior distribution—i.e., n > 50—provides
+only marginal gain in accuracy, which might not be worth trading off
+with computational efficiency. We suggest balancing the simulated sam-
+ple size from the posterior distribution of H with the computational
+resources available to the user, preferring a minimum of n = 50 and
+opting for larger sample sizes based on time and resource constraints.
+Keywords: detrended fluctuation analysis, fractal fluctuation, fractional,
+long-range correlation, physiology, variability
+1
+
+Springer Nature 2021 LATEX template
+2
+Bayesian method for estimating the Hurst exponent
+Introduction
+A robust measure of the strength of long-range correlations in time series
+is the Hurst exponent, H, named by Mandelbrot [1] in honor of pioneering
+work by Edwin Hurst in hydrology [2]. In the parlance of linear statistics, H
+quantifies how the measurements’ SD-like variations grow across progressively
+longer timescales, indicating how the correlation among sequential measure-
+ments might decay across longer separations in time. H describes a single
+fractal-scaling estimate of power-law decay in autocorrelation ρ for lag k as
+ρk = |k + 1|2H − 2|k|2H + |k − 1|2H, for which H reveals the degree of persis-
+tence (0.5 < H < 1.0; i.e., large values are typically followed by large values)
+or anti-persistence (0 < H < 0.5; i.e., small values typically follow large values
+and vice versa).
+H has become a central inferential statistic in diverse fields, including
+meteorology [3–5], economics [6–10], ethology [11, 12], bioinformatics [13–15],
+and physiology [16–19]. In behavioral sciences, successful examples of infer-
+ences made using the H statistic include interpretations about feedforward
+and forward processes in postural control [20–22], system-wide coordination
+[23, 24], cognition [25–29], and perception-action [30–32], among countless
+others. H has also proved to be an effective measure differentiating among
+adults with healthy and pathological cardiovascular functioning [33–35], as
+well as movement systems [36–41]. H is also becoming a statistical bench-
+mark for developing rehabilitative interventions [42–44] and quantifying the
+effectiveness of those interventions [45–47].
+The most common method of estimating H is detrended fluctuation
+analysis (DFA) [48, 49]. DFA’s ability to assess the strength of long-range cor-
+relations embedded in time series that seem non-stationary and to prevent
+the false detection of long-range correlations that are a byproduct of non-
+stationarity make it superior to many other methods. Numerical analysis has
+shown that DFA confers several advantages when the data trend’s functional
+form is not known a priori [50, 51]. Nonetheless, DFA has several shortcomings
+which none of the existing alternatives overcome [52–60]. For instance, DFA
+does not accurately assess the strength of long-range correlations when the
+time series is brief [54, 55, 59], producing a positive bias in its central tendency
+in addition to a large dispersion [52, 53, 56–58, 60]. DFA requires time series
+consisting of at least 500 measurements to accurately estimate H, severely
+limiting its application under time constraints or when collecting longer time
+series is not practical, such as in pathological populations who cannot partic-
+ipate in a study for an extended time due to fatigue [56]. Furthermore, DFA
+is precariously sensitive to the time series length, typically overestimating H,
+a trend present in long time series but exaggerated when used with brief time
+series[53, 61].
+An alternative approach to estimating H—not well-known in behavioral
+sciences—is a Bayesian approach used to assess the Hurst-Kolmogorov (HK)
+
+Springer Nature 2021 LATEX template
+Bayesian method for estimating the Hurst exponent
+3
+process in hydrology [62]. In this method—which we call the ”HK method,”
+Tyralis and Koutsoyiannis [62] proposed a Bayesian-inspired technique that
+defines the posterior distribution from which to sample H.
+We previously compared the performance of the HK method and the DFA
+using simulated and empirical time series [63]. Using synthetic time series with
+a priori known values of H, we demonstrated that the HK method consis-
+tently outperforms DFA in three ways. The HK method (i) accurately assesses
+long-range correlations when the measurement time series is short, (ii) shows
+minimal dispersion about the central tendency, and (iii) yields a point esti-
+mate that does not depend on the length of the measurement time series or its
+underlying Hurst exponent. Furthermore, comparing the two methods using
+empirical human behavioral time series supported these simulation results. We
+also showed that the HK method balances the Type I and Type II errors asso-
+ciated with inferential statistics performed on the estimated ˆH (We use ˆH to
+distinguish the estimated value of the Hurst exponent from the ground truth
+H). It reduces the likelihood of the Type II error by not missing an effect of
+an independent factor when it exists, without increasing the likelihood of the
+Type I error by finding an effect of an independent factor when it does not
+exist. DFA nonetheless confers an advantage in computing time—owing to the
+simple and linear nature of computations, even though these results provide a
+convincing argument for choosing the computationally-expensive HK method
+over DFA. Therefore, computational efficiency, particularly for high through-
+put and real-time applications, is critical to successfully implementing the HK
+method.
+The HK method is computationally expensive, owing to its roots in the
+Bayesian framework. The computation time increases exponentially with the
+time series length N. When performed on a personal computer, the computa-
+tion time could easily exceed several hours for N ≥ 1024—typical time series
+length in behavioral sciences (e.g., stride interval time series, RT time series).
+This problem becomes even more challenging when dealing with physiological
+measurements recorded over longer times (e.g., breathing rate variability, heart
+rate variability, functional near-infrared spectroscopy, fNIRS) or at higher
+frequencies (e.g., the center of pressure, CoP, electroencephalogram, EEG,
+electromyography, EMG). Moreover, the computational limitation makes it
+impractical to implement the HK method in real-time paradigms, such as
+biofeedback and brain-computer interfaces. Computationally optimizing the
+HK method for accurately estimating H, i.e., ˆH, is, therefore, critical for pro-
+moting the adoption of the HK method as a standard approach to estimating
+the Hurst exponent in behavioral sciences.
+Here, we provide data on the accuracy of the Hurst exponent, estimated
+using the HK method for synthetic time series as a function of a priori known
+values of H, time series length, and the number of samples from the poste-
+rior distribution of H—a parameter related to the Bayesian estimation that
+critically influences the accuracy of ˆH. Our results will guide the selection of
+
+Springer Nature 2021 LATEX template
+4
+Bayesian method for estimating the Hurst exponent
+the minimum sample of H from the posterior distribution of H necessary for
+estimating ˆH for a given level of accuracy.
+Methods
+The HK method for estimating the Hurst exponent
+As noted above, a recently introduced Bayesian approach to estimating H [62]
+shows remarkable promise in addressing fundamental limitations with DFA.
+In previous work, we have demonstrated that the HK method outperforms
+DFA in several contexts [63]. Our current interest is investigating the HK
+method’s performance trade-offs related to computational efficiency. Results
+presented later in Section 1 demonstrate that the HK method is entirely accu-
+rate in recovering H from time series even when sacrificing some accuracy
+for enhanced computational efficiency. Below, we provide a brief overview of
+the HK method while referring the reader to the foundational work for addi-
+tional mathematical details and proofs [62]. Our notation generally follows
+that original work.
+The foundation for the method originates in the definition of the auto-
+correlation function for the so-called Hurst-Kolmogorov (HK) process [64]
+as:
+ρk = |k + 1|2H/2 − 2|k|2H/2 + |k − 1|2H,
+k = 0, 1, . . . ,
+(1)
+such that H is the Hurst exponent, k is the time lag, and ρk is the autocor-
+relation function at each successive value of k. If H = 0.5, then ρk is 1 when
+k = 0 but zero for k > 0. If 0 < H < 0.5, then ρk is negative at lag 1 before
+damping zero when k > 1. Lastly, if 0.5 < H < 1, then ρk is positive and
+slowly decays towards zero; and as H → 1, ρk asymptotically approaches 0.
+As noted, the HK method is a Bayesian approach to estimating H [62].
+In the foundational work, Tyralis & Koutsoyiannis [62] derived a method to
+sample from the posterior distribution of H given by:
+π(ϕ|xn) ∝ |Rn|−1/2 [eT
+nR−1
+n enxT
+nR−1
+n xn − (eT
+nR−1
+n en)2]−(n−1)/2
+(eT
+nR−1
+n en)n/2−1,
+(2)
+The natural logarithm of Eq. (2) is then given by:
+ln π(ϕ|xn) ∝ 1
+2 ln |Rn| − (n − 1)
+2
+ln [eT
+nR−1
+n enxT
+nR−1
+n xn − (eT
+nR−1
+n en)2]
++n − 2
+2
+ln (eT
+nR−1
+n en), (3)
+
+Springer Nature 2021 LATEX template
+Bayesian method for estimating the Hurst exponent
+5
+where Rn is the autocorrelation matrix with elements ri,j where i, j =
+1, 2, 3, . . ., n, en = (1, 1, 1, . . ., 1)T is a vector of ones with n elements, | . . . |
+notes a determinant, the superscript of −1 in R−1
+n
+is a matrix inverse, and
+the superscript T is a matrix transpose. The right-hand products in Eq. (3)
+are derived from the quadratic forms of the inverse of a symmetric, positive
+definite autocorrelation matrix (Levinson Algorithm; Algorithm 4.7.2, Golub
+& Van Loan [65], p. 235) for a given xt and ρk.
+Accept-reject algorithms are standard tools for sampling from posterior dis-
+tributions and serve as the backbone of implementing the HK method [66]. Let
+f(x) be a probability density function (PDF) from which it is difficult to sam-
+ple. f(x) is the “target distribution” and can be sampled using Monte Carlo
+methods. First, one samples a simpler “proposal distribution,” Mg(x) that
+has the same domain as f(x) and M is a constant large enough to ensure that
+g(x) ≥ f(x). In theory, the proposal distribution, g(x), can be any number of
+distributions, such as uniform, Gaussian, exponential, etc. However, the algo-
+rithm gains computational efficiency when the overall shape of g(x) is similar
+to f. Second, f(x) is evaluated at the value obtained by sampling g(x), the pro-
+posal distribution. Third, a sample is drawn from U(x) ∼ Uniform(0, Mg(x)).
+If U(x) ≤ f(x), then the value proposed by sampling g(x) is accepted as a valid
+sample. Otherwise, the proposal is rejected, and the algorithm is re-initialized.
+This process repeats until n samples are obtained, where n is the number
+of samples desired from the posterior distribution. We seek to understand
+appropriate values of n that balance estimation accuracy and computational
+efficiency.
+In experiments reported in Section 1 and Section 1, we employ this accept-
+reject algorithm to sample H from its posterior distribution (Algorithm A.5,
+Robert & Casella [66], p. 49). The target distribution, f(x) is Eq. (3) and
+g(x) ∼ Uniform(0, 1). That uniform distribution makes sense for g(x) because
+it shares the same domain of H and hence Eq. (3), namely (0, 1) [62]. A numer-
+ical optimization routine is used to determine M by finding the maximum
+of Eq. (3) as a function of H. The point estimate of H is then taken as the
+median of the posterior distribution of H. Time series were analyzed using the
+R [67] programming environment using the inferH() function as part of the
+“HKprocess” package [68].
+Generating synthetic time series with a priori known
+values of the Hurst exponent
+The Davies-Harte algorithm [69] was used to generate fractional Gaussian noise
+(fGn), which can be tuned to exhibit varying degrees and direction of auto-
+correlation consistent with Eq. (1). fGn time series were generated in R [67]
+using the function fgn sim() from the package “fractalRegression” [70]. The
+function fgn sim() has two inputs: the time series length, N, and the Hurst
+exponent, H. We generated 1, 000 synthetic fGn time series for each combi-
+nation of six different time series lengths (N = 32, 64, 128, 256, 512, 1024) and
+
+Springer Nature 2021 LATEX template
+6
+Bayesian method for estimating the Hurst exponent
+nine different a priori known values of H (H = 0.1, 0.2, . . ., 0.9). We submit-
+ted all synthetic time series to the HK method in R [67] using the function
+inferH() from the package “HKprocess” [68]. The function inferH() has two
+inputs: the time series, xN, and the simulated sample size from the posterior
+distribution of H, n. The HK method was performed for a progressively larger
+sample from the posterior distribution of H, covering an extensive range with
+the sample size ranging from 1 to 25 with increments of 1 and from 25 to 500
+with increments of 25, i.e., n = 1, 2, . . . , 25, 50, . . ., 500.
+Results
+Figs. 1 & 2 provide a summary visualization of the simulation results
+for each combination of the a priori known values of the Hurst exponent
+(H = 0.1, 0.2, . . ., 0.9), the time series length (N = 32, 64, . . ., 1024), and
+the sample size of H desired from the posterior distribution of H, n =
+1, 2, . . . , 25, 50, . . ., 500. As a general preview,
+ˆH estimated using the HK
+method closely matches the actual H for time series containing as few as
+128 values (Fig. 1, middle left). For shorter time series—N = 32, 64, the HK
+method visibily overestimates ˆH for smaller actual H and underestimates ˆH
+for larger actual H (Figs. 1, top left and top right, respectively). Shorter time
+series—N = 32, 64, 128—show more closely matching values of ˆH and H for
+larger posterior samples of H. Still, this trend was not apparent for longer
+time series—N = 256, 512, 1024 (Fig. 1, middle right, bottom left, and bottom
+right, respectively). Nonetheless, the sample size of H desired from the poste-
+rior distribution does not seem to influence the fidelity of ˆH for a sufficiently
+large sample size of H desired from the posterior distribution, i.e., n = 50.
+When N = 32, a very short time series compared to the DFA standard
+of > 500, the estimated ˆH shows a large discrepancy (> 0.1) with the actual
+H in terms of the absolute error (Fig. 2, top left). Although this discrepancy
+sharply reduced with the sample size of H desired from the posterior distri-
+bution, almost reaching an asymptote by n = 25, the absolute error remains
+considerably high even for n = 500. For a relatively longer yet considerably
+short time series—N = 64, the absolute error reduces with the sample size of
+H desired from the posterior distribution, reaching a lower asymptotic value
+of < 0.1 (Fig. 2, top right). However, this discrepancy is still sufficient to mask
+the typically observed differences in the Hurst exponent of empirical time series
+across two groups. For instance, the Hurst exponent of stride-to-stride interval
+time series during walking shows a difference of the order of 0.1 across vari-
+ous task conditions(e.g., [42–44]. However, a discrepancy of the order of 0.1 in
+the estimation of H can potentially mask these differences, resulting in false
+negatives in statistical tests. The trend was comparable for time series with
+N = 124 except for the absolute error reaching a lower asymptotic value of
+∼ 0.05 (Fig. 2, middle left).
+
+Springer Nature 2021 LATEX template
+Bayesian method for estimating the Hurst exponent
+7
+Fig. 1 The Hurst exponent, ˆ
+H, estimated using the HK method closely matches
+the actual H for time series containing as few as 128 values. Each panel plots the
+Mean H for 1, 000 synthetic time series with N = 32, 64, 128, 256, 512, 1024, a priori known
+values of H ranging from 0.1 to 0.9, and the sample size of H desired from the posterior
+distribution of H, n = 1, 2, . . . , 25, 50, . . . , 500. Horizontal colored lines indicate the actual
+H, and error bars indicate 95% CI across 1000 simulations.
+When N = 256, the absolute error in the estimated ˆH falls within a much
+lower range of tolerance (< 0.05) even with a very small sample of H from the
+posterior distribution (Fig. 2, middle right). Again, the absolute error sharply
+reduces with n, reaching an even lower asymptotic value of ∼ 0.04 by n = 25.
+Longer time series with N = 512 and N = 1024 also show similar trends
+except for much lower asymptotic values of absolute error: < 0.03 and < 0.02,
+respectively, by n = 25 (Fig. 2, bottom left and bottom right, respectively). In
+
+N = 32
+N = 64
+0.9
+0.9
+0.8
+HOOOH
+0.8
+0.7
+0.7
+0.6
+0.6
+<H
+<H
+0.5
+0.5
+0.4
+0.4
+0.3
+0.3
+0.2
+0.2
+0.1
+0.1
+5
+5
+n
+n
+N = 128
+N = 256
+0.9
+0.9
+0.8
+0.8
+0.7
+0.7
+0.6
+0.6
+H
+H
+0.5
+0.5
+0.4
+0.4
+0.3
+0.3
+0.2
+0.2
+0.1
+0.1
+2
+n
+n
+N = 512
+N = 1024
+0.9
+0.9
+0.8
+0.8
+0.7
+0.7
+0.6
+0.6
+H
+<H
+0.5
+0.5
+0.4
+0.4
+0.3
+0.3
+0.2
+0.2
+0.1
+0.1
+5
+n
+nSpringer Nature 2021 LATEX template
+8
+Bayesian method for estimating the Hurst exponent
+Fig. 2 The absolute error in the estimation of the Hurst exponent,
+ˆ
+H, using
+the HK method sharply reduced with the sample size of H desired from the
+posterior distribution of H, reaching an asymptote at n = 50. Using a larger
+simulated sample from the posterior distribution of H—i.e., n > 50—does not influence the
+accuracy of the estimated H. Each panel plots the Mean absolute error in the estimated H
+for 1, 000 synthetic time series with N = 32, 64, 128, 256, 512, 1024, a priori known values of
+H ranging from 0.1 to 0.9, and the sample size of H desired from the posterior distribution
+of H, n = 1, 2, . . . , 25, 50, . . . , 500. Error bars indicate 95% CI across 1000 simulations.
+short, a relatively small sample size of H desired from the posterior distribu-
+tion when using the accept-reject algorithm of the HKM suffices to estimate
+ˆH with very high accuracy. Increasing the sample size of H desired from the
+posterior distribution considerably increases the computational cost but con-
+fers no additional advantage in terms of the accuracy of estimating the Hurst
+exponent.
+
+0.175
+0.15
+H = 0.1
+N = 32
+N = 64
+H = 0.6
+H = 0.2
+H = 0.7
+0.15
+0.125
+H = 0.3
+H = 0.8
+H = 0.4
+H = 0.9
+H =
+= 0.5
+0.125
+0.1
+0.1
+0.075
+0.075
+0.05
+III!!
+0.05
+0.025
+5
+20
+5
+C
+20
+C
+10
+n
+n
+0.075
+0.075
+N = 128
+N = 256
+0.06
+0.06
+0.045
+0.045
+H
+0.03
+0.03
+重亚严亚亚
+0.015
+0.015
+0
+0
+5
+C
+n
+n
+0.05
+0.05
+N = 512
+N = 1024
+0.04
+0.04
+0.03
+0.03
+0.02
+0.02
+0.01
+0.01
+0
+0
+5
+5
+0
+n
+nSpringer Nature 2021 LATEX template
+Bayesian method for estimating the Hurst exponent
+9
+Discussion
+The HK method offers several advantages over DFA in estimating the Hurst
+exponent of a time series [63]. However, these advantages come at the cost of
+computation time. The HK method is computationally expensive owing to its
+roots in the Bayesian framework. Computationally optimizing the HK method
+for accurately estimating ˆH is, therefore, critical for promoting the adoption
+of the HK method over DFA for estimating the Hurst exponent in behav-
+ioral sciences. To address this issue, we have provided data on the accuracy of
+the Hurst exponent estimated using the HK method for synthetic time series
+as a function of a priori known values of H, the time series length, and the
+sample size of H from the posterior distribution of H—a parameter related
+to the Bayesian estimation that critically influences the accuracy of ˆH and
+computation time. The simulated sample from the posterior distribution of H
+as small as n = 50 suffices to estimate the Hurst exponent with reasonable
+accuracy. Using a larger simulated sample from the posterior distribution of
+H—i.e., n > 50—provides only a marginal gain in accuracy, which might not
+be worth trading off with computational efficiency. We suggest balancing the
+simulated sample size from the posterior distribution of H with the compu-
+tational resources available to the user, preferring a minimum of n = 50 and
+opting for larger sample sizes based on time and resource constraints. Our
+results allow the reader to make such judgments.
+Empirical data pose several other issues that might undermine the accuracy
+of H estimated using the HK method, such as strong trends [71–73], nonsta-
+tionarities [71, 74], and “crossovers”—i.e., when correlations do not follow the
+same scaling law for all timescales and a crossover is observed between different
+scaling regions [49, 50, 75, 76]. However, because these anomalies, particularly
+the crossovers, often appear at longer timescales, it seems reasonable to pro-
+mote the systematic use of this method, irrespective of these reserves. Future
+work could investigate how trends, nonstationarities, and crossovers influence
+the estimation accuracy using the Bayesian approach.
+In summary, the HK method offers several advantages over DFA for esti-
+mating the Hurst exponent of a time series, especially when it is short. What
+may prevent, however, the adoption of the HK method is significantly long
+computation time, especially when analyzing time series containing several
+hundred to thousands of measurements—which is frequently the case in behav-
+ioral sciences. To minimize the computation time of the HK method, we have
+provided critical information for identifying the minimum simulated sample
+from the posterior distribution of H. This information could aid the selection
+of correct parameters that allow the estimation of H in real-time settings, such
+as biofeedback paradigms and brain-computer interfaces, where computation
+time is often limited.
+Acknowledgments.
+This work was supported by the Center for Research
+in Human Movement Variability at the University of Nebraska at Omaha,
+
+Springer Nature 2021 LATEX template
+10
+Bayesian method for estimating the Hurst exponent
+the University of Nebraska Collaboration Initiative, the NSF award 212491,
+the NIH awards P20GM109090 and R01NS114282, the NASA EPSCoR
+mechanism, and the IARPA WatchID award.
+Author contributions.
+Conceptualization: M.M. and A.D.L.; Methodol-
+ogy: M.M., T.W., J.H.S., and A.D.L.; Formal analysis: M.M.; Data curation:
+M.M.; Writing – Original draft: M.M.; Writing – Review & Editing: M.M.,
+T.W., J.H.S., and A.D.L.; Visualization: M.M.; Funding acquisition: A.D.L.
+Declarations.
+The authors declare no competing financial interests.
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf,len=1257
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='12064v1  [q-bio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='QM]  28 Jan 2023  Springer Nature 2021 LATEX template  Optimizing a Bayesian method for estimating  the Hurst exponent in behavioral sciences  Madhur Mangalam1*, Taylor Wilson1, Joel Sommerfeld1  and Aaron D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Likens1*  1Division of Biomechanics and Research Development,  Department of Biomechanics, and Center for Research in Human  Movement Variability, University of Nebraska at Omaha,  University Dr S, Omaha, 68182, NE, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Corresponding author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' E-mail(s):  mmangalam@unomaha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' alikens@unomaha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Abstract  The Bayesian Hurst-Kolmogorov (HK) method estimates the Hurst  exponent of a time series more accurately than the age-old detrended  fluctuation analysis (DFA), especially when the time series is short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  However, this advantage comes at the cost of computation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The  computation time increases exponentially with N, easily exceeding sev-  eral hours for N = 1024, limiting the utility of the HK method in  real-time paradigms, such as biofeedback and brain-computer interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  To address this issue, we have provided data on the estimation accu-  racy of H for synthetic time series as a function of a priori known  values of H, the time series length, and the simulated sample size  from the posterior distribution—a critical step in the Bayesian esti-  mation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The simulated sample from the posterior distribution  as small as n = 25 suffices to estimate H with reasonable accuracy  for a time series as short as 256 measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Using a larger simu-  lated sample from the posterior distribution—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', n > 50—provides  only marginal gain in accuracy, which might not be worth trading off  with computational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' We suggest balancing the simulated sam-  ple size from the posterior distribution of H with the computational  resources available to the user, preferring a minimum of n = 50 and  opting for larger sample sizes based on time and resource constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Keywords: detrended fluctuation analysis, fractal fluctuation, fractional,  long-range correlation, physiology, variability  1  Springer Nature 2021 LATEX template  2  Bayesian method for estimating the Hurst exponent  Introduction  A robust measure of the strength of long-range correlations in time series  is the Hurst exponent, H, named by Mandelbrot [1] in honor of pioneering  work by Edwin Hurst in hydrology [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' In the parlance of linear statistics, H  quantifies how the measurements’ SD-like variations grow across progressively  longer timescales, indicating how the correlation among sequential measure-  ments might decay across longer separations in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' H describes a single  fractal-scaling estimate of power-law decay in autocorrelation ρ for lag k as  ρk = |k + 1|2H − 2|k|2H + |k − 1|2H, for which H reveals the degree of persis-  tence (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5 < H < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', large values are typically followed by large values)  or anti-persistence (0 < H < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', small values typically follow large values  and vice versa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  H has become a central inferential statistic in diverse fields, including  meteorology [3–5], economics [6–10], ethology [11, 12], bioinformatics [13–15],  and physiology [16–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' In behavioral sciences, successful examples of infer-  ences made using the H statistic include interpretations about feedforward  and forward processes in postural control [20–22], system-wide coordination  [23, 24], cognition [25–29], and perception-action [30–32], among countless  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' H has also proved to be an effective measure differentiating among  adults with healthy and pathological cardiovascular functioning [33–35], as  well as movement systems [36–41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' H is also becoming a statistical bench-  mark for developing rehabilitative interventions [42–44] and quantifying the  effectiveness of those interventions [45–47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  The most common method of estimating H is detrended fluctuation  analysis (DFA) [48, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' DFA’s ability to assess the strength of long-range cor-  relations embedded in time series that seem non-stationary and to prevent  the false detection of long-range correlations that are a byproduct of non-  stationarity make it superior to many other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Numerical analysis has  shown that DFA confers several advantages when the data trend’s functional  form is not known a priori [50, 51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Nonetheless, DFA has several shortcomings  which none of the existing alternatives overcome [52–60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' For instance, DFA  does not accurately assess the strength of long-range correlations when the  time series is brief [54, 55, 59], producing a positive bias in its central tendency  in addition to a large dispersion [52, 53, 56–58, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' DFA requires time series  consisting of at least 500 measurements to accurately estimate H, severely  limiting its application under time constraints or when collecting longer time  series is not practical, such as in pathological populations who cannot partic-  ipate in a study for an extended time due to fatigue [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Furthermore, DFA  is precariously sensitive to the time series length, typically overestimating H,  a trend present in long time series but exaggerated when used with brief time  series[53, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  An alternative approach to estimating H—not well-known in behavioral  sciences—is a Bayesian approach used to assess the Hurst-Kolmogorov (HK)  Springer Nature 2021 LATEX template  Bayesian method for estimating the Hurst exponent  3  process in hydrology [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' In this method—which we call the ”HK method,”  Tyralis and Koutsoyiannis [62] proposed a Bayesian-inspired technique that  defines the posterior distribution from which to sample H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  We previously compared the performance of the HK method and the DFA  using simulated and empirical time series [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Using synthetic time series with  a priori known values of H, we demonstrated that the HK method consis-  tently outperforms DFA in three ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The HK method (i) accurately assesses  long-range correlations when the measurement time series is short, (ii) shows  minimal dispersion about the central tendency, and (iii) yields a point esti-  mate that does not depend on the length of the measurement time series or its  underlying Hurst exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Furthermore, comparing the two methods using  empirical human behavioral time series supported these simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' We  also showed that the HK method balances the Type I and Type II errors asso-  ciated with inferential statistics performed on the estimated ˆH (We use ˆH to  distinguish the estimated value of the Hurst exponent from the ground truth  H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' It reduces the likelihood of the Type II error by not missing an effect of  an independent factor when it exists, without increasing the likelihood of the  Type I error by finding an effect of an independent factor when it does not  exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' DFA nonetheless confers an advantage in computing time—owing to the  simple and linear nature of computations, even though these results provide a  convincing argument for choosing the computationally-expensive HK method  over DFA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Therefore, computational efficiency, particularly for high through-  put and real-time applications, is critical to successfully implementing the HK  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  The HK method is computationally expensive, owing to its roots in the  Bayesian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The computation time increases exponentially with the  time series length N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' When performed on a personal computer, the computa-  tion time could easily exceed several hours for N ≥ 1024—typical time series  length in behavioral sciences (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', stride interval time series, RT time series).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  This problem becomes even more challenging when dealing with physiological  measurements recorded over longer times (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', breathing rate variability, heart  rate variability, functional near-infrared spectroscopy, fNIRS) or at higher  frequencies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', the center of pressure, CoP, electroencephalogram, EEG,  electromyography, EMG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Moreover, the computational limitation makes it  impractical to implement the HK method in real-time paradigms, such as  biofeedback and brain-computer interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Computationally optimizing the  HK method for accurately estimating H, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', ˆH, is, therefore, critical for pro-  moting the adoption of the HK method as a standard approach to estimating  the Hurst exponent in behavioral sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Here, we provide data on the accuracy of the Hurst exponent, estimated  using the HK method for synthetic time series as a function of a priori known  values of H, time series length, and the number of samples from the poste-  rior distribution of H—a parameter related to the Bayesian estimation that  critically influences the accuracy of ˆH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Our results will guide the selection of  Springer Nature 2021 LATEX template  4  Bayesian method for estimating the Hurst exponent  the minimum sample of H from the posterior distribution of H necessary for  estimating ˆH for a given level of accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Methods  The HK method for estimating the Hurst exponent  As noted above, a recently introduced Bayesian approach to estimating H [62]  shows remarkable promise in addressing fundamental limitations with DFA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  In previous work, we have demonstrated that the HK method outperforms  DFA in several contexts [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Our current interest is investigating the HK  method’s performance trade-offs related to computational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Results  presented later in Section 1 demonstrate that the HK method is entirely accu-  rate in recovering H from time series even when sacrificing some accuracy  for enhanced computational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Below, we provide a brief overview of  the HK method while referring the reader to the foundational work for addi-  tional mathematical details and proofs [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Our notation generally follows  that original work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  The foundation for the method originates in the definition of the auto-  correlation function for the so-called Hurst-Kolmogorov (HK) process [64]  as:  ρk = |k + 1|2H/2 − 2|k|2H/2 + |k − 1|2H,  k = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' ,  (1)  such that H is the Hurst exponent, k is the time lag, and ρk is the autocor-  relation function at each successive value of k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' If H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5, then ρk is 1 when  k = 0 but zero for k > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' If 0 < H < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5, then ρk is negative at lag 1 before  damping zero when k > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Lastly, if 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5 < H < 1, then ρk is positive and  slowly decays towards zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' and as H → 1, ρk asymptotically approaches 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  As noted, the HK method is a Bayesian approach to estimating H [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  In the foundational work, Tyralis & Koutsoyiannis [62] derived a method to  sample from the posterior distribution of H given by:  π(ϕ|xn) ∝ |Rn|−1/2 [eT  nR−1  n enxT  nR−1  n xn − (eT  nR−1  n en)2]−(n−1)/2  (eT  nR−1  n en)n/2−1,  (2)  The natural logarithm of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' (2) is then given by:  ln π(ϕ|xn) ∝ 1  2 ln |Rn| − (n − 1)  2  ln [eT  nR−1  n enxT  nR−1  n xn − (eT  nR−1  n en)2]  +n − 2  2  ln (eT  nR−1  n en), (3)  Springer Nature 2021 LATEX template  Bayesian method for estimating the Hurst exponent  5  where Rn is the autocorrelation matrix with elements ri,j where i, j =  1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', n, en = (1, 1, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', 1)T is a vector of ones with n elements, | .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' |  notes a determinant, the superscript of −1 in R−1  n  is a matrix inverse, and  the superscript T is a matrix transpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The right-hand products in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' (3)  are derived from the quadratic forms of the inverse of a symmetric, positive  definite autocorrelation matrix (Levinson Algorithm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Algorithm 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='2, Golub  & Van Loan [65], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 235) for a given xt and ρk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Accept-reject algorithms are standard tools for sampling from posterior dis-  tributions and serve as the backbone of implementing the HK method [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Let  f(x) be a probability density function (PDF) from which it is difficult to sam-  ple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' f(x) is the “target distribution” and can be sampled using Monte Carlo  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' First, one samples a simpler “proposal distribution,” Mg(x) that  has the same domain as f(x) and M is a constant large enough to ensure that  g(x) ≥ f(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' In theory, the proposal distribution, g(x), can be any number of  distributions, such as uniform, Gaussian, exponential, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' However, the algo-  rithm gains computational efficiency when the overall shape of g(x) is similar  to f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Second, f(x) is evaluated at the value obtained by sampling g(x), the pro-  posal distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Third, a sample is drawn from U(x) ∼ Uniform(0, Mg(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  If U(x) ≤ f(x), then the value proposed by sampling g(x) is accepted as a valid  sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Otherwise, the proposal is rejected, and the algorithm is re-initialized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  This process repeats until n samples are obtained, where n is the number  of samples desired from the posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' We seek to understand  appropriate values of n that balance estimation accuracy and computational  efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  In experiments reported in Section 1 and Section 1, we employ this accept-  reject algorithm to sample H from its posterior distribution (Algorithm A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5,  Robert & Casella [66], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 49).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The target distribution, f(x) is Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' (3) and  g(x) ∼ Uniform(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' That uniform distribution makes sense for g(x) because  it shares the same domain of H and hence Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' (3), namely (0, 1) [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' A numer-  ical optimization routine is used to determine M by finding the maximum  of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' (3) as a function of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The point estimate of H is then taken as the  median of the posterior distribution of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Time series were analyzed using the  R [67] programming environment using the inferH() function as part of the  “HKprocess” package [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Generating synthetic time series with a priori known  values of the Hurst exponent  The Davies-Harte algorithm [69] was used to generate fractional Gaussian noise  (fGn), which can be tuned to exhibit varying degrees and direction of auto-  correlation consistent with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' fGn time series were generated in R [67]  using the function fgn sim() from the package “fractalRegression” [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The  function fgn sim() has two inputs: the time series length, N, and the Hurst  exponent, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' We generated 1, 000 synthetic fGn time series for each combi-  nation of six different time series lengths (N = 32, 64, 128, 256, 512, 1024) and  Springer Nature 2021 LATEX template  6  Bayesian method for estimating the Hurst exponent  nine different a priori known values of H (H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' We submit-  ted all synthetic time series to the HK method in R [67] using the function  inferH() from the package “HKprocess” [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The function inferH() has two  inputs: the time series, xN, and the simulated sample size from the posterior  distribution of H, n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The HK method was performed for a progressively larger  sample from the posterior distribution of H, covering an extensive range with  the sample size ranging from 1 to 25 with increments of 1 and from 25 to 500  with increments of 25, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', n = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' , 25, 50, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Results  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 1 & 2 provide a summary visualization of the simulation results  for each combination of the a priori known values of the Hurst exponent  (H = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='9), the time series length (N = 32, 64, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', 1024), and  the sample size of H desired from the posterior distribution of H, n =  1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' , 25, 50, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' As a general preview,  ˆH estimated using the HK  method closely matches the actual H for time series containing as few as  128 values (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 1, middle left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' For shorter time series—N = 32, 64, the HK  method visibily overestimates ˆH for smaller actual H and underestimates ˆH  for larger actual H (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 1, top left and top right, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Shorter time  series—N = 32, 64, 128—show more closely matching values of ˆH and H for  larger posterior samples of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Still, this trend was not apparent for longer  time series—N = 256, 512, 1024 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 1, middle right, bottom left, and bottom  right, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Nonetheless, the sample size of H desired from the poste-  rior distribution does not seem to influence the fidelity of ˆH for a sufficiently  large sample size of H desired from the posterior distribution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', n = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  When N = 32, a very short time series compared to the DFA standard  of > 500, the estimated ˆH shows a large discrepancy (> 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1) with the actual  H in terms of the absolute error (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 2, top left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Although this discrepancy  sharply reduced with the sample size of H desired from the posterior distri-  bution, almost reaching an asymptote by n = 25, the absolute error remains  considerably high even for n = 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' For a relatively longer yet considerably  short time series—N = 64, the absolute error reduces with the sample size of  H desired from the posterior distribution, reaching a lower asymptotic value  of < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 2, top right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' However, this discrepancy is still sufficient to mask  the typically observed differences in the Hurst exponent of empirical time series  across two groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' For instance, the Hurst exponent of stride-to-stride interval  time series during walking shows a difference of the order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1 across vari-  ous task conditions(e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', [42–44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' However, a discrepancy of the order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1 in  the estimation of H can potentially mask these differences, resulting in false  negatives in statistical tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The trend was comparable for time series with  N = 124 except for the absolute error reaching a lower asymptotic value of  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='05 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 2, middle left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  Bayesian method for estimating the Hurst exponent  7  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 1 The Hurst exponent, ˆ  H, estimated using the HK method closely matches  the actual H for time series containing as few as 128 values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Each panel plots the  Mean H for 1, 000 synthetic time series with N = 32, 64, 128, 256, 512, 1024, a priori known  values of H ranging from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='9, and the sample size of H desired from the posterior  distribution of H, n = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' , 25, 50, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' , 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Horizontal colored lines indicate the actual  H, and error bars indicate 95% CI across 1000 simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  When N = 256, the absolute error in the estimated ˆH falls within a much  lower range of tolerance (< 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='05) even with a very small sample of H from the  posterior distribution (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 2, middle right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Again, the absolute error sharply  reduces with n, reaching an even lower asymptotic value of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='04 by n = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Longer time series with N = 512 and N = 1024 also show similar trends  except for much lower asymptotic values of absolute error: < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='03 and < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='02,  respectively, by n = 25 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' 2, bottom left and bottom right, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' In  N = 32  N = 64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='8  HOOOH  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='6  <H  <H  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='1  5  5  n  n  N = 128  N = 256  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='6  H  H  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' 2 The absolute error in the estimation of the Hurst exponent,  ˆ  H, using  the HK method sharply reduced with the sample size of H desired from the  posterior distribution of H, reaching an asymptote at n = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' Each panel plots the Mean absolute error in the estimated H  for 1, 000 synthetic time series with N = 32, 64, 128, 256, 512, 1024, a priori known values of  H ranging from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' Error bars indicate 95% CI across 1000 simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  short, a relatively small sample size of H desired from the posterior distribu-  tion when using the accept-reject algorithm of the HKM suffices to estimate  ˆH with very high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='01  0  0  5  5  0  n  nSpringer Nature 2021 LATEX template  Bayesian method for estimating the Hurst exponent  9  Discussion  The HK method offers several advantages over DFA in estimating the Hurst  exponent of a time series [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' However, these advantages come at the cost of  computation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The HK method is computationally expensive owing to its  roots in the Bayesian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Computationally optimizing the HK method  for accurately estimating ˆH is, therefore, critical for promoting the adoption  of the HK method over DFA for estimating the Hurst exponent in behav-  ioral sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' To address this issue, we have provided data on the accuracy of  the Hurst exponent estimated using the HK method for synthetic time series  as a function of a priori known values of H, the time series length, and the  sample size of H from the posterior distribution of H—a parameter related  to the Bayesian estimation that critically influences the accuracy of ˆH and  computation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' The simulated sample from the posterior distribution of H  as small as n = 50 suffices to estimate the Hurst exponent with reasonable  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Using a larger simulated sample from the posterior distribution of  H—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', n > 50—provides only a marginal gain in accuracy, which might not  be worth trading off with computational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' We suggest balancing the  simulated sample size from the posterior distribution of H with the compu-  tational resources available to the user, preferring a minimum of n = 50 and  opting for larger sample sizes based on time and resource constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Our  results allow the reader to make such judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Empirical data pose several other issues that might undermine the accuracy  of H estimated using the HK method, such as strong trends [71–73], nonsta-  tionarities [71, 74], and “crossovers”—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', when correlations do not follow the  same scaling law for all timescales and a crossover is observed between different  scaling regions [49, 50, 75, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' However, because these anomalies, particularly  the crossovers, often appear at longer timescales, it seems reasonable to pro-  mote the systematic use of this method, irrespective of these reserves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Future  work could investigate how trends, nonstationarities, and crossovers influence  the estimation accuracy using the Bayesian approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  In summary, the HK method offers several advantages over DFA for esti-  mating the Hurst exponent of a time series, especially when it is short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' What  may prevent, however, the adoption of the HK method is significantly long  computation time, especially when analyzing time series containing several  hundred to thousands of measurements—which is frequently the case in behav-  ioral sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' To minimize the computation time of the HK method, we have  provided critical information for identifying the minimum simulated sample  from the posterior distribution of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' This information could aid the selection  of correct parameters that allow the estimation of H in real-time settings, such  as biofeedback paradigms and brain-computer interfaces, where computation  time is often limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  This work was supported by the Center for Research  in Human Movement Variability at the University of Nebraska at Omaha,  Springer Nature 2021 LATEX template  10  Bayesian method for estimating the Hurst exponent  the University of Nebraska Collaboration Initiative, the NSF award 212491,  the NIH awards P20GM109090 and R01NS114282, the NASA EPSCoR  mechanism, and the IARPA WatchID award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Author contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Conceptualization: M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Methodol-  ogy: M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=',  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  Declarations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='  The authors declare no competing financial interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' : Bodywide fluctuations support manual exploration: Fractal fluc-  tuations in posture predict perception of heaviness and length via  effortful touch by the hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' : Global broadcasting  of local fractal fluctuations in a bodywide distributed system supports  perception via effortful touch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Chaos, Solitons & Fractals 135, 109740  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' Human Movement Science  26(4), 555–589 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=': Gait instability and  fractal dynamics of older adults with a “cautious” gait: Why do cer-  tain older adults walk fearfully?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content=' Gait & Posture 21(2), 178–185 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
+page_content='gaitpost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=',  Likens,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=':  Leveraging  a  virtual  alley  with  con-  tinuously  varying  width  modulates  step  width  variability  during  self-paced treadmill walking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=' Neuroscience Letters 763, 136193  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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+page_content=': Gait variability  is altered in older adults when listening to auditory stimuli with differing  temporal structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/btFLT4oBgHgl3EQfYS80/content/2301.12064v1.pdf'}
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diff --git a/dtFJT4oBgHgl3EQf_i1w/content/tmp_files/2301.11695v1.pdf.txt b/dtFJT4oBgHgl3EQf_i1w/content/tmp_files/2301.11695v1.pdf.txt
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+LegendreTron: Uprising Proper Multiclass Loss Learning
+Kevin H. Lam
+University of New South Wales
+khflam@gmail.com
+Christian Walder
+Google Research
+cwalder@google.com
+Spiridon Penev
+University of New South Wales
+s.penev@unsw.edu.au
+Richard Nock
+Google Research
+richardnock@google.com
+Abstract
+Loss functions serve as the foundation of su-
+pervised learning and are often chosen prior to
+model development. To avoid potentially ad
+hoc choices of losses, statistical decision theory
+describes a desirable property for losses known
+as properness, which asserts that Bayes’ rule
+is optimal. Recent works have sought to learn
+losses and models jointly. Existing methods do
+this by fitting an inverse canonical link function
+which monotonically maps R to [0, 1] to estimate
+probabilities for binary problems. In this paper,
+we extend monotonicity to maps between RC−1
+and the projected probability simplex ˜∆C−1 by
+using monotonicity of gradients of convex func-
+tions. We present LegendreTron as a novel
+and practical method that jointly learns proper
+canonical losses and probabilities for multiclass
+problems. Tested on a benchmark of domains
+with up to 1,000 classes, our experimental re-
+sults show that our method consistently outper-
+forms the natural multiclass baseline under a
+t-test at 99% significance on all datasets with
+greater than 10 classes.
+1
+Introduction
+Loss functions are a pillar of machine learning (ML). In
+supervised learning, a loss provides a measure of discrep-
+ancy between the underlying ground truth and a model’s
+predictions. A learning algorithm attempts to minimise
+this discrepancy by adjusting the model. In other words,
+the loss governs how a model learns. The consequence
+of the bad choice of a loss is oblivious to the qualities of
+the learning pipeline: it means a poor model in the end.
+This brings forth the question: which loss is best for the
+problem at hand?
+Statistical decision theory answers this by turning to ad-
+missible losses [Savage, 1971]; also referred to as proper
+losses or proper scoring rules [Gneiting and Raftery, 2007].
+Proper losses are those for which the posterior expected
+loss value is minimised when probability predictions co-
+incide with the true underlying probabilities. That is, a
+proper loss is one that can induce probability estimates
+that are admissible or optimal. Proper losses have been
+extensively studied in Shuford et al. [1966], Gr¨unwald and
+Dawid [2004], Reid and Williamson [2010], Williamson
+et al. [2016], with the latter two works extending losses to
+proper composite forms in binary and multiclass settings.
+Only a handful of proper losses, such as the square and
+log losses, are commonly used in ML. This is not sur-
+prising: properness is an intensional property and does
+not provide any candidate function. While eliciting some
+members is possible, extending further requires tuning
+or adapting the loss as part of the ML task.
+There has been a recent surge of interest in doing so
+for supervised learning, including Mei and Moura [2018],
+Grabocka et al. [2019], Streeter [2019], Liu et al. [2020],
+Siahkamari et al. [2020], Sypherd et al. [2022]. However,
+no connections are made to properness to formulate the
+losses in these works. On the other hand, a series of
+recent works have used properness to formulate losses
+including Nock and Nielsen [2008], Nock and Menon
+[2020], Walder and Nock [2020].
+Notably, the latter
+two works have proposed algorithms to learn both the
+link function and linear predictor of logistic regression
+models by considering both functions to be unknown
+but learnable; thereby extending Single Index Models
+[Hardle et al., 1993, Mei and Moura, 2018] and algorithms
+designed to learn them [Kakade et al., 2011]. Despite the
+impressive progress in these works, no references have
+been made to proper losses for multiclass problems.
+Background
+To approach multiclass problems in a
+principled manner, we generalise logistic regression as
+follows. For a given invertible and monotonic (see Defi-
+nition A.1) link function ψ that maps [0, 1] to R and an
+input-label pair (x, y) with x ∈ Rp and y ∈ {−1, 1}, logis-
+tic regression learns a model of the form Pr(Y = 1|x) =
+ψ−1(w⊤x + b) by fitting a coefficient vector w ∈ Rp and
+an intercept b ∈ R. A class prediction is then formed
+as ˆy = arg maxy∈{−1,1} Pr(Y = y|x).
+The crucial el-
+ement of logistic regression lies in the invertible and
+monotonic link function that connects probabilities to
+predictors. Invertibility of the link allows one to identify
+a unique probability estimate to associate with the pre-
+dictor. Monotonicity of the link enforces an order to class
+predictions as elements of x either increase or decrease
+monotonically, so that the decision boundary between
+1
+arXiv:2301.11695v1  [stat.ML]  27 Jan 2023
+
+classes is unique. Loosely speaking, the generalisation of
+these ideas to multiclass problems with C ≥ 2 classes is
+to form probability estimates by using a monotonic link
+function ψ such that ψ−1(x) = (p1, p2, . . . , pC−1) with
+�C−1
+k=1 pk ≤ 1.
+Motivation
+To approach a multiclass problem with
+C > 2 classes, one would typically pose the problem as
+multiple 1-vs-rest or 1-vs-1 component problems. Each
+component problem consists of positive and negative la-
+bels where the former refers to a class of interest, and
+the latter refers to all other classes in 1-vs-rest or to a
+single other class of interest in 1-vs-1. An unfortunate
+consequence in the design of these reductions to binary
+problems is that they do not include the admissibility
+constraint that probability estimates should rank classes
+in the same way that true probabilities do. Without loss
+of generality to the 1-vs-1 approach, we observe this in
+the following theorem.
+Theorem 1.1. Suppose we use the 1-vs-rest approach to
+estimate probabilities for a multiclass problem with C > 2
+classes. Then we learn models of the form
+Pr( ˜Y = c|x) = ψ−1
+k (w⊤
+k x + bk)
+where c =
+�
++1
+when y = k
+−1
+otherwise
+for k = 1, . . . , C. Probabil-
+ity estimates for any class k is admissible if and only if
+ψ−1
+k (w⊤
+k x + bk) > ψ−1
+i
+(w⊤
+i x + bi) for all i ̸= k.
+To avoid solving C 1-vs-rest problems through con-
+strained optimisation, we desire an approach that allows
+us to model multiclass probabilities simultaneously, while
+learning proper multiclass losses which can induce admis-
+sible probability estimates for all C classes directly. We
+illustrate this can be done by modelling the canonical
+link function which connects probability estimates with
+a proper loss (see Definition 4.1 and remarks therein).
+In order to model canonical links flexibly, we form them
+as composite functions with a fixed component and a
+learnable component.
+Contributions
+Our main contributions are as follows:
+• We derive necessary and sufficient conditions for a
+composite function in RC−1 to be monotonic and the
+gradient of a twice-differentiable convex function;
+• We derive sufficient conditions for a composite func-
+tion in RC−1 to be monotonic and the gradient of a
+twice-differentiable strictly convex function;
+• We present LegendreTron as a novel and prac-
+tical way of learning proper canonical losses and
+probabilities concurrently in the multiclass problem
+setting.
+Organisation
+In Section 2, we review existing works
+which similarly aim to learn losses and models concur-
+rently. In Section 3, we first describe properness and
+proper canonical losses. In Section 4, we design multi-
+class canonical link functions through Legendre functions
+and the (u, v)-geometric structure, and provide conditions
+for composite functions to be monotonic and gradients of
+convex functions. We then describe our method, Legen-
+dreTron, in detail within Section 5. Lastly, numerical
+comparisons are provided in Section 6 before concluding
+in Section 7.
+2
+Related Work
+Tron family of link-learning algorithms
+The no-
+tion of searching for proper losses was first established
+within Nock and Nielsen [2008]. The SlIsotron algo-
+rithm was later presented in Kakade et al. [2011], as the
+first algorithm designed to learn a model of the form
+Pr(Y = 1|x) = u(w⊤x) for binary problems, which in-
+volves learning the unknown link function u : R → [0, 1]
+assumed to be 1-Lipschitz and non-decreasing, and the
+vector w ∈ Rp used to form the linear predictor w⊤x.
+The algorithm iterates between Lipschitz isotonic regres-
+sion to estimate u and gradient updates to estimate w. A
+notable and practical shortcoming of SlIsotron is that
+the isotonic regression steps to update u do not guarantee
+u to map to [0, 1]. The BregmanTron algorithm was
+later proposed in Nock and Menon [2020], to refine the
+SlIsotron algorithm by addressing this and providing
+convergence guarantees. By utilising the connection be-
+tween proper losses and their canonical link functions
+outlined in Section 4, the BregmanTron replaced the
+link function u with the inverse canonical link ˜ψ−1 which
+guaranteed probability estimates to lie in [0, 1].
+ISGP-Linkgistic algorithm
+The idea of using the
+(u, v)-geometric structure in combination with Legendre
+functions to learn canonical link functions has recently
+been explored in the work of Walder and Nock [2020]
+to propose the ISGP-Linkgistic algorithm to learn
+a model of the form Pr(Y = 1|x) = (u ◦ v−1)(w⊤x).
+By the squaring and integration of a Gaussian Process
+(GP) to yield the Integrated Squared Gaussian Process
+(ISGP), monotonicity and invertibility of v−1 : R → R is
+guaranteed. The ISGP-Linkgistic algorithm exploits
+this property by choosing a fixed squashing function u
+separate from the a priori ISGP distributed v−1. In-
+ference is performed with a stochastic EM algorithm
+where the E-step fixes the linear predictor w⊤x and ap-
+plies a Laplace approximation the latent GP to compute
+Eq(v−1|w)[log p(y|x, v−1)], and the M-step maximises this
+expectation with respect to w. The ISGP-Linkgistic
+algorithm takes a Bayesian approach to learning proper
+2
+
+canonical losses jointly with a probability estimator by
+posterior sampling of inverse canonical links.
+3
+Definitions and Properties of Losses
+In this section, we revisit the notions of proper losses to
+formulate proper canonical losses in the multiclass setting.
+We follow the definitions and notations of Williamson
+et al. [2016] and describe key properties therein, for our
+discussion of composite multiclass losses.
+Let C ≥ 2 as the total number of classes. Our setting is
+multiclass probability estimation. Denote the (C − 1)-
+dimensional probability simplex as
+∆C−1 =
+�
+p ∈ RC
++ :
+C
+�
+i=1
+pi = 1
+�
+,
+and its relative interior as
+ri(∆C−1) =
+�
+p ∈ RC
++ :
+C
+�
+i=1
+pi = 1, pi ∈ (0, 1), ∀i
+�
+.
+Suppose we have a dataset D of N pairs {(xn, yn)}N
+n=1
+where each xn ∈ X = Rp and yn ∈ Y = {1, . . . , C}
+denotes an input and a single label respectively. We
+aim to learn a function h : X → ∆C−1 such that ˆyn ∈
+arg maxc∈{1,...,C} P(yn = c|xn) closely matches yn.
+Consider
+the
+label
+as
+a
+random
+variable
+Y
+∼
+Categorical(p) with prior class probabilities p ∈ ∆C−1.
+We denote q ∈ ∆C−1 as the estimated probabilities in the
+following definitions. To assess the quality of probability
+estimates, a loss function can be defined generally as
+ℓ : ∆C−1 → RC
++,
+ℓ(q) = (ℓ1(q), . . . , ℓC(q))⊤
+where ℓi is the partial loss for predicting q when y = i.
+For a given label y, we can return to scalar-valued losses
+by referring to the y-th partial loss ℓy.
+Definition 3.1 (conditional Bayes Risk). The condi-
+tional risk associated with ℓ is defined as L(p, q) =
+EY ∼Categorical(p)[ℓY (q)] for all p, q ∈ ∆C−1.
+The best
+achievable conditional risk associated with a loss is termed
+the conditional Bayes risk and is defined as
+L :∆C−1 → R+,
+L(p) =
+inf
+q∈∆C−1 L(p, q) =
+inf
+q∈∆C−1 EY ∼Categorical(p)[ℓY (q)].
+It is well known that L is concave.
+Definition 3.2 (Proper Losses). A loss ℓ is proper if
+and only if L is minimized when q = p. In other words,
+L(p) = L(p, p) ≤ L(p, q) for all p, q ∈ ∆C−1. Losses
+where the inequality is strict when p ̸= q, are termed
+strictly proper losses.
+Remark
+Properness is an essential property of losses,
+as optimising a model with respect to a proper loss guides
+the model’s probability estimates towards true underly-
+ing prior class probabilities. Examples of proper losses
+include the square, log and Matsushita losses.
+To draw the connection between a proper loss and its con-
+ditional Bayes risk, we require definitions of subgradients
+and Bregman divergences.
+Subgradients are a gener-
+alisation of gradients and are particularly useful when
+analysing convex functions that may not be differentiable.
+Subgradients
+For a convex set S ⊆ Rn, the subdiffer-
+ential of a convex function f : S → (−∞, +∞] at x ∈ S
+is defined as
+∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ ≤ f(y) − f(x), ∀y ∈ Rn}
+where an element φ ∈ ∂f(x) is called a subgradient of
+f at x.
+By convention, we define ∂f(x) = ∅ for all
+x /∈ S.
+Moreover, f is strictly convex if and only if
+∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ < f(y) − f(x), ∀y ∈ Rn}.
+Bregman divergence
+For a convex set S ⊆ Rn, and a
+continuously-differentiable and strictly convex function f :
+S → (−∞, +∞], the Bregman divergence with generator
+f is defined for all x, y ∈ S as
+Df(x, y) = f(x) − f(y) − ⟨∇f(y), x − y⟩.
+The following result is a rewritten characterisation of
+proper losses through their “Bregman representation”,
+and explicates the connection between a proper loss and
+its conditional Bayes risk.
+Proposition 3.3 ([Williamson et al., 2016, Proposition
+7]). Let ℓ : ∆C−1 → RC
++ be a loss. ℓ is a (strictly) proper
+loss if and only if there exists a (strictly) convex function
+f : ∆C−1 → R such that for all q ∈ ∆C−1, there exists a
+subgradient φ ∈ ∂f(q) such that
+L(p, q) = −(p − q)⊤φ − f(q) for all p ∈ ∆C−1.
+Moreover, if L is differentiable on ri(∆C−1) then
+L(p, q) = (p − q)⊤ℓ(q) + L(q)
+where ℓ is the unique proper loss associated with L with
+the property ∇L(p) = ℓ(p), ∀p ∈ ri(∆C−1).
+Remark
+We note that L(p, q) is a Bregman divergence
+if and only if ℓ is strictly proper due to the requirement
+of strict convexity of f.
+In this work, we seek to learn strictly proper losses ℓ
+by exploiting the connection ∇L(p) = ℓ(p) described
+3
+
+in Proposition 3.3. In Section 4, we extend this con-
+nection between probabilities and predictors in RC−1
+through canonical link functions, and describe in detail
+how strictly proper losses can be learned through this
+extended connection.
+4
+Designing Multiclass Canonical Links
+In this section, we provide definitions of canonical link
+functions, Legendre functions and the (u, v)-geometric
+structure.
+The latter two structures are essential for
+the design and learning of canonical link functions. We
+show that designing a canonical link amounts to de-
+signing a composite function that is the gradient of a
+twice-differentiable and convex function. To this end, we
+present our key theoretical contributions: conditions for
+composite functions to be gradients of convex functions.
+Composite Form
+It is often desirable to link predic-
+tors with their probability estimates through an invert-
+ible link function ψ : ∆C−1 → RC. This allows one to
+uniquely identify probabilities while working with general
+predictors. It also allows one to define loss functions more
+generally as ℓψ = ℓ ◦ ψ−1 which are referred to as proper
+composite losses when ℓ is proper. Williamson et al. [2016,
+Proposition 13] shows that a proper composite loss ℓψ is
+uniquely represented by ℓ and ψ when ℓψ is continuous
+and invertible.
+Proper Canonical Form
+As elements of ∆C−1 are
+uniquely determined by the first C − 1 components, the
+above properties can be more naturally described by the
+projected probability simplex:
+˜∆C−1 =
+�
+˜p ∈ RC−1
++
+:
+C−1
+�
+i=1
+˜pi ≤ 1
+�
+.
+Define the projection map
+Π : ∆C−1 → ˜∆C−1,
+Π(p) = (p1, . . . , pC−1) for all p ∈ ∆C−1,
+and its inverse
+Π−1 : ˜∆C−1 → ∆C−1,
+Π−1(˜p) =
+�
+˜p1, . . . , ˜pC−1, 1 −
+C−1
+�
+i=1
+˜pi
+�
+for all ˜p ∈ ˜∆C−1.
+Definition 4.1. The projected conditional Bayes risk
+is defined as ˜L = L ◦ Π−1. Suppose ˜L is differentiable.
+Then the canonical link function is defined as
+˜ψ : ˜∆C−1 → RC−1,
+˜ψ(˜p) = −∇˜L(˜p).
+Williamson et al. [2016, Corollary 32] shows that given
+a proper loss ℓ, the function ℓ ◦ Π−1 ◦ ˜ψ−1 has com-
+ponents which are convex with respect to the input
+domain.
+We refer to such losses as proper canoni-
+cal losses to distinguish them from proper composite
+losses. The connection between a differentiable condi-
+tional Bayes risk, a proper loss, and a canonical link,
+shown by Proposition 3.3 and Definition 4.1, is given by
+ℓ = ∇L = −((−∇˜L ◦ Π) · JΠ) = −(( ˜ψ ◦ Π) · JΠ) where
+JΠ is the Jacobian of Π. This illustrates that one can
+learn proper canonical losses by modelling either the
+conditional Bayes risk or its associated canonical link.
+Properties of Legendre functions
+Let f : RC−1 →
+R be continuously differentiable and strictly convex. We
+refer to f as a Legendre function. The Legendre-Fenchel
+conjugate of f, denoted by f ∗, is defined as
+f ∗ : S → R,
+f ∗(x∗) = ⟨(∇f)−1(x∗), x∗⟩ − f
+�
+(∇f)−1(x∗)
+�
+.
+where S = {∇f(x) : x ∈ RC−1}, and f is Legendre if
+and only if f ∗ is Legendre. Rockafellar [1970, Theorem
+26.5] shows that when the latter holds, (f ∗)∗ = f, and
+∇f is continuous and invertible with ∇f ∗ = (∇f)−1.
+(u, v)-geometric structure
+Amari [2016], Nock et al.
+[2016], Walder and Nock [2020] state that a general dually
+flat structure on RC−1 can be defined in terms of an
+arbitrary strictly convex function ξ.
+Let u and v be
+differentiable invertible functions. The pair (u, v) give a
+dually flat structure on RC−1 if and only if ∇ξ = u ◦ v−1.
+We consider the (u, v)-geometric structure of the Bregman
+divergence D(−˜L)∗ which gives ˜ψ−1 = u ◦ v−1.
+Designing links
+In this work, we focus on the case
+when −˜L is differentiable. Note that −˜L is convex since
+Π−1 is affine and −L is convex. Properties of Legendre
+functions allow us to move from −˜L to its Legendre-
+Fenchel conjugate (−˜L)∗, and similarly allow us to move
+from the canonical link ˜ψ to its inverse ˜ψ−1. The (u, v)-
+geometric structure then allows us to flexibly learn ˜ψ−1
+by splitting it into a learnable component v−1 and a fixed
+component u. Fixing u to be a suitable squashing func-
+tion ensures that ˜ψ−1 maps to ˜∆C−1; thereby allowing
+us to uniquely identify multiclass probabilities associated
+with predictors from RC−1. On the other hand, v−1 can
+be parameterised by an invertible neural network which
+allows ˜ψ−1 to adapt to the multiclass problem at hand.
+Legendre functions and the (u, v)-geometric structure
+together yield a more natural and practical design of the
+canonical link through its inverse since it is often much
+easier to map inputs from an unbounded space such as
+RC−1, to a bounded space such as ˜∆C−1. Figure 1 illus-
+trates how the inverse of the canonical link is modelled
+4
+
+˜ψ−1
+v−1
+u
+probability estimates
+˜∆C−1
+predictors
+RC−1
+transformed predictors
+RC−1
+Figure 1. Relationship between predictors and probability es-
+timates through the inverse of the canonical link function
+under the (u, v)-geometric structure.
+using the (u, v)-geometric structure. Loosely speaking,
+v−1 allows one to find better logit representations before
+they are squashed to probabilities.
+Under the (u, v)-geometric structure, if one can prove
+that u ◦ v−1 maps to ˜∆C−1 and is the gradient of a
+Legendre function f, then one can set (−˜L)∗ = f and
+∇(−˜L)∗ = u ◦ v−1 as its corresponding inverse canoni-
+cal link function by using properties of Legendre func-
+tions. This requires showing u ◦ v−1 is the gradient of
+a twice-differentiable and strictly convex function. In
+the following two theorems, we provide conditions where
+this assertion holds for general composite functions. We
+defer the background, supporting theorems and proofs of
+the following results to Sections A, D and E within the
+Appendices.
+Theorem 4.2. Let f : RC−1 → RC−1 and g : RC−1 →
+RC−1 be differentiable. Then the following conditions are
+equivalent:
+1. f ◦ g = ∇F where F is a twice-differentiable convex
+function.
+2. The Jacobian Jf◦g(x) is symmetric for all x ∈ RC−1.
+3. Jf◦g(x) is positive semi-definite for all x ∈ RC−1.
+4. f ◦ g is monotone.
+Proof sketch of Theorem 4.2
+To claim that a func-
+tion f : RC−1 → RC−1 is the gradient of a convex func-
+tion g : RC−1 → R, requires f to satisfy maximal cyclical
+monotonicity. This is a more abstract notion of mono-
+tonicity within domains in higher dimensions, and en-
+compasses two notions of monotonicity, namely maximal
+monotonicity and cyclical monotonicity. It turns out
+that it is sufficient to consider monotonicity as maximal
+monotonicity is automatically guaranteed as our domain
+is RC−1.
+Theorem 4.2 characterises when a composite function
+is the gradient of a convex function. It also serves as
+a convenient and practical criteria to aid model design
+through a check of positive semi-definiteness for the Jaco-
+bian Jf◦g. The implications of Theorem 4.2 are profound
+as it allows us to derive the following sufficient condi-
+tions under which the composition of gradients of convex
+functions is the gradient of a Legendre function.
+Theorem 4.3. Let f : RC−1 → S and g : RC−1 → RC−1
+be differentiable where S ⊆ RC−1, and Jf(x) and Jg(x)
+are symmetric and positive definite for all x ∈ RC−1.
+Then f ◦g is the gradient of a twice-differentiable Legendre
+function.
+Proof sketch of Theorem 4.3
+Theorem 4.2 tells us
+it is sufficient to check for positive semi-definiteness of
+a composite function’s Jacobian. Our proof involves a
+check that all eigenvalues of the Jacobian are positive.
+This asserts that the composite function is the gradient
+of a twice-differentiable and strictly convex function.
+To use the (u, v)-geometric structure from Section 3 with
+Theorem 4.3, we can set f = u and g = v−1 within
+Theorem 4.3. This presents an additional requirement
+that the functions f and g are also invertible. In Section
+5, we show how these requirements can be met with our
+proposed algorithm, LegendreTron.
+5
+Learning Proper Canonical
+Multiclass Losses: LegendreTron
+In this section, we present LegendreTron, our main
+algorithmic contribution for learning proper canonical
+losses for multiclass probability estimation. With the
+theory of Legendre functions, (u, v)-geometric structure
+and Theorem 4.3 in hand to support our approach, we
+now present LegendreTron in detail, as an extension
+of Generalised Linear Models and Single Index Models
+for Multinomial Logistic Regression.
+Model
+Given a dataset D = {(xn, yn)}N
+n=1, we have
+the classification model
+yn|xn ∼ Categorical
+�
+ˆp(zn)
+�
+where zn = Wxn + b
+where W ∈ R(C−1)×p, b ∈ RC−1 and ˆp(zn) = (u ◦
+v−1)(zn) with u chosen as a squashing function that
+maps to ˜∆C−1 and v−1 = ∇g for a twice-differentiable
+and strictly convex function g. We leave the specification
+of a suitable squashing function u as a modelling choice
+and provide a natural choice at the end of this section.
+For any B ∈ Z+, let g1, g2, . . . gB be fully input convex
+neural networks (FICNN) investigated in Amos et al.
+[2017]. We set v−1 = ∇g = (∇g1) ◦ (∇g2) ◦ · · · ◦ (∇gB).
+For each gi, we use the same architecture as Huang et al.
+5
+
+[2021] which is described as
+zi,1 = l+
+i,1(x)
+zi,k = li,k(x) + l+
+i,k(s(zi,k−1)) for k = 2, . . . , M + 1,
+hi(x) = s(zi,M+1),
+gi(x) = s(wi,0)hi(x) + s(wi,1)∥x∥2
+2
+where we denote l+
+i,k as a linear layer with positive
+weights, li,k as a linear layer with unconstrained weights,
+wi,0, wi,1 ∈ R are unconstrained parameters and s(x) =
+log(1 + ex) is the softplus function with s(x) denoting
+the softplus function applied elementwise on x. In partic-
+ular, li,M+1 and l+
+i,M+1 are linear layers that map to R
+while for each k = 1, . . . M, li,k and l+
+i,k are hidden layers
+that map to RH for a chosen dimension size H ∈ Z+.
+With this setup, each gi is strongly convex (and therefore
+strictly convex) with an invertible gradient and positive
+definite Hessian for all x ∈ RC−1 due to the quadratic
+term within each gi.
+We conclude this section by showing that, equipped with
+a suitable squashing function u, any function learned by
+LegendreTron is a valid inverse canonical link function.
+We turn to a modified version of the LogSumExp function
+previously studied in Nielsen and Hadjeres [2018] and
+describe its main properties within the following theorem.
+Theorem 5.1. Let f(x) = log
+�
+1 + �C−1
+k=1 exp(xk)
+�
+.
+The key properties of f are:
+• f is strictly convex with invertible gradient
+u : RC−1 → ˜∆C−1,
+u(x) =
+�
+exp(xi)
+1 + �C−1
+k=1 exp(xk)
+�
+1≤i≤C−1
+.
+• the Hessian of f, given by Ju(x), is positive definite
+for all x ∈ RC−1.
+We refer to f and u as LogSumExp+ and softmax+ re-
+spectively. Let v−1 : RC−1 → RC−1 be defined as
+v−1 = (∇g1) ◦ (∇g2) ◦ · · · ◦ (∇gB)
+where g1, g2, . . . gB are FICNNs. Then any function u ◦
+v−1 learned by LegendreTron is the gradient of a
+twice-differentiable Legendre function and is therefore,
+the inverse of a canonical link function.
+With this specification, we can deduce that any function
+u ◦ v−1 learned via LegendreTron is the gradient of a
+twice-differentiable Legendre function which can serve as
+an inverse canonical link function. Algorithm 1 describes
+LegendreTron in detail.
+Algorithm 1 LegendreTron
+Input: sample S ⊂ D, number of iterations T, number
+of FICNNs B, hidden layer dimension size H, number
+of layers M, squashing function u.
+Initialise W and b.
+Initialise g1, g2, . . . gB each with M layers of dimension
+size H, and denote their joint set of parameters θ.
+for i = 1 to T do
+Set v−1 = (∇g1) ◦ (∇g2) ◦ · · · ◦ (∇gB).
+for each (xn, yn) ∈ S do
+Compute zn = Wxn + b.
+Compute ˆp(zn) = (u ◦ v−1)(zn).
+end for
+Compute ES[L(ˆp(z), y)] by Monte Carlo where L is
+the log-likelihood of the Categorical distribution.
+Update W, b and θ by backpropagation.
+end for
+Output: W, b and g1, g2, . . . gB.
+Remark
+We note that the specification of u remains
+as a modelling choice, and that its importance lies in
+the requirement that it yields a function u ◦ v−1 which
+maps to ˜∆C−1 and is the gradient of a twice-differentiable
+Legendre function. We have chosen softmax+ since it
+serves as the natural multiclass analogue of the classical
+sigmoid function.
+6
+Experiments
+In this section, we provide numerical comparisons be-
+tween LegendreTron, multinomial logistic regression
+and other existing methods that also aim to jointly learn
+models and proper canonical losses.
+Remark
+As LogSumExp+ is twice-differentiable and
+Legendre, its gradient softmax+ is a valid inverse canoni-
+cal link function since it maps to ˜∆C−1. However, we note
+that setting ˜ψ−1 = softmax+ results in learning only the
+parameters W and b which coincides with multinomial
+logistic regression and generalised linear models. Here
+˜ψ(˜p) =
+�
+˜pi
+1−�C−1
+k=1 ˜pk
+�
+1≤i≤C−1 with corresponding proper
+loss ℓ = −(( ˜ψ ◦ Π) · JΠ).
+For our experiments, we set softmax+ as the squashing
+function u for both LegendreTron and Multinomial
+Logistic Regression.
+For a practical and numerically
+stable implementation, we also map probability estimates
+to the log scale by deriving an alternate Log-Sum-Exp
+trick for softmax+. We defer the full experimental details
+to Appendix G. All experiments were performed using
+PyTorch [Paszke et al., 2019] and took roughly one CPU
+6
+
+Table 1. Test AUC for generalised linear models with various
+link methods (ordering in decreasing average). See text for
+details.
+MNIST FMNIST
+LegendreTron
+99.9%
+99.2%
+ISGP-Linkgistic
+99.9%
+99.2%
+GP-Linkgistic
+99.9%
+99.1%
+Logistic regression
+99.9%
+98.5%
+GLMTron
+99.6%
+98.1%
+BregmanTron
+99.7%
+97.9%
+BregmanTronlabel
+99.6%
+97.7%
+BregmanTronapprox 99.3%
+94.6%
+SlIsotron
+94.6%
+90.7%
+month to complete1.
+MNIST Binary Problems
+Binary problems are a
+special case of our setting where C = 2, so Legen-
+dreTron is readily applicable. In Table 1, we compared
+LegendreTron against ISGP-Linkgistic [Walder and
+Nock, 2020] and BregmanTron [Nock and Menon,
+2020], as both algorithms also aim to learn proper canon-
+ical losses for binary problems.
+We also compared
+with other baselines in these two works including the
+SlIsotron algorithm from Kakade et al. [2011]. Ex-
+periment details can be found in Section 6 of Nock and
+Menon [2020]. Our model successfully matches the (bi-
+nary specific) ISGP-Linkgistic baseline, which was the
+strongest algorithm in test AUC performance from the
+experiments of Walder and Nock [2020].
+MNIST Multiclass Problems
+For the three MNIST-
+like datasets [LeCun et al., 2010, Xiao et al., 2017,
+Clanuwat et al., 2018], we compared LegendreTron
+against multinomial logistic regression and ISGP-
+Linkgistic, since the latter is the strongest algorithm in
+ten-class classification test accuracy performance based
+on the experiments within Walder and Nock [2020].
+ISGP-Linkgistic approaches the multiclass problem
+by learning proper canonical losses for the 10 component
+1-vs-rest problems. Our experimental results in Figure
+2 show that LegendreTron and multinomial logistic
+regression outperform the ISGP-Linkgistic baseline on
+all three datasets. These results illustrate our conjecture
+that properness with respect to losses and models in com-
+ponent problems in a multiclass setting, does not imply
+optimality of class predictions or probability estimates.
+By respecting the true problem structure, proper multi-
+class losses allow the model to learn probability estimates
+1The total run time for our experiments is favourable
+relative to the reported two CPU months for the ISGP-
+Linkgistic algorithm from Walder and Nock [2020].
+that are able to better distinguish between all the classes
+at hand. Our results also show that LegendreTron
+either matches or outperforms multinomial logistic regres-
+sion on all three datasets. This is most notable on the
+Kuzushiji-MNIST dataset where LegendreTron out-
+performs multinomial logistic regression by a reasonable
+margin.
+Other Multiclass Problems and Label Noise
+We
+also compared LegendreTron against multinomial lo-
+gistic regression on 15 datasets that are publicly available
+from the LIBSVM library [Chang and Lin, 2011], the
+UCI machine learning repository [Asuncion and New-
+man, 2007, Dua and Graff, 2017], and the Statlog project
+[King et al., 1995]. We note that we did not compare
+our proposed method with other multiclass classification
+methods such as kernel methods explored in Zien and
+Ong [2007] and Li et al. [2018], as these methods are
+centred on the task of classification, whereas our focus
+is on jointly learning multiclass probabilities and proper
+canonical losses through the canonical link function. To
+assess the robustness against label noise, we also compare
+the classification accuracy of LegendreTron and multi-
+nomial logistic regression where labels in the training set
+are corrupted with probability η. That is, for any true
+label yn, we instead train our models on the potentially
+corrupted label given by
+˜yn =
+�
+yn
+with probability 1 − η,
+c
+with probability η where c ∈ Y \ {yn} .
+We applied symmetric label noise in our experiments
+which is the case where the probability of ˜yn = c for
+each c ∈ Y \ {yn} is
+η
+C−1. We run both LegendreTron
+and multinomial logistic regression for each dataset 20
+times, where each run randomly splits the dataset into
+80% training and 20% testing sets. Our results in Table
+2 show that LegendreTron outperforms multinomial
+logistic regression under a t-test at 99% significance for
+most datasets and label noise settings. The performance
+of LegendreTron is on par with multinomial logistic re-
+gression on the svmguide2, wine and iris datasets. Multi-
+nomial logistic regression only statistically outperforms
+LegendreTron on the dna dataset. LegendreTron
+consistently outperforms multinomial logistic regression
+especially strongly on problems where the number of
+classes is greater than 10. We conjecture this can be
+due to the greater expressiveness of logit representations
+induced by the diffeomorphism u ◦ v−1 learned by Leg-
+endreTron, and the sensitivity of multinomial logistic
+regression to noise and potential measurement errors.
+7
+
+10000
+20000
+30000
+40000
+50000
+60000
+60
+70
+80
+90
+Training Set Size
+Classification Accuracy (%)
+FMNIST / MLR
+KMNIST / MLR
+MNIST / MLR
+FMNIST / ISGP
+KMNIST / ISGP
+MNIST / ISGP
+FMNIST / LT
+KMNIST / LT
+MNIST / LT
+Figure 2. Test performance v.s. training set size for the MNIST, Kuzushiji-MNIST and Fashion-MNIST datasets. We compare
+the ten-class classification accuracy of LegendreTron (LT), multinomial logistic regression (MLR) and ISGP-Linkgistic
+(ISGP) where the ISGP combines 10 one-vs-rest binary models while the former two algorithms model the probabilities of all
+10 classes jointly.
+Table 2. Average test classification accuracies (%) for LegendreTron (LT) and multinomial logistic regression (MLR) on
+LIBSVM, UCI and Statlog datasets; at varying levels of label noise (η). Numbers of the method are bolded when it performs
+statistically better at a significance level of 99% under a t-test. Absence of bolding indicates both methods have statistically
+similar performance.
+Dataset
+# Features # Classes
+η = 0%
+η = 20%
+η = 50%
+LT
+MLR
+LT
+MLR
+LT
+MLR
+aloi
+128
+1,000
+88.11±0.03
+10.34±0.42
+83.03±0.06
+7.07±0.45
+75.23±0.07
+3.53±0.29
+sector
+55,197
+105
+89.71±0.18
+8.77±0.73
+81.00±0.28
+4.12±0.44
+57.38±0.31
+3.17±0.47
+letter
+16
+26
+79.82±0.30
+53.37±0.25
+74.17±0.21
+51.24±0.28
+64.28±0.26
+46.78±0.41
+news20
+62,061
+20
+75.65±0.72
+63.09±0.58
+73.48±0.20
+50.49±1.16
+51.72±0.16
+31.54±1.83
+Sensorless
+48
+11
+88.31±0.19
+34.42±0.46
+82.63±0.99
+32.70±0.50
+52.02±0.78
+29.35±0.84
+vowel
+10
+11
+79.72±1.03
+44.58±1.08
+63.77±1.36
+43.44±1.17
+40.94±1.61
+35.42±1.45
+usps
+256
+10
+95.23±0.16
+93.79±0.17
+92.88±0.15
+92.95±0.19
+90.23±0.26
+90.48±0.27
+segment
+19
+7
+95.95±0.24
+87.86±0.40
+92.21±0.40
+87.28±0.40
+86.56±0.47
+82.75±0.46
+satimage
+36
+6
+86.97±0.19
+83.93±0.28
+84.93±0.25
+81.16±0.28
+77.44±0.29
+77.39±0.29
+glass
+36
+6
+58.72±1.94
+52.09±1.88
+53.72±1.98
+50.47±2.11
+42.56±1.92
+45.47±1.67
+vehicle
+18
+4
+76.91±0.65
+64.94±0.43
+73.59±0.79
+63.06±0.53
+60.94±1.25
+55.18±1.20
+dna
+180
+3
+92.79±0.30
+94.43±0.19
+82.61±0.51
+89.55±0.31
+58.23±1.05
+64.18±0.81
+svmguide2
+20
+3
+56.01±1.40
+56.01±1.40
+56.01±1.40
+56.01±1.40
+51.65±2.81
+52.41±3.04
+wine
+13
+3
+96.94±1.14
+97.78±0.59
+90.97±1.92
+96.25±0.99
+69.44±2.89
+77.36±2.46
+iris
+4
+3
+86.67±3.89
+83.00±2.08
+80.00±3.71
+81.50±2.27
+63.50±5.13
+70.67±3.83
+8
+
+7
+Conclusion
+In this work, we proposed a general approach which
+jointly learns proper canonical losses and multiclass prob-
+abilities. Our contributions advance the recent work on
+learning losses with probabilities based on the seminal
+work within Kakade et al. [2011], Nock and Menon [2020],
+Walder and Nock [2020] by providing a natural exten-
+sion to the multiclass setting. The practical nature and
+generality of our model is owed to the general parame-
+terisation of Fully Input Convex Neural Networks, with
+theoretical support from Legendre functions, structures
+from information geometry and hallmark results from
+convex analysis.
+By grounding losses in properness for the multiclass set-
+ting, we have demonstrated that our model improves
+upon existing methods that aim to solve multiclass prob-
+lems through binary reductions, and also outperforms the
+natural baseline of multinomial logistic regression. Sepa-
+rately, we have also provided conditions under which a
+composition of gradients of differentiable convex functions
+is the gradient of another differentiable convex function.
+We anticipate that our results will find applications in
+multiclass classification and probability estimation, as
+well as variational inference.
+References
+Shun´ıchi Amari. Information geometry and its applica-
+tions, volume 194. Springer, 2016.
+Brandon Amos, Lei Xu, and J. Zico Kolter. Input convex
+neural networks. In Doina Precup and Yee Whye Teh,
+editors, Proceedings of the 34th International Confer-
+ence on Machine Learning, volume 70 of Proceedings
+of Machine Learning Research, pages 146–155. PMLR,
+06–11 Aug 2017.
+Edgar Asplund. A monotone convergence theorem for
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+10
+
+A
+Convex Analysis: Relevant Background and List of Theorems
+A.1
+Background
+To motivate the results studied in this section, we first note that in general, the composition of two monotone
+functions in RC−1 is not necessarily another monotone function in RC−1. This means that methods to design
+monotonic functions in R cannot be applied to functions defined on RC−1, leaving the methods discussed in Section 2
+unsuitable for the general multiclass setting. Separately, we note that the composition of two gradients of differentiable
+convex functions is not necessarily the gradient of another convex function. In general, to claim that a function
+f : RC−1 → RC−1 is the gradient of a convex function g : RC−1 → R, requires f to satisfy a notion of monotonicity
+generalised to higher dimensions. The connection between convex functions and their gradients is well known in
+convex analysis via the notion of maximal cyclically monotone functions. This is a combination of two notions
+of monotonicity: maximal monotonicity and cyclical monotonicity. These are defined within the following list of
+definitions and theorems.
+A.2
+List of Theorems
+Definition A.1 ([Rockafellar et al., 2009, Definition 12.1]). A function f : RC−1 → RC−1 is monotone if ⟨f(x) −
+f(z), x − z⟩ ≥ 0 for all x, z ∈ RC−1. Moreover, it is strictly monotone when the inequality is strict whenever x ̸= z.
+The following two definitions require the notion of the graph of a function f : RC−1 → RC−1 which is defined as
+gph(f) = {(x, y) : x ∈ RC−1, y ∈ f(x)}.
+Definition A.2 ([Bauschke and Combettes, 2011, Definition 20.20]). Let f : RC−1 → RC−1 be a monotone function.
+Then f is maximally monotone if there exists no monotone function g : RC−1 → RC−1 such that gph(f) ⊊ gph(g).
+Definition A.3 ([Bauschke and Combettes, 2011, Definition 22.10]). Let f : RC−1 → RC−1. For an arbitrary integer
+n ≥ 2, f is n-cyclically monotone if for any {(xi, yi)}i=1,...,n ⊂ gph(f) it follows that
+n
+�
+i=1
+⟨yi, xi+1 − xi⟩ ≤ 0 where xn+1 = x1.
+f is cyclically monotone if it is n-cyclically monotone for any integer n ≥ 2. In addition, if gph(f) ̸⊂ gph(g) for any
+cyclically monotone function g ̸= f then f is maximal cyclically monotone.
+Theorem A.4 ([Rockafellar et al., 2009, Theorems 12.17 & 12.25]). Let f : RC−1 → RC−1. Then f = ∇h for a
+differentiable convex function h : RC−1 → R if and only if f is maximal cyclically monotone. That is, f is maximally
+monotone and cyclically monotone.
+Theorem A.5 ([Rockafellar et al., 2009, Proposition 12.3]). Let f : RC−1 → RC−1 be a differentiable function. Then
+f is monotone if and only if ∇f(x) is positive semi-definite for all x ∈ RC−1. Moreover, if ∇f(x) is positive definite
+for all x ∈ RC−1 \ {0} then f is strictly monotone.
+Theorem A.6 ([Bauschke and Combettes, 2011, Theorem 21.1, Minty’s Theorem]). Let f : RC−1 → RC−1 be a
+monotone function. Then f is maximal monotone if and only if range(Id + f) = RC−1 where Id is the identity
+function.
+Theorem A.7 ([Borwein and Wiersma, 2007, Theorem 3]). Let f : RC−1 → RC−1 be maximally monotone and
+continuously differentiable. Then f(x) = ∇F(x) + Lx where F is a differentiable convex function, and L is a skew
+symmetric matrix.
+Theorem A.8 ([Meenakshi and Rajian, 1999, Theorem 3]). Let A, B ∈ R(C−1)×(C−1) be symmetric and positive
+semi-definite matrices. Then AB is positive semi-definite if and only if it is symmetric.
+Theorem A.9 ([Bhatia, 2013, Theorem VIII.4.6]). Let V ⊂ R(C−1)×(C−1) be a real vector space whose elements are
+matrices with real eigenvalues. Denote λi(M) as the i-th smallest eigenvalue for any matrix M ∈ V . Let A, B ∈ V
+then
+λi(A) + λ1(B) ≤ λi(A + B) ≤ λi(A) + λC−1(B).
+11
+
+A.3
+Remarks
+Theorem A.4 serves as a criterion and characterisation of differentiable convex functions through their gradients.
+Theorems A.6 to A.8 are hallmark results from the rich literature of convex analysis and monotone operators that tie
+together conditions under which a differentiable composite function is the gradient of a convex function. Notably,
+Theorem A.7 is a rewritten version of the Asplund decomposition of maximal monotone operators [Asplund, 1968]
+which tells us it suffices to focus on maximal monotonicity. We refer the reader to Appendix D for the usage of
+Theorems A.5 to A.8 in the proof of Theorem 4.2.
+Theorem A.9 allows us to obtain a lower bound on the smallest eigenvalue of the sum of two real-valued matrices
+with real eigenvalues. This is particularly useful to prove positive definiteness in Theorem 4.3. We refer the reader to
+Appendix E for its usage in the proof of Theorem 4.3.
+B
+Proof of equivalent conditions on subdifferentials for strictly convex functions
+(⇒) Suppose f is strictly convex and assume for a proof by contradiction that there exists some x, y ∈ domf such
+that x ̸= y with f(x) + ⟨φ, y − x⟩ ≥ f(y) for some φ ∈ ∂f(x).
+Fix λ ∈ (0, 1). Then we have
+f(x) + ⟨φ, (λx + (1 − λ)y) − x⟩ = f(x) + (1 − λ)⟨φ, y − x⟩
+≤ f(λx + (1 − λ)y) by definition of a subgradient
+< λf(x) + (1 − λ)f(y) by strict convexity of f
+≤ f(x) + (1 − λ)⟨φ, y − x⟩ by the above assumption.
+Thus, we have a contradiction so we must have the subdifferential of f for all x ∈ domf is given by
+∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ < f(y) − f(x), ∀y ∈ Rn} .
+(⇐) Suppose the subdifferential of f for any x ∈ domf is given by
+∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ < f(y) − f(x), ∀y ∈ Rn} .
+Fix x, y ∈ domf and λ ∈ (0, 1). Consider φ ∈ ∂f(λx + (1 − λ)y). Then we have
+f(λx + (1 − λ)y) + (1 − λ)⟨φ, x − y⟩ < f(x),
+f(λx + (1 − λ)y) + λ⟨φ, y − x⟩ < f(y).
+Multiplying the first inequality by λ and the second by (1 − λ), summing them gives us f(λx + (1 − λ)y) <
+λf(x) + (1 − λ)f(y). This holds for arbitrary x, y ∈ domf and λ ∈ (0, 1) so it follows that f is strictly convex.
+C
+Proof of Proposition 3.3
+(⇒) Fix q ∈ ∆C−1. Suppose ℓ is proper. Then we have
+L(p, q) = p⊤ℓ(q) = q⊤ℓ(q) + (p − q)⊤ℓ(q) = L(q) + (p − q)⊤ℓ(q)
+and also,
+0 ≤ L(p, q) − L(p, p) = L(q) + (p − q)⊤ℓ(q) − L(p)
+=⇒ −(p − q)⊤ℓ(q) ≤ −L(p) − (−L(q)).
+Recall that L is concave so it follows that −L is convex. Hence, −ℓ(q) ∈ ∂(−L)(q) which means −ℓ(q) is a subgradient
+of −L at q and L(p, q) = −(−L(q)) − (p − q)⊤(−ℓ(q)).
+(⇐) Suppose there exists a convex function f : ∆C−1 → R such that for all q ∈ ∆C−1, there exists a subgradient
+φ ∈ ∂f(q) and L(p, q) = −f(q) − (p − q)⊤φ.
+12
+
+For all p ∈ ∆C−1, we have
+L(p, q) − L(p, p) = f(p) − f(q) − (p − q)⊤φ
+≥ 0 since φ is a subgradient of f at q
+=⇒ L(p, p) ≤ L(p, q).
+Hence, ℓ is a proper loss.
+To prove that ℓ is strictly proper if and only if there exists a strictly convex function f : ∆C−1 → R such that for all
+q ∈ ∆C−1, there exists a subgradient φ ∈ ∂f(q) such that L(p, q) = −(p − q)⊤φ − f(q) for all p ∈ ∆C−1. This follows
+immediately by definitions of strictly proper losses and subdifferentials from which the above inequalities become
+strict.
+We are left to prove that L(p, q) = (p − q)⊤ℓ(q) + L(q) when L is differentiable. We first note that L is concave so
+−L is convex. Recall that L(p, q) = p⊤ℓ(q) = L(q) + (p − q)⊤ℓ(q) from the workings within Appendix C. Setting
+f = −L for Proposition 3.3, we can deduce −ℓ(q) = −∇L(q)∀q ∈ ri(∆C−1) for a proper loss ℓ which follows by the
+uniqueness of subgradients for differentiable functions. That is, ∇L(q) = ℓ(q), ∀q ∈ ri(∆C−1).
+D
+Proof of Theorem 4.2
+(1) =⇒ (2). This follows from Schwarz’s theorem on the equality of mixed partial derivatives. (2) =⇒ (3). This
+follows from Theorem A.8 since the Jacobian of a composite function is a product of matrices. (3) =⇒ (4). This
+follows from Theorem A.5. We are left to prove (4) =⇒ (1).
+(4) =⇒ (1). As range(Id + f ◦ g) = RC−1, it follows from Theorem A.6 that f ◦ g is maximally monotone. From
+Theorem A.7, (f ◦ g)(x) = ∇F(x) + Lx for a differentiable convex function F and a skew-symmetric matrix L. Since
+f ◦ g is differentiable then it follows that F is twice-differentiable. This gives us Jf◦g = ∇2F + L⊤ where ∇2F is
+symmetric by Schwarz’s theorem on the equality of mixed partial derivatives. Theorems A.5 and A.8 tells us that
+Jf◦g is also symmetric. As Jf◦g and ∇2F are both symmetric, then we must have L⊤ = 0 = L. That is, f ◦ g = ∇F
+where F is twice-differentiable and convex.
+E
+Proof of Theorem 4.3
+Fix x ∈ RC−1. The Jacobian of f ◦ g is given by
+Jf◦g(x) = Jf(g(x))Jg(x).
+Here we aim to prove that Jf◦g(x) is positive definite. We first note that Jg(x) is invertible since |Jg(x)| > 0. Now,
+note that Jf◦g(x) is similar to the matrix
+(Jg(x))
+1
+2 Jf(g(x))Jg(x)(Jg(x))− 1
+2 = (Jg(x))
+1
+2 Jf(g(x))(Jg(x))
+1
+2
+where the square root of the matrix Jg(x) is given by (Jg(x))
+1
+2 which is known to be symmetric since Jg(x) is symmetric
+and positive definite. Since Jf(g(x)) is also symmetric, it follows that (Jg(x))
+1
+2 Jf(g(x))(Jg(x))
+1
+2 is symmetric. As
+Jg(x) and Jf(g(x)) are positive definite, we have
+���(Jg(x))
+1
+2 Jf(g(x))(Jg(x))
+1
+2
+��� = |Jf(g(x))| |(Jg(x))| > 0.
+It follows that (Jg(x))
+1
+2 Jf(g(x))(Jg(x))
+1
+2 is positive definite, meaning it has positive eigenvalues λ1, . . . , λC−1 ∈ R
+that can be denoted such that λ1 ≤ λ2 ≤ · · · ≤ λC−1. Since similar matrices have the same eigenvalues, it follows
+that λ1, . . . , λC−1 are also the eigenvalues of Jf◦g(x).
+Denote S = 1
+2(Jf◦g(x) + (Jf◦g(x))⊤) and A = 1
+2(Jf◦g(x) − (Jf◦g(x))⊤) as the symmetric and skew-symmetric parts
+of Jf◦g(x) respectively. It is well known that for any skew-symmetric matrix A and any z ∈ RC−1, we have z⊤Az = 0.
+To prove that Jf◦g(x) is positive definite, it suffices to prove that z⊤Jf◦g(x)z = z⊤Sz > 0 for any z ∈ RC−1 \ {0}.
+Firstly, recall that all eigenvalues of Jf◦g(x) are real and positive, and the fact that the transpose of Jf◦g(x),
+(Jf◦g(x))⊤, has the same eigenvalues as Jf◦g(x). That is, all eigenvalues of (Jf◦g(x))⊤ are real and positive. Secondly,
+13
+
+S = 1
+2(Jf◦g(x) + (Jf◦g(x))⊤) is symmetric so all of its eigenvalues must be real. Hence, Theorem A.9 gives us the
+following bound for the smallest eigenvalue λ1(S)
+λ1(S) ≥ λ1
+�1
+2Jf◦g(x)
+�
++ λ1
+�1
+2(Jf◦g(x))⊤
+�
+= 1
+2
+�
+λ1(Jf◦g(x)) + λ1((Jf◦g(x))⊤)
+�
+> 0.
+The Rayleigh quotient for S and any z ∈ RC−1 \ {0}, is given by z⊤Sz
+∥z∥2 , and satisfies the inequality
+λ1(S) ≤ z⊤Sz
+∥z∥2 ≤ λC−1(S).
+Hence, we have
+z⊤Sz
+∥z∥2 ≥ λ1(S) > 0 for all z ∈ RC−1 \ {0} .
+Thus, z⊤Jf◦g(x)z = z⊤Sz > 0, ∀z ∈ RC−1 \{0} and so, Jf◦g(x) is positive definite. This holds for arbitrary x ∈ RC−1
+so it follows that f ◦ g is the gradient of a twice-differentiable convex function F by Theorem 4.2 with F being
+strictly convex since Jf◦g(x) is positive definite. In other words, f ◦ g is the gradient of a twice-differentiable Legendre
+function.
+F
+Proof of Theorem 5.1
+Proof of Properties of LogSumExp+ and softmax+
+Since positive definiteness of Ju(x) for all x ∈ RC−1
+implies strict convexity of f and strict convexity of f implies invertibility of u, it suffices to prove that Ju(x) is
+positive definite for all x ∈ RC−1.
+Fix x ∈ RC−1. For ease of notation, we denote M as Ju(x) where Mij refers to the entry within the i-th row and
+j-th column of Ju(x). Consider any row i ∈ {1, . . . , C − 1}. We have
+Mii =
+exp(xi)
+1 + �C−1
+k=1 exp(xk)
+�
+1 −
+exp(xi)
+1 + �C−1
+k=1 exp(xk)
+�
+,
+Mij = −
+exp(xi)
+1 + �C−1
+k=1 exp(xk)
+exp(xj)
+1 + �C−1
+k=1 exp(xk)
+.
+Observe that Mii−�
+j̸=i |Mij| =
+exp(xi)
+1+�C−1
+k=1 exp(xk)
+�
+1 −
+�C−1
+k=1 exp(xk)
+1+�C−1
+k=1 exp(xk)
+�
+> 0. This holds for arbitrary i ∈ {1, . . . , C −1}
+so it follows that Ju(x) is strictly diagonally dominant. This implies that Ju(x) is positive definite so it follows that
+f is strictly convex. This completes the proof of the key properties of the LogSumExp+ function and its gradient
+softmax+.
+Proof of functions learned by LegendreTron are inverse canonical links
+We first note that v−1 = (∇g1) ◦
+(∇g2) ◦ · · · ◦ (∇gB) is indeed invertible since the RHS is invertible by the strong convexity of g1, g2, . . . , gB. Since
+each ∇gi is symmetric and positive definite, it follows that v−1 is the gradient of a twice-differentiable Legendre
+function by applying Theorem 4.3 recursively. It follows from Theorem 4.2 that Jv−1(x) is symmetric. We also have
+that |Jv−1(x)| > 0 so Jv−1(x) is positive definite for all x ∈ RC−1.
+Recall that LogSumExp+ is twice-differentiable with gradient u = softmax+ and Hessian Ju(x) being strictly
+diagonally dominant. That is, Ju(x) is symmetric and positive definite. Applying Theorem 4.3 on u ◦ v−1 allows us
+to deduce that u ◦ v−1 is the gradient of a twice-differentiable Legendre function that maps to ˜∆C−1 so u ◦ v−1 can
+be set as the inverse of an implicit canonical link function.
+14
+
+G
+Experimental Details
+G.1
+Network Architecture and Optimisation Details
+Experiment details on architecture and optimisation parameters for LegendreTron (LT) and multinomial logistic
+regression (MLR). Here we denote α as the learning rate, λ as weight decay, γ as the multiplicative rate of decay
+applied to α every S epochs through a step-wise learning rate scheduler. We used the Adam optimiser for all
+experiments.
+Dataset(s)
+Model B H M
+α
+γ
+S Epochs Batch Size
+MNIST/FMNIST/KMNIST
+LT
+1
+4
+4
+0.001
+0.7
+4
+200
+128
+MNIST/FMNIST/KMNIST
+MLR
+\
+\
+\
+0.001
+0.7
+4
+200
+128
+aloi
+LT
+2
+2
+4
+0.01
+0.95 4
+360
+64
+aloi
+MLR
+\
+\
+\
+0.01
+0.95 4
+360
+64
+LIBSVM/UCI/Statlog (other datasets)
+LT
+2
+2
+4
+0.01
+0.95 4
+240
+64
+LIBSVM/UCI/Statlog (other datasets)
+MLR
+\
+\
+\
+0.01
+0.95 4
+240
+64
+G.2
+LogSumExp trick for softmax+
+Let u = softmax+ and consider x ∈ RC−1. We have
+log(Π−1(u(x))) =
+�
+log
+�
+exp(x1)
+1 + �C−1
+k=1 exp(xk)
+�
+, . . . , log
+�
+exp(xC−1)
+1 + �C−1
+k=1 exp(xk)
+�
+, log
+�
+1
+1 + �C−1
+k=1 exp(xk)
+��⊤
+where log on the LHS is applied elementwise. We seek an alternate expression for log(Π−1(u(x))) that is numerically
+stable.
+Let x∗ = max(x1, . . . , xC−1) and S = exp(−x∗) + �C−1
+k=1 exp(xk − x∗). We can write
+log(Π−1(u(x))) =
+�
+log
+�exp(x1 − x∗)
+S
+�
+, . . . , log
+�exp(xC−1 − x∗)
+S
+�
+, log
+�exp(−x∗)
+S
+��⊤
+= (x1 − x∗ − log(S), . . . , xC−1 − x∗ − log(S), −x∗ − log(S))⊤ .
+It can be observed that this expression is numerically stable for any large values of x∗.
+15
+
diff --git a/dtFJT4oBgHgl3EQf_i1w/content/tmp_files/load_file.txt b/dtFJT4oBgHgl3EQf_i1w/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2a72d7c98c7862e2d88b312add55c0a62061512e
--- /dev/null
+++ b/dtFJT4oBgHgl3EQf_i1w/content/tmp_files/load_file.txt
@@ -0,0 +1,981 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf,len=980
+page_content='LegendreTron: Uprising Proper Multiclass Loss Learning  Kevin H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Lam  University of New South Wales  khflam@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='com  Christian Walder  Google Research  cwalder@google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='com  Spiridon Penev  University of New South Wales  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='penev@unsw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='au  Richard Nock  Google Research  richardnock@google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='com  Abstract  Loss functions serve as the foundation of su-  pervised learning and are often chosen prior to  model development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' To avoid potentially ad  hoc choices of losses, statistical decision theory  describes a desirable property for losses known  as properness, which asserts that Bayes’ rule  is optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Recent works have sought to learn  losses and models jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Existing methods do  this by fitting an inverse canonical link function  which monotonically maps R to [0, 1] to estimate  probabilities for binary problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In this paper,  we extend monotonicity to maps between RC−1  and the projected probability simplex ˜∆C−1 by  using monotonicity of gradients of convex func-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We present LegendreTron as a novel  and practical method that jointly learns proper  canonical losses and probabilities for multiclass  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Tested on a benchmark of domains  with up to 1,000 classes, our experimental re-  sults show that our method consistently outper-  forms the natural multiclass baseline under a  t-test at 99% significance on all datasets with  greater than 10 classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  1  Introduction  Loss functions are a pillar of machine learning (ML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In  supervised learning, a loss provides a measure of discrep-  ancy between the underlying ground truth and a model’s  predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A learning algorithm attempts to minimise  this discrepancy by adjusting the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In other words,  the loss governs how a model learns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The consequence  of the bad choice of a loss is oblivious to the qualities of  the learning pipeline: it means a poor model in the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  This brings forth the question: which loss is best for the  problem at hand?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Statistical decision theory answers this by turning to ad-  missible losses [Savage, 1971];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' also referred to as proper  losses or proper scoring rules [Gneiting and Raftery, 2007].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Proper losses are those for which the posterior expected  loss value is minimised when probability predictions co-  incide with the true underlying probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, a  proper loss is one that can induce probability estimates  that are admissible or optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Proper losses have been  extensively studied in Shuford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [1966], Gr¨unwald and  Dawid [2004], Reid and Williamson [2010], Williamson  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2016], with the latter two works extending losses to  proper composite forms in binary and multiclass settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Only a handful of proper losses, such as the square and  log losses, are commonly used in ML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This is not sur-  prising: properness is an intensional property and does  not provide any candidate function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' While eliciting some  members is possible, extending further requires tuning  or adapting the loss as part of the ML task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  There has been a recent surge of interest in doing so  for supervised learning, including Mei and Moura [2018],  Grabocka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2019], Streeter [2019], Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2020],  Siahkamari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2020], Sypherd et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' However,  no connections are made to properness to formulate the  losses in these works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' On the other hand, a series of  recent works have used properness to formulate losses  including Nock and Nielsen [2008], Nock and Menon  [2020], Walder and Nock [2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Notably, the latter  two works have proposed algorithms to learn both the  link function and linear predictor of logistic regression  models by considering both functions to be unknown  but learnable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' thereby extending Single Index Models  [Hardle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 1993, Mei and Moura, 2018] and algorithms  designed to learn them [Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2011].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Despite the  impressive progress in these works, no references have  been made to proper losses for multiclass problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Background  To approach multiclass problems in a  principled manner, we generalise logistic regression as  follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' For a given invertible and monotonic (see Defi-  nition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1) link function ψ that maps [0, 1] to R and an  input-label pair (x, y) with x ∈ Rp and y ∈ {−1, 1}, logis-  tic regression learns a model of the form Pr(Y = 1|x) =  ψ−1(w⊤x + b) by fitting a coefficient vector w ∈ Rp and  an intercept b ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A class prediction is then formed  as ˆy = arg maxy∈{−1,1} Pr(Y = y|x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The crucial el-  ement of logistic regression lies in the invertible and  monotonic link function that connects probabilities to  predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Invertibility of the link allows one to identify  a unique probability estimate to associate with the pre-  dictor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Monotonicity of the link enforces an order to class  predictions as elements of x either increase or decrease  monotonically, so that the decision boundary between  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='11695v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='ML]  27 Jan 2023  classes is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Loosely speaking, the generalisation of  these ideas to multiclass problems with C ≥ 2 classes is  to form probability estimates by using a monotonic link  function ψ such that ψ−1(x) = (p1, p2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , pC−1) with  �C−1  k=1 pk ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Motivation  To approach a multiclass problem with  C > 2 classes, one would typically pose the problem as  multiple 1-vs-rest or 1-vs-1 component problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Each  component problem consists of positive and negative la-  bels where the former refers to a class of interest, and  the latter refers to all other classes in 1-vs-rest or to a  single other class of interest in 1-vs-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' An unfortunate  consequence in the design of these reductions to binary  problems is that they do not include the admissibility  constraint that probability estimates should rank classes  in the same way that true probabilities do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Without loss  of generality to the 1-vs-1 approach, we observe this in  the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Suppose we use the 1-vs-rest approach to  estimate probabilities for a multiclass problem with C > 2  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then we learn models of the form  Pr( ˜Y = c|x) = ψ−1  k (w⊤  k x + bk)  where c =  �  +1  when y = k  −1  otherwise  for k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Probabil-  ity estimates for any class k is admissible if and only if  ψ−1  k (w⊤  k x + bk) > ψ−1  i  (w⊤  i x + bi) for all i ̸= k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  To avoid solving C 1-vs-rest problems through con-  strained optimisation, we desire an approach that allows  us to model multiclass probabilities simultaneously, while  learning proper multiclass losses which can induce admis-  sible probability estimates for all C classes directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We  illustrate this can be done by modelling the canonical  link function which connects probability estimates with  a proper loss (see Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1 and remarks therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  In order to model canonical links flexibly, we form them  as composite functions with a fixed component and a  learnable component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Contributions  Our main contributions are as follows:  We derive necessary and sufficient conditions for a  composite function in RC−1 to be monotonic and the  gradient of a twice-differentiable convex function;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We derive sufficient conditions for a composite func-  tion in RC−1 to be monotonic and the gradient of a  twice-differentiable strictly convex function;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We present LegendreTron as a novel and prac-  tical way of learning proper canonical losses and  probabilities concurrently in the multiclass problem  setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Organisation  In Section 2, we review existing works  which similarly aim to learn losses and models concur-  rently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Section 3, we first describe properness and  proper canonical losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Section 4, we design multi-  class canonical link functions through Legendre functions  and the (u, v)-geometric structure, and provide conditions  for composite functions to be monotonic and gradients of  convex functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We then describe our method, Legen-  dreTron, in detail within Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Lastly, numerical  comparisons are provided in Section 6 before concluding  in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  2  Related Work  Tron family of link-learning algorithms  The no-  tion of searching for proper losses was first established  within Nock and Nielsen [2008].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The SlIsotron algo-  rithm was later presented in Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2011], as the  first algorithm designed to learn a model of the form  Pr(Y = 1|x) = u(w⊤x) for binary problems, which in-  volves learning the unknown link function u : R → [0, 1]  assumed to be 1-Lipschitz and non-decreasing, and the  vector w ∈ Rp used to form the linear predictor w⊤x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The algorithm iterates between Lipschitz isotonic regres-  sion to estimate u and gradient updates to estimate w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A  notable and practical shortcoming of SlIsotron is that  the isotonic regression steps to update u do not guarantee  u to map to [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The BregmanTron algorithm was  later proposed in Nock and Menon [2020], to refine the  SlIsotron algorithm by addressing this and providing  convergence guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' By utilising the connection be-  tween proper losses and their canonical link functions  outlined in Section 4, the BregmanTron replaced the  link function u with the inverse canonical link ˜ψ−1 which  guaranteed probability estimates to lie in [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  ISGP-Linkgistic algorithm  The idea of using the  (u, v)-geometric structure in combination with Legendre  functions to learn canonical link functions has recently  been explored in the work of Walder and Nock [2020]  to propose the ISGP-Linkgistic algorithm to learn  a model of the form Pr(Y = 1|x) = (u ◦ v−1)(w⊤x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  By the squaring and integration of a Gaussian Process  (GP) to yield the Integrated Squared Gaussian Process  (ISGP), monotonicity and invertibility of v−1 : R → R is  guaranteed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The ISGP-Linkgistic algorithm exploits  this property by choosing a fixed squashing function u  separate from the a priori ISGP distributed v−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In-  ference is performed with a stochastic EM algorithm  where the E-step fixes the linear predictor w⊤x and ap-  plies a Laplace approximation the latent GP to compute  Eq(v−1|w)[log p(y|x, v−1)], and the M-step maximises this  expectation with respect to w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The ISGP-Linkgistic  algorithm takes a Bayesian approach to learning proper  2  canonical losses jointly with a probability estimator by  posterior sampling of inverse canonical links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  3  Definitions and Properties of Losses  In this section, we revisit the notions of proper losses to  formulate proper canonical losses in the multiclass setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We follow the definitions and notations of Williamson  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2016] and describe key properties therein, for our  discussion of composite multiclass losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Let C ≥ 2 as the total number of classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our setting is  multiclass probability estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Denote the (C − 1)-  dimensional probability simplex as  ∆C−1 =  �  p ∈ RC  + :  C  �  i=1  pi = 1  �  ,  and its relative interior as  ri(∆C−1) =  �  p ∈ RC  + :  C  �  i=1  pi = 1, pi ∈ (0, 1), ∀i  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Suppose we have a dataset D of N pairs {(xn, yn)}N  n=1  where each xn ∈ X = Rp and yn ∈ Y = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , C}  denotes an input and a single label respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We  aim to learn a function h : X → ∆C−1 such that ˆyn ∈  arg maxc∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=',C} P(yn = c|xn) closely matches yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Consider  the  label  as  a  random  variable  Y  ∼  Categorical(p) with prior class probabilities p ∈ ∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We denote q ∈ ∆C−1 as the estimated probabilities in the  following definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' To assess the quality of probability  estimates, a loss function can be defined generally as  ℓ : ∆C−1 → RC  +,  ℓ(q) = (ℓ1(q), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , ℓC(q))⊤  where ℓi is the partial loss for predicting q when y = i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  For a given label y, we can return to scalar-valued losses  by referring to the y-th partial loss ℓy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1 (conditional Bayes Risk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The condi-  tional risk associated with ℓ is defined as L(p, q) =  EY ∼Categorical(p)[ℓY (q)] for all p, q ∈ ∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The best  achievable conditional risk associated with a loss is termed  the conditional Bayes risk and is defined as  L :∆C−1 → R+,  L(p) =  inf  q∈∆C−1 L(p, q) =  inf  q∈∆C−1 EY ∼Categorical(p)[ℓY (q)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  It is well known that L is concave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 (Proper Losses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A loss ℓ is proper if  and only if L is minimized when q = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In other words,  L(p) = L(p, p) ≤ L(p, q) for all p, q ∈ ∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Losses  where the inequality is strict when p ̸= q, are termed  strictly proper losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Remark  Properness is an essential property of losses,  as optimising a model with respect to a proper loss guides  the model’s probability estimates towards true underly-  ing prior class probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Examples of proper losses  include the square, log and Matsushita losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  To draw the connection between a proper loss and its con-  ditional Bayes risk, we require definitions of subgradients  and Bregman divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Subgradients are a gener-  alisation of gradients and are particularly useful when  analysing convex functions that may not be differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Subgradients  For a convex set S ⊆ Rn, the subdiffer-  ential of a convex function f : S → (−∞, +∞] at x ∈ S  is defined as  ∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ ≤ f(y) − f(x), ∀y ∈ Rn}  where an element φ ∈ ∂f(x) is called a subgradient of  f at x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  By convention, we define ∂f(x) = ∅ for all  x /∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Moreover, f is strictly convex if and only if  ∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ < f(y) − f(x), ∀y ∈ Rn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Bregman divergence  For a convex set S ⊆ Rn, and a  continuously-differentiable and strictly convex function f :  S → (−∞, +∞], the Bregman divergence with generator  f is defined for all x, y ∈ S as  Df(x, y) = f(x) − f(y) − ⟨∇f(y), x − y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The following result is a rewritten characterisation of  proper losses through their “Bregman representation”,  and explicates the connection between a proper loss and  its conditional Bayes risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3 ([Williamson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2016, Proposition  7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let ℓ : ∆C−1 → RC  + be a loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' ℓ is a (strictly) proper  loss if and only if there exists a (strictly) convex function  f : ∆C−1 → R such that for all q ∈ ∆C−1, there exists a  subgradient φ ∈ ∂f(q) such that  L(p, q) = −(p − q)⊤φ − f(q) for all p ∈ ∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Moreover, if L is differentiable on ri(∆C−1) then  L(p, q) = (p − q)⊤ℓ(q) + L(q)  where ℓ is the unique proper loss associated with L with  the property ∇L(p) = ℓ(p), ∀p ∈ ri(∆C−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Remark  We note that L(p, q) is a Bregman divergence  if and only if ℓ is strictly proper due to the requirement  of strict convexity of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  In this work, we seek to learn strictly proper losses ℓ  by exploiting the connection ∇L(p) = ℓ(p) described  3  in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Section 4, we extend this con-  nection between probabilities and predictors in RC−1  through canonical link functions, and describe in detail  how strictly proper losses can be learned through this  extended connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  4  Designing Multiclass Canonical Links  In this section, we provide definitions of canonical link  functions, Legendre functions and the (u, v)-geometric  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The latter two structures are essential for  the design and learning of canonical link functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We  show that designing a canonical link amounts to de-  signing a composite function that is the gradient of a  twice-differentiable and convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' To this end, we  present our key theoretical contributions: conditions for  composite functions to be gradients of convex functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Composite Form  It is often desirable to link predic-  tors with their probability estimates through an invert-  ible link function ψ : ∆C−1 → RC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This allows one to  uniquely identify probabilities while working with general  predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' It also allows one to define loss functions more  generally as ℓψ = ℓ ◦ ψ−1 which are referred to as proper  composite losses when ℓ is proper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Williamson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2016,  Proposition 13] shows that a proper composite loss ℓψ is  uniquely represented by ℓ and ψ when ℓψ is continuous  and invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Proper Canonical Form  As elements of ∆C−1 are  uniquely determined by the first C − 1 components, the  above properties can be more naturally described by the  projected probability simplex:  ˜∆C−1 =  �  ˜p ∈ RC−1  +  :  C−1  �  i=1  ˜pi ≤ 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Define the projection map  Π : ∆C−1 → ˜∆C−1,  Π(p) = (p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , pC−1) for all p ∈ ∆C−1,  and its inverse  Π−1 : ˜∆C−1 → ∆C−1,  Π−1(˜p) =  �  ˜p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , ˜pC−1, 1 −  C−1  �  i=1  ˜pi  �  for all ˜p ∈ ˜∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The projected conditional Bayes risk  is defined as ˜L = L ◦ Π−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Suppose ˜L is differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Then the canonical link function is defined as  ˜ψ : ˜∆C−1 → RC−1,  ˜ψ(˜p) = −∇˜L(˜p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Williamson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2016, Corollary 32] shows that given  a proper loss ℓ, the function ℓ ◦ Π−1 ◦ ˜ψ−1 has com-  ponents which are convex with respect to the input  domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We refer to such losses as proper canoni-  cal losses to distinguish them from proper composite  losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The connection between a differentiable condi-  tional Bayes risk, a proper loss, and a canonical link,  shown by Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3 and Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1, is given by  ℓ = ∇L = −((−∇˜L ◦ Π) · JΠ) = −(( ˜ψ ◦ Π) · JΠ) where  JΠ is the Jacobian of Π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This illustrates that one can  learn proper canonical losses by modelling either the  conditional Bayes risk or its associated canonical link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Properties of Legendre functions  Let f : RC−1 →  R be continuously differentiable and strictly convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We  refer to f as a Legendre function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The Legendre-Fenchel  conjugate of f, denoted by f ∗, is defined as  f ∗ : S → R,  f ∗(x∗) = ⟨(∇f)−1(x∗), x∗⟩ − f  �  (∇f)−1(x∗)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  where S = {∇f(x) : x ∈ RC−1}, and f is Legendre if  and only if f ∗ is Legendre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Rockafellar [1970, Theorem  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='5] shows that when the latter holds, (f ∗)∗ = f, and  ∇f is continuous and invertible with ∇f ∗ = (∇f)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  (u, v)-geometric structure  Amari [2016], Nock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  [2016], Walder and Nock [2020] state that a general dually  flat structure on RC−1 can be defined in terms of an  arbitrary strictly convex function ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Let u and v be  differentiable invertible functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The pair (u, v) give a  dually flat structure on RC−1 if and only if ∇ξ = u ◦ v−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We consider the (u, v)-geometric structure of the Bregman  divergence D(−˜L)∗ which gives ˜ψ−1 = u ◦ v−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Designing links  In this work, we focus on the case  when −˜L is differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Note that −˜L is convex since  Π−1 is affine and −L is convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Properties of Legendre  functions allow us to move from −˜L to its Legendre-  Fenchel conjugate (−˜L)∗, and similarly allow us to move  from the canonical link ˜ψ to its inverse ˜ψ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The (u, v)-  geometric structure then allows us to flexibly learn ˜ψ−1  by splitting it into a learnable component v−1 and a fixed  component u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Fixing u to be a suitable squashing func-  tion ensures that ˜ψ−1 maps to ˜∆C−1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' thereby allowing  us to uniquely identify multiclass probabilities associated  with predictors from RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' On the other hand, v−1 can  be parameterised by an invertible neural network which  allows ˜ψ−1 to adapt to the multiclass problem at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Legendre functions and the (u, v)-geometric structure  together yield a more natural and practical design of the  canonical link through its inverse since it is often much  easier to map inputs from an unbounded space such as  RC−1, to a bounded space such as ˜∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Figure 1 illus-  trates how the inverse of the canonical link is modelled  4  ˜ψ−1  v−1  u  probability estimates  ˜∆C−1  predictors  RC−1  transformed predictors  RC−1  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Relationship between predictors and probability es-  timates through the inverse of the canonical link function  under the (u, v)-geometric structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  using the (u, v)-geometric structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Loosely speaking,  v−1 allows one to find better logit representations before  they are squashed to probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Under the (u, v)-geometric structure, if one can prove  that u ◦ v−1 maps to ˜∆C−1 and is the gradient of a  Legendre function f, then one can set (−˜L)∗ = f and  ∇(−˜L)∗ = u ◦ v−1 as its corresponding inverse canoni-  cal link function by using properties of Legendre func-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This requires showing u ◦ v−1 is the gradient of  a twice-differentiable and strictly convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In  the following two theorems, we provide conditions where  this assertion holds for general composite functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We  defer the background, supporting theorems and proofs of  the following results to Sections A, D and E within the  Appendices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1 and g : RC−1 →  RC−1 be differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then the following conditions are  equivalent:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' f ◦ g = ∇F where F is a twice-differentiable convex  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The Jacobian Jf◦g(x) is symmetric for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Jf◦g(x) is positive semi-definite for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' f ◦ g is monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Proof sketch of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2  To claim that a func-  tion f : RC−1 → RC−1 is the gradient of a convex func-  tion g : RC−1 → R, requires f to satisfy maximal cyclical  monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This is a more abstract notion of mono-  tonicity within domains in higher dimensions, and en-  compasses two notions of monotonicity, namely maximal  monotonicity and cyclical monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' It turns out  that it is sufficient to consider monotonicity as maximal  monotonicity is automatically guaranteed as our domain  is RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 characterises when a composite function  is the gradient of a convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' It also serves as  a convenient and practical criteria to aid model design  through a check of positive semi-definiteness for the Jaco-  bian Jf◦g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The implications of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 are profound  as it allows us to derive the following sufficient condi-  tions under which the composition of gradients of convex  functions is the gradient of a Legendre function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → S and g : RC−1 → RC−1  be differentiable where S ⊆ RC−1, and Jf(x) and Jg(x)  are symmetric and positive definite for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Then f ◦g is the gradient of a twice-differentiable Legendre  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Proof sketch of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 tells us  it is sufficient to check for positive semi-definiteness of  a composite function’s Jacobian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our proof involves a  check that all eigenvalues of the Jacobian are positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  This asserts that the composite function is the gradient  of a twice-differentiable and strictly convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  To use the (u, v)-geometric structure from Section 3 with  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3, we can set f = u and g = v−1 within  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This presents an additional requirement  that the functions f and g are also invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Section  5, we show how these requirements can be met with our  proposed algorithm, LegendreTron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  5  Learning Proper Canonical  Multiclass Losses: LegendreTron  In this section, we present LegendreTron, our main  algorithmic contribution for learning proper canonical  losses for multiclass probability estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' With the  theory of Legendre functions, (u, v)-geometric structure  and Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3 in hand to support our approach, we  now present LegendreTron in detail, as an extension  of Generalised Linear Models and Single Index Models  for Multinomial Logistic Regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Model  Given a dataset D = {(xn, yn)}N  n=1, we have  the classification model  yn|xn ∼ Categorical  �  ˆp(zn)  �  where zn = Wxn + b  where W ∈ R(C−1)×p, b ∈ RC−1 and ˆp(zn) = (u ◦  v−1)(zn) with u chosen as a squashing function that  maps to ˜∆C−1 and v−1 = ∇g for a twice-differentiable  and strictly convex function g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We leave the specification  of a suitable squashing function u as a modelling choice  and provide a natural choice at the end of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  For any B ∈ Z+, let g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' gB be fully input convex  neural networks (FICNN) investigated in Amos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  [2017].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We set v−1 = ∇g = (∇g1) ◦ (∇g2) ◦ · · · ◦ (∇gB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  For each gi, we use the same architecture as Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  5  [2021] which is described as  zi,1 = l+  i,1(x)  zi,k = li,k(x) + l+  i,k(s(zi,k−1)) for k = 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , M + 1,  hi(x) = s(zi,M+1),  gi(x) = s(wi,0)hi(x) + s(wi,1)∥x∥2  2  where we denote l+  i,k as a linear layer with positive  weights, li,k as a linear layer with unconstrained weights,  wi,0, wi,1 ∈ R are unconstrained parameters and s(x) =  log(1 + ex) is the softplus function with s(x) denoting  the softplus function applied elementwise on x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In partic-  ular, li,M+1 and l+  i,M+1 are linear layers that map to R  while for each k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' M, li,k and l+  i,k are hidden layers  that map to RH for a chosen dimension size H ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  With this setup, each gi is strongly convex (and therefore  strictly convex) with an invertible gradient and positive  definite Hessian for all x ∈ RC−1 due to the quadratic  term within each gi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We conclude this section by showing that, equipped with  a suitable squashing function u, any function learned by  LegendreTron is a valid inverse canonical link function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We turn to a modified version of the LogSumExp function  previously studied in Nielsen and Hadjeres [2018] and  describe its main properties within the following theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f(x) = log  �  1 + �C−1  k=1 exp(xk)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The key properties of f are:  f is strictly convex with invertible gradient  u : RC−1 → ˜∆C−1,  u(x) =  �  exp(xi)  1 + �C−1  k=1 exp(xk)  �  1≤i≤C−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  the Hessian of f, given by Ju(x), is positive definite  for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We refer to f and u as LogSumExp+ and softmax+ re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let v−1 : RC−1 → RC−1 be defined as  v−1 = (∇g1) ◦ (∇g2) ◦ · · · ◦ (∇gB)  where g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' gB are FICNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then any function u ◦  v−1 learned by LegendreTron is the gradient of a  twice-differentiable Legendre function and is therefore,  the inverse of a canonical link function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  With this specification, we can deduce that any function  u ◦ v−1 learned via LegendreTron is the gradient of a  twice-differentiable Legendre function which can serve as  an inverse canonical link function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Algorithm 1 describes  LegendreTron in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Algorithm 1 LegendreTron  Input: sample S ⊂ D, number of iterations T, number  of FICNNs B, hidden layer dimension size H, number  of layers M, squashing function u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Initialise W and b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Initialise g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' gB each with M layers of dimension  size H, and denote their joint set of parameters θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  for i = 1 to T do  Set v−1 = (∇g1) ◦ (∇g2) ◦ · · · ◦ (∇gB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  for each (xn, yn) ∈ S do  Compute zn = Wxn + b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Compute ˆp(zn) = (u ◦ v−1)(zn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  end for  Compute ES[L(ˆp(z), y)] by Monte Carlo where L is  the log-likelihood of the Categorical distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Update W, b and θ by backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  end for  Output: W, b and g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' gB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Remark  We note that the specification of u remains  as a modelling choice, and that its importance lies in  the requirement that it yields a function u ◦ v−1 which  maps to ˜∆C−1 and is the gradient of a twice-differentiable  Legendre function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We have chosen softmax+ since it  serves as the natural multiclass analogue of the classical  sigmoid function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  6  Experiments  In this section, we provide numerical comparisons be-  tween LegendreTron, multinomial logistic regression  and other existing methods that also aim to jointly learn  models and proper canonical losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Remark  As LogSumExp+ is twice-differentiable and  Legendre, its gradient softmax+ is a valid inverse canoni-  cal link function since it maps to ˜∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' However, we note  that setting ˜ψ−1 = softmax+ results in learning only the  parameters W and b which coincides with multinomial  logistic regression and generalised linear models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Here  ˜ψ(˜p) =  �  ˜pi  1−�C−1  k=1 ˜pk  �  1≤i≤C−1 with corresponding proper  loss ℓ = −(( ˜ψ ◦ Π) · JΠ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  For our experiments, we set softmax+ as the squashing  function u for both LegendreTron and Multinomial  Logistic Regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  For a practical and numerically  stable implementation, we also map probability estimates  to the log scale by deriving an alternate Log-Sum-Exp  trick for softmax+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We defer the full experimental details  to Appendix G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' All experiments were performed using  PyTorch [Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2019] and took roughly one CPU  6  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Test AUC for generalised linear models with various  link methods (ordering in decreasing average).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' See text for  details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  MNIST FMNIST  LegendreTron  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9%  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2%  ISGP-Linkgistic  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9%  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2%  GP-Linkgistic  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9%  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1%  Logistic regression  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9%  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='5%  GLMTron  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6%  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1%  BregmanTron  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7%  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9%  BregmanTronlabel  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6%  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7%  BregmanTronapprox 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3%  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6%  SlIsotron  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6%  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7%  month to complete1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  MNIST Binary Problems  Binary problems are a  special case of our setting where C = 2, so Legen-  dreTron is readily applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Table 1, we compared  LegendreTron against ISGP-Linkgistic [Walder and  Nock, 2020] and BregmanTron [Nock and Menon,  2020], as both algorithms also aim to learn proper canon-  ical losses for binary problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We also compared  with other baselines in these two works including the  SlIsotron algorithm from Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2011].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Ex-  periment details can be found in Section 6 of Nock and  Menon [2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our model successfully matches the (bi-  nary specific) ISGP-Linkgistic baseline, which was the  strongest algorithm in test AUC performance from the  experiments of Walder and Nock [2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  MNIST Multiclass Problems  For the three MNIST-  like datasets [LeCun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2010, Xiao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2017,  Clanuwat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2018], we compared LegendreTron  against multinomial logistic regression and ISGP-  Linkgistic, since the latter is the strongest algorithm in  ten-class classification test accuracy performance based  on the experiments within Walder and Nock [2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  ISGP-Linkgistic approaches the multiclass problem  by learning proper canonical losses for the 10 component  1-vs-rest problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our experimental results in Figure  2 show that LegendreTron and multinomial logistic  regression outperform the ISGP-Linkgistic baseline on  all three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' These results illustrate our conjecture  that properness with respect to losses and models in com-  ponent problems in a multiclass setting, does not imply  optimality of class predictions or probability estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  By respecting the true problem structure, proper multi-  class losses allow the model to learn probability estimates  1The total run time for our experiments is favourable  relative to the reported two CPU months for the ISGP-  Linkgistic algorithm from Walder and Nock [2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  that are able to better distinguish between all the classes  at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our results also show that LegendreTron  either matches or outperforms multinomial logistic regres-  sion on all three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This is most notable on the  Kuzushiji-MNIST dataset where LegendreTron out-  performs multinomial logistic regression by a reasonable  margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Other Multiclass Problems and Label Noise  We  also compared LegendreTron against multinomial lo-  gistic regression on 15 datasets that are publicly available  from the LIBSVM library [Chang and Lin, 2011], the  UCI machine learning repository [Asuncion and New-  man, 2007, Dua and Graff, 2017], and the Statlog project  [King et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 1995].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We note that we did not compare  our proposed method with other multiclass classification  methods such as kernel methods explored in Zien and  Ong [2007] and Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2018], as these methods are  centred on the task of classification, whereas our focus  is on jointly learning multiclass probabilities and proper  canonical losses through the canonical link function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' To  assess the robustness against label noise, we also compare  the classification accuracy of LegendreTron and multi-  nomial logistic regression where labels in the training set  are corrupted with probability η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, for any true  label yn, we instead train our models on the potentially  corrupted label given by  ˜yn =  �  yn  with probability 1 − η,  c  with probability η where c ∈ Y \\ {yn} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We applied symmetric label noise in our experiments  which is the case where the probability of ˜yn = c for  each c ∈ Y \\ {yn} is  η  C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We run both LegendreTron  and multinomial logistic regression for each dataset 20  times, where each run randomly splits the dataset into  80% training and 20% testing sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our results in Table  2 show that LegendreTron outperforms multinomial  logistic regression under a t-test at 99% significance for  most datasets and label noise settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The performance  of LegendreTron is on par with multinomial logistic re-  gression on the svmguide2, wine and iris datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Multi-  nomial logistic regression only statistically outperforms  LegendreTron on the dna dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' LegendreTron  consistently outperforms multinomial logistic regression  especially strongly on problems where the number of  classes is greater than 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We conjecture this can be  due to the greater expressiveness of logit representations  induced by the diffeomorphism u ◦ v−1 learned by Leg-  endreTron, and the sensitivity of multinomial logistic  regression to noise and potential measurement errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  7  10000  20000  30000  40000  50000  60000  60  70  80  90  Training Set Size  Classification Accuracy (%)  FMNIST / MLR  KMNIST / MLR  MNIST / MLR  FMNIST / ISGP  KMNIST / ISGP  MNIST / ISGP  FMNIST / LT  KMNIST / LT  MNIST / LT  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Test performance v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' training set size for the MNIST, Kuzushiji-MNIST and Fashion-MNIST datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We compare  the ten-class classification accuracy of LegendreTron (LT), multinomial logistic regression (MLR) and ISGP-Linkgistic  (ISGP) where the ISGP combines 10 one-vs-rest binary models while the former two algorithms model the probabilities of all  10 classes jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Average test classification accuracies (%) for LegendreTron (LT) and multinomial logistic regression (MLR) on  LIBSVM, UCI and Statlog datasets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' at varying levels of label noise (η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Numbers of the method are bolded when it performs  statistically better at a significance level of 99% under a t-test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Absence of bolding indicates both methods have statistically  similar performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
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+page_content='83  8  7  Conclusion  In this work, we proposed a general approach which  jointly learns proper canonical losses and multiclass prob-  abilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Our contributions advance the recent work on  learning losses with probabilities based on the seminal  work within Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' [2011], Nock and Menon [2020],  Walder and Nock [2020] by providing a natural exten-  sion to the multiclass setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The practical nature and  generality of our model is owed to the general parame-  terisation of Fully Input Convex Neural Networks, with  theoretical support from Legendre functions, structures  from information geometry and hallmark results from  convex analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  By grounding losses in properness for the multiclass set-  ting, we have demonstrated that our model improves  upon existing methods that aim to solve multiclass prob-  lems through binary reductions, and also outperforms the  natural baseline of multinomial logistic regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Sepa-  rately, we have also provided conditions under which a  composition of gradients of differentiable convex functions  is the gradient of another differentiable convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We anticipate that our results will find applications in  multiclass classification and probability estimation, as  well as variational inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  References  Shun´ıchi Amari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Information geometry and its applica-  tions, volume 194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Brandon Amos, Lei Xu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Zico Kolter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Input convex  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Doina Precup and Yee Whye Teh,  editors, Proceedings of the 34th International Confer-  ence on Machine Learning, volume 70 of Proceedings  of Machine Learning Research, pages 146–155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' PMLR,  06–11 Aug 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Edgar Asplund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A monotone convergence theorem for  sequences of nonlinear mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Felix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Browder,  editor, Proceedings of Symposia in Pure Mathemat-  ics, volume 18, pages 1–9, Chicago, IL, USA, 1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  American Mathematical Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Arthus Asuncion and David Newman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' UCI repository of  machine learning databases, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Heinz H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Bauschke and Patrick L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Combettes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Convex  Analysis and Monotone Operator Theory in Hilbert  Spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' CMS Books in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Springer, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  ISBN 9781441994660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Rajendra Bhatia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Matrix Analysis, volume 169 of Gradu-  ate Texts in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Springer New York, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  ISBN 9781461206538.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Jonathan Borwein and Herre Wiersma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Asplund decom-  position of monotone operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' SIAM Journal on  Optimization, 18(3):946–960, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Chih-Chung Chang and Chih-Jen Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' LIBSVM: A li-  brary for support vector machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' ACM Transactions  on Intelligent Systems and Technology, 2:27:1–27:27,  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Tarin Clanuwat, Mikel Bober-Irizar, Asanobu Kita-  moto, Alex Lamb, Kazuaki Yamamoto, and David  Ha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Deep learning for classical japanese literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  CoRR, abs/1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='01718, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Dheeru Dua and Casey Graff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' UCI machine learning  repository, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Tilmann Gneiting and Adrian E Raftery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Strictly proper  scoring rules, prediction, and estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Journal of  the American Statistical Association, 102(477):359–378,  2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Josif Grabocka, Randolf Scholz, and Lars Schmidt-  Thieme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Learning surrogate losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' arXiv preprint  arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='10108, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Peter D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
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+page_content='  Varia-  tional Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Grundlehren der mathematischen Wis-  senschaften.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Springer Berlin Heidelberg, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' ISBN  9783540627722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Leonard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Savage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Elicitation of personal probabilities  and expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Journal of the American Statistical  Association, 66(336):783–801, 1971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' ISSN 01621459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Emir H Shuford, Arthur Albert, and H Edward Massen-  gill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Admissible probability measurement procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Psychometrika, 31(2):125–145, 1966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Ali Siahkamari, Xide Xia, Venkatesh Saligrama, David  Casta˜n´on, and Brian Kulis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Learning to approximate  a bregman divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Larochelle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Ranzato,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Hadsell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Balcan, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Lin, editors, Advances  in Neural Information Processing Systems, volume 33,  pages 3603–3612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Matthew Streeter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Learning effective loss functions effi-  ciently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' CoRR, abs/1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='00103, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Tyler Sypherd, Mario Diaz, John Kevin Cava, Gautam  Dasarathy, Peter Kairouz, and Lalitha Sankar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A tun-  able loss function for robust classification: Calibration,  landscape, and generalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' IEEE Transactions on  Information Theory, 68(9):6021–6051, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Christian Walder and Richard Nock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' All your loss are  belong to bayes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Larochelle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Ranzato, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Had-  sell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Balcan, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Lin, editors, Advances in  Neural Information Processing Systems, volume 33,  pages 18505–18517.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Robert C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Williamson, Elodie Vernet, and Mark D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Reid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Composite multiclass losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Journal of Machine Learn-  ing Research, 17(222):1–52, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Han Xiao, Kashif Rasul, and Roland Vollgraf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Fashion-  mnist: a novel image dataset for benchmarking ma-  chine learning algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' CoRR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Alexander Zien and Cheng Soon Ong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Multiclass multiple  kernel learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In Proceedings of the 24th International  Conference on Machine Learning, pages 1191–1198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Association for Computing Machinery, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' ISBN  9781595937933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  10  A  Convex Analysis: Relevant Background and List of Theorems  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1  Background  To motivate the results studied in this section, we first note that in general, the composition of two monotone  functions in RC−1 is not necessarily another monotone function in RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This means that methods to design  monotonic functions in R cannot be applied to functions defined on RC−1, leaving the methods discussed in Section 2  unsuitable for the general multiclass setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Separately, we note that the composition of two gradients of differentiable  convex functions is not necessarily the gradient of another convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In general, to claim that a function  f : RC−1 → RC−1 is the gradient of a convex function g : RC−1 → R, requires f to satisfy a notion of monotonicity  generalised to higher dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The connection between convex functions and their gradients is well known in  convex analysis via the notion of maximal cyclically monotone functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This is a combination of two notions  of monotonicity: maximal monotonicity and cyclical monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' These are defined within the following list of  definitions and theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2  List of Theorems  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1 ([Rockafellar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2009, Definition 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' A function f : RC−1 → RC−1 is monotone if ⟨f(x) −  f(z), x − z⟩ ≥ 0 for all x, z ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Moreover, it is strictly monotone when the inequality is strict whenever x ̸= z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The following two definitions require the notion of the graph of a function f : RC−1 → RC−1 which is defined as  gph(f) = {(x, y) : x ∈ RC−1, y ∈ f(x)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 ([Bauschke and Combettes, 2011, Definition 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='20]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1 be a monotone function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Then f is maximally monotone if there exists no monotone function g : RC−1 → RC−1 such that gph(f) ⊊ gph(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3 ([Bauschke and Combettes, 2011, Definition 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' For an arbitrary integer  n ≥ 2, f is n-cyclically monotone if for any {(xi, yi)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=',n ⊂ gph(f) it follows that  n  �  i=1  ⟨yi, xi+1 − xi⟩ ≤ 0 where xn+1 = x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  f is cyclically monotone if it is n-cyclically monotone for any integer n ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In addition, if gph(f) ̸⊂ gph(g) for any  cyclically monotone function g ̸= f then f is maximal cyclically monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='4 ([Rockafellar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2009, Theorems 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='17 & 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='25]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then f = ∇h for a  differentiable convex function h : RC−1 → R if and only if f is maximal cyclically monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, f is maximally  monotone and cyclically monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='5 ([Rockafellar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=', 2009, Proposition 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1 be a differentiable function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then  f is monotone if and only if ∇f(x) is positive semi-definite for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Moreover, if ∇f(x) is positive definite  for all x ∈ RC−1 \\ {0} then f is strictly monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6 ([Bauschke and Combettes, 2011, Theorem 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1, Minty’s Theorem]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1 be a  monotone function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then f is maximal monotone if and only if range(Id + f) = RC−1 where Id is the identity  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7 ([Borwein and Wiersma, 2007, Theorem 3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let f : RC−1 → RC−1 be maximally monotone and  continuously differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then f(x) = ∇F(x) + Lx where F is a differentiable convex function, and L is a skew  symmetric matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='8 ([Meenakshi and Rajian, 1999, Theorem 3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let A, B ∈ R(C−1)×(C−1) be symmetric and positive  semi-definite matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then AB is positive semi-definite if and only if it is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9 ([Bhatia, 2013, Theorem VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let V ⊂ R(C−1)×(C−1) be a real vector space whose elements are  matrices with real eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Denote λi(M) as the i-th smallest eigenvalue for any matrix M ∈ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Let A, B ∈ V  then  λi(A) + λ1(B) ≤ λi(A + B) ≤ λi(A) + λC−1(B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  11  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3  Remarks  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='4 serves as a criterion and characterisation of differentiable convex functions through their gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorems A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6 to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='8 are hallmark results from the rich literature of convex analysis and monotone operators that tie  together conditions under which a differentiable composite function is the gradient of a convex function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Notably,  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7 is a rewritten version of the Asplund decomposition of maximal monotone operators [Asplund, 1968]  which tells us it suffices to focus on maximal monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We refer the reader to Appendix D for the usage of  Theorems A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='5 to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='8 in the proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9 allows us to obtain a lower bound on the smallest eigenvalue of the sum of two real-valued matrices  with real eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This is particularly useful to prove positive definiteness in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We refer the reader to  Appendix E for its usage in the proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  B  Proof of equivalent conditions on subdifferentials for strictly convex functions  (⇒) Suppose f is strictly convex and assume for a proof by contradiction that there exists some x, y ∈ domf such  that x ̸= y with f(x) + ⟨φ, y − x⟩ ≥ f(y) for some φ ∈ ∂f(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Fix λ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then we have  f(x) + ⟨φ, (λx + (1 − λ)y) − x⟩ = f(x) + (1 − λ)⟨φ, y − x⟩  ≤ f(λx + (1 − λ)y) by definition of a subgradient  < λf(x) + (1 − λ)f(y) by strict convexity of f  ≤ f(x) + (1 − λ)⟨φ, y − x⟩ by the above assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Thus, we have a contradiction so we must have the subdifferential of f for all x ∈ domf is given by  ∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ < f(y) − f(x), ∀y ∈ Rn} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  (⇐) Suppose the subdifferential of f for any x ∈ domf is given by  ∂f(x) = {φ ∈ Rn : ⟨φ, y − x⟩ < f(y) − f(x), ∀y ∈ Rn} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Fix x, y ∈ domf and λ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Consider φ ∈ ∂f(λx + (1 − λ)y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then we have  f(λx + (1 − λ)y) + (1 − λ)⟨φ, x − y⟩ < f(x),  f(λx + (1 − λ)y) + λ⟨φ, y − x⟩ < f(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Multiplying the first inequality by λ and the second by (1 − λ), summing them gives us f(λx + (1 − λ)y) <  λf(x) + (1 − λ)f(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This holds for arbitrary x, y ∈ domf and λ ∈ (0, 1) so it follows that f is strictly convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  C  Proof of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3  (⇒) Fix q ∈ ∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Suppose ℓ is proper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Then we have  L(p, q) = p⊤ℓ(q) = q⊤ℓ(q) + (p − q)⊤ℓ(q) = L(q) + (p − q)⊤ℓ(q)  and also,  0 ≤ L(p, q) − L(p, p) = L(q) + (p − q)⊤ℓ(q) − L(p)  =⇒ −(p − q)⊤ℓ(q) ≤ −L(p) − (−L(q)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Recall that L is concave so it follows that −L is convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Hence, −ℓ(q) ∈ ∂(−L)(q) which means −ℓ(q) is a subgradient  of −L at q and L(p, q) = −(−L(q)) − (p − q)⊤(−ℓ(q)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  (⇐) Suppose there exists a convex function f : ∆C−1 → R such that for all q ∈ ∆C−1, there exists a subgradient  φ ∈ ∂f(q) and L(p, q) = −f(q) − (p − q)⊤φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  12  For all p ∈ ∆C−1, we have  L(p, q) − L(p, p) = f(p) − f(q) − (p − q)⊤φ  ≥ 0 since φ is a subgradient of f at q  =⇒ L(p, p) ≤ L(p, q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Hence, ℓ is a proper loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  To prove that ℓ is strictly proper if and only if there exists a strictly convex function f : ∆C−1 → R such that for all  q ∈ ∆C−1, there exists a subgradient φ ∈ ∂f(q) such that L(p, q) = −(p − q)⊤φ − f(q) for all p ∈ ∆C−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This follows  immediately by definitions of strictly proper losses and subdifferentials from which the above inequalities become  strict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  We are left to prove that L(p, q) = (p − q)⊤ℓ(q) + L(q) when L is differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We first note that L is concave so  −L is convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Recall that L(p, q) = p⊤ℓ(q) = L(q) + (p − q)⊤ℓ(q) from the workings within Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Setting  f = −L for Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3, we can deduce −ℓ(q) = −∇L(q)∀q ∈ ri(∆C−1) for a proper loss ℓ which follows by the  uniqueness of subgradients for differentiable functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, ∇L(q) = ℓ(q), ∀q ∈ ri(∆C−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  D  Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2  (1) =⇒ (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This follows from Schwarz’s theorem on the equality of mixed partial derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' (2) =⇒ (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This  follows from Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='8 since the Jacobian of a composite function is a product of matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' (3) =⇒ (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This  follows from Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We are left to prove (4) =⇒ (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  (4) =⇒ (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' As range(Id + f ◦ g) = RC−1, it follows from Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='6 that f ◦ g is maximally monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' From  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7, (f ◦ g)(x) = ∇F(x) + Lx for a differentiable convex function F and a skew-symmetric matrix L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Since  f ◦ g is differentiable then it follows that F is twice-differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This gives us Jf◦g = ∇2F + L⊤ where ∇2F is  symmetric by Schwarz’s theorem on the equality of mixed partial derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Theorems A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='5 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='8 tells us that  Jf◦g is also symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' As Jf◦g and ∇2F are both symmetric, then we must have L⊤ = 0 = L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, f ◦ g = ∇F  where F is twice-differentiable and convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  E  Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3  Fix x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' The Jacobian of f ◦ g is given by  Jf◦g(x) = Jf(g(x))Jg(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Here we aim to prove that Jf◦g(x) is positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We first note that Jg(x) is invertible since |Jg(x)| > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Now,  note that Jf◦g(x) is similar to the matrix  (Jg(x))  1  2 Jf(g(x))Jg(x)(Jg(x))− 1  2 = (Jg(x))  1  2 Jf(g(x))(Jg(x))  1  2  where the square root of the matrix Jg(x) is given by (Jg(x))  1  2 which is known to be symmetric since Jg(x) is symmetric  and positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Since Jf(g(x)) is also symmetric, it follows that (Jg(x))  1  2 Jf(g(x))(Jg(x))  1  2 is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' As  Jg(x) and Jf(g(x)) are positive definite, we have  ���(Jg(x))  1  2 Jf(g(x))(Jg(x))  1  2  ��� = |Jf(g(x))| |(Jg(x))| > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  It follows that (Jg(x))  1  2 Jf(g(x))(Jg(x))  1  2 is positive definite, meaning it has positive eigenvalues λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , λC−1 ∈ R  that can be denoted such that λ1 ≤ λ2 ≤ · · · ≤ λC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Since similar matrices have the same eigenvalues, it follows  that λ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , λC−1 are also the eigenvalues of Jf◦g(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Denote S = 1  2(Jf◦g(x) + (Jf◦g(x))⊤) and A = 1  2(Jf◦g(x) − (Jf◦g(x))⊤) as the symmetric and skew-symmetric parts  of Jf◦g(x) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' It is well known that for any skew-symmetric matrix A and any z ∈ RC−1, we have z⊤Az = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  To prove that Jf◦g(x) is positive definite, it suffices to prove that z⊤Jf◦g(x)z = z⊤Sz > 0 for any z ∈ RC−1 \\ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Firstly, recall that all eigenvalues of Jf◦g(x) are real and positive, and the fact that the transpose of Jf◦g(x),  (Jf◦g(x))⊤, has the same eigenvalues as Jf◦g(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, all eigenvalues of (Jf◦g(x))⊤ are real and positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Secondly,  13  S = 1  2(Jf◦g(x) + (Jf◦g(x))⊤) is symmetric so all of its eigenvalues must be real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Hence, Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='9 gives us the  following bound for the smallest eigenvalue λ1(S)  λ1(S) ≥ λ1  �1  2Jf◦g(x)  �  + λ1  �1  2(Jf◦g(x))⊤  �  = 1  2  �  λ1(Jf◦g(x)) + λ1((Jf◦g(x))⊤)  �  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  The Rayleigh quotient for S and any z ∈ RC−1 \\ {0}, is given by z⊤Sz  ∥z∥2 , and satisfies the inequality  λ1(S) ≤ z⊤Sz  ∥z∥2 ≤ λC−1(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Hence, we have  z⊤Sz  ∥z∥2 ≥ λ1(S) > 0 for all z ∈ RC−1 \\ {0} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Thus, z⊤Jf◦g(x)z = z⊤Sz > 0, ∀z ∈ RC−1 \\{0} and so, Jf◦g(x) is positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This holds for arbitrary x ∈ RC−1  so it follows that f ◦ g is the gradient of a twice-differentiable convex function F by Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 with F being  strictly convex since Jf◦g(x) is positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' In other words, f ◦ g is the gradient of a twice-differentiable Legendre  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  F  Proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1  Proof of Properties of LogSumExp+ and softmax+  Since positive definiteness of Ju(x) for all x ∈ RC−1  implies strict convexity of f and strict convexity of f implies invertibility of u, it suffices to prove that Ju(x) is  positive definite for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Fix x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' For ease of notation, we denote M as Ju(x) where Mij refers to the entry within the i-th row and  j-th column of Ju(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Consider any row i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , C − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We have  Mii =  exp(xi)  1 + �C−1  k=1 exp(xk)  �  1 −  exp(xi)  1 + �C−1  k=1 exp(xk)  �  ,  Mij = −  exp(xi)  1 + �C−1  k=1 exp(xk)  exp(xj)  1 + �C−1  k=1 exp(xk)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Observe that Mii−�  j̸=i |Mij| =  exp(xi)  1+�C−1  k=1 exp(xk)  �  1 −  �C−1  k=1 exp(xk)  1+�C−1  k=1 exp(xk)  �  > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This holds for arbitrary i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , C −1}  so it follows that Ju(x) is strictly diagonally dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This implies that Ju(x) is positive definite so it follows that  f is strictly convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' This completes the proof of the key properties of the LogSumExp+ function and its gradient  softmax+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Proof of functions learned by LegendreTron are inverse canonical links  We first note that v−1 = (∇g1) ◦  (∇g2) ◦ · · · ◦ (∇gB) is indeed invertible since the RHS is invertible by the strong convexity of g1, g2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , gB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Since  each ∇gi is symmetric and positive definite, it follows that v−1 is the gradient of a twice-differentiable Legendre  function by applying Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3 recursively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' It follows from Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2 that Jv−1(x) is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We also have  that |Jv−1(x)| > 0 so Jv−1(x) is positive definite for all x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Recall that LogSumExp+ is twice-differentiable with gradient u = softmax+ and Hessian Ju(x) being strictly  diagonally dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' That is, Ju(x) is symmetric and positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Applying Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='3 on u ◦ v−1 allows us  to deduce that u ◦ v−1 is the gradient of a twice-differentiable Legendre function that maps to ˜∆C−1 so u ◦ v−1 can  be set as the inverse of an implicit canonical link function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  14  G  Experimental Details  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='1  Network Architecture and Optimisation Details  Experiment details on architecture and optimisation parameters for LegendreTron (LT) and multinomial logistic  regression (MLR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' Here we denote α as the learning rate, λ as weight decay, γ as the multiplicative rate of decay  applied to α every S epochs through a step-wise learning rate scheduler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We used the Adam optimiser for all  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Dataset(s)  Model B H M  α  γ  S Epochs Batch Size  MNIST/FMNIST/KMNIST  LT  1  4  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7  4  200  128  MNIST/FMNIST/KMNIST  MLR  \\  \\  \\  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='7  4  200  128  aloi  LT  2  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='95 4  360  64  aloi  MLR  \\  \\  \\  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='95 4  360  64  LIBSVM/UCI/Statlog (other datasets)  LT  2  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='95 4  240  64  LIBSVM/UCI/Statlog (other datasets)  MLR  \\  \\  \\  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='95 4  240  64  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='2  LogSumExp trick for softmax+  Let u = softmax+ and consider x ∈ RC−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We have  log(Π−1(u(x))) =  �  log  �  exp(x1)  1 + �C−1  k=1 exp(xk)  �  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , log  �  exp(xC−1)  1 + �C−1  k=1 exp(xk)  �  , log  �  1  1 + �C−1  k=1 exp(xk)  ��⊤  where log on the LHS is applied elementwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We seek an alternate expression for log(Π−1(u(x))) that is numerically  stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  Let x∗ = max(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , xC−1) and S = exp(−x∗) + �C−1  k=1 exp(xk − x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' We can write  log(Π−1(u(x))) =  �  log  �exp(x1 − x∗)  S  �  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , log  �exp(xC−1 − x∗)  S  �  , log  �exp(−x∗)  S  ��⊤  = (x1 − x∗ − log(S), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content=' , xC−1 − x∗ − log(S), −x∗ − log(S))⊤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  It can be observed that this expression is numerically stable for any large values of x∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
+page_content='  15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/dtFJT4oBgHgl3EQf_i1w/content/2301.11695v1.pdf'}
diff --git a/eNE2T4oBgHgl3EQfbQcn/content/tmp_files/2301.03882v1.pdf.txt b/eNE2T4oBgHgl3EQfbQcn/content/tmp_files/2301.03882v1.pdf.txt
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+Generational variance reduction in Monte Carlo criticality
+simulations as a way of mitigating unwanted correlations
+Kévin Fröhlicher,∗,a Eric Dumonteil,b Loïc Thulliez,b Julien Taforeau,a and
+Mariya Brovchenkoa
+aInstitut de Radioprotection et de Sûreté Nucléaire (IRSN)
+31 avenue de la Division Leclerc, 92260, Fontenay-aux-Roses, France
+bIRFU, CEA, Université Paris-Saclay
+91191, Gif-sur-Yvette, France
+∗Email: kevin.frohlicher@irsn.fr
+Number of pages:
+38
+Number of tables:
+4
+Number of figures:
+18
+arXiv:2301.03882v1  [cond-mat.stat-mech]  10 Jan 2023
+
+Abstract
+Monte Carlo criticality simulations are widely used in nuclear safety demonstrations, as they
+offer an arbitrarily precise estimation of global and local tallies while making very few assumptions.
+However, since the inception of such numerical approaches, it is well known that bias might affect
+both the estimation of errors on these tallies and the tallies themselves. In particular, stochastic
+modeling approaches developed in the past decade have shed light on the prominent role played by
+spatial correlations through a phenomenon called neutron clustering. This effect is particularly of
+great significance when simulating loosely coupled systems (i.e., with a high dominance ratio). In
+order to tackle this problem, this paper proposes to recast the power iteration technique of Monte
+Carlo criticality codes into a variance reduction technique called Adaptative Multilevel Splitting.
+The central idea is that iterating over neutron generations can be seen as pushing a sub-population
+of neutrons towards a generational detector (instead of a spatial detector as variance reduction
+techniques usually do). While both approaches allow for neutron population control, the former
+blindly removes or splits neutrons.
+In contrast, the latter optimizes spatial, generational, and
+spectral attributes of neutrons when they are removed or split through an adjoint flux estimation,
+hence tempering both generational and spatial correlations. This is illustrated in the present article
+with a simple case of a bare slab reactor in the one speed theory on which the Adaptive Multilevel
+Splitting was applied and compared to variations of the Monte Carlo power iteration method used
+in neutron transport. Besides looking at the resulting efficiency of the methods, this work also aims
+at highlighting the main mechanisms of the Adaptive Multilevel Splitting in criticality calculations.
+Keywords — Monte Carlo Criticality Simulations, Neutron Clustering, Power Iteration, Variance
+Reduction, Adaptive Multilevel Splitting
+2
+
+I.
+INTRODUCTION
+For a long time, dating back 80 years, the simulation of neutron transport in multiplicative
+media has been one of the main motivations leading the development of intensive systems (digital)
+calculation capabilities and the Monte Carlo algorithm itself. Nuclear engineers and researchers
+still consider Monte Carlo methods as high fidelity methods, compared to deterministic ones, since
+they estimate global and local tallies with an arbitrary precision while making very few hypotheses.
+Nuclear data uncertainties are often considered as the only source of uncertainty (while others
+such as technological uncertainties are usually neglected or ignored), aside from the stochastic
+fluctuations intrinsic to the very nature of the method. Therefore, Monte Carlo simulations are
+widely used as reference calculations when validating new models/methods.
+Criticality calculations have been used for decades in reactor physics to characterize the
+behavior of multiplicative nuclear systems through their keff by solving the transport critical equa-
+tion [1, 2, 3, 4, 5]. This equation takes the form of an eigenvalue equation in which fixed neutron
+sources are neglected (for instance, spontaneous fissions), and the production term of the equation
+is modified to ensure that the neutron population remains constant through generations. Solving
+this k-eigenvalue equation by Monte Carlo methods is generally done using an iterative algorithm
+based on the power iteration method, and therefore allows characterizing the fundamental mode of
+the system as if it was exactly critical. Despite fundamental questions related to the inner nature
+of the problem that is solved due to the renormalization of fission neutrons by the keff [6], this
+method has made a consensus when it comes to criticality calculations. It is now widely used not
+only in nuclear criticality safety but also in reactor physics. For loosely coupled systems, however,
+it can exhibit convergence issues [7] that can lead to potentially significant errors in estimating
+global and local tallies and their statistical uncertainties. By loosely coupled systems, we mean
+systems in which neutrons may have difficulty travelling from one part of the geometry to another
+over several generations, typically large systems.
+Indeed, in the late 60’s, different works shed light on the biases on the keff estimation in crit-
+icality calculations [8, 9, 10, 11, 12] which were however increasingly used by the nuclear industry.
+Later, Ueki et al. [13], and Dumonteil et al. [14] highlighted respectively the fact that generational
+and spatial correlations were also a source of biases in the spatial flux estimation. Additionally,
+different works [15] pointed out that tallies estimators are usually built from observations drawn
+3
+
+in successive generations of neutrons which lead to an actual underestimation bias of the tallies
+uncertainty [16, 13].
+At the heart of these observations lies the fact that, while both types of correlations (genera-
+tional and spatial) are deeply rooted in the fission phenomenon and therefore also develop in actual
+nuclear configurations [17], their magnitude might indeed soar in numerical simulations due to the
+combination of the population control and the small number of neutrons that can be simulated
+compared to natural systems. In particular, the so-called neutron clustering effect has received
+considerable attention in the past decade. It is typical of branching spatial processes since its
+origin is found in the asymmetry between neutron captures, which occur everywhere, and neutron
+births, which can only happen in the vicinity of other neutrons. Whenever the system is loosely
+coupled, and even in the presence of absorbing boundaries [18], the asymmetry creates spatial
+patterns of randomly distributed neutron clusters. This results in the under-sampling of some
+regions and ultimately leads to biased estimates of the global (e.g., keff) and local (e.g., flux) tallies
+[19], which can have drastic consequences when feedback effects are taken into account through
+multi-physics coupling [20, 21]. This phenomenon, called neutron clustering, has been investigated
+using statistical mechanics tools and, in particular, could be modeled using the so-called branching
+Brownian motion, which couples a Galton-Watson birth-death process to standard Brownian mo-
+tion [14, 18, 22, 23]. Although neutron clustering is usually mitigated by sampling more particles
+into the Monte Carlo simulation, different strategies have been tested to avoid the occurrence of
+this phenomenon. While attenuating the phenomenon, neither the introduction of two-time scales
+that reproduce the effect of delayed neutrons nor the presence or absence of population control
+[24] affect this qualitative picture [25, 26]. Because the persistence of neutron families was the key
+to counter this effect in simulations, beneficial modifications of the Monte Carlo power iteration
+method were recently investigated [27, 20, 28].
+Starting from these last observations, this paper proposes a different approach to tackle
+generational and spatial correlations (hence, to temper Monte Carlo criticality biases). The ob-
+servation that drives our approach is that the power iteration randomly kills or splits neutrons
+during population control. The only way to ensure that neutron families extinction is slowed down
+is to restart neutrons that will survive for many generations. Hence, the paradigm change here
+consists of seeing the population control acting on a super/subcritical medium as a way to either
+4
+
+select neutrons or enforce neutrons persistence through generations. In other words, the goal is
+to estimate the asymptotic state of our system conditioned on its survival: such approaches are
+known in mathematics as Fleming-Viot processes [29, 30]. These processes can also be seen as an
+estimator for rare events [31] and therefore as a variance reduction techniques [32] which primarily
+aims at "pushing" neutron to a given "detector" without introducing any bias in the estimates of
+tallies associated to this detector. These techniques can use an importance map whose quality will
+condition the improvement in the method efficiency. In the present case, our detector could be a
+generational detector, and the importance map could be the adjoint flux [33, 34, 35] that could be
+estimated on-the-fly or using external codes. A generalization of such Fleming-Viot processes that
+allows for handling importance functions has recently appeared. This method is based on the use
+of particle splitting and using an on-the-fly estimation of the importance levels at which particles
+are split [36]. It has been named Adaptative Multilevel Splitting (AMS) and has been adapted to
+neutron transport in the context of shielding calculations [37, 38]. The present paper will show
+that modification of this variance reduction technique that has proven successful in shielding cal-
+culations can also help mitigate correlations and biases in Monte Carlo criticality calculations. It
+will also show that AMS can be used alone or on top of other population control techniques (such
+as the branchless collision method [15]).
+The paper is organized as follows. In Section II, the Adaptive Multilevel Splitting method,
+and its extension to criticality calculations are presented, while Section III outlines the main numer-
+ical results and discussions about methods performances. All methods were compared regarding
+keff and flux estimations, as well as their impact on spatial and generational correlations.
+II.
+ADAPTIVE MULTILEVEL SPLITTING
+II.A.
+Original algorithm for particle transport
+The Adaptive Multilevel Splitting (AMS) is a method initially developed in applied math-
+ematics to compute rare events probability. Initially intended for continuous Markov chains [36],
+it was then adapted to discrete Markov chains [39] and used in particle transport for attenuation
+and radiation protection problems [40, 41].
+The concept is to re-sample particles towards a detector iteratively. The key idea underlying
+the method is to re-sample particle histories closer and closer to a detector. To this aim, neutron
+5
+
+histories are first simulated from birth to death (disappearance of all its particles by capture,
+leakage, Russian Roulette) and ranked following an importance criterion. According to the ranking,
+the least important histories are deleted, and histories re-sampled among the remaining ones. The
+general algorithm is illustrated in Figure 1. The general algorithm is here described for analog
+transport of particles, it is however possible to use the AMS in a weighted Monte Carlo game [39].
+Initialize
+N neutron
+histories/tracks
+Transport
+particles
+All
+particles
+are dead ?
+Ranking tracks
+Stopping criterion
+(I(K) = IMAX)
+met ?
+Re-sample
+new tracks
+End of iterations
+Collision
+Splitting
+event ?
+Create new
+branch in track
+Add point
+in branch
+Increasing
+importance
+in branch ?
+Add point
+in branch
+Order tracks
+I(1) ≤ I(2) ≤ ... ≤ I(N)
+Define kill
+level as I(K)
+Kill Ki tracks
+with I ≤ I(K)
+Sample Ki new
+tracks from the
+N − Ki remaining
+tracks (with
+I > I(K))
+LEGEND
+Step
+Substep
+Test
+yes
+no
+yes
+yes
+no
+yes
+no
+Fig. 1. AMS algorithm
+II.A.1.
+AMS tree structure and transport step
+The AMS consists of successive fixed source simulations, where each batch , i.e. each sim-
+ulation, is composed of N tracks (initially independent) representing N particle histories. Here,
+a particle history is the whole trajectory of a particle and its progeny arising from collisions and
+splitting events, from the birth of the initial particle to the death of all its progeny. At each colli-
+sion, the outgoing particle of the collision is assigned an importance value using a cost function (see
+Section II.A.4). If the particle importance is higher than the previous branch point importance,
+the particle is saved as a point in the AMS structure. Each track initially starts with a unique
+6
+
+branch, and new branches are appended every time a splitting event occurs (it can be physical
+like fission or numerical like splitting in a weighted Monte Carlo game). At any time, a track
+importance is equal to the maximum importance of its branches, and the importance of a branch
+is equal to the maximum importance amongst its points. The resulting tree structure is illustrated
+in Figure 2.
+AMS BATCH
+Iteration number
+TRACK 1
+...
+TRACK N
+Importance
+BRANCH 1
+BRANCH 2
+...
+Importance
+POINT 1
+POINT 2
+...
+Position
+Direction
+Energy
+Time / Generation
+Weight
+Importance
+Fig. 2. AMS track/branch/point structure
+II.A.2.
+Ranking the histories
+Once all particles in an iteration i are dead (by capture, leakage, Russian Roulette), the N
+tracks are ranked in increasing order of importance. At this point, a kill level Ikill is defined by
+the importance of the K-th worst track, where K is a user-defined parameter.
+I(i)
+kill ≡ I(i)(K)
+(1)
+When a track has reached the detector, its importance is set to infinity. At the end of an iteration,
+the algorithm samples new tracks according to the following description if the stopping criterion
+7
+
+that is defined hereinafter has not been met.
+AMS iterations stop when
+I(i)
+kill = I(i)
+MAX
+(2)
+where I(i)
+MAX is the maximum track importance at iteration i. If the algorithm iterated correctly
+(see discussion on the importance in Section II.A.4), it should stop when
+I(i)
+kill = I(i)(K) = ∞.
+(3)
+This equation implies that tracks K to N have reached the detector (since their importance is
+superior to Ii(K)), hence, at least N − K + 1 tracks have reached the detector.
+II.A.3.
+Sampling new particles
+After the kill level has been computed, all tracks whose importance is lower or equal to this
+level are deleted from the batch structure. Since multiple tracks can have the same importance,
+the number of deleted tracks is not necessarily equal to K (it can be higher), and we denote it Ki
+at iteration i, where Ki ≡ card(S) ≥ K, with S defined as
+S =
+�
+k, k ∈ [1; N] | I(i)(k) ≤ Ikill
+�
+.
+(4)
+To keep the total number of tracks constant, Ki tracks are sampled uniformly among the
+remaining ones to be duplicated to make up for the deleted ones. When a track is selected for
+duplication, the first point of importance greater than the kill level is copied into the new track.
+The new track thus created is simulated as described in Section II.A.1. This is illustrated by Figure
+3.
+Once the AMS algorithm has stopped (we note the last iteration I), scores are computed
+using the following estimator
+�φdetector = φ(I)
+detector × αAMS.
+(5)
+where �φdetector is an unbiased estimator of φdetector, φ(I)
+detector is the estimation of score φdetector
+based on all iterations tallies using classical Monte Carlo estimators (e.g., track length or collision
+8
+
+I(1)
+kill
+x
+Detector
+y
+TRACK 1
+TRACK 2
+TRACK 3
+(a) Iteration 1
+I(2)
+kill
+x
+Detector
+y
+TRACK 1
+TRACK 2
+TRACK 3
+(b) Iteration 2
+I(3)
+kill
+x
+Detector
+y
+TRACK 1
+TRACK 2
+TRACK 3
+(c) Iteration 3
+Fig. 3. AMS iterations with a detector defined in the (x, y) plane, with N = 3 and K = 1. The
+closer the detector, the more important the particle is.
+.
+estimators) and αAMS is defined by
+αAMS ≡
+I�
+i=1
+�
+1 − Ki
+N
+�
+.
+(6)
+While αAMS is used to correct tallies so that results remain unbiased, it can also be interpreted
+as an estimation of the probability to reach the detector. Although it is not described here, it is
+possible to define an on-the-fly scoring procedure to compute scores outside the detector.
+II.A.4.
+About the importance function
+The importance function is a function that maps RL → R, where L is the number of pa-
+rameters considered to compute the importance (position, direction, energy, ...). Its purpose is
+to rank tracks in the AMS (see Section II.A.2) and should be chosen to push neutron histories
+towards the detector. The optimal choice for that function should lead to the best estimation of
+the probability αAMS leading to the minimum variance [42]. In particle transport, although there
+9
+
+is no formal demonstration for the AMS, the solution of the adjoint Boltzmann equation for the
+detector [35] is generally considered to be the optimal choice.
+Although there are no further requirements, it is best to avoid importance functions pre-
+senting discrete levels that could lead to aggregates of particles. Indeed, for a discrete importance
+function, if the N −K+1 particles with the highest importance were on the same level, the splitting
+level would be equal to I(i)
+MAX < ∞, and the iterations would stop before enough particles have
+reached the detector.
+Finally, since the importance function is only used to rank particles, only the relative impor-
+tance between two particles matters, making the AMS a reasonably robust and easy to use method
+[41].
+II.B.
+Adaptation to criticality calculations
+For subcritical systems, the neutron population tends to go extinct with time/generationsa.
+Therefore, it is clear that the lower the keff, the less likely a neutron history is to survive over several
+generations, and reaching a distant generation is then a rare event. In criticality calculations, the
+AMS is used to re-sample histories and push them across generations.
+Moreover, it has been
+specified in Section II.A.1 that any collision point could be added to the AMS structure, which
+implies that any collision point could be used for the re-sampling of neutrons. Compared to the
+power iteration, where new neutrons are sampled at fission sites only, this induces a non-negligible
+difference in terms of the precise equation solved by the algorithm due to spectral and spatial
+heterogeneity effects as explained by Cullen et al. in Ref. [6]. However, to ease the comparison
+with the power iteration method, only fission points can be saved, as it is possible to store any
+stopping point as long as the system remains Markovian.
+In a subcritical system, keff can be interpreted as the probability for a neutron to go from one
+generation to the next. With that in mind, the probability for one neutron history with initially
+one particle to reach generation G is
+Psurvive(G) = kG
+eff.
+(7)
+aOne can artificially define a generation as a neutron trajectory between birth and death by absorption or
+leakage. Therefore, neutrons born by fission are considered in the next generation of the particle that caused the
+fission.
+10
+
+Hence, tracking neutrons over generations in a subcritical system can also be considered as an
+attenuation problem over generations when no population control is done, making this a suitable
+scope for using the AMS. The idea is then to define a detector in generation (i.e., a target generation
+towards which neutrons will be pushed by the re-sampling algorithm) and to track neutrons not in
+time but over successive generations. For this purpose, in the subsequent sections of this article,
+the importance function used to rank tracks will be of the following form
+I(rrr, g) = g + f(rrr)
+(8)
+where g is the neutron generation to push neutrons over generations, and 0 ≤ f(rrr) ≤ 1 is a function
+of space used to discriminate neutrons of the same generation so that the importance function is
+not discrete (see Section II.A.4). The resulting algorithm is compared to the Power Iteration in
+Figure 4.
+N fission sites
+initialize
+FISSION BANK
+N neutrons
+PARTICLE DEATH
+fission
+capture
+leakage
+sample N neutrons
+then empty bank
+fill fission
+bank
+Transport neutrons over 1 generation
+capture
+leakage
+Iterate
+over G
+cycles
+(a) PI: iterates over fission neutrons (1 generation
+per iteration) after being initialized with an arbi-
+trary fission distribution.
+Neutrons are sampled
+from fission neutrons of the last iteration.
+N analog tracks
+initialize
+N TRACKS
+Ki new tracks
+TRACKS DEATH
+all branches are dead
+either by capture, leakage, ...
+delete Ki tracks
+sample Ki
+new tracks
+rank the
+N tracks
+Transport tracks over several generations
+tracks structures are filled at collisions
+Iterate until
+N − K + 1 tracks
+have reached
+generation G
+(b) AMS in criticality:
+iterates over re-sampled
+tracks (multiple generations per iteration) after be-
+ing initially fed with N analog tracks.
+Fig. 4. Comparison scheme between the Power Iteration (PI) and AMS used for criticality.
+The probability of reaching the detector defined by Equation 6 could therefore be compared
+to the keff given as a probability of survival (see Equation 7)
+αAMS =
+I�
+i=1
+�
+1 − Ki
+N
+�
+= kG
+eff
+(9)
+11
+
+where I is the total number of AMS iterations, and G is the target generation. Therefore we can
+build the following estimation of the keff
+keff =
+� I�
+i=1
+�
+1 − Ki
+N
+��1/G
+.
+(10)
+While this holds for subcritical systems, it is no longer valid when the system is critical
+or supercritical.
+In the description above, the neutron population is not constrained by some
+population control mechanism, which allows for fluctuations in the system’s number of particles.
+This mechanism can induce population growth for systems close to criticality (and supercritical
+systems), thus increasing the number of branches inside a track. Since it is necessary to take
+those branches into account during the re-sampling step, the number of re-sampled branches may
+increase as iterations go by, leading to slower and slower iterations (as well as more and more
+memory used). Besides, as in fixed source calculations, neutron histories must end at some point
+to be able to rank the tracks as previously described, which could be troublesome in critical and
+supercritical regimes. Thus, the branchless collision method [15] was used to limit the number of
+branches inside a track (equal to one if no splitting is used), preventing these issues. For a system
+with leakage, making particles carry population fluctuations through statistical weights produces
+a numerically subcritical system (no particles are produced by splitting, and some disappear by
+leaking out of the geometry). Hence, it is possible to reproduce a population attenuation over
+generations that appeals to the use of the AMS whatever the keff if the branchless collision method
+is used.
+III.
+APPLICATION TO A ONE-DIMENSIONAL SLAB REACTOR
+To characterize the AMS behavior regarding criticality calculations, the method was tested
+on a one-dimensional bare slab reactor. We tested the method on a simple case in one dimension
+with mono-energetic neutrons, thus limiting the number of particles needed to explore the space
+and allowing us to compare results to a simple analytical solution.
+12
+
+III.A.
+Bare slab properties
+The modeled system is a one dimensional homogeneous bare slab reactor with leakage on
+the sides, the total size of the slab being 100 cm, from xmin = −50.0 cm to xmax = 50.0 cm. The
+slab size was chosen so the system would be loosely coupled considering the cross sections of the
+system, presented in Table I. Three reactions are possible following a collision in analog transport:
+fission, capture, and isotropic scattering. The cross sections were arbitrarily chosen to model a
+slightly supercritical system to assess the capability of the AMS to model supercritical systems
+using the branchless collision method, the resulting keff being equal to 1.03437. The simplicity of
+TABLE I
+Physical properties for homogeneous 1D rods
+Mean number of fission neutrons (¯ν)
+2.383
+Neutron speed (v)
+2.2 × 104 cm.s−1
+Macroscopic cross sections
+Fission (Σf)
+0.250 cm−1
+Absorption (Σa)
+0.575 cm−1
+Scattering (Σs)
+0.425 cm−1
+Total (Σtot)
+1.00 cm−1
+the system also allowed us to compute an analytical solution using diffusion theory [43], which is
+used as a comparison in the following results
+φ(x) = φ0 cos
+�
+π
+2(a + z0)x
+�
+(11)
+with φ0 depending on the normalization, a being the reactor half size (here a = 50.0 cm) and z0
+is the linear extrapolated end point of the reactor and is defined as
+z0 =
+2
+3Σtr
+(12)
+where Σtr is the transport cross section, which is equal to the total macroscopic cross section Σt
+since all collisions are isotropic in the laboratory referential.
+Different calculation options were tested and compared to assess the effects of each regarding
+clustering and variance estimation. The sets of options corresponding to each case are described
+in Table II. Four different simulations were done for the power iteration to distinguish between
+13
+
+the effects of the methods used. As a matter of fact, collisions were simulated either by in an
+analog way or by using the branchless collision method. As for the population control operated
+between cycles, two sampling methods were used, a simple sampling with replacement and the
+combing method [44]. For the AMS, since the system is supercritical, no simulation with analog
+collisions was done since it would lead to a divergence of the particle number over generations,
+hence computation cost issues.
+TABLE II
+Description of calculation parameters
+Case
+Population control
+Collisions
+Importance (AMS only)
+PI analog
+sampling with replacement
+analog
+PI branchless
+sampling with replacement
+branchless
+PI combing
+combing
+analog
+PI combing branchless
+combing
+branchless
+AMS branchless
+AMS
+branchless
+g + cos
+� πx
+2a
+�
+All the calculations presented below started from a uniform fission distribution and were done
+with 1000 neutrons per cycle (N = 1000 initial independent tracks for the AMS) over G = 1000
+successive generations in M = 1000 independent runs. Having too few particles per generation to
+facilitate clustering in all cases was deliberate to study the effects of methods on neutron clustering.
+Finally, estimators used in this work for the flux and the keff rely on the on-the-fly scoring
+procedure detailed in Ref. [41]. In each generation i, the flux was computed using the collision
+estimator and normalized so its spatial shape could be averaged over successive generations. The
+keff estimator is based on the physical interpretation of the keff, and was computed as the ratio of
+neutrons produced in a generation over the ones produces in the previous generation.
+III.B.
+Convergence of inactive cycles and behavior of the Shannon entropy
+Firstly, the convergence of the keff estimates in each generation, and the Shannon entropy
+[45] of the system were considered to set the number of inactive cycles. Firstly, the convergence
+of the keff is shown on Figure 5 as the mean keff per generation, computed in M independent
+simulations, as a function of the cycle number
+keff(g) = 1
+M
+M
+�
+m=1
+N (m)
+g
+N (m)
+g−1
+(13)
+14
+
+where N (m)
+g
+is the number of neutrons born in generation g for simulation m. Its convergence is
+quite fast for every calculation. Apart from statistical fluctuations that have no impact on the
+mean value, as seen later, all methods seem to converge towards the same value.
+0
+200
+400
+600
+800
+1000
+Generation (g)
+1.0200
+1.0225
+1.0250
+1.0275
+1.0300
+1.0325
+1.0350
+1.0375
+1.0400
+keff(g)
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+Fig. 5. Convergence of the average keff (over 1000 independent runs) with 3σ confidence intervals.
+Cases PI branchless, PI combing branchless, and AMS branchless show the same results, with
+narrow confidence intervals.
+Secondly, the Shannon entropy was used to assess the spatial flux convergence [45] and set
+the number of generations that have been discarded when computing average scores. Its averaged
+value over M independent simulation has been computed in each generation as such
+H(g) = 1
+M
+M
+�
+m=1
+�
+−
+Nbins
+�
+l=1
+φ(m)
+g
+(xl)
+φ(m)
+g,tot
+log2
+�
+φ(m)
+g
+(xl)
+φ(m)
+g,tot
+��
+(14)
+where Nbins is the number of spatial bins along the x (here 100 bins), φ(m)
+g
+(xl) is the normalized
+flux estimated in generation g in bin xl for simulation m, and φ(m)
+g,tot is the normalized flux at
+cycle g for simulation m integrated over x. The results are plotted in Figure 6. As expected, the
+entropy converges slower than the keff. All cases were considered to have reached an acceptable
+convergence for g = 200. For the rest of the article, the number of inactive cycles was set to 200.
+15
+
+0
+200
+400
+600
+800
+1000
+Generation g
+6.1
+6.2
+6.3
+6.4
+6.5
+6.6
+6.7
+H(g)
+cosinus
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+Fig. 6. Evolution of the mean entropy over generations.
+Unlike the keff, the Shannon entropy, as defined in Equation 14, and presented in Figure
+6, does not converge to the same asymptotic value for all the different methods and is lower
+than the theoretical value for a cosine shape distribution in all cases.
+Moreover, the entropy
+presents oscillations when the AMS is used.
+This phenomenon is likely due to how the AMS
+injects particles into the simulation and can be decomposed into two underlying mechanisms: the
+numerical subcriticality of our system (1) and the re-sampling of new particles by the AMS (2), as
+portrayed in Figure 7. Indeed, as explained in Section II.B, the system was set to be numerically
+subcritical thanks to the branchless collision method to model an attenuation problem for the AMS.
+Thus, without population control, the population progressively goes extinct over generations (see
+mechanism (1) on Figure 7). As for the re-sampling of new particles, detailed in Section II.A.3,
+the algorithm samples about K new tracks close to an importance level defined by the kill level
+of the current iteration. Since the generation of a particle mainly drives the importance value, as
+stated by Equation 8, we have
+g ≤ Ikill(i) ≤ g + 1.
+(15)
+The new tracks sampled by the algorithm will therefore start either in generation g with an
+16
+
+Generation / importance
+N particles 
+ N collisions
+Ikill
+Numerically subcritical 
+ less collisions at 
+each generations 
+(1)
+AMS injects Ki new tracks in g / g+1 
+(branchless 
+ Ki new particles) 
+(2)
+generation g
+generation g+1
+Fig. 7. AMS population control mechanisms. In this example, all neutrons that were re-sampled
+appeared in generation g.
+importance higher than Ikill(i), or in generation g + 1 (illustrated by the dashed area on Figure
+7). This will result in a much higher increase in the total population sampled in these generations
+(see mechanism (2) on Figure 7). Intuitively, the more particles in the system, the closer (and
+smoother) their distribution will be to the natural distribution. Hence, as the system loses particles,
+the flux estimation gets noisier due to statistical fluctuations. Although these fluctuations have
+no visible impact on the average estimate, they slightly modify the entropy. Consequently, when
+the number of particles in the system is increased by the re-sampling of the AMS in generations
+g and g + 1, the flux estimate in generation g + 1 gets smoother than in previous generations,
+inducing an increase in the entropy (which will then decrease as particles disappear, until the
+next re-sampling step, and so on).
+To reduce the amplitude of these fluctuations, one could
+reduce the number of re-sampled particles at each iteration by reducing the value of K. It would
+also increase the frequency of the entropy since the re-sampling of particles would occur more
+frequently. To illustrate the phenomenon, the mean number of collisions (unweighted) and the
+corresponding entropy per generation were computed and plotted on Figure 8 for K/N = 25% and
+K/N = 10%. Making the system less subcritical (numerically) should also reduce the frequency of
+17
+
+the oscillations; however, it should not modify the amplitude of the oscillations. Another way to
+make the oscillations disappear without changing the simulation would be to compute the Shannon
+entropy over a coarser spatial mesh, which would lessen the spatial fluctuations.
+0
+200
+400
+600
+800
+1000
+Generation (g)
+1300.0
+1412.5
+1525.0
+1637.5
+1750.0
+Number of collisions
+6.300
+6.375
+6.450
+6.525
+6.600
+H(g)
+K/N = 25%
+K/N = 10%
+Fig. 8. Mean entropy (solid lines) and mean number of collision points (dashed lines) per generation
+for the AMS + branchless case, for K/N = 10% and K/N = 25%.
+In a nutshell, the AMS does not seem to lengthen nor abridge the convergence period.
+Besides, the observed oscillations of the flux entropy it might produce are natural and do not
+affect the average flux estimation.
+III.C.
+Fundamental mode estimates
+The fundamental mode of a multiplicative system described by the k-eigenvalue equation is
+characterized by the highest eigenvalue k0 = keff and the associated eigenvector : the fundamental
+flux distribution.
+For the system described earlier, the keff distribution over 800 actives cycles in 1000 in-
+dependent simulations is plotted in Figure 9. Cases with branchless collision show quite similar
+distributions, with much less dispersion around their mean value than for the non-branchless cases.
+Hence, regarding the keff estimation, the branchless collision method seems to be the main con-
+18
+
+tributor to the variance reduction, while the differences between population control methods are
+not very significant.
+0.85
+0.90
+0.95
+1.00
+1.05
+1.10
+1.15
+1.20
+keff
+PI
+analog
+PI
+branchless
+PI
+combing
+PI
+combing
+branchless
+AMS
+branchless
+keff = 1.03437
+Fig. 9. Distribution of the keff after convergence. Dashed lines represent the first, second and third
+quartiles of the empirical distribution.
+Besides the eigenvalue, the fundamental flux was also computed over 800 successive genera-
+tions in 1000 independent simulations, and is plotted on Figure 10. The first striking observation
+is the lack of consistency between the solutions of the different methods, even with 3σ confidence
+intervals. Although they do not include the analytical solution within their 3σ confidence inter-
+val, the cases that show the less difference with the analytical cosine are the power iteration with
+branchless collision and combing used for population control case, and the AMS combined with
+branchless caseb.
+These observed deformations of the flux shape are likely due to clustering effects that affect
+bThe analytical solution was computed using the diffusion theory, this is why minor discrepancies are expected,
+especially on the sides.
+19
+
+the estimation of the mean spatial flux. Since our goal was to compare methods behavior regarding
+clustering, those effects were expected due to the low number of particles simulated in each batch,
+and increasing their number would tend to mitigate clustering effects until they disappear.
+−40
+−20
+0
+20
+40
+x [cm]
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+1.6
+φ(x) [a.u.]
+Diffusion
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+Fig. 10. Spatial flux profile with 3σ confidence interval (top) with the relative (center) and absolute
+(bottom) discrepancies against the analytical cosine-shaped solution.
+By flattening the average flux distribution, the presence of neutron clusters should increase
+the entropy of the average distribution since the entropy of a uniform distribution is higher than the
+entropy of a cosine distribution. At the same time, the estimation of the spatial flux in a generation
+is noisier than its average over multiple generations, which tend to lower the entropy, and clusters
+in a generation should lower the entropy even more. This could explain the different asymptotic
+values displayed in Figure 6. Table III displays the values of the average spatial flux entropy, as
+well as the asymptotic value to wich the generational entropy converges (the one shown in Figure
+6). We can see that the the averaged flux entropy is systematically higher than the reference
+solution entropy due to flatter spatial shapes than the analytical diffusion solution, whereas the
+asymptotic entropy reached in a generation is systematically lower due to statistical noise (which
+could be reduced if the number of bins used to compute the entropy were to be decreased). In
+that regard, the AMS branchless and PI combing branchless cases present the lowest discrepancies
+20
+
+(about the same order of magnitude for both methods) with the analytical solution, which implies
+less noise in the spatial estimation of the flux and an average value closer to the analytical solution
+than the other cases.
+TABLE III
+Values for the asymptotic entropy reached during source convergence and for the flux distribution
+averaged over active cycles for each case. The differences are computed with respect to the analyt-
+ical solution; a negative difference means that the distribution is more ordered than the analytical
+one (in terms of entropy), while a positive difference means that the distribution is less ordered
+than the analytical one (closer to a uniform distribution).
+Case
+Converged entropy
+Averaged flux entropy
+value
+difference
+value
+difference
+Analytical solution
+6.4673
+-
+6.4673
+-
+PI analog
+6.0525
+−4.148 × 10−1
+6.5424
+7.511 × 10−2
+PI branchless
+6.2427
+−2.246 × 10−1
+6.4975
+3.020 × 10−2
+PI combing
+6.1838
+−2.835 × 10−1
+6.5088
+4.154 × 10−2
+PI combing branchless
+6.3976
+−6.969 × 10−2
+6.4687
+1.375 × 10−3
+AMS branchless
+6.3629
+−1.044 × 10−1
+6.4704
+3.168 × 10−3
+The observed bias on the average flux shape related to the clustering phenomenon is further
+examined in the following section.
+III.D.
+Effects of the AMS on clustering
+To assess the probability for clusters to appear, spatial correlations were computed using
+empirical estimations of Pearson’s correlation coefficient between each spatial bin defined by
+ρij = Cov [φ(xi), φ(xj)]
+σ [φ(xi)] σ [φ(xj)]
+(16)
+where Cov [φ(xi), φ(xj)] is the covariance between flux estimations in spatial bins xi and xj, and
+σ [φ(xi)] is the standard deviation of the flux in spatial bin xi. The results are presented on Figures
+11 and 12 for 100 spatial bins. While cases PI analog, PI branchless, and PI combing show similar
+levels of spatial correlations (see Figure 11), combing branchless and AMS branchless cases present
+almost nonexistent spatial correlations as seen in Figure 12. Since these correlations are deeply
+linked to the probability for clusters to form [22], this implies that the two above mentioned cases
+are the least likely to present neutron cluster problems. High correlation levels are linked to the
+number of correlated pairs of particles in the system, whose number increases as generations go by
+21
+
+because of independent familyc extinctions [23, 27].
+−50−25 0
+25 50
+x [cm]
+−50
+−25
+0
+25
+50
+x [cm]
+-1.0
+0.0
+1.0
+Correlation factor
+(a) PI analog
+−50−25 0
+25 50
+x [cm]
+−50
+−25
+0
+25
+50
+x [cm]
+-1.0
+0.0
+1.0
+Correlation factor
+(b) PI combing
+−50−25 0
+25 50
+x [cm]
+−50
+−25
+0
+25
+50
+x [cm]
+-1.0
+0.0
+1.0
+Correlation factor
+(c) PI branchless
+Fig. 11. Spatial correlations (scale set from −1 to 1)
+−50−25 0
+25 50
+x [cm]
+−50
+−25
+0
+25
+50
+x [cm]
+-0.1
+0.0
+0.1
+Correlation factor
+(a) PI combing branchless
+−50−25 0
+25 50
+x [cm]
+−50
+−25
+0
+25
+50
+x [cm]
+-0.1
+0.0
+0.1
+Correlation factor
+(b) AMS branchless
+Fig. 12. Spatial correlations (scale set from −0.1 to 0.1)
+cA neutron family is defined as the set of all neutrons descending from the same ancestor amongst neutrons
+initially present.
+22
+
+Regarding the loss of independent neutron families, Figure 13 shows that both the branchless
+collision method and population control play a nonnegligible role in preserving uncorrelated pairs
+of particles. Indeed, both the combing method and the AMS seem to allow for more neutron
+lineages to be conserved over generations.
+100
+101
+102
+103
+Generation
+100
+101
+102
+103
+104
+Mean number of families
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+Fig. 13. Mean number of families over generations (the number of families at generation 0 is equal
+to 1000 for all cases).
+In the power iteration method, the death of a particle can occur from physical phenomena
+during the transport stage or by being combed out or not selected for duplication during the
+population control step.
+To look at these two mechanisms in more detail, Figures 14 and 15
+present the number of independent families removed from the simulation throughout the transport
+stage and during the population control step, respectively.
+Regarding the death occurring during transport, their relative number is higher when the
+branchless collision is not used, as seen in Figure 14, because the method reduces the number of
+uncorrelated pairs that disappear during the transport step by preventing families from dying from
+capture.
+Clusters of particles can form due to the asymmetry between particle death, which is likely
+to happen everywhere in the core, and the birth of new particles, which happen only at fission
+23
+
+10−3
+10−2
+10−1
+100
+101
+102
+103
+104
+Absolute
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+100
+101
+102
+103
+Generation
+0
+20
+40
+60
+Rel. [%]
+Fig. 14. Absolute (top) and relative (bottom) mean number of independent neutron families killed
+by birth/death process over generations
+sites. Regulating the particle population thus also affects the formation of clusters by removing
+independent families (which are not sampled during the population control step), reducing the
+number of uncorrelated particles in the process. It also contributes to regrouping particles into
+areas of the geometry because the probability of sampling a particle from the fission bank in a region
+of the geometry will depend on the density of particles inside that region, hence favoring high-
+density regions like clusters. In that regard, the combing is expected to be less "cluster-friendly"
+than sampling with replacement since particles can be sampled a limited number of times by
+combing. As seen in Figure 15, the combing method shows excellent results with a meager killing
+24
+
+rate, around a few percent. At the same time, the AMS does not appear in the absolute results
+(top figure) because the AMS does not remove particles during re-sampling. It is because it never
+kills independent families since the "population control" operated during the re-sampling step, see
+Section II.A.3, only regenerates particles. Obtaining the same effect without taking into account
+any importance function would eventually be possible by modeling the system as a Fleming-Viot
+particle systemd. Eventually, these observations are consistent with the findings of recent work
+on the role of population control on clustering in Monte Carlo iterated-fission-source calculations
+[27]. It is interesting to notice that using branchless collision when population control is done by
+sampling with replacement (case PI branchless on Figure 15) causes more families to be terminated
+than the analog collisions (case PI analog). This is because analog collisions induced more death
+during transport, so the total number of independent families is lower once the population control
+step is reached, as seen on the bottom plot of Figure 15 presenting a relative number of families
+being killed in the case PI analog.
+As a reminder, the number of particles per cycle was deliberately too low to enable the
+formation of neutron clusters to compare the methods regarding clustering issues. In the end, both
+the AMS and the combing method helped reduce clustering effects by preserving more independent
+families if combined with the branchless collision.
+In a production calculation, the number of
+particles would be higher to reduce the bias on the average value. However, for loosely coupled
+systems where this bias is limiting regarding the number of particles simulated in each generation,
+decreasing the required number of neutrons by using an appropriate method would be attractive
+regarding the global performances of the calculation.
+III.E.
+Variance estimation
+Besides a bias on the mean flux estimates due to clustering, criticality calculations can also
+present a bias on variance estimates since scores are averaged over correlated generations. In order
+to evaluate the bias on the flux variance estimation along the x-axis of the geometry, generational
+correlation coefficients were computed as a function of the neutron position along x. Like spatial
+dTo characterize the state of this system conditioned on its survival
+25
+
+10−3
+10−2
+10−1
+100
+101
+102
+103
+104
+Absolute
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+100
+101
+102
+103
+Generation
+0
+10
+20
+30
+Rel. [%]
+Fig. 15. Absolute (top) and relative (bottom) mean number of independent neutron families killed
+by population control over generations
+correlations, the generational correlations were estimated using Pearson’s correlation coefficient
+ρg(xl) = Cov [φ0(xl), φg(xl)]
+σ [φ0(xl)] σ [φg(xl)]
+(17)
+where ρg(xl) is the correlation coefficient for the flux estimate in spatial bin xl between two gen-
+erations g apart, computed from M independent simulations, φ0(xl) and φg(xl) are flux estimates
+in spatial bin xl in the first and k + 1-th active generations respectively, and σ [φ0(xl)] σ [φg(xl)]
+is the product of their standard deviation. Figure 16 illustrates the behavior of the generational
+26
+
+correlations in different space bins in the case PI analog, which is expected to be the worst-case
+scenario regarding correlations. In this figure, two local maxima appear along the x-axis (around
+-25 cm and 25 cm, which corresponds to 1/4 and 3/4 of the slab length), and three local minima
+around -50, 0 and 50 cm (0, 1/2 and 1 of the total length) in each generation. This behavior has
+already been observed in previous work and is due to excitation of the eigenvector higher modes
+as explained in Ref. [46]. To compare the different calculations, a slice along the x-axis is plotted
+in Figure 17, around x = 25 cm which is one of the locations where correlations are the strongest.
+This figure highlights that generational correlations drop quickly to negligible levels when combing
+or AMS are combined with the branchless collision method. In a nutshell, the real variance should
+be very close to the apparent one given by the Monte Carlo calculation in those two cases. Com-
+puting the cycle correlations allows us to compute the real variance when estimating the Figure of
+Merit.
+x [cm]
+−40
+−20
+0
+20
+40
+Generation (g)
+0
+200
+400
+600
+800
+ρg(x)
+-0.24
+-0.10
+0.03
+0.17
+0.31
+0.45
+0.59
+0.72
+0.86
+1.00
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ρg(x)
+Fig. 16. Cycle correlations for the PI analog case.
+In order to compare the efficiency of the methods, the Figure of Merit (FoM) for the flux
+27
+
+0
+100
+200
+300
+400
+500
+600
+700
+800
+Generation (g)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+ρg
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+Fig. 17. Cycle correlations for x = 23.5 cm.
+was computed in each spatial bin xl as such
+FoM(xl) =
+1
+σ2corr(xl)Tcalc
+(18)
+where Tcalc is the calculation time and σ2
+corr is the variance of the score which was computed
+accounting for generational correlations using Bienaymé’s identity such that
+σ2
+corr(xl) = σ2(xl)
+N
+�
+1 + 2
+G−1
+�
+g=1
+�
+1 − g
+G
+�
+ρk(xl)
+�
+(19)
+where σ2(xl) is the variance between estimations of the flux in spatial bin xl, N is the size of
+the sample used to compute the average flux, G is the number of active cycles and ρk(xl) is the
+generational correlations coefficients defined in Equation 17.
+The computation times are presented in Table IV. All methods show similar orders of mag-
+nitude, with combing overall faster than the rest and AMS slightly slower. The combing speed is
+due to the way source neutrons are sampled, which is more efficient than sampling with replace-
+ment. Concerning the AMS, the transport part is slightly faster than in the power iteration due
+28
+
+to the smaller number of collisions occurring in some generations (see Figure 8). It appears that
+a nonnegligible amount of time is spent in the function that adds points into the AMS structure,
+which could probably be optimized.
+TABLE IV
+Computation time [s] for each calculation
+Case
+Total
+Transport
+Sampling
+Scoring
+Sorting tracks
+Adding points
+PI analog
+1.822 × 104
+1.896 × 103
+7.954 × 103
+6.134 × 103
+(10) %
+(43) %
+(33) %
+PI branchless
+1.779 × 104
+1.859 × 103
+7.805 × 103
+5.949 × 103
+(10 %)
+(43 %)
+(33 %)
+PI combing
+1.497 × 104
+2.066 × 103
+4.377 × 103
+6.245 × 103
+(13 %)
+(29 %)
+(41 %)
+PI combing branchless
+1.392 × 104
+1.896 × 103
+3.990 × 103
+5.885 × 103
+(13 %)
+(28 %)
+(42 %)
+AMS branchless
+2.094 × 104
+1.660 × 103
+4.166 × 101
+1.199 × 104
+3.638 × 101
+3.867 × 103
+(7 %)
+(0 %)
+(57 %)
+(0 %)
+(18 %)
+The resulting FoM for the spatial flux is shown in Figure 18. Cases PI combing branchless
+and AMS branchless display better FoM, about one to two orders of magnitude more than the three
+other cases for all x. Overall, preserving the maximum number of independent pairs of particles
+through appropriate population control, combined with the branchless collision method, which
+reduces the variance between fission chains length, improves the Figure of Merit of the spatial flux.
+In that sense, the AMS seems to be an equivalent alternative to the combing method.
+29
+
+−40
+−20
+0
+20
+40
+x [cm]
+10−6
+10−5
+10−4
+10−3
+10−2
+FoM
+PI analog
+PI branchless
+PI combing
+PI combing branchless
+AMS branchless
+Fig. 18. Figure of Merit for the flux estimation over x.
+IV.
+CONCLUSION
+In this work, the Adaptive Multilevel Splitting (AMS) algorithm initially designed for vari-
+ance reduction and used in fixed source simulations has been extended to Monte Carlo neutron
+criticality calculations. The results obtained with this methodology were compared to the ones
+obtained with the power iteration algorithm used in Monte Carlo calculations on a one-dimensional
+homogeneous reactor slab. To assess for the population control impact on correlations and cluster-
+ing, multiple population control methods were used in the power iteration. The results produced
+by the different methods were compared regarding the average keff and spatial flux, as well as
+spatial and generational correlations.
+Due to the fact that the AMS does not kill particles like usual population control techniques, it
+has allowed to highly reduce correlations levels. It has been combined with the branchless collision
+method and has showed results almost identical to those obtained with the power iteration when
+the combing and the branchless collision methods were used. Compared to the other cases (power
+iteration with sampling with replacement and/or analog collisions), the AMS branchless and the
+30
+
+combing branchless displayed spatial and generational correlation levels close to nil, resulting in
+almost no clustering, despite a low number of neutrons per generation. Overall, we managed to
+compute a fundamental flux distribution using the AMS with branchless collisions with a Figure of
+Merit (FoM) multiplied by 100 compared to an elementary power iteration, thus close in magnitude
+to the power iteration using the combing and branchless collisions methods.
+The importance function chosen in the numerical applications remained quite simple due to
+the nature of the system. Indeed, we do not expect much improvement in the Figure of Merit by
+changing the spatial shape of the importance in one-speed homogeneous problems. Modeling more
+complex systems with a non-trivial adjoint solution should be necessary to further characterize
+this method’s behavior, especially for loosely coupled systems. In these systems, neutrons would
+have difficulties reaching certain regions, thus making the effects of the importance function even
+more significant and potentially potentially improving the FoM compared to the combing used in
+combination with branchless collisions.
+Another opening for this work could be to investigate, on the contrary, approaches that
+totally eliminate the importance map. Indeed, the idea of using the AMS in criticality simulations
+was to characterize the asymptotic behavior of a system (e.g., the keff and the fundamental flux)
+conditioned to its survival. This approach does, in essence, not require an importance function to
+rank tracks and push neutron histories through time. It could be possible to get rid of this function
+by treating the system as a Fleming-Viot process, thus benefiting from the population control to
+regenerate particles without killing independent families.
+Finally, and more importantly, since the AMS has been capable of computing a steady-state
+spatial flux distribution, regardless of the reactivity of the system, it should be conceivable to
+take a step further and use it to model transients in kinetics calculations. The target detector
+would therefore be defined in specific time bins, e.g., one could be interested in reducing the
+variance of the power distribution during the power peak. In order to achieve variance reduction
+in specific time bins, the importance function would have to account for particles position in time.
+Hence it would be helpful to be able to compute a time-dependent adjoint flux. Going from a
+time-independent adjoint flux to a time-dependent one would also allow taking delayed neutron
+precursors importance into account. Indeed, AMS branches can also carry the particle type as
+a parameter, making it possible to use multiple importance functions depending on the particles
+31
+
+nature.
+32
+
+ACKNOWLEDGMENTS
+The authors would like to thanks Benjamin Dechenaux for his useful remarks on the present
+article, as well as Tony Lelièvre for helpful discussions on the Adaptive Multilevel Splitting method.
+33
+
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+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf,len=895
+page_content='Generational variance reduction in Monte Carlo criticality  simulations as a way of mitigating unwanted correlations  Kévin Fröhlicher,∗,a Eric Dumonteil,b Loïc Thulliez,b Julien Taforeau,a and  Mariya Brovchenkoa  aInstitut de Radioprotection et de Sûreté Nucléaire (IRSN)  31 avenue de la Division Leclerc, 92260, Fontenay-aux-Roses, France  bIRFU, CEA, Université Paris-Saclay  91191, Gif-sur-Yvette, France  ∗Email: kevin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='frohlicher@irsn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='fr  Number of pages:  38  Number of tables:  4  Number of figures:  18  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='03882v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='stat-mech]  10 Jan 2023  Abstract  Monte Carlo criticality simulations are widely used in nuclear safety demonstrations, as they  offer an arbitrarily precise estimation of global and local tallies while making very few assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  However, since the inception of such numerical approaches, it is well known that bias might affect  both the estimation of errors on these tallies and the tallies themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In particular, stochastic  modeling approaches developed in the past decade have shed light on the prominent role played by  spatial correlations through a phenomenon called neutron clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This effect is particularly of  great significance when simulating loosely coupled systems (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', with a high dominance ratio).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In  order to tackle this problem, this paper proposes to recast the power iteration technique of Monte  Carlo criticality codes into a variance reduction technique called Adaptative Multilevel Splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The central idea is that iterating over neutron generations can be seen as pushing a sub-population  of neutrons towards a generational detector (instead of a spatial detector as variance reduction  techniques usually do).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' While both approaches allow for neutron population control, the former  blindly removes or splits neutrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In contrast, the latter optimizes spatial, generational, and  spectral attributes of neutrons when they are removed or split through an adjoint flux estimation,  hence tempering both generational and spatial correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This is illustrated in the present article  with a simple case of a bare slab reactor in the one speed theory on which the Adaptive Multilevel  Splitting was applied and compared to variations of the Monte Carlo power iteration method used  in neutron transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Besides looking at the resulting efficiency of the methods, this work also aims  at highlighting the main mechanisms of the Adaptive Multilevel Splitting in criticality calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Keywords — Monte Carlo Criticality Simulations, Neutron Clustering, Power Iteration, Variance  Reduction, Adaptive Multilevel Splitting  2  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  INTRODUCTION  For a long time, dating back 80 years, the simulation of neutron transport in multiplicative  media has been one of the main motivations leading the development of intensive systems (digital)  calculation capabilities and the Monte Carlo algorithm itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Nuclear engineers and researchers  still consider Monte Carlo methods as high fidelity methods, compared to deterministic ones, since  they estimate global and local tallies with an arbitrary precision while making very few hypotheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Nuclear data uncertainties are often considered as the only source of uncertainty (while others  such as technological uncertainties are usually neglected or ignored), aside from the stochastic  fluctuations intrinsic to the very nature of the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Therefore, Monte Carlo simulations are  widely used as reference calculations when validating new models/methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Criticality calculations have been used for decades in reactor physics to characterize the  behavior of multiplicative nuclear systems through their keff by solving the transport critical equa-  tion [1, 2, 3, 4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This equation takes the form of an eigenvalue equation in which fixed neutron  sources are neglected (for instance, spontaneous fissions), and the production term of the equation  is modified to ensure that the neutron population remains constant through generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Solving  this k-eigenvalue equation by Monte Carlo methods is generally done using an iterative algorithm  based on the power iteration method, and therefore allows characterizing the fundamental mode of  the system as if it was exactly critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Despite fundamental questions related to the inner nature  of the problem that is solved due to the renormalization of fission neutrons by the keff [6], this  method has made a consensus when it comes to criticality calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It is now widely used not  only in nuclear criticality safety but also in reactor physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' For loosely coupled systems, however,  it can exhibit convergence issues [7] that can lead to potentially significant errors in estimating  global and local tallies and their statistical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' By loosely coupled systems, we mean  systems in which neutrons may have difficulty travelling from one part of the geometry to another  over several generations, typically large systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Indeed, in the late 60’s, different works shed light on the biases on the keff estimation in crit-  icality calculations [8, 9, 10, 11, 12] which were however increasingly used by the nuclear industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Later, Ueki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [13], and Dumonteil et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [14] highlighted respectively the fact that generational  and spatial correlations were also a source of biases in the spatial flux estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Additionally,  different works [15] pointed out that tallies estimators are usually built from observations drawn  3  in successive generations of neutrons which lead to an actual underestimation bias of the tallies  uncertainty [16, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  At the heart of these observations lies the fact that, while both types of correlations (genera-  tional and spatial) are deeply rooted in the fission phenomenon and therefore also develop in actual  nuclear configurations [17], their magnitude might indeed soar in numerical simulations due to the  combination of the population control and the small number of neutrons that can be simulated  compared to natural systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In particular, the so-called neutron clustering effect has received  considerable attention in the past decade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It is typical of branching spatial processes since its  origin is found in the asymmetry between neutron captures, which occur everywhere, and neutron  births, which can only happen in the vicinity of other neutrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Whenever the system is loosely  coupled, and even in the presence of absorbing boundaries [18], the asymmetry creates spatial  patterns of randomly distributed neutron clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This results in the under-sampling of some  regions and ultimately leads to biased estimates of the global (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', keff) and local (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', flux) tallies  [19], which can have drastic consequences when feedback effects are taken into account through  multi-physics coupling [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This phenomenon, called neutron clustering, has been investigated  using statistical mechanics tools and, in particular, could be modeled using the so-called branching  Brownian motion, which couples a Galton-Watson birth-death process to standard Brownian mo-  tion [14, 18, 22, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Although neutron clustering is usually mitigated by sampling more particles  into the Monte Carlo simulation, different strategies have been tested to avoid the occurrence of  this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' While attenuating the phenomenon, neither the introduction of two-time scales  that reproduce the effect of delayed neutrons nor the presence or absence of population control  [24] affect this qualitative picture [25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Because the persistence of neutron families was the key  to counter this effect in simulations, beneficial modifications of the Monte Carlo power iteration  method were recently investigated [27, 20, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Starting from these last observations, this paper proposes a different approach to tackle  generational and spatial correlations (hence, to temper Monte Carlo criticality biases).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The ob-  servation that drives our approach is that the power iteration randomly kills or splits neutrons  during population control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The only way to ensure that neutron families extinction is slowed down  is to restart neutrons that will survive for many generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Hence, the paradigm change here  consists of seeing the population control acting on a super/subcritical medium as a way to either  4  select neutrons or enforce neutrons persistence through generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In other words, the goal is  to estimate the asymptotic state of our system conditioned on its survival: such approaches are  known in mathematics as Fleming-Viot processes [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' These processes can also be seen as an  estimator for rare events [31] and therefore as a variance reduction techniques [32] which primarily  aims at "pushing" neutron to a given "detector" without introducing any bias in the estimates of  tallies associated to this detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' These techniques can use an importance map whose quality will  condition the improvement in the method efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In the present case, our detector could be a  generational detector, and the importance map could be the adjoint flux [33, 34, 35] that could be  estimated on-the-fly or using external codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' A generalization of such Fleming-Viot processes that  allows for handling importance functions has recently appeared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This method is based on the use  of particle splitting and using an on-the-fly estimation of the importance levels at which particles  are split [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It has been named Adaptative Multilevel Splitting (AMS) and has been adapted to  neutron transport in the context of shielding calculations [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The present paper will show  that modification of this variance reduction technique that has proven successful in shielding cal-  culations can also help mitigate correlations and biases in Monte Carlo criticality calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It  will also show that AMS can be used alone or on top of other population control techniques (such  as the branchless collision method [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In Section II, the Adaptive Multilevel Splitting method,  and its extension to criticality calculations are presented, while Section III outlines the main numer-  ical results and discussions about methods performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' All methods were compared regarding  keff and flux estimations, as well as their impact on spatial and generational correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  ADAPTIVE MULTILEVEL SPLITTING  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Original algorithm for particle transport  The Adaptive Multilevel Splitting (AMS) is a method initially developed in applied math-  ematics to compute rare events probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Initially intended for continuous Markov chains [36],  it was then adapted to discrete Markov chains [39] and used in particle transport for attenuation  and radiation protection problems [40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The concept is to re-sample particles towards a detector iteratively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The key idea underlying  the method is to re-sample particle histories closer and closer to a detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' To this aim, neutron  5  histories are first simulated from birth to death (disappearance of all its particles by capture,  leakage, Russian Roulette) and ranked following an importance criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' According to the ranking,  the least important histories are deleted, and histories re-sampled among the remaining ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The  general algorithm is illustrated in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The general algorithm is here described for analog  transport of particles, it is however possible to use the AMS in a weighted Monte Carlo game [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Initialize  N neutron  histories/tracks  Transport  particles  All  particles  are dead ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Ranking tracks  Stopping criterion  (I(K) = IMAX)  met ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Re-sample  new tracks  End of iterations  Collision  Splitting  event ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Create new  branch in track  Add point  in branch  Increasing  importance  in branch ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Add point  in branch  Order tracks  I(1) ≤ I(2) ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' ≤ I(N)  Define kill  level as I(K)  Kill Ki tracks  with I ≤ I(K)  Sample Ki new  tracks from the  N − Ki remaining  tracks (with  I > I(K))  LEGEND  Step  Substep  Test  yes  no  yes  yes  no  yes  no  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' AMS algorithm  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  AMS tree structure and transport step  The AMS consists of successive fixed source simulations, where each batch , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' each sim-  ulation, is composed of N tracks (initially independent) representing N particle histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Here,  a particle history is the whole trajectory of a particle and its progeny arising from collisions and  splitting events, from the birth of the initial particle to the death of all its progeny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' At each colli-  sion, the outgoing particle of the collision is assigned an importance value using a cost function (see  Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' If the particle importance is higher than the previous branch point importance,  the particle is saved as a point in the AMS structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Each track initially starts with a unique  6  branch, and new branches are appended every time a splitting event occurs (it can be physical  like fission or numerical like splitting in a weighted Monte Carlo game).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' At any time, a track  importance is equal to the maximum importance of its branches, and the importance of a branch  is equal to the maximum importance amongst its points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The resulting tree structure is illustrated  in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  AMS BATCH  Iteration number  TRACK 1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  TRACK N  Importance  BRANCH 1  BRANCH 2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Importance  POINT 1  POINT 2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Position  Direction  Energy  Time / Generation  Weight  Importance  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' AMS track/branch/point structure  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Ranking the histories  Once all particles in an iteration i are dead (by capture, leakage, Russian Roulette), the N  tracks are ranked in increasing order of importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' At this point, a kill level Ikill is defined by  the importance of the K-th worst track, where K is a user-defined parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  I(i)  kill ≡ I(i)(K)  (1)  When a track has reached the detector, its importance is set to infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' At the end of an iteration,  the algorithm samples new tracks according to the following description if the stopping criterion  7  that is defined hereinafter has not been met.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  AMS iterations stop when  I(i)  kill = I(i)  MAX  (2)  where I(i)  MAX is the maximum track importance at iteration i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' If the algorithm iterated correctly  (see discussion on the importance in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4), it should stop when  I(i)  kill = I(i)(K) = ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (3)  This equation implies that tracks K to N have reached the detector (since their importance is  superior to Ii(K)), hence, at least N − K + 1 tracks have reached the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Sampling new particles  After the kill level has been computed, all tracks whose importance is lower or equal to this  level are deleted from the batch structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Since multiple tracks can have the same importance,  the number of deleted tracks is not necessarily equal to K (it can be higher), and we denote it Ki  at iteration i, where Ki ≡ card(S) ≥ K, with S defined as  S =  �  k, k ∈ [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' N] | I(i)(k) ≤ Ikill  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (4)  To keep the total number of tracks constant, Ki tracks are sampled uniformly among the  remaining ones to be duplicated to make up for the deleted ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' When a track is selected for  duplication, the first point of importance greater than the kill level is copied into the new track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The new track thus created is simulated as described in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This is illustrated by Figure  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Once the AMS algorithm has stopped (we note the last iteration I), scores are computed  using the following estimator  �φdetector = φ(I)  detector × αAMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (5)  where �φdetector is an unbiased estimator of φdetector, φ(I)  detector is the estimation of score φdetector  based on all iterations tallies using classical Monte Carlo estimators (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', track length or collision  8  I(1)  kill  x  Detector  y  TRACK 1  TRACK 2  TRACK 3  (a) Iteration 1  I(2)  kill  x  Detector  y  TRACK 1  TRACK 2  TRACK 3  (b) Iteration 2  I(3)  kill  x  Detector  y  TRACK 1  TRACK 2  TRACK 3  (c) Iteration 3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' AMS iterations with a detector defined in the (x, y) plane, with N = 3 and K = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The  closer the detector, the more important the particle is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  estimators) and αAMS is defined by  αAMS ≡  I�  i=1  �  1 − Ki  N  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (6)  While αAMS is used to correct tallies so that results remain unbiased, it can also be interpreted  as an estimation of the probability to reach the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Although it is not described here, it is  possible to define an on-the-fly scoring procedure to compute scores outside the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  About the importance function  The importance function is a function that maps RL → R, where L is the number of pa-  rameters considered to compute the importance (position, direction, energy, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Its purpose is  to rank tracks in the AMS (see Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2) and should be chosen to push neutron histories  towards the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The optimal choice for that function should lead to the best estimation of  the probability αAMS leading to the minimum variance [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In particle transport, although there  9  is no formal demonstration for the AMS, the solution of the adjoint Boltzmann equation for the  detector [35] is generally considered to be the optimal choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Although there are no further requirements, it is best to avoid importance functions pre-  senting discrete levels that could lead to aggregates of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Indeed, for a discrete importance  function, if the N −K+1 particles with the highest importance were on the same level, the splitting  level would be equal to I(i)  MAX < ∞, and the iterations would stop before enough particles have  reached the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Finally, since the importance function is only used to rank particles, only the relative impor-  tance between two particles matters, making the AMS a reasonably robust and easy to use method  [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Adaptation to criticality calculations  For subcritical systems, the neutron population tends to go extinct with time/generationsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Therefore, it is clear that the lower the keff, the less likely a neutron history is to survive over several  generations, and reaching a distant generation is then a rare event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In criticality calculations, the  AMS is used to re-sample histories and push them across generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Moreover, it has been  specified in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1 that any collision point could be added to the AMS structure, which  implies that any collision point could be used for the re-sampling of neutrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Compared to the  power iteration, where new neutrons are sampled at fission sites only, this induces a non-negligible  difference in terms of the precise equation solved by the algorithm due to spectral and spatial  heterogeneity effects as explained by Cullen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' However, to ease the comparison  with the power iteration method, only fission points can be saved, as it is possible to store any  stopping point as long as the system remains Markovian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In a subcritical system, keff can be interpreted as the probability for a neutron to go from one  generation to the next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' With that in mind, the probability for one neutron history with initially  one particle to reach generation G is  Psurvive(G) = kG  eff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (7)  aOne can artificially define a generation as a neutron trajectory between birth and death by absorption or  leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Therefore, neutrons born by fission are considered in the next generation of the particle that caused the  fission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  10  Hence, tracking neutrons over generations in a subcritical system can also be considered as an  attenuation problem over generations when no population control is done, making this a suitable  scope for using the AMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The idea is then to define a detector in generation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', a target generation  towards which neutrons will be pushed by the re-sampling algorithm) and to track neutrons not in  time but over successive generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' For this purpose, in the subsequent sections of this article,  the importance function used to rank tracks will be of the following form  I(rrr, g) = g + f(rrr)  (8)  where g is the neutron generation to push neutrons over generations, and 0 ≤ f(rrr) ≤ 1 is a function  of space used to discriminate neutrons of the same generation so that the importance function is  not discrete (see Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The resulting algorithm is compared to the Power Iteration in  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  N fission sites  initialize  FISSION BANK  N neutrons  PARTICLE DEATH  fission  capture  leakage  sample N neutrons  then empty bank  fill fission  bank  Transport neutrons over 1 generation  capture  leakage  Iterate  over G  cycles  (a) PI: iterates over fission neutrons (1 generation  per iteration) after being initialized with an arbi-  trary fission distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Neutrons are sampled  from fission neutrons of the last iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  N analog tracks  initialize  N TRACKS  Ki new tracks  TRACKS DEATH  all branches are dead  either by capture, leakage, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  delete Ki tracks  sample Ki  new tracks  rank the  N tracks  Transport tracks over several generations  tracks structures are filled at collisions  Iterate until  N − K + 1 tracks  have reached  generation G  (b) AMS in criticality:  iterates over re-sampled  tracks (multiple generations per iteration) after be-  ing initially fed with N analog tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Comparison scheme between the Power Iteration (PI) and AMS used for criticality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The probability of reaching the detector defined by Equation 6 could therefore be compared  to the keff given as a probability of survival (see Equation 7)  αAMS =  I�  i=1  �  1 − Ki  N  �  = kG  eff  (9)  11  where I is the total number of AMS iterations, and G is the target generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Therefore we can  build the following estimation of the keff  keff =  � I�  i=1  �  1 − Ki  N  ��1/G  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (10)  While this holds for subcritical systems, it is no longer valid when the system is critical  or supercritical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In the description above, the neutron population is not constrained by some  population control mechanism, which allows for fluctuations in the system’s number of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  This mechanism can induce population growth for systems close to criticality (and supercritical  systems), thus increasing the number of branches inside a track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Since it is necessary to take  those branches into account during the re-sampling step, the number of re-sampled branches may  increase as iterations go by, leading to slower and slower iterations (as well as more and more  memory used).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Besides, as in fixed source calculations, neutron histories must end at some point  to be able to rank the tracks as previously described, which could be troublesome in critical and  supercritical regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Thus, the branchless collision method [15] was used to limit the number of  branches inside a track (equal to one if no splitting is used), preventing these issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' For a system  with leakage, making particles carry population fluctuations through statistical weights produces  a numerically subcritical system (no particles are produced by splitting, and some disappear by  leaking out of the geometry).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Hence, it is possible to reproduce a population attenuation over  generations that appeals to the use of the AMS whatever the keff if the branchless collision method  is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  APPLICATION TO A ONE-DIMENSIONAL SLAB REACTOR  To characterize the AMS behavior regarding criticality calculations, the method was tested  on a one-dimensional bare slab reactor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' We tested the method on a simple case in one dimension  with mono-energetic neutrons, thus limiting the number of particles needed to explore the space  and allowing us to compare results to a simple analytical solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  12  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Bare slab properties  The modeled system is a one dimensional homogeneous bare slab reactor with leakage on  the sides, the total size of the slab being 100 cm, from xmin = −50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0 cm to xmax = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The  slab size was chosen so the system would be loosely coupled considering the cross sections of the  system, presented in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Three reactions are possible following a collision in analog transport:  fission, capture, and isotropic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The cross sections were arbitrarily chosen to model a  slightly supercritical system to assess the capability of the AMS to model supercritical systems  using the branchless collision method, the resulting keff being equal to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='03437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The simplicity of  TABLE I  Physical properties for homogeneous 1D rods  Mean number of fission neutrons (¯ν)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='383  Neutron speed (v)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2 × 104 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='s−1  Macroscopic cross sections  Fission (Σf)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='250 cm−1  Absorption (Σa)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='575 cm−1  Scattering (Σs)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='425 cm−1  Total (Σtot)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='00 cm−1  the system also allowed us to compute an analytical solution using diffusion theory [43], which is  used as a comparison in the following results  φ(x) = φ0 cos  �  π  2(a + z0)x  �  (11)  with φ0 depending on the normalization, a being the reactor half size (here a = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0 cm) and z0  is the linear extrapolated end point of the reactor and is defined as  z0 =  2  3Σtr  (12)  where Σtr is the transport cross section, which is equal to the total macroscopic cross section Σt  since all collisions are isotropic in the laboratory referential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Different calculation options were tested and compared to assess the effects of each regarding  clustering and variance estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The sets of options corresponding to each case are described  in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Four different simulations were done for the power iteration to distinguish between  13  the effects of the methods used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' As a matter of fact, collisions were simulated either by in an  analog way or by using the branchless collision method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' As for the population control operated  between cycles, two sampling methods were used, a simple sampling with replacement and the  combing method [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' For the AMS, since the system is supercritical, no simulation with analog  collisions was done since it would lead to a divergence of the particle number over generations,  hence computation cost issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='TABLE II  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='Description of calculation parameters  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='Case  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='Population control  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='Collisions  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='Importance (AMS only)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='PI analog  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='sampling with replacement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='analog  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='PI branchless  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='sampling with replacement  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='branchless  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='PI combing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='combing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='analog  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='PI combing branchless  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='combing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='branchless  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='AMS branchless  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='AMS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='branchless  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='g + cos  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='� πx  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2a  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='All the calculations presented below started from a uniform fission distribution and were done  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='with 1000 neutrons per cycle (N = 1000 initial independent tracks for the AMS) over G = 1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='successive generations in M = 1000 independent runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Having too few particles per generation to  facilitate clustering in all cases was deliberate to study the effects of methods on neutron clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Finally, estimators used in this work for the flux and the keff rely on the on-the-fly scoring  procedure detailed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In each generation i, the flux was computed using the collision  estimator and normalized so its spatial shape could be averaged over successive generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The  keff estimator is based on the physical interpretation of the keff, and was computed as the ratio of  neutrons produced in a generation over the ones produces in the previous generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Convergence of inactive cycles and behavior of the Shannon entropy  Firstly, the convergence of the keff estimates in each generation, and the Shannon entropy  [45] of the system were considered to set the number of inactive cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Firstly, the convergence  of the keff is shown on Figure 5 as the mean keff per generation, computed in M independent  simulations, as a function of the cycle number  keff(g) = 1  M  M  �  m=1  N (m)  g  N (m)  g−1  (13)  14  where N (m)  g  is the number of neutrons born in generation g for simulation m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Its convergence is  quite fast for every calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Apart from statistical fluctuations that have no impact on the  mean value, as seen later, all methods seem to converge towards the same value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  0  200  400  600  800  1000  Generation (g)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0200  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0225  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0250  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0275  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0300  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0325  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0350  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0375  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0400  keff(g)  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Convergence of the average keff (over 1000 independent runs) with 3σ confidence intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Cases PI branchless, PI combing branchless, and AMS branchless show the same results, with  narrow confidence intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Secondly, the Shannon entropy was used to assess the spatial flux convergence [45] and set  the number of generations that have been discarded when computing average scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Its averaged  value over M independent simulation has been computed in each generation as such  H(g) = 1  M  M  �  m=1  �  −  Nbins  �  l=1  φ(m)  g  (xl)  φ(m)  g,tot  log2  �  φ(m)  g  (xl)  φ(m)  g,tot  ��  (14)  where Nbins is the number of spatial bins along the x (here 100 bins), φ(m)  g  (xl) is the normalized  flux estimated in generation g in bin xl for simulation m, and φ(m)  g,tot is the normalized flux at  cycle g for simulation m integrated over x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The results are plotted in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' As expected, the  entropy converges slower than the keff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' All cases were considered to have reached an acceptable  convergence for g = 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' For the rest of the article, the number of inactive cycles was set to 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  15  0  200  400  600  800  1000  Generation g  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='7  H(g)  cosinus  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Evolution of the mean entropy over generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Unlike the keff, the Shannon entropy, as defined in Equation 14, and presented in Figure  6, does not converge to the same asymptotic value for all the different methods and is lower  than the theoretical value for a cosine shape distribution in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Moreover, the entropy  presents oscillations when the AMS is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  This phenomenon is likely due to how the AMS  injects particles into the simulation and can be decomposed into two underlying mechanisms: the  numerical subcriticality of our system (1) and the re-sampling of new particles by the AMS (2), as  portrayed in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Indeed, as explained in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='B, the system was set to be numerically  subcritical thanks to the branchless collision method to model an attenuation problem for the AMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Thus, without population control, the population progressively goes extinct over generations (see  mechanism (1) on Figure 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' As for the re-sampling of new particles, detailed in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='3,  the algorithm samples about K new tracks close to an importance level defined by the kill level  of the current iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Since the generation of a particle mainly drives the importance value, as  stated by Equation 8, we have  g ≤ Ikill(i) ≤ g + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  (15)  The new tracks sampled by the algorithm will therefore start either in generation g with an  16  Generation / importance  N particles  N collisions  Ikill  Numerically subcritical  less collisions at  each generations  (1)  AMS injects Ki new tracks in g / g+1  (branchless  Ki new particles)  (2)  generation g  generation g+1  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' AMS population control mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In this example, all neutrons that were re-sampled  appeared in generation g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  importance higher than Ikill(i), or in generation g + 1 (illustrated by the dashed area on Figure  7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This will result in a much higher increase in the total population sampled in these generations  (see mechanism (2) on Figure 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Intuitively, the more particles in the system, the closer (and  smoother) their distribution will be to the natural distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Hence, as the system loses particles,  the flux estimation gets noisier due to statistical fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Although these fluctuations have  no visible impact on the average estimate, they slightly modify the entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Consequently, when  the number of particles in the system is increased by the re-sampling of the AMS in generations  g and g + 1, the flux estimate in generation g + 1 gets smoother than in previous generations,  inducing an increase in the entropy (which will then decrease as particles disappear, until the  next re-sampling step, and so on).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  To reduce the amplitude of these fluctuations, one could  reduce the number of re-sampled particles at each iteration by reducing the value of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It would  also increase the frequency of the entropy since the re-sampling of particles would occur more  frequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' To illustrate the phenomenon, the mean number of collisions (unweighted) and the  corresponding entropy per generation were computed and plotted on Figure 8 for K/N = 25% and  K/N = 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Making the system less subcritical (numerically) should also reduce the frequency of  17  the oscillations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' however, it should not modify the amplitude of the oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Another way to  make the oscillations disappear without changing the simulation would be to compute the Shannon  entropy over a coarser spatial mesh, which would lessen the spatial fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  0  200  400  600  800  1000  Generation (g)  1300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='5  1525.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  1637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='5  1750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  Number of collisions  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='300  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='375  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='450  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='525  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='600  H(g)  K/N = 25%  K/N = 10%  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Mean entropy (solid lines) and mean number of collision points (dashed lines) per generation  for the AMS + branchless case, for K/N = 10% and K/N = 25%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In a nutshell, the AMS does not seem to lengthen nor abridge the convergence period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Besides, the observed oscillations of the flux entropy it might produce are natural and do not  affect the average flux estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Fundamental mode estimates  The fundamental mode of a multiplicative system described by the k-eigenvalue equation is  characterized by the highest eigenvalue k0 = keff and the associated eigenvector : the fundamental  flux distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  For the system described earlier, the keff distribution over 800 actives cycles in 1000 in-  dependent simulations is plotted in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Cases with branchless collision show quite similar  distributions, with much less dispersion around their mean value than for the non-branchless cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Hence, regarding the keff estimation, the branchless collision method seems to be the main con-  18  tributor to the variance reduction, while the differences between population control methods are  not very significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='15  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='20  keff  PI  analog  PI  branchless  PI  combing  PI  combing  branchless  AMS  branchless  keff = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='03437  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Distribution of the keff after convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Dashed lines represent the first, second and third  quartiles of the empirical distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Besides the eigenvalue, the fundamental flux was also computed over 800 successive genera-  tions in 1000 independent simulations, and is plotted on Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The first striking observation  is the lack of consistency between the solutions of the different methods, even with 3σ confidence  intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Although they do not include the analytical solution within their 3σ confidence inter-  val, the cases that show the less difference with the analytical cosine are the power iteration with  branchless collision and combing used for population control case, and the AMS combined with  branchless caseb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  These observed deformations of the flux shape are likely due to clustering effects that affect  bThe analytical solution was computed using the diffusion theory, this is why minor discrepancies are expected,  especially on the sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  19  the estimation of the mean spatial flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Since our goal was to compare methods behavior regarding  clustering, those effects were expected due to the low number of particles simulated in each batch,  and increasing their number would tend to mitigate clustering effects until they disappear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  −40  −20  0  20  40  x [cm]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='6  φ(x) [a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=']  Diffusion  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Spatial flux profile with 3σ confidence interval (top) with the relative (center) and absolute  (bottom) discrepancies against the analytical cosine-shaped solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  By flattening the average flux distribution, the presence of neutron clusters should increase  the entropy of the average distribution since the entropy of a uniform distribution is higher than the  entropy of a cosine distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' At the same time, the estimation of the spatial flux in a generation  is noisier than its average over multiple generations, which tend to lower the entropy, and clusters  in a generation should lower the entropy even more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This could explain the different asymptotic  values displayed in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Table III displays the values of the average spatial flux entropy, as  well as the asymptotic value to wich the generational entropy converges (the one shown in Figure  6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' We can see that the the averaged flux entropy is systematically higher than the reference  solution entropy due to flatter spatial shapes than the analytical diffusion solution, whereas the  asymptotic entropy reached in a generation is systematically lower due to statistical noise (which  could be reduced if the number of bins used to compute the entropy were to be decreased).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In  that regard, the AMS branchless and PI combing branchless cases present the lowest discrepancies  20  (about the same order of magnitude for both methods) with the analytical solution, which implies  less noise in the spatial estimation of the flux and an average value closer to the analytical solution  than the other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  TABLE III  Values for the asymptotic entropy reached during source convergence and for the flux distribution  averaged over active cycles for each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The differences are computed with respect to the analyt-  ical solution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' a negative difference means that the distribution is more ordered than the analytical  one (in terms of entropy), while a positive difference means that the distribution is less ordered  than the analytical one (closer to a uniform distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Case  Converged entropy  Averaged flux entropy  value  difference  value  difference  Analytical solution  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4673 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4673 PI analog  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0525  −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='148 × 10−1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='5424  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='511 × 10−2  PI branchless  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2427  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='246 × 10−1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4975  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='020 × 10−2  PI combing  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1838  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='835 × 10−1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='5088  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='154 × 10−2  PI combing branchless  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='3976  −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='969 × 10−2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4687  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='375 × 10−3  AMS branchless  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='3629  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='044 × 10−1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4704  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='168 × 10−3  The observed bias on the average flux shape related to the clustering phenomenon is further  examined in the following section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Effects of the AMS on clustering  To assess the probability for clusters to appear, spatial correlations were computed using  empirical estimations of Pearson’s correlation coefficient between each spatial bin defined by  ρij = Cov [φ(xi), φ(xj)]  σ [φ(xi)] σ [φ(xj)]  (16)  where Cov [φ(xi), φ(xj)] is the covariance between flux estimations in spatial bins xi and xj, and  σ [φ(xi)] is the standard deviation of the flux in spatial bin xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The results are presented on Figures  11 and 12 for 100 spatial bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' While cases PI analog, PI branchless, and PI combing show similar  levels of spatial correlations (see Figure 11), combing branchless and AMS branchless cases present  almost nonexistent spatial correlations as seen in Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Since these correlations are deeply  linked to the probability for clusters to form [22], this implies that the two above mentioned cases  are the least likely to present neutron cluster problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' High correlation levels are linked to the  number of correlated pairs of particles in the system, whose number increases as generations go by  21  because of independent familyc extinctions [23, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  −50−25 0  25 50  x [cm]  −50  −25  0  25  50  x [cm]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  Correlation factor  (a) PI analog  −50−25 0  25 50  x [cm]  −50  −25  0  25  50  x [cm]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  Correlation factor  (b) PI combing  −50−25 0  25 50  x [cm]  −50  −25  0  25  50  x [cm]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  Correlation factor  (c) PI branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Spatial correlations (scale set from −1 to 1)  −50−25 0  25 50  x [cm]  −50  −25  0  25  50  x [cm]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1  Correlation factor  (a) PI combing branchless  −50−25 0  25 50  x [cm]  −50  −25  0  25  50  x [cm]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1  Correlation factor  (b) AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Spatial correlations (scale set from −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='1)  cA neutron family is defined as the set of all neutrons descending from the same ancestor amongst neutrons  initially present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  22  Regarding the loss of independent neutron families, Figure 13 shows that both the branchless  collision method and population control play a nonnegligible role in preserving uncorrelated pairs  of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Indeed, both the combing method and the AMS seem to allow for more neutron  lineages to be conserved over generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  100  101  102  103  Generation  100  101  102  103  104  Mean number of families  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Mean number of families over generations (the number of families at generation 0 is equal  to 1000 for all cases).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In the power iteration method, the death of a particle can occur from physical phenomena  during the transport stage or by being combed out or not selected for duplication during the  population control step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  To look at these two mechanisms in more detail, Figures 14 and 15  present the number of independent families removed from the simulation throughout the transport  stage and during the population control step, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Regarding the death occurring during transport, their relative number is higher when the  branchless collision is not used, as seen in Figure 14, because the method reduces the number of  uncorrelated pairs that disappear during the transport step by preventing families from dying from  capture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Clusters of particles can form due to the asymmetry between particle death, which is likely  to happen everywhere in the core, and the birth of new particles, which happen only at fission  23  10−3  10−2  10−1  100  101  102  103  104  Absolute  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  100  101  102  103  Generation  0  20  40  60  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [%]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Absolute (top) and relative (bottom) mean number of independent neutron families killed  by birth/death process over generations  sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Regulating the particle population thus also affects the formation of clusters by removing  independent families (which are not sampled during the population control step), reducing the  number of uncorrelated particles in the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It also contributes to regrouping particles into  areas of the geometry because the probability of sampling a particle from the fission bank in a region  of the geometry will depend on the density of particles inside that region, hence favoring high-  density regions like clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In that regard, the combing is expected to be less "cluster-friendly"  than sampling with replacement since particles can be sampled a limited number of times by  combing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' As seen in Figure 15, the combing method shows excellent results with a meager killing  24  rate, around a few percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' At the same time, the AMS does not appear in the absolute results  (top figure) because the AMS does not remove particles during re-sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It is because it never  kills independent families since the "population control" operated during the re-sampling step, see  Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='3, only regenerates particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Obtaining the same effect without taking into account  any importance function would eventually be possible by modeling the system as a Fleming-Viot  particle systemd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Eventually, these observations are consistent with the findings of recent work  on the role of population control on clustering in Monte Carlo iterated-fission-source calculations  [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It is interesting to notice that using branchless collision when population control is done by  sampling with replacement (case PI branchless on Figure 15) causes more families to be terminated  than the analog collisions (case PI analog).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This is because analog collisions induced more death  during transport, so the total number of independent families is lower once the population control  step is reached, as seen on the bottom plot of Figure 15 presenting a relative number of families  being killed in the case PI analog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  As a reminder, the number of particles per cycle was deliberately too low to enable the  formation of neutron clusters to compare the methods regarding clustering issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In the end, both  the AMS and the combing method helped reduce clustering effects by preserving more independent  families if combined with the branchless collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In a production calculation, the number of  particles would be higher to reduce the bias on the average value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' However, for loosely coupled  systems where this bias is limiting regarding the number of particles simulated in each generation,  decreasing the required number of neutrons by using an appropriate method would be attractive  regarding the global performances of the calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Variance estimation  Besides a bias on the mean flux estimates due to clustering, criticality calculations can also  present a bias on variance estimates since scores are averaged over correlated generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In order  to evaluate the bias on the flux variance estimation along the x-axis of the geometry, generational  correlation coefficients were computed as a function of the neutron position along x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Like spatial  dTo characterize the state of this system conditioned on its survival  25  10−3  10−2  10−1  100  101  102  103  104  Absolute  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  100  101  102  103  Generation  0  10  20  30  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [%]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Absolute (top) and relative (bottom) mean number of independent neutron families killed  by population control over generations  correlations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' the generational correlations were estimated using Pearson’s correlation coefficient  ρg(xl) = Cov [φ0(xl),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' φg(xl)]  σ [φ0(xl)] σ [φg(xl)]  (17)  where ρg(xl) is the correlation coefficient for the flux estimate in spatial bin xl between two gen-  erations g apart,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' computed from M independent simulations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' φ0(xl) and φg(xl) are flux estimates  in spatial bin xl in the first and k + 1-th active generations respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' and σ [φ0(xl)] σ [φg(xl)]  is the product of their standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Figure 16 illustrates the behavior of the generational  26  correlations in different space bins in the case PI analog, which is expected to be the worst-case  scenario regarding correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In this figure, two local maxima appear along the x-axis (around  25 cm and 25 cm, which corresponds to 1/4 and 3/4 of the slab length), and three local minima  around -50, 0 and 50 cm (0, 1/2 and 1 of the total length) in each generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This behavior has  already been observed in previous work and is due to excitation of the eigenvector higher modes  as explained in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' To compare the different calculations, a slice along the x-axis is plotted  in Figure 17, around x = 25 cm which is one of the locations where correlations are the strongest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  This figure highlights that generational correlations drop quickly to negligible levels when combing  or AMS are combined with the branchless collision method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In a nutshell, the real variance should  be very close to the apparent one given by the Monte Carlo calculation in those two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Com-  puting the cycle correlations allows us to compute the real variance when estimating the Figure of  Merit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  x [cm]  −40  −20  0  20  40  Generation (g)  0  200  400  600  800  ρg(x)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='86  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  ρg(x)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Cycle correlations for the PI analog case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In order to compare the efficiency of the methods, the Figure of Merit (FoM) for the flux  27  0  100  200  300  400  500  600  700  800  Generation (g)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='0  ρg  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Cycle correlations for x = 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='5 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  was computed in each spatial bin xl as such  FoM(xl) =  1  σ2corr(xl)Tcalc  (18)  where Tcalc is the calculation time and σ2  corr is the variance of the score which was computed  accounting for generational correlations using Bienaymé’s identity such that  σ2  corr(xl) = σ2(xl)  N  �  1 + 2  G−1  �  g=1  �  1 − g  G  �  ρk(xl)  �  (19)  where σ2(xl) is the variance between estimations of the flux in spatial bin xl,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' N is the size of  the sample used to compute the average flux,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' G is the number of active cycles and ρk(xl) is the  generational correlations coefficients defined in Equation 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The computation times are presented in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' All methods show similar orders of mag-  nitude, with combing overall faster than the rest and AMS slightly slower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The combing speed is  due to the way source neutrons are sampled, which is more efficient than sampling with replace-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Concerning the AMS, the transport part is slightly faster than in the power iteration due  28  to the smaller number of collisions occurring in some generations (see Figure 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It appears that  a nonnegligible amount of time is spent in the function that adds points into the AMS structure,  which could probably be optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  TABLE IV  Computation time [s] for each calculation  Case  Total  Transport  Sampling  Scoring  Sorting tracks  Adding points  PI analog  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='822 × 104  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='896 × 103  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='954 × 103  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='134 × 103  (10) %  (43) %  (33) %  PI branchless  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='779 × 104  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='859 × 103  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='805 × 103  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='949 × 103  (10 %)  (43 %)  (33 %)  PI combing  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='497 × 104  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='066 × 103  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='377 × 103  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='245 × 103  (13 %)  (29 %)  (41 %)  PI combing branchless  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='392 × 104  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='896 × 103  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='990 × 103  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='885 × 103  (13 %)  (28 %)  (42 %)  AMS branchless  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='094 × 104  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='660 × 103  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='166 × 101  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='199 × 104  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='638 × 101  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='867 × 103  (7 %)  (0 %)  (57 %)  (0 %)  (18 %)  The resulting FoM for the spatial flux is shown in Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Cases PI combing branchless  and AMS branchless display better FoM, about one to two orders of magnitude more than the three  other cases for all x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Overall, preserving the maximum number of independent pairs of particles  through appropriate population control, combined with the branchless collision method, which  reduces the variance between fission chains length, improves the Figure of Merit of the spatial flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  In that sense, the AMS seems to be an equivalent alternative to the combing method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  29  −40  −20  0  20  40  x [cm]  10−6  10−5  10−4  10−3  10−2  FoM  PI analog  PI branchless  PI combing  PI combing branchless  AMS branchless  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Figure of Merit for the flux estimation over x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  CONCLUSION  In this work, the Adaptive Multilevel Splitting (AMS) algorithm initially designed for vari-  ance reduction and used in fixed source simulations has been extended to Monte Carlo neutron  criticality calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The results obtained with this methodology were compared to the ones  obtained with the power iteration algorithm used in Monte Carlo calculations on a one-dimensional  homogeneous reactor slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' To assess for the population control impact on correlations and cluster-  ing, multiple population control methods were used in the power iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The results produced  by the different methods were compared regarding the average keff and spatial flux, as well as  spatial and generational correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Due to the fact that the AMS does not kill particles like usual population control techniques, it  has allowed to highly reduce correlations levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It has been combined with the branchless collision  method and has showed results almost identical to those obtained with the power iteration when  the combing and the branchless collision methods were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Compared to the other cases (power  iteration with sampling with replacement and/or analog collisions), the AMS branchless and the  30  combing branchless displayed spatial and generational correlation levels close to nil, resulting in  almost no clustering, despite a low number of neutrons per generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Overall, we managed to  compute a fundamental flux distribution using the AMS with branchless collisions with a Figure of  Merit (FoM) multiplied by 100 compared to an elementary power iteration, thus close in magnitude  to the power iteration using the combing and branchless collisions methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  The importance function chosen in the numerical applications remained quite simple due to  the nature of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Indeed, we do not expect much improvement in the Figure of Merit by  changing the spatial shape of the importance in one-speed homogeneous problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Modeling more  complex systems with a non-trivial adjoint solution should be necessary to further characterize  this method’s behavior, especially for loosely coupled systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In these systems, neutrons would  have difficulties reaching certain regions, thus making the effects of the importance function even  more significant and potentially potentially improving the FoM compared to the combing used in  combination with branchless collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Another opening for this work could be to investigate, on the contrary, approaches that  totally eliminate the importance map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Indeed, the idea of using the AMS in criticality simulations  was to characterize the asymptotic behavior of a system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', the keff and the fundamental flux)  conditioned to its survival.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' This approach does, in essence, not require an importance function to  rank tracks and push neutron histories through time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' It could be possible to get rid of this function  by treating the system as a Fleming-Viot process, thus benefiting from the population control to  regenerate particles without killing independent families.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Finally, and more importantly, since the AMS has been capable of computing a steady-state  spatial flux distribution, regardless of the reactivity of the system, it should be conceivable to  take a step further and use it to model transients in kinetics calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' The target detector  would therefore be defined in specific time bins, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=', one could be interested in reducing the  variance of the power distribution during the power peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' In order to achieve variance reduction  in specific time bins, the importance function would have to account for particles position in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  Hence it would be helpful to be able to compute a time-dependent adjoint flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Going from a  time-independent adjoint flux to a time-dependent one would also allow taking delayed neutron  precursors importance into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content=' Indeed, AMS branches can also carry the particle type as  a parameter, making it possible to use multiple importance functions depending on the particles  31  nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
+page_content='  32  ACKNOWLEDGMENTS  The authors would like to thanks Benjamin Dechenaux for his useful remarks on the present  article, as well as Tony Lelièvre for helpful discussions on the Adaptive Multilevel Splitting method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE2T4oBgHgl3EQfbQcn/content/2301.03882v1.pdf'}
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+Springer Nature 2021 LATEX template
+Parallelized computational 3D video
+microscopy of freely moving organisms at
+multiple gigapixels per second
+Kevin C. Zhou1,2,6*, Mark Harfouche2, Colin L.
+Cooke3, Jaehee Park2, Pavan C. Konda1, Lucas
+Kreiss1, Kanghyun Kim1, Joakim J¨onsson1, Jed
+Doman2, Paul Reamey2, Veton Saliu2, Clare B.
+Cook1,2, Maxwell Zheng2, Jack P. Bechtel2, Aur´elien
+B`egue2, Matthew McCarroll5, Jennifer Bagwell4, Gregor
+Horstmeyer2, Michel Bagnat4 and Roarke Horstmeyer1,2,3*
+1Department of Biomedical Engineering, Duke University,
+Durham, NC 27708, USA.
+2Ramona Optics Inc., 1000 W Main St., Durham, NC 27701, USA.
+3Department of Electrical and Computer Engineering, Duke
+University, Durham, NC 27708, USA.
+4Department of Cell Biology, Duke University, Durham, NC
+27710, USA.
+5Department of Pharmaceutical Chemistry, University of
+California, San Francisco, CA, USA.
+6Current affiliation: Department of Electrical Engineering and
+Computer Sciences, University of California, Berkeley, CA, USA.
+*Corresponding author(s). E-mail(s): kevinczhou@berkeley.edu;
+roarke.w.horstmeyer@duke.edu;
+Abstract
+To study the behavior of freely moving model organisms such as zebrafish
+(Danio rerio) and fruit flies (Drosophila) across multiple spatial scales, it
+would be ideal to use a light microscope that can resolve 3D information
+over a wide field of view (FOV) at high speed and high spatial resolu-
+tion. However, it is challenging to design an optical instrument to achieve
+1
+arXiv:2301.08351v1  [physics.optics]  19 Jan 2023
+
+Springer Nature 2021 LATEX template
+2
+3D-RAPID
+all of these properties simultaneously. Existing techniques for large-FOV
+microscopic imaging and for 3D image measurement typically require
+many sequential image snapshots, thus compromising speed and through-
+put. Here, we present 3D-RAPID, a computational microscope based on
+a synchronized array of 54 cameras that can capture high-speed 3D topo-
+graphic videos over a 135-cm2 area, achieving up to 230 frames per second
+at throughputs exceeding 5 gigapixels (GPs) per second. 3D-RAPID
+features a 3D reconstruction algorithm that, for each synchronized tem-
+poral snapshot, simultaneously fuses all 54 images seamlessly into a
+globally-consistent composite that includes a coregistered 3D height
+map. The self-supervised 3D reconstruction algorithm itself trains a
+spatiotemporally-compressed convolutional neural network (CNN) that
+maps raw photometric images to 3D topography, using stereo overlap
+redundancy and ray-propagation physics as the only supervision mecha-
+nism. As a result, our end-to-end 3D reconstruction algorithm is robust
+to generalization errors and scales to arbitrarily long videos from arbi-
+trarily sized camera arrays. The scalable hardware and software design
+of 3D-RAPID addresses a longstanding problem in the field of behavioral
+imaging, enabling parallelized 3D observation of large collections of freely
+moving organisms at high spatiotemporal throughputs, which we demon-
+strate in ants (Pogonomyrmex barbatus), fruit flies, and zebrafish larvae.
+Keywords: parallelized microscopy, camera array, computational microscopy,
+behavioral imaging, self-supervised learning, 3D imaging
+1 Introduction
+Quantifying the behavior and locomotion of freely-moving model organisms,
+such as the fruit fly (Drosophila) and zebrafish (Danio rerio), is essential
+in a wide variety of applications, including neuroscience [1–3], developmen-
+tal biology [4], disease modeling [5, 6], drug discovery [7, 8], and toxicology
+[9, 10]. Particularly for high-throughput screening in these applications, it is
+desirable to monitor the behaviors of tens or hundreds of organisms simulta-
+neously, thus requiring high-speed imaging over large fields of view (FOVs) at
+high spatial resolution, and ideally with the ability to observe behavior in 3D.
+Such an imaging system would allow researchers to bridge the gap between
+microscopic phenotypic expression and natural, multi-organism behavior that
+manifest across more macroscopic scales, such as shoaling [11, 12], courtship
+and aggression behaviors [13, 14], exploration [15, 16], and hunting [16–20].
+Common approaches for behavioral recording utilize 2D wide-field micro-
+scopes with low-magnification optics to cover as large a FOV as possible.
+However, due to physical space-bandwidth product (SBP) limitations of con-
+ventional optics [21–23], standard imaging systems are forced to accept a
+tradeoff between image resolution and FOV (that is, can only record at low
+resolution when observing a large FOV). Such systems are commonly used to
+track the location of large populations of organisms in high-content screening
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+3
+applications for toxicology and pharmacology [24–26], but cannot record key
+morphological features and behavioral signatures that require high-resolution
+capture. Techniques that enhance SBP to facilitate high-resolution imaging
+over large areas, such as Fourier ptychography (FP) [27–29] and mechanical
+sample translation [30, 31], often require multiple sequential measurements,
+which compromises imaging speed and throughput. Approaches that perform
+closed-loop mechanical tracking to record single organisms freely moving in 2D
+with scanning mirrors [32] or moving cameras [16] are not scalable and thus
+cannot longitudinally observe multiple organisms simultaneously.
+Number of overlapping cameras
+cam (1,1)
+cam (1,6)
+cam (9,1)
+cam (9,6)
+a
+c
+0
+1
+2
+3
+4
+5
+6
+d
+12.5 cm
+10.8 cm
+54-camera array
+Reflection 
+illumination
+Object
+Transmission 
+illumination
+b
+⋯
+⋯
+⋯
+⋯
+~66% Horizontal overlap
+Parallax-aware stitching and 3D estimation
+cam (1,1)
+cam (1,2)
+cam (1,6)
+cam (9,1)
+cam (9,5)
+cam (9,6)
+3D height map
+height
+4 mm
+0 mm
+Photometric composite
+1.35 cm
+1 cm
+2 mm
+Fig. 1 Overview of 3D-RAPID. a, Computational microscope setup, consisting of a 9×6
+= 54 array of finite-conjugate imaging systems, jointly recording across a 135-cm2 area.
+LED arrays serve as the illumination source, both in transmission and reflection. b, 9×6
+array of cameras and lenses. c, Overlap map of the object plane, demonstrating roughly
+66% horizontal overlap redundancy between neighboring cameras (and minimal overlap in
+the vertical dimension). Four example camera FOVs are denoted with green dotted boxes,
+identified by (row,column) coordinates. d, The MCAM captures 54 synchronized videos at
+>5-GP/sec throughputs, which are stitched to form a high-speed video sequence of globally-
+consistent composites and the corresponding 3D height maps.
+Conventional wide-field techniques also lack 3D information, which poten-
+tially precludes observation of important behaviors, such as vertical displace-
+ment and out-of-plane tilt changes in zebrafish larvae [20, 33, 34] and 3D
+limb coordination and kinematics in various insects [35–38]. Commonly used
+3D microscopy techniques such as diffraction tomography [39–43], light sheet
+microscopy [44–46], and optical coherence tomography (OCT) [47–50], are not
+well-suited for behavioral imaging, since they often require multiple sequential
+measurements for 3D estimation and inertially-limited scanners that sacrifice
+speed. Furthermore, while such techniques can achieve micrometer-scale spa-
+tial resolutions, they typically do so over millimeter-scale FOVs rather than
+
+Springer Nature 2021 LATEX template
+4
+3D-RAPID
+the multi-centimeter-scale FOVs necessary for imaging freely-moving organ-
+isms. Thus, these techniques are typically limited to imaging one immobilized
+organism at a time (e.g., embedded in agarose, tethered [37, 38], or paralyzed),
+which prevents behavior studies.
+Parallelized, camera array-based imaging systems have also been proposed
+to increase imaging system SBP and overall measurement throughput [51–55];
+however, none of these prior approaches have demonstrated scalable, high-
+speed, high-resolution, wide-FOV, 3D imaging. In particular, several of these
+approaches were designed for 2D macroscopic photographic applications, which
+face several challenges for miniaturization for microscopy applications, or fea-
+ture a primary objective lens that limits the maximum achievable system SBP
+(see Discussion). Various macroscale 3D depth imaging techniques have also
+been developed, such as time-of-flight light detection and ranging (LiDAR)
+[56], coherent LiDAR [57–61], structured light [62], stereo vision [63], and
+active stereo vision techniques [64]. However, such 3D imaging systems have
+throughputs typically limited to 10s of megapixels (MPs) per second and gen-
+erally have poor spatial resolutions on the order of millimeters, making them
+ill-suited for behavioral imaging of small model organisms. Further, active
+patterned illumination techniques do not scale to high pixel counts, typically
+require multiple measurements (thus compromising speed), and may directly
+impact the organism’s behavior.
+Here, we present 3D Reconstruction with an Array-based Parallelized
+Imaging Device (3D-RAPID), a new computational 3D microscope based on
+an array of 9×6 = 54 temporally synchronized cameras, capable of acquiring
+continuous high-speed video of dynamic 3D topographies over a 135-cm2 lateral
+FOV at 10s of micrometer 3D spatial resolution and at spatiotemporal data
+rates exceeding 5 gigapixels (GPs) per second (Fig. 1). We demonstrate three
+operating modes of our microscope, which can be flexibly chosen depending on
+whether to prioritize speed (up to 230 frames per second (fps)) or spatial SBP
+(up to 146 MP/frame). We also present a new scalable computational 3D recon-
+struction algorithm that, for each synchronized snapshot, simultaneously forms
+a globally-consistent photometric composite and a coregistered 3D height map
+based on a ray-based physical model. The 3D reconstruction itself trains an
+underparameterized, spatiotemporally-compressed convolutional neural net-
+work (CNN) that maps multi-ocular inputs to the 3D topographies, using
+ray propagation physics and consistency in the overlapped regions as the
+only supervision. Thus, after computational reconstruction of just a few video
+frames (<20), 3D-RAPID can rapidly generate photometric composites and
+3D height maps for the remaining video frames non-iteratively.
+3D-RAPID thus solves a longstanding problem in the field of behavioral
+imaging of freely moving organisms that previously only admitted low-
+throughput solutions. To the best of our knowledge, prior to our work, there
+was no imaging system that could sustainably image at such high spatiotem-
+poral throughputs (>5 GP/sec) in 3D. These new capabilities have allowed us
+to capture novel 3D measurements of freely moving organism behavior, which
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+5
+we have extensively tested in a series of experiments with three model organ-
+isms: zebrafish larvae, fruit flies, and ants. In particular, the large FOV of
+3D-RAPID enabled imaging of multiple freely behaving organisms in parallel,
+while the dynamic 3D reconstructions and high spatial resolution and imag-
+ing speeds enabled 3D tracking of fine features, such as ant leg joints during
+exploration, zebrafish larva eye orientation during feeding, and fruit fly pose
+while grooming.
+2 High-throughput 3D video with 3D-RAPID
+2.1 3D-RAPID hardware design
+The 3D-RAPID hardware is based on a multi-camera array microscope
+(MCAM) architecture [55, 65], consisting of 54 synchronized micro-camera
+units spaced by 13.5 mm and tiled in a 9×6 configuration. Each micro-camera
+captures up to 3120 × 4208 pixels (1.1-µm pitch), for a total of ∼700 megapix-
+els per snapshot. The data is transmitted to computer memory via PCIe at ∼5
+GB/sec. Unlike conventional microscopy, 3D-RAPID is configured to acquire
+multi-view videos. That is, almost every point in the synthesized ∼12.5×10.8-
+cm2 is viewed from at least two perspectives. To achieve this, we axially
+positioned the lenses (Supply Chain Optics, f = 26.23 mm) to obtain a mag-
+nification of M ≈ 0.11, leading to ∼66% overlap in the sample plane field
+of view (FOV) between cameras adjacent along the longer camera dimension
+(Fig. 1c). This overlap redundancy enables 3D estimation using stereoscopic
+parallax cues. The sample is illuminated in transmission or reflection using
+planar arrays of white LEDs covered by diffusers (Fig. 1a).
+2.2 Tradeoff space of lateral resolution, field of view, and
+frame rate
+Our 3D-RAPID system has flexibility to downsample or crop the individual
+sensor pixels or use fewer cameras to increase the frame rate. The overall
+data throughput is limited by the slower of two factors: the data transfer rate
+from the sensors to the computer RAM (∼5 GB/sec) or the sensor readout
+rate, which is a function of the sensor crop shape and downsample factor.
+Streaming all 54 cameras without downsampling or cropping runs into the
+data transfer rate-limited frame rate of ∼7 fps. To achieve higher frame rates,
+we present results with a 1536×4096 sensor crop using either 4×, 2×, or no
+downsampling, allowing us to achieve up to 230, 60, or 15 fps, respectively,
+while maintaining roughly the same overall throughput of ∼5 GP/sec (Table
+1). While excluding half of the sensor rows all but eliminates FOV overlap
+in the vertical dimension, the benefits are two-fold: increased frame rate and
+reduced rolling shutter artifacts (see Methods 5.1).
+
+Springer Nature 2021 LATEX template
+6
+3D-RAPID
+Downsample factor
+1× (none)
+2×
+4×
+Per-camera dims
+1536×4096
+768×2048
+384×1024
+Composite dims
+13000×11250
+6500×5625
+3250×2810
+Composite SBP
+146.3 MP
+36.6 MP
+9.1 MP
+Frame rate
+15 fps
+60 fps
+230 fps
+Exposure
+20 ms
+5 ms
+2.5 ms
+Raw pixel rate
+5.1 GP/sec
+5.1 GP/sec
+4.9 GP/sec
+Composite pixel rate
+2.2 GP/sec
+2.2 GP/sec
+2.1 GP/sec
+Image pixel pitch
+9.6 µm
+19.2 µm
+38.4 µm
+Table 1 The three imaging configurations.
+2.3 Seamless image registration, stitching, and 3D
+estimation
+For each video frame, the 3D-RAPID algorithm fuses the 54 synchronously
+acquired images, via gradient descent using a pixel-intensity-based loss, into
+a continuous, seamless, expanded-FOV composite image, and simultaneously
+estimates a coregistered 3D height map (Fig. 2a). In fact, these two tasks
+are intimately related – to form a high-quality registration, it is necessary to
+account for parallax distortions induced by height deviations from a planar
+sample scene that would otherwise thwart simple registration using homo-
+graphic transformations (Fig. 2b) [66–68]. To achieve this, the algorithm starts
+with calibration of the 6-degree-of-freedom poses (x, y, z, roll, pitch, yaw),
+camera distortions, and intensity variations by registering and stitching 54
+images of a flat, patterned target (Methods 5.3). Estimating the 3D height
+map of the sample of interest relative to this calibration plane is tantamount
+to rendering the images registerable using homographies (Fig. 2b). In par-
+ticular, the per-pixel deformation vectors that undo the parallax shifts (i.e.,
+orthorectify the images) have magnitudes that are directly proportional to the
+per-pixel heights, h(r) (i.e., the height map), given by [68]
+h(robj + rrectify) = f
+∥rrectify∥
+∥robj − rvanish∥
+�
+1 + 1
+M
+�
+(1)
+where f = 26.23 mm is the effective focal length of the lens, M ≈ 0.11 is
+the linear magnification, robj is the apparent 2D position of the object in the
+pixel (before orthorectification), rvanish is the vanishing point to which all lines
+perpendicular to the sample plane appear to converge, and rrectify is the 2D
+orthorectification vector pointing towards the vanishing point (Fig. 2b). rvanish
+can be determined from the camera pose, as the point in the sample plane that
+intersects with the perpendicular line that passes through the principal point
+in the thin lens model. The orthorectification vectors rrectify, and therefore
+the height map, for each object position robj can be determined by registering
+images (via photometric pixel values) from different perspectives. The accuracy
+of the height map thus depends on the object having photometrically textured
+(i.e., not uniform) surfaces that enable unique image registration, a condition
+which the model organisms we imaged satisfied.
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+7
+a
+b
+c
+d
+Ant anaglyph
+Zebrafish anaglyph
+Near focal plane
+Above focal plane
+2 mm
+1 mm
+Fig. 2 Computational 3D reconstruction and stitching algorithm for 3D-RAPID. a, The
+algorithm starts with raw RGB images (only one shown for clarity), along with coregistered
+images from the cameras to left and right, as CNN inputs. CNN generates camera-centric
+height maps, which in turn dictate orthorectification fields (see b and Eq. 1). Orthorecti-
+ficaton fields and camera poses + distortions constitute registration parameters, dictating
+where and how each image should be backprojected in the stitched photometric compos-
+ite and 3D height map. The backprojection step is then reversed (reprojection) to form
+forward predictions of the RGB images and camera-centric height maps. Errors (photomet-
+ric MSE and height MSE) guide the optimization of the CNN. b, The physical ray model,
+intuitively showing how orthorectification facilitates stitching of non-telecentric images and
+height maps. c, The patch-based joint training/stitching/3D reconstruction algorithm. At
+each gradient descent iteration, random coordinates are chosen (red star); all cameras that
+view a given point are isolated. A patch is cropped out from each camera image surrounding
+the randomly sampled point, along with the corresponding left/right camera images to serve
+as the multi-ocular stereo inputs to the CNN to predict the patch height map. These patches
+undergo the procedure outlined in a to form a mini photometric and 3D height reconstruc-
+tions to update the CNN. Zeros are assigned to stereo input pixels when unavailable (e.g.,
+at the edge of the object plane FOV), to preserve convolutionality when applying the CNN
+to the entire camera images to generate the full-size reconstructions. d, Analyphs, whereby
+the three stereo inputs are color-coded as RGB channels, showing the parallax that is used
+to estimate 3D.
+Thus, the optimization problem is to jointly register all 54 images using
+the pixel-wise photometric loss, using the orthorectification maps (which are
+directly proportional to the height maps via Eq. 1) as the deformation model
+on top of the fixed, pre-calibrated camera parameters, including distortions
+(Fig. 2a,b). In practice, since viewpoint-dependent photometric appearance
+can affect image registration, we also employed normalized high-pass filtering
+
+Multi-ocular stereo input from MCAM
+Left
+Right
+Camera
+Camera
+CNN
+camera
+camera
+centric
+image
+image
+image
+height
+Photometric
+Registration
+3D height
+Backproject
+Backproject
+composite
+parameters
+map
+Equation
+Dewarp
+Orthorectification
+fields
+Reproject
+Reproject
+War
+Warp
+Camera6Dposes
+& distortions
+Photometric
+Height
+Photometric
+Height
+forward
+LOSS
+forward
+MSE
+MSE
+prediction
+predictionObjectplaneFOV
+00
+2
+Shared
+Shared
+b
+P
+Update CNN
+Miniphotometric
+RGB
+3Dheighti
++3Dheight
+reconstruction
+０１2345６
+PatchMSE
+Numberofobservingcamerasrvanish
+rectif
+robj
+brd
+brd
+brd
+stitch
+stitch
+robj + rrectify
+stitch
+stitchSpringer Nature 2021 LATEX template
+8
+3D-RAPID
+to standardize photometric appearance (Methods 5.2 and Supplementary Sec.
+S3.5).
+2.4 Spatiotemporally-compressed 3D video via
+end-to-end physics-supervised learning
+Instead of optimizing the height maps directly, we reparameterized the height
+maps as the output of a fully-convolutional encoder-decoder CNN that takes
+the multi-view stereo images as inputs. This reparameterization has two inter-
+pretations, depending on whether we emphasize the CNN or the ray-based
+physical model. On the one hand, the CNN can be thought to act entirely as a
+training-data-free regularizer (i.e., deep image prior (DIP) [69]) that safeguards
+against 3D reconstruction artifacts that may otherwise arise from practical
+deviations from modeling assumptions that thwart image registration [68]. For
+example, using the CNN as a regularizer can be useful when the sample has a
+different appearance when viewed from different angles, which can be caused
+by uneven illumination, angle-dependent scattering responses, or varying pixel
+responses. Since we wish to reconstruct hundreds to thousands of 3D video
+frames, it would be prohibitively slow to independently reconstruct every indi-
+vidual video frame, with or without CNNs. Thus, we use one shared DIP, with
+each frame encoded by the raw multi-ocular stereo photometric inputs.
+On the other hand, this leads to the second interpretation of a self-
+supervised or physics-supervised learning problem, in which the image reg-
+istration of the overlapped MCAM image frames, governed by a ray-based
+thin lens physical model (Eq. 1), provides the physics-based supervision that
+guides the CNN training (Fig. 2a,c). The CNN can then be used to generalize
+to other MCAM data, both spatially (other micro-cameras) and temporally
+(other video frames).
+This dual interpretation of our CNN-regularized, physics-supervised learn-
+ing approach reveals several advantages. First, since we employ a fully-
+convolutional CNN, we can optimize on arbitrarily-sized image patches (Fig.
+2c) that can fit in GPU memory, and then perform non-iterative forward
+inference on arbitrarily-large full-size images (Fig. S4). Thus, our proposed
+approach is scalable and generalizable to arbitrarily many cameras, each with
+arbitrarily many pixels, for arbitrarily many video frames. For implementation
+details on patch-based training, see Sec. 2.5, Fig. 2c, and Supplementary Sec.
+S3. Second, the CNN acts as a spatiotemporally-compressed representation
+of the 3D height map videos, thus avoiding the need to iteratively optimize
+every single 3D video frame. Third, this spatiotemporal compression offers
+additional regularizing effects on top of the dataset-free, DIP-based regular-
+ization. As there are far fewer parameters in the CNN than height map pixels
+across all MCAM video frames, overfitting becomes less likely. Furthermore,
+the CNN implicitly enforces consistency across space and time, thus, for exam-
+ple, avoiding variance induced by independent optimization runs on different
+frames. Fourth, our approach has an inherent fail-safe against CNN general-
+ization errors, unlike other deep learning-based approaches, since the ground
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+9
+truth is implicitly always available via the overlap redundancy of the MCAM
+along with the physical model.
+2.5 Patch-based learning from multi-ocular stereo inputs
+While Fig. 2a summarizes the ideal joint 3D reconstruction, stitching, and
+training method, in practice we are constrained by GPU memory. Thus, we
+train the CNN using a random patch sampling approach (Fig. 2c). Briefly,
+at each optimization iteration, we sample nbatch (batch size) random points
+within the composite FOV (one shown in Fig. 2c). All cameras viewing each
+point are selected, from which patches surrounding that point are extracted
+from each camera view. Thereafter, these nbatch groups of selected patches
+independently undergo the procedure outlined in Fig. 2a. Once CNN training
+is done, the backprojection step in Fig. 2a is carried out for each full temporal
+frame to create the stitched RGBH 3D reconstructions (Fig. S4). For more
+implementation details, see Supplementary Sec. S3.
+As mentioned in the previous section (Sec. 2.4), the CNN is supplied multi-
+view inputs of the same sample scene (as shown in Fig. 2a,c), whose goal is to
+improve the generalizability of the CNN. These neighboring views are stacked
+along the channel input dimension in a way that preserves convolutionality, so
+that patch training and full-FOV inference are consistent (Supplementary Sec.
+S3). This is beneficial because monocular stereo depth estimation is insuffi-
+cient for objects whose appearances don’t change significantly as a function of
+depth. For example, when imaging a fruit fly or zebrafish larva, it is difficult to
+distinguish between height-dependent magnification changes and natural vari-
+ation in organism size. Thus, we train our CNN to solve a multi-ocular stereo
+3D estimation problem, which is better-posed, as the 3D supervision signal
+itself is derived from the registration of the multi-ocular data (Supplementary
+Sec. S2). In this paper, we use 3 stereo inputs or fewer (center, left, and right,
+if available).
+3 Results
+3.1 3D-RAPID system characterization
+Our 3D-RAPID system has a full-pitch lateral resolution of ∼25 µm and
+DOF of ∼9.4 mm, based on imaging a USAF resolution target and translat-
+ing a patterned target axially (see Supplementary Sec. S1). We validated the
+height precision and accuracy of our 3D-RAPID system by imaging precisely
+machined (to within 0.3 µm) and interferometrically characterized gauge blocks
+(Mitutoyo). As expected, accuracy and precision of the reconstructed height
+improve when imaging at higher spatial resolution, which facilitates more accu-
+rate measurement of parallax shifts (see Supplementary Sec. S5). Specifically,
+we achieved sub-20 µm accuracy and precision in the 15-fps configuration, and
+∼37 µm and ∼74 µm accuracy and precision in the 230-fps configuration. See
+Supplementary Sec. S1 for detailed characterization results.
+
+Springer Nature 2021 LATEX template
+10
+3D-RAPID
+Fig. 3 Zebrafish larvae (10 dpf) swimming in an open arena with interspersed microcap-
+sulated food particles (AP100), acquired at 60 fps for 10 sec (Supplementary Videos 1-3). a,
+3D height map and photometric composites of the zoomed-out FOV, projected across every
+50th temporal frame (0.83 sec) to highlight dynamics. The height map assigns an arbitrary
+value to the otherwise empty background. b, Photometric and height map frames of a single
+tracked fish feeding on AP100. The first 5 frames are spaced by 500 ms while the remaining
+frames are spaced by 16.7 ms (the full frame rate). c, The same fish’s head height, elevation
+angle (pitch), and eye vergence angle (illustrated in inset) throughout the 10-sec video. d-e,
+Another example of a zebrafish feeding event. Note the change in eye vergence before and
+after the feeding event in both b and d. f, A zoomed-in region of a, showing 3 individual
+larvae in varying states of activity. The small red tracks are the drifting and floating AP100
+food particles. g Fish head height vs. elevation angle for all 40 fish over time. Lines define
+the approximate physical limits due to geometric fish mobility constraints. h, Kernel density
+estimates of the height distributions of the zebrafish and AP100 food particles. Eye vergence
+vs. head height (i) and vs. elevation angle (j) plots are color-coded by the maximum height
+the fish attained in the 10-sec video. Fixed effect components of the linear mixed-effects
+regression lines are plotted (p = 0.33 and p < 10−5) for i and j, respectively).
+3.2 Zebrafish larvae (Danio rerio)
+We applied 3D-RAPID to several 10-sec videos of zebrafish larvae (Danio
+rerio) freely swimming in a large 97 mm × 130 mm open arena using the
+60-fps and 230-fps configurations (Table 1) across three separate experiments,
+the first of which was on 10-dpf fish feeding on microcapsule food particles
+(AP100) (Supplementary Videos 1 (60 fps), 2 (230 fps), and 3 (60 fps with
+tracking)). Fig. 3 summarizes the results for the 60-fps video of the 10-dpf fish
+feeding on AP100, most of which are floating at or near the water surface (Fig.
+3h). We tracked all 40 fish using a simple particle-tracking algorithm (Methods
+5.4; Supplementary Video 3). The high throughput of 3D-RAPID allowed us
+to observe fine detail over a very wide FOV, capturing multiple rapid feeding
+events (∼10s of ms), as shown in Fig. 3b,d. From the photometric images,
+
+3D height.map
+b
+c
+30
+80
+20
+60
+t = 500 ms
+6t=16.7ms
+1 mm
+eal
+40
+0.5
+2
+2.2mn
+Teat
+-30
+0
+2
+10
+1 mm
+Time (s)
+30
+80
+20
+60
+1.5
+St = 167 ms
+eat
+t=16.7ms
+40
+0.5
+20
+5.2mm
+-20 
+eat
+-30
+0
+2
+6
+8
+10
+1mm
+Time (s)
+h
+2.5
+b
+Fish
+15
+Probability
+1.5
+0
+-15
+0.5
+0
+0.5
+1.5
+2
+0
+0.5
+1.5
+2
+2.5
+Height (mm)
+Height (mm)
+80
+2.4 ,mm
+2.4 mm.
+I food
+60
+540
+40
+0mm
+0mm
+20
+1 cm
+1 mm
+Photometric composite
+0
+0.5
+20
+Height(mm)
+Elevationangle (°)Springer Nature 2021 LATEX template
+3D-RAPID
+11
+we can see that the larvae turn their bodies laterally so that their ventrally
+positioned mouths can access the overhead floating food. We also observe eye
+convergence once the larvae identify and approach the target, as shown in
+previous studies [17–19]. The eye angles rapidly deconverge after food capture
+(Fig. 3c,e). The older fish (20 dpf) exhibit similar eye behavior when feeding
+on brine shrimp (Supplementary Videos 4, 5).
+The 3D topographic information enabled by our technique reveals how the
+larvae axially approach their targets from below, including their head heights
+and elevation (pitch) angles during these feeding events (Fig. 3b-e) [20]. Note
+that the larvae’s head height matches that of the targeted food particle during
+ingestion (see also in Supplementary Videos 1, 2, 4, 5), offering validation of
+our technique.
+In addition to making organism-level observations, the high throughput
+of 3D-RAPID enabled us to make population-level inferences by aggregating
+height and elevation angle information for all 40 individually-tracked larvae
+for all in-frame time points. The results show a roughly linear trend between
+height and elevation angle (Fig. 3g), which can be explained based on the
+mobility constraints defined by the length of the larvae and the water depth.
+For example, if the head is at the bottom of the arena, then the elevation angle
+must be negative. Assuming a larval length of L = 4 mm and a water depth
+of H = 2.3 mm, these geometric constraints on the elevation angle, φ, for a
+fish at height, h, are
+φmin(h) = sin−1(h/L),
+φmax(h) = sin−1((H − h)/L),
+(2)
+which are plotted in Fig. 3g. This offers additional validation of the accuracy of
+our 3D height maps, suggesting future applications in studying fish locomotion
+dynamics [34]. We also estimated the probability distributions of the heights
+of the larvae and the food particles (Fig. 3h), both of which are bimodal.
+Predominantly, the larvae dwell at the bottom of the arena, only occasionally
+venturing upwards to hunt or forage for food.
+Finally, we also analyzed population-level correlations between eye vergence
+angle (Methods 5.4), a property observable in the photometric images, and the
+fish height and elevation angle, which are derived from our 3D height maps
+(Fig. 3i,j), across n = 39 fish (one stationary fish excluded). Specifically, we
+used a linear mixed-effects model, where height or elevation angle is the fixed
+effect and dependence among images from the same fish are accounted for as
+random effects. Analyses of variance suggest that while fish height is not a
+statistically significant linear predictor of eye vergence angle (p = 0.33), fish
+elevation angle is (p < 10−5). This is consistent with the fact that when the
+fish is swimming upwards, it is likely focusing on a food particle close to the
+surface. On the other hand, the fish can still be close to the surface following
+a feeding event, immediately after which the eyes deconverge (Fig. 3b-e).
+With the 230-fps configuration of our system, we can trade off spatial
+resolution to temporally resolve higher-speed zebrafish larval locomotion. For
+example, compare the beginning of Supplementary Videos 6 and 7, which
+
+Springer Nature 2021 LATEX template
+12
+3D-RAPID
+Fig. 4 Adult fruit flies freely moving across a flat, noise-patterned surface, acquired at 60
+fps for 8 sec (Supplementary Videos 8-10). a, 3D height map and photometric composites
+of the zoomed-out FOV. The white-outlined red lines are the trajectories the 50 flies take.
+The green-circled flies are analyzed in the other figure panels. b, Select photometric and
+height map frames of a single tracked fly, exhibiting several grooming behaviors (hi = hind-
+leg grooming, fo = foreleg or head grooming, mi = mid leg participation, ab = abdominal
+grooming). The time points of the frames are indicated by dotted lines in the plot below,
+which in turn highlights the changing heights of the head, thorax, and abdomen for the
+different grooming actions. c-g, The same information for 5 additional flies. h Kernel densi-
+ties of the heights of head, thorax, and abdomen for various behaviors. Differences of head
+(p < 10−7), thorax (p < 10−16), and abdomen (p < 10−62) heights across behaviors are
+statistically significant (n = 43 flies).
+feature rapidly swimming zebrafish larvae, captured at 60 fps and 230 fps,
+respectively. Similarly, we can resolve the 4D fish dynamics as it attempts to
+swallow a live brine shrimp (Supplementary Videos 4 (60 fps) and 5 (230 fps)).
+3.3 Fruit flies (Drosophila hydei)
+Next, we applied 3D-RAPID to image and track 50 freely exploring adult fruit
+flies (Drosophila hydei) under the 60-fps (Supplementary Videos 8 and 10) and
+230-fps (Supplementary Video 9) configurations. Fig. 4 summarizes the results
+for the 60-fps configuration for six individual flies exhibiting various behaviors.
+Supplementary Video 10 shows tracking of all 50 flies. The 3D height map
+offers additional insights into such grooming behaviors, building upon works
+
+3D height map
+TO
+hi/mi
+0.267 s
+2.6
+一Head
+Thorax
+Abdomen
+1.6
+45678
+time(s)
+time(s
+time(s)
+e
+0.767
+3.267 s
+3 mm
+0 mm
+1 cm
+2
+Photometric composite
+5678
+time (s)
+time (s)
+time (s)
+Hindleg groom
+Foreleggroom
+Abdomengroom
+Stand
+Walk
+All behavior
+h
+Head
+nsity
+Thorax
+Abdomen
+1.5
+2
+2.5
+31
+1.5
+2
+2.5
+3 1
+1.5
+2.5
+1.5
+2
+2.5
+3 1
+1.5
+2.5
+31
+2.5
+Height (mm)
+Height(mm)
+Height (mm)
+Height (mm)
+Height (mm)
+Height(mm)Springer Nature 2021 LATEX template
+3D-RAPID
+13
+that study freely-moving flies in 2D [70, 71] and 3D in single tethered flies
+[37]. In particular, we observed changes in fly height and body tilt as the flies
+transition between different grooming behaviors. In Fig. 4b, as an individual
+fly transitions between grooming with its hindlegs and forelegs, the abdomen
+moves up and down, respectively, relative to the head and thorax. When a
+middle leg joins the grooming (Fig. 4b, arrowheads), there is a subtle change
+in abdomen height relative to head height. In Fig. 4c, our method correctly
+predicts an elevated height as one fly climbs atop another. At 2.5 sec, the
+fly’s height drops, consistent with the straightened leg joints. A similar body
+tilt trend is observed for foreleg vs. hindleg grooming in this fly, as well as
+in Fig. 4d, e, and f. In Fig. 4f, we see another instance of the fly’s leg joints
+fully extended at 1.767 sec, resulting in a reduced overall height. Further, we
+observe that the abdomen takes on a different relative height during abdominal
+grooming compared to hindleg grooming. Finally, in Fig. 4g, although the fly
+is grooming its forelegs throughout the video, it reduces its overall height after
+1 sec, consistent with its extended leg posture.
+To analyze population trends, we annotated video frames across n = 43
+flies flies with one of five behaviors: hindleg grooming, foreleg/head grooming,
+abdomen grooming, standing still, and walking (Fig. 4h). Flies that exited the
+FOV were excluded. We tested for cross-behavioral differences in heights of
+the head, thorax, and abdomen using three separate linear categorical mixed-
+effects models, accounting for random effects due to correlations among video
+frames from the same fly. Analyses of variance suggest that behavior groups
+are a statistically significant predictor of the heights of the head (p < 10−7),
+thorax (p < 10−16), and abdomen (p < 10−62).
+3.4 Harvester ants (Pogonomyrmex barbatus)
+We also imaged freely exploring red harvester ants (Pogonomyrmex barba-
+tus) under the 60-fps (Supplementary Video 11) and 230-fps (Supplementary
+Video 12) configurations. The 60-fps results are summarized in Fig. 5. From
+the static 3D height map frame, it is immediately obvious that the body is
+sloped downward, from the head to the abdomen [72]. We used the dynamic
+3D reconstructions enabled by 3D-RAPID to track the femur-tibia joints of all
+six legs of an individual ant (Fig. 5b,c; Methods 5.4), providing information
+about the kinematics of ant locomotion. The joint trajectories are plotted in
+Fig. 5c, showing that the high-frequency (∼3-4 Hz) oscillations from walking
+kinematics are anti-correlated (180◦ out of phase) between left and right legs.
+This oscillation frequency remains relatively constant throughout the ant’s
+journey. Further, the forelegs and hindlegs on the same side of the body are
+correlated, but anti-correlated with the mid legs on the same side of the body.
+These behaviors are consistent with the well-known alternating tripod gait pat-
+tern in ants [36, 72, 73], which persists even as the curvature of ant trajectory
+changes in our tracked ant.
+We also observe changes in lower-frequency gait patterns as the ant makes
+multiple turns throughout its exploration. In the first ∼1.5 sec, as the ant is
+
+Springer Nature 2021 LATEX template
+14
+3D-RAPID
+Fig. 5 Harvester ants freely moving across a flat, noise-patterned surface, acquired at 60
+fps for 10 sec (Supplementary Videos 11-12). a, Photometric composite and 3D height map
+of the zoomed-out FOV. One of the ants’ trajectories is color-coded by time, progressing
+from blue to red over a 5.5-sec duration, and is analyzed in b and c. b, Temporal snapshots
+of a single tracked ant along the trajectory in a. The blue and red dots are the femur-tibia
+joints for the ant’s 6 legs (L = left, R = right, F = foreleg, M = middle leg, H = hindleg). c,
+The 3D positions of the femur-tibia joints over the 5.5-sec trajectory. The lateral dimensions
+(xy) are defined relative to the ant’s orientation, as illustrated in b.
+turning right, we see a reduced oscillation amplitude in the mid and hindlegs
+on the right side in both the y and z directions; however, for the x direction,
+we see the opposite trend (see Fig. 5b for the ant-centric coordinate system
+definition). Between 1.5 and 3 sec, as the ant is turning left, we see the opposite
+motions as in the first 1.5 sec – the oscillation amplitudes in the mid and
+hindlegs on the left are reduced in both the y and z directions, while amplitude
+of the right mid leg motion in the x direction is reduced. From 3 to 4.5 sec, the
+ant once again is turning right and we see similar trends as in the first 1.5 sec.
+Overall, this reduction in motion in y and z on the side of the ant corresponding
+to the direction the ant is turning is consistent with prior knowledge [73].
+Interestingly, the amplitudes of the foreleg oscillations on both the left and
+right sides in both y and z remain relatively constant throughout the entire
+5.5 sec, suggesting a lesser role in the biomechanics of changing directions.
+Finally, we observe a low-frequency oscillation (with a period of ∼4 sec)
+in the x direction for all 6 legs that is correlated with the curvature of the
+ant’s trajectory. Unlike the high-frequency (3-4 Hz) walking kinematics, which
+are anti-correlated between left and right, these low-frequencies are correlated
+between left and right legs, suggesting left-right coordination when the ant is
+
+a
+3D height map
+2 mm
+0.100s
+0.767 s
+1.433 s
+3.433:
+4.100 s
+4.767 s
+5.433 s
+++x**++*
+m
+y (mm)
+(mm
+z (mm)
+o
+PIW
+4 mm
+0 mm
+1 cm
+2
+5
+0
+1
+2
+3
+4
+5
+0
+4
+2
+3
+4
+5
+Photometric composite
+time (s)
+time (s)
+time (s)Springer Nature 2021 LATEX template
+3D-RAPID
+15
+turning. These low-frequencies in the x direction further are correlated between
+the forelegs and mid legs, but anti-correlated with the hindlegs.
+4 Discussion
+We have presented 3D-RAPID, a new computational microscope with a unique
+capability of dynamic topographic 3D imaging at 10s-of-µm resolution and
+accuracy, over >130-cm2 FOV at throughputs exceeding 5 GP/sec. To handle
+the large data load, we devised an efficient, end-to-end, physics-supervised,
+CNN-based, joint 3D reconstruction and stitching algorithm that scales to
+arbitrarily long videos and arbitrarily sized camera arrays. The high through-
+put of 3D-RAPID enabled us to study several freely-behaving model organisms
+at high speed and high resolution over a very large FOV. Thus, our technique
+fills a unique niche, enabling new ways for scientists to study small features of
+individual organisms over a large FOV that allows unconstrained social inter-
+actions of multiple organisms in parallel in 3D at high speed. For example,
+3D-RAPID could be applied to study dueling behavior in ants [74], sexual
+behavior in fruit flies [75], and feeding decisions in fruit flies [76].
+3D-RAPID differs from other camera array-based techniques [51–55] in
+several ways, stemming from the challenge of adapting to microscopy applica-
+tions. In particular, due to the large magnification requirements, the cameras
+need to be physically packed more tightly, which is a practical challenge due
+to mechanical constraints and heat dissipation management. Some approaches
+alleviate this challenge by using a primary objective lens to magnify the object
+to an intermediate image plane, which is then imaged by a camera array. How-
+ever, this strategy limits scalability, as the primary objective’s intrinsic SBP
+would limit the total imaging throughput. Instead, we solved this problem by
+tiling all of the array’s CMOS sensors at the chip-scale onto a common multi-
+layer PCB, which is connected to a single FPGA for unified data routing.
+This allows for extremely tight packing and scalability by simply adding more
+sensors. Finally, 3D-RAPID also differs from light field imaging, because our
+cameras exhibit almost the theoretical minimum amount of overlap necessary
+for 3D surface estimation – this is an important design consideration because
+it allows us to maximize the SBP. In particular, to our knowledge, 3D-RAPID
+is the 3D imaging system with the highest sustained throughput to date.
+While we have presented several convincing 3D behavioral imaging demon-
+strations, there are several avenues for improvement. The hardware configu-
+ration could be adjusted to improve the 3D height reconstruction accuracy,
+which depends on how accurately parallax shifts can be detected to match
+corresponding features from different cameras. In Supplementary Sec. S5, we
+derive several equations detailing how height accuracy is impacted by hardware
+design parameters, suggesting that decreasing the focal length and increas-
+ing the magnification and sensor-to-sensor spacing improve height accuracy.
+Furthermore, since the reconstruction algorithm is agnostic to the contrast
+mechanism, it would also be possible to incorporate other optical contrast
+
+Springer Nature 2021 LATEX template
+16
+3D-RAPID
+mechanisms into 3D-RAPID, such as fluorescence to correlate behaviors with
+molecular signatures. Finally, throughput could be improved beyond 5 GP/sec
+by alleviating data transfer bottlenecks to the computer.
+In summary, we have presented a high-throughput computational 3D topo-
+graphic microscope as a new platform for studying the behavior of multiple
+freely-moving organisms at high speed and resolution over a very wide area.
+We expect our technique to be broadly applicable to elucidate new behavioral
+phenomena, not only in zebrafish, fruit flies, and ants, but also other model
+organisms such as tadpoles (X. laevis and X. tropicalis) and nematodes (C.
+elegans).
+5 Methods
+5.1 Temporal synchronization of the camera array
+Ideally, all sensor pixels should be fully synchronized with a global shutter,
+not only within each sensor, but also across sensors. This would ensure that
+between different views of the same object, after accounting for camera poses,
+the only discrepancies are due to parallax shifts and not sample motion. For
+example, if two camera views of a moving object with zero height were desyn-
+chronized, lateral motion could be interpreted as a parallax shift, leading to
+an erroneous height estimate. In practice, each of our sensors exhibits a rolling
+shutter, whereby only a single pixel value can be read out at a given time for
+a given sensor, row by row from the top-left to bottom-right corner in a raster
+scan pattern. This means that the bottom of a given sensor is captured later
+than the top of the sensor immediately below. However, across independent
+sensors, this rolling shutter readout pattern is synchronized to within 10 µs,
+limited by the serial communication interface (I2C with a 100-kHz clock).
+To mitigate the rolling shutter effects, we employed two strategies. First, we
+cropped the sensors so that there is only significant overlap in the horizontal
+dimension for stitching, in which the desynchronization is much less severe.
+Second, we calculated that with exposures of 2.5 ms for 4× downsampling, 5
+ms for 2× downsampling, and 20 ms for no downsampling, artifacts would be
+minimal. For a detailed discussion and calculations, see Supplementary Sec.
+S4.
+5.2 Achieving robustness to illumination variation
+Since the optimization metric of our approach is the mean square per-pixel
+photometric error, we would achieve optimal performance when the sample has
+a camera-independent photometric appearance. This condition would require
+not only uniform response across all pixels of all cameras, but also that the
+sample is isotropically emanating light in all directions. The latter property is
+in practice difficult to achieve, requiring either perfectly diffuse illumination
+or a diffusely scattering sample, regardless of the illumination direction. In
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+17
+addition to the regularizing effects of the CNN/DIP, we employed two addi-
+tional strategies to reduce the effects of camera-dependent appearance. First,
+as part of the camera pose pre-calibration procedure, we also jointly optimized
+per-camera second-order 2D polynomials (with cross terms) to correct the
+slowly-varying image intensity variation (whether caused by uneven illumina-
+tion or camera response), using the same photometric stitching loss. Thus, the
+pre-calibration step not only ensures geometric consistency of the 54 images,
+but also photometric continuity. For more details, see Methods 5.3, below.
+Second, for terrestrial organisms illuminated in reflection, we employed a
+two-step optimization process, where we first optimize the CNN to register the
+images using the RGB intensities. In the second step, we continue optimizing
+the CNN, except this time registering normalized high-pass-filtered versions of
+the photometric images, which reduces illumination-induced differences in pho-
+tometric appearance and emphasizes edges (Supplementary Sec. S3.5). This
+two-step procedure effectively removes artifacts in the 3D height maps that
+would otherwise result from camera-dependent photometric appearances.
+5.3 Calibration of camera pose, distortion, and intensity
+variation
+The first step in the 3D estimation pipeline was to calibrate the cameras’
+geometric and photometric properties. Specifically, the geometric properties
+include their 6D pose (3D position + 3D orientation) and second-order radial
+distortions (e.g., pincushion or barrel distortions). The photometric proper-
+ties include the pixel intensity variations both within individual cameras and
+across different cameras. These may arise due to vignetting, uneven illumi-
+nation, pixel response variation, or angle-dependent scattering of the sample.
+To estimate the calibration parameters, we imaged a flat, epi-illuminated,
+homogeneously-patterned calibration target with the MCAM and registered
+the resulting 54 images, enforcing both geometric and photometric consistency
+in the overlapped regions.
+The calibration procedure follows the optimization procedure outlined in
+Fig. 2a, excluding the height map-related orthorectification portion. In partic-
+ular, let x0 and y0 be two vectors representing the ideal 2D spatial coordinates
+of the camera pixels – that is, a 2D rectangular grid of equally-spaced points
+(e.g., 1536×4096). Next, let Dθ{·, ·} be an image deformation operation that
+maps from the ideal camera coordinates to a common global coordinate space
+(the object plane), parameterized by the camera parameters, θ. See Supple-
+mentary Sec. 1 of Ref. [68] for specific implementation details of Dθ. Let θi be
+the camera parameters for the ith camera, so that
+xi, yi = Dθi{x0, y0}
+(3)
+represents the (de)warped coordinates of the ith camera in a common object
+plane.
+
+Springer Nature 2021 LATEX template
+18
+3D-RAPID
+Let Ii,0 be a vector of the same length as x0 and y0, indicating the measured
+photometric intensity at every pixel coordinate for the ith camera. Although
+the debayered images have 3 color channels, here, for simplicity, we assume
+a single-channel image. Further, let Cφ,x0,y0{·} be a photometric correction
+operation, parameterized by φ, so that
+Ii = Cφi,x0,y0{Ii,0}
+(4)
+represents the photometrically-adjusted intensity values for the ith camera.
+The dependence on x0 and y0 indicates that the photometric correction is
+spatially-varying. Specifically, we used a second-order polynomial correction,
+Ii = Cφi,x0,y0{Ii,0} = (ai,0 + ai,1x0 + ai,2y0 + ai,3x0 ⊙ x0+
+ai,4y0 ⊙ y0 + ai,5x0 ⊙ y0) ⊙ Ii,0,
+(5)
+where
+⊙
+represents
+element-wise
+multiplication
+and
+φi
+=
+{ai,0, ai,1, ai,2, ai,3, ai,4, ai,5}. In sum, assuming θi and φi are optimized,
+then {xi, yi, Ii,0} represents the corrected ith camera data, accounting for
+distortion and photometric variation.
+Next, let {x, y, I} be three vectors representing the flattened concatenation
+of {xi, yi, Ii,0} for all i. We then initialize a blank matrix, R[·, ·], representing
+the stitched reconstruction, into which we backproject the collection of points,
+R[x, y] ← I,
+(6)
+with interpolation, as x and y are continuously valued. When specific coordi-
+nates are visited more than once, the values are averaged. The result of Eq. 6 is
+an estimate of the stitched composite for a given set of {θi, φi}54
+i=1. To update
+these parameters, we form a forward prediction from R[·, ·] by reprojecting
+back into the camera spaces, as follows:
+Ipred = R[x, y].
+(7)
+Ipred should match I when the camera images are well-registered and the cor-
+rected photometric intensities match in overlapped regions. Thus, we minimize
+the error metric,
+MSE = ∥Ipred − I∥2,
+(8)
+with respect to {θi, φi}54
+i=1 via gradient descent. Since the image target is
+homogeneous, we also include a regularization term,
+�
+i
+stdev(Ii),
+(9)
+which enforces a homogeneous reconstruction. Here, the standard deviation
+(stdev) is taken across all the pixels in one image.
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+19
+Finally, we apply the calibrated parameters, {θi, φi}54
+i=1, to each frame of
+the videos of the freely-moving organisms. To homogenize the background in
+the case of zebrafish, which uses transmission illumination instead of the epi-
+illuminated calibration target, we apply a second calibration step that only
+optimizes the photometric correction parameters, {φi}54
+i=1, using the maximum
+projection of the video across time, which eliminates all moving objects.
+5.4 Organism tracking and pose determination
+To track the fruit flies, zebrafish larvae, and harvester ants, we first thresh-
+olded the photometric composites to segment each organism and compute each
+of their centroids across all video frames. We then employed a simple particle-
+tracking algorithm, matching the organisms by finding the closest centroid
+in the subsequent video frame. In the case of clashing match proposals, we
+assigned matches that minimized the sum of the total absolute lateral displace-
+ments. To track the ants’ 6 femur-tibia joints, we incorporated the observation
+that the joint heights are local maxima in the 3D height maps for segmentation,
+and employed a similar particle-tracking algorithm.
+To determine the orientation of the organisms, we performed principal
+component analysis (PCA) on the thresholded pixel coordinates and took the
+first principal component (PC) as the organism’s orientation. In the case of
+zebrafish, we used the height map coordinates to perform PCA in 3D, thereby
+allowing us to compute the elevation angles in Fig. 3. We resolved the sign
+ambiguity of the PC either by enforcing the dot products of PCs of the tracked
+organism in consecutive frames to be positive, or by computing the rela-
+tive displacement between the unweighted centroid and the intensity-weighted
+centroid and forcing the PC to point in the same direction.
+The fish eye vergence angles were estimated by thresholding the green chan-
+nel of the photometric intensity images to identify the eyes. The orientations
+of the eyes were estimated using the regionprops command in MATLAB,
+which finds the angle of the major axis of the ellipse with the equivalent sec-
+ond moments. The vergence angle is then computed as the angle between the
+two eyes.
+5.5 Biological samples and data acquisition
+Zebrafish stocks were bred and maintained following IACUC guidelines and as
+previously described [77]. Zebrafish were stored at 28°C with daily feeding and
+water changes, and cycled through 14 hours of light and 10 hours of darkness
+per day. Free swimming fish were imaged at larval stages between 5 dpf and
+20 dpf. Specifically, zebrafish larvae were transferred from culture chambers
+using a transfer pipette to a clear plastic imaging arena (with lateral inner
+dimensions 97 mm × 130 mm), which was filled with system water a few mm
+deep. The arena was then placed on the sample stage of the MCAM system.
+The z position of the stage was adjusted such that the zebrafish larvae were all
+within the DOF of the lenses. The system was left undisturbed with the LED
+
+Springer Nature 2021 LATEX template
+20
+3D-RAPID
+illumination panels turned on for at least 5 minutes to allow the zebrafish to
+acclimate, after which multiple MCAM videos were acquired using a custom
+Python script. After video acquisition, the arena was removed and replaced
+with a flat patterned calibration target. We focused the target with the z stage
+using a Laplacian-based sharpness metric and captured a single frame (all 54
+cameras), which would serve to calibrate the camera poses and distortions for
+all videos captured during that imaging session.
+The wild-type red harvester ants and fruit flies (available from various
+vendors on Amazon) were maintained at room temperature. When ready for
+imaging, we positioned and focused a flat patterned calibration target, which
+serves two purposes: 1) for camera calibration, just as for the zebrafish videos
+described in the previous paragraph, and 2) to serve as a flat substrate for the
+ants and fruit flies to walk upon. The patterned target, although not required,
+serves as a global reference in the 3D height maps. Alternatively, the substrate
+could be monochrome/featureless or transparent (e.g., a glass sheet), as was the
+case for the zebrafish imaging configuration, in which case the 3D height map
+would assign an arbitrary height value to the background without affecting
+the 3D accuracy of the organisms themselves.
+The ants or fruit flies were inserted into a Falcon tube and released onto
+the center of the flat substrate, after which we immediately ran the same
+custom Python script to acquire MCAM videos. If necessary, the insects were
+re-collected in the tubes and re-released into the arena for repeated imaging.
+After video acquisition, we acquired a single frame of the calibration target
+alone, just as we did after zebrafish video acquisition.
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+21
+References
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+Acknowledgements
+We would like to thank Kristin Branson, Srinivas Turaga, Timothy Dunn,
+Archan Chakraborty, and Maximilian Hoffmann for their helpful feedback
+on the manuscript. Research reported in this publication was supported
+by the Office of Research Infrastructure Programs (ORIP), Office Of The
+Director, National Institutes Of Health of the National Institutes Of Health
+and the National Institute Of Environmental Health Sciences (NIEHS) of
+the National Institutes of Health under Award Number R44OD024879, the
+National Cancer Institute (NCI) of the National Institutes of Health under
+Award Number R44CA250877, the National Institute of Biomedical Imag-
+ing and Bioengineering (NIBIB) of the National Institutes of Health under
+Award Number R43EB030979, the National Science Foundation under Award
+Number 2036439, and the Duke Coulter Translational Partnership Award.
+Author contributions
+KCZ and RH conceived the idea and initiated the research. KCZ developed the
+algorithms and theory, with the help of CLC, JP, PCK, and RH. KCZ wrote
+the code for and performed 3D video reconstruction and stitching, animal
+tracking, and data analysis. MH, JD, PR, VS, CBC, MZ, and RH developed
+the MCAM hardware and acquisition software. KCZ acquired and analyzed
+the biological data, with the help of JPB, JB, AB, GH, and RH. JD and KCZ
+created the supplementary videos. KCZ wrote the manuscript and created the
+figures, with input from all authors. RH and MB supervised the research.
+Disclosures
+RH and MH are cofounders of Ramona Optics, Inc., which is commercializing
+multi-camera array microscopes. MH, JP, JD, PR, VS, CBC, MZ, JPB, and
+GH are or were employed by Ramona Optics, Inc. during the course of this
+research. KCZ is a consultant for Ramona Optics, Inc.
+Data availability
+Data will be available at https://doi.org/10.7924/r4db86b1q.
+Code availability
+Code will be available at https://github.com/kevinczhou/3D-RAPID.
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+29
+Supplementary information
+S1 System characterization: lateral resolution,
+axial precision and accuracy, and depth of
+field
+We performed several experiments to characterize the performance of our com-
+putational 3D imaging system, starting with imaging of a USAF resolution
+target near the center and edge of the field of view (FOV) of a single cam-
+era (Fig. S1a,b). Our system can resolve group 5 elements 2-3, corresponding
+to a bar width of 12-13 µm or a full-pitch lateral resolution of ∼25 µm. We
+then characterized the depth of field (DOF) by axially translating the same
+flat patterned target used in Figs. 4 and 5, using a motorized stage (Zaber)
+in increments of 0.25 mm. This defines the axial FOV of our 3D reconstruc-
+tions. For each axial position, we computed a contrast metric based on the
+mean image gradient magnitude (Fig. S1c). The full width at half maximum
+(FWHM) of this curve is 9.434 mm, which is similar to value obtained by
+fitting the curve to the intensity of a Gaussian beam,
+I(z) =
+I0
+1 + (z−z0)2
+z2
+R
++ Ib,
+(S1)
+where I0 and Ib are the arbitrary amplitude and offset, z0 is the focal position,
+and 2zR is the DOF, corresponding to when the lateral resolution degrades by
+√
+2. Least-squares fitting yields 2zR = 9.402 mm. In practice, the DOF may
+be smaller if the neighboring cameras are not focused to the same plane, such
+that the focus regions are offset.
+Finally, we characterized the accuracy and precision of our 3D height maps
+by imaging 6 gauge blocks (Mitutoyo), precisely machined and characterized
+to be within 0.3 µm of their nominal values: 1.000, 1.020, 1.050, 1.100, 1.200,
+and 1.400 mm (Fig. S1d,e). We computed the accuracy as the absolute error
+between the estimated and ground truth heights, aggregated across all pixels
+within each gauge block, and the precision as the standard deviation of the
+height estimates across each gauge block, which are summarized in Table S1
+for all three configurations in Table 1. Since there is an arbitrary global height
+offset, we chose the one that minimizes the MSE between the estimated and
+ground truth heights [68].
+S2 Generalization experiments
+Here, we show that the multiocular stereo CNN trained on a subset of frames
+can generalize well to unseen frames. As validation we compare this general-
+ization performance to that of a monocular stereo CNN (i.e., one that only
+takes in a single image as the input). To make these comparisons, we picked
+two independent subsets of the video frames. In Set 1, we took about 15 frames
+
+Springer Nature 2021 LATEX template
+30
+3D-RAPID
+Fig. S1 System characterization experiments. a, b, USAF resolution test chart image near
+the center and edge of the FOV of one camera without downsampling. c, Image contrast of
+a patterned target as a function of axial position. d, Stitched photometric composite of 6
+precisely-machined gauge blocks placed on a green patterned target (captured with the 60-
+fps configuration), with their nominal thicknesses denoted. e, The reconstructed 3D height
+map of the gauge blocks. Accuracy and precision are quantified in Table S1.
+Ground truth
+1× downsamp
+2× downsamp
+4× downsamp
+height
+Acc.
+Prec.
+Acc.
+Prec.
+Acc.
+Prec.
+0
+44.3
+19.3
+25.3
+17.2
+60.0
+55.9
+1000
+8.9
+17.5
+12.0
+32.2
+50.6
+69.4
+1020
+4.1
+11.2
+18.1
+24.3
+51.6
+72.7
+1050
+3.2
+18.5
+4.3
+25.7
+14.8
+63.8
+1100
+7.9
+17.7
+7.8
+28.6
+12.7
+68.7
+1200
+5.2
+24.1
+0.4
+33.0
+20.3
+88.9
+1400
+55.0
+8.7
+1.0
+27.7
+49.4
+100.4
+mean
+18.4
+16.7
+9.8
+26.9
+37.1
+74.3
+Table S1 Accuracy (absolute error from ground truth) and precision (standard
+deviation) of the height estimation of the 6 gauge blocks (and background) in Fig. S1a,b
+for all three downsampling configurations. All values are in µm.
+equally spaced temporarily across the video. In Set 2, we took another 15
+equally spaced frames at half a period offset with respect to Set 1. For exam-
+ple, if the video was 601 frames, then Set 1 would consist of frames 1, 41, 81,
+... 561, 601 and Set 2 would consist of frames 20, 60, 100, ...540, 580. We then
+trained two independent multiocular CNNs, one on Set 1, the other on Set 2,
+and compared the 3D height map predictions on both sets. The idea is that
+in the absence of ground truths, the physics-supervised CNN predictions on
+training set examples could serve as pseudo-truths. For comparison, we also
+trained a monocular CNN on Set 1 and compared predictions on Set 1 and
+Set 2.
+Figs. S2 and S3 show the comparisons among these three CNNs for both
+zebrafish and fruit flies. In both organisms, the multiocular CNNs generalize
+well to unseen video frames, based on comparisons between images from the
+CNN trained on Set 1 and the one trained on Set 2. However, for zebrafish,
+
+Center
+Edge
+a
+b
+Photometric composite
+1.000 mm
+1.050 mm
+1.200 mm
+1.020 mm
+1.100 mm
+1.400 mm
+150 μm
+ cm
+50
+3D height map
+C
+30
+FWHM = 9.4 mm
+20
+10
+-20 
+-10
+0
+10
+20
+30
+-0.1 mm
+1.5mm
+z position (mm)Springer Nature 2021 LATEX template
+3D-RAPID
+31
+2.8 mm
+0 mm
+1 mm
+2.8 mm
+0 mm
+1 mm
+a
+b
+Pseudo-truth
+Pseudo-truth
+Fig. S2 Generalization performance of multiocular and monocular CNNs trained on frames
+from a video of freely swimming zebrafish. a, First row shows an example from Set 1 and
+3D height predictions of three different CNNs – two multiocular CNNs, trained on Set 1 and
+Set 2, and one monocular CNN trained on Set 1. Second row shows predictions on Set 2. b,
+Zoom-in of the red boxes in a. Arrowheads point out features for which the multiocular CNN
+generalized well, but not the monocular CNN, as evaluated by comparing the predictions
+the respective pseudo-truth.
+the monocular CNN (trained on Set 1) generalizes poorly (to Set 2). This
+is evidenced by erroneous heights of several zebrafish’s heads or tails, as it
+is difficult to determine the heights of the fish based on appearance alone –
+magnification-based cues are confounded by natural size variation. Similarly,
+the monocular CNN incorrectly estimates the heights of the sunken food par-
+ticles. This is likely due to the fact that the vast majority of food particles are
+floating, and since the food particles have no discernible height indicators, the
+monocular CNN simply uniformly assigns the floating height to all particles.
+While the monocular CNN performs better for the fruit flies than for zebrafish,
+it still makes a few errors, e.g., when one fly is climbing on top of another.
+
+Photometric
+Multiocular, trained on Set 1
+Multiocular, trained on Set 2
+Monocular, trained on Set 1
+Pseudo-truth
+Set
+Pseudo-truth
+Set
+Image from Photometric
+Multiocular, trained on Set 1
+Multiocular, trained on Set 2
+Monocular, trained on Set
+Image from Set 1
+Image from Set 2Springer Nature 2021 LATEX template
+32
+3D-RAPID
+Such fly behavior was rare in our captured video, so the monocular CNN had
+fewer training examples to learn the semantic cues to accurately predict the
+elevated height, whereas the multiocular CNN was able to predict the elevated
+height from the parallax cues.
+4.5 mm
+0 mm
+2 mm
+Fig. S3 Generalization performance of multiocular and monocular CNNs trained on frames
+from a video of fruit flies. First row shows an example from Set 1 and 3D height predictions
+of three different CNNs – two multiocular CNNs, trained on Set 1 and Set 2, and one
+monocular CNN trained on Set 1. Second row shows predictions on Set 2.
+S3 Implementation details on patch-based
+training with multi-ocular stereo inputs
+Here, we expand upon the explanation of our patch-based CNN training
+procedure given in Sec. 2.5 and Fig. 2c.
+S3.1 Determining the observing cameras and the
+coordinates
+We start with the camera pose calibration based on a flat patterned target
+(Methods 5.3) to generate a “visitation log”, V . V is an nrow × ncolumn × 54
+× 2 tensor look-up table specifying which of the 54 cameras view a certain spa-
+tial position in the reconstruction coordinate system as well as the respective
+(row,column) pixel coordinates in the camera coordinate system that map to
+that position. The formation process of V is somewhat similar to the backpro-
+jection step of the reconstruction (Fig. 2a), but instead of backprojecting the
+RGBH values, we backproject the (row, column) coordinates. This visitation
+
+Photometric
+Multiocular, trained on Set 1
+Multiocular, trained on Set 2
+Monocular, trained on Set 1
+Pseudo-truth
+from Set
+Pseudo-truth
+Set
+Image from :Springer Nature 2021 LATEX template
+3D-RAPID
+33
+log facilitates rapid retrieval of the relevant cameras for each randomly sam-
+pled position. Note that since we want to avoid rolling shutter artifacts that
+may occur where the bottom of one camera overlaps with the top of the camera
+below (Methods 5.1 and Supplementary Sec. S4), we only consider horizontal
+overlap.
+S3.2 Selecting random patches
+Given this visitation log, we select nbatch random 2D coordinates in the recon-
+struction frame of reference for each CNN training iteration. For each of these
+random coordinates, we retrieve the relevant cameras and their corresponding
+camera-centric coordinates. For each camera image, we then crop out a square
+patch of width wpatch centered at the sampled coordinates. If these coordinates
+are within wpatch/2 of a camera image edge, they are shifted so that the patch
+remains within the image.
+For each image patch, we also extract patches from the left and right cam-
+eras and stack them along the channel dimension of the CNN input, which
+the CNN can exploit for 3D estimation (Fig. 2c). To do this in a manner con-
+sistent with both training on patches and inference on full-sized images, we
+homographically transformed the left/right neighboring images into the frame
+of reference of the central camera in question, as if the sample were flat (more
+precisely, coincident with the pre-calibration reference plane; Sec. 2.3, Meth-
+ods 5.3). If the sample were completely flat, then the transformed neighboring
+images would theoretically be identical to the image captured by the camera
+in question where their viewpoints overlap. However, if the sample exhibits
+height variation, the transformed neighboring images would exhibit parallax
+shifts in proportion to the height variation. When there is no left or right
+camera (i.e, the first or last column of cameras), we input blank images (all
+zeros). Similarly, when either the left or right patch overlaps with the edge
+of its respective camera, we assign zeros to the missing regions. Note that in
+this scenario, we cannot shift the left/right patch away from the edge, as we
+could above, because the left/right patch must remain coaligned with the main
+(central) patch so that we maintain full convolutionality for the inference step
+(Supplementary Sec. S3.8). Furthermore, we do not want to exclude training
+cases where the central patch is close to the edge of the camera, as these cases
+appear when applied to full-size camera images during the inference step.
+We note that the number of cameras observing a particular point can range
+from 1 - 3, since we only consider horizontal overlap. When only one camera
+views a particular point (the left and right edges of the reconstruction) during
+training, we reject the resulting patch as there’s nothing to register. To account
+for the fact that the number of patches may vary for each batch element, we use
+tensorflow’s [78] tf.RaggedTensor construct, which allows some dimensions
+of a tensor to have slices with different lengths. In our experiments, we used
+nbatch =1, 2, and 8 for the 1×, 2×, and 4× downsampling cases.
+
+Springer Nature 2021 LATEX template
+34
+3D-RAPID
+S3.3 CNN architecture
+The input to the CNN has nine channels, corresponding to three stacked RGB
+inputs – the camera image whose height we wish to predict, followed by the left
+and right camera views (Fig. 2c). The output of the CNN is a single-channel
+height map, obtained by summing across the channel dimension of the final
+convolutional layer.
+The encoder-decoder CNN architectures were based on one basic building
+block, consisting of the following operations in sequence:
+1. 3 × 3 convolution, k filters, stride=1, padding=‘same’,
+2. Batch normalization,
+3. Leaky ReLU,
+4. 1 × 1 convolution, k filters, stride=1, padding=‘valid’,
+5. Batch normalization,
+6. Leaky ReLU (unless final block of the CNN),
+where k is a free hyperparameter, specifying the number of filters in the
+convolution layers. In the case of an upsample block, a 2× nearest-neighbor
+upsampling procedure is applied before the block. In the case of a downsample
+block, a 2×2 max pooling operation is applied after the block.
+The full, symmetric encoder-decoder CNN architecture is described by a list
+of positive integers, each of which specifies the k for an upsample/downsample
+block pair. For example, [8, 16, 32] indicates three downsample blocks with k
+= 8, 16, and 32 filters, followed by three upsample blocks with k = 32, 16,
+and 8 filters. In our experiments, we set k = 32 for all upsample/downsample
+blocks, but varied the number of blocks between 3 and 6 (i.e., [32, 32, 32] and
+[32, 32, 32, 32, 32, 32]), depending on the sensor downsampling.
+S3.4 Data-dependent loss function
+The data-dependent loss function is computed based on the model depicted in
+Fig. 2a, where 2-3 image patches are used instead of 54 full-size images. Specif-
+ically, the 4-channel (RGBH) image patches are backprojected onto a blank
+“canvas” according to the camera poses and height map-derived orthorectifi-
+cation fields (Eq. 1). The same coordinates are then used to reproject back
+to camera-centric coordinates to obtain the forward predictions. The data-
+dependent loss function is thus the MSE between forward predictions and the
+original RGBH patches.
+S3.5 Normalized high-pass filtering
+For terrestrial samples, which were illuminated in reflection, we found that reg-
+istering the RGB images sometimes led to artifacts due to camera-dependent
+photometric appearance. This can be caused by illumination variation across
+the FOV due to off-axis LED panel geometry and anisotropic, non-Lambertian
+reflections, causing different amounts of light entering each camera. To combat
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+35
+these effects, we used normalized high-pass filtered versions of the images,
+�Iσ(x, y) =
+I(x, y) ⊛ exp
+�
+− x2+y2
+4σ2
+�
+I(x, y) ⊛ exp
+�
+− x2+y2
+2σ2
+�,
+(S2)
+where ⊛ denotes 2D convolution. Thus, Eq. S2 is the ratio of two Gaussian-
+blurred versions of I(x, y), the grayscale-converted RGB image, with widths
+σ and
+√
+2σ. Like high-pass filtering, applying Eq. S2 to the images highlights
+edges and attenuates DC and low-frequency features. The motivation for tak-
+ing a ratio rather than subtracting (i.e., difference of Gaussians) is so that
+the spatial fluctuations are normalized and therefore illumination-variation-
+independent, thereby facilitating registration. To capture different scales, we
+used three values of σ for the three image channels (σ = 1, 2, 4).
+S3.6 Regularization of the height maps
+In addition to the CNN reparameterization (i.e., DIP) of the height maps as a
+regularizer [43, 68, 69], we also incorporated two additive regularization terms
+to the overall loss function: height map consistency regularization and support
+regularization. The height map consistency regularization enforces agreement
+in height values in overlapped regions of camera images and simply comes from
+the fourth channel of the RGBH images, whose contribution can be scaled
+by a hyperparameter, λheight. We observed smoothing effects with increasing
+λheight. The object support regularization relies on a segmentation mask of the
+background pixels, whose height values we enforce to be a particular constant
+(e.g., 0) via an L2 loss. In other words,
+losssupport = λsupport
+�
+x,y
+mask background(x, y)(h(x, y) − h0)2,
+(S3)
+where mask background(x, y) is the segmentation mask, h(x, y) is the height map
+output of the CNN, h0 is the known background height value, and λheight is
+the regularization coefficient. In this paper, we used a simple intensity-based
+threshold on the green channel of the photometric images, as our backgrounds
+are relatively homogeneous, although other segmentation strategies may be
+used.
+S3.7 Additional training details
+We optimized the loss function, consisting of the aforementioned data-
+dependent and regularization terms, using the Adam Optimizer [79]. Depend-
+ing on the downsampling configuration, we used a different patch size and
+number of patches per iteration: one 1024×1024 patch (no downsampling), two
+768×768 patches (2× downsampling), and eight 384×384 patches (4× down-
+sampling). These patches were randomly selected from a subset of the recorded
+
+Springer Nature 2021 LATEX template
+36
+3D-RAPID
+video frames – for the 2× and 4× downsampling configurations, we selected
+from 15-16 frames evenly distributed frames, while for the no downsampling
+configuration, we used 8 frames (due to memory constraints).
+For the reflection-illuminated terrestrial samples, we performed a two-
+step training procedure, where we first optimized with RGB images using
+λheight = 500 (Supplementary Sec. S3.6) to scale the height channel (with units
+of mm) and λsupport = 0 (Eq. S3) for 30k iterations. Thereafter, we ran 70k
+iterations with the normalized high-pass filtering (Supplementary Sec. S3.5)
+and λheight = 50 and λsupport = 100. For aquatic samples, high-pass filtering
+was not necessary because they were illuminated in transmission. Thus, we
+used a one-step training procedure with 70k iterations with λheight = 50 and
+λsupport = 100.
+S3.8 Inference step - generating the full-size RGBH
+videos
+Once the CNN is trained to map from multi-ocular stereo inputs to a 3D height
+map using the patch-based procedure, we can apply the CNN to sequences
+of full-sized MCAM video streams that includes unseen frames (Fig. S4).
+Essentially, this refers to the backprojection step in Fig. 2a. Since iterative
+optimization is no longer necessary after the CNN is fully trained, generating
+new 3D video frames can be done quickly. For example, one application might
+involve a human observer selecting a particular region of interest within the
+large FOV, whose 3D height map the computer would then generate in real
+time.
+…
+…
+…
+…
+…
+…
+…
+Video input stream at ~5 GP/sec
+Apply multi-ocular CNN
+3D reconstruction
+Output 3D video frames
+Fig. S4 Inference step post patch-based training (Fig. 2c) that generates the stitched
+composites and coregistered 3D height map on potentially unseen video frames.
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+37
+S4 Reducing the impact of the per-camera
+rolling shutter
+Each sensor exhibits a rolling shutter, whereby the pixels begin integrating
+sequentially every δt = (230 MHz)−1 = 4.35 ns and are read out in a raster
+scan pattern row by row from the top left to bottom right (with the longer
+sensor dimension as the horizontal dimension). Although the rolling shutters
+are synchronized to within 10 µs across cameras, there is still significant asyn-
+chrony in overlapped regions of neighboring camera FOVs, thus thwarting
+accurate 3D estimation. Here, we consider asynchrony in 1) vertically over-
+lapped FOVs and 2) horizontally overlapped FOVs. The former asynchrony
+is much more serious, as the bottom row of the upper sensor is not reached
+until after δt × lrow × lcol, where lrow and lcol are the number of pixels per
+row and column, respectively. Using the full sensor without downsampling
+(lrow = 4208, lrow = 3120), the time delay between the last row of the upper
+sensor and the first row of the lower sensor is ∼57 ms. In practice, the delay
+is even larger due to horizontal and vertical blanking (dead time between row
+and column reads). To circumvent this problem, we thus reduced the number
+of rows approximately in half (3120 to 1536) to ensure the smallest overlap
+between vertically adjacent cameras that still allowed for a contiguous com-
+posite FOV. This also has the added benefit of increasing the sensor frame
+rate.
+Asychrony in horizontally overlapped FOVs is less serious, but still an
+important consideration. Using the full sensor without downsampling, the time
+delay between corresponding rows of perfectly aligned camera FOVs is only
+δt × lrow, or approximately 20 µs, which is negligible. In practice, however,
+there is a vertical offset due to slight camera misalignments, so that the time
+delay is δt × lrow × lmisalign. Based on stitching a flat target, we determined
+that the worst-case vertical misalignment was lmisalign = 100 rows, leading to a
+2-ms delay between when the corresponding pixels in horizontally neighboring
+cameras begin to expose. To ensure significant temporal overlap (at least 90%)
+in the exposure periods, we thus exposed for 2 ms/(1 − 0.9) = 20 ms.
+For 2× and 4× downsampling, the asynchrony is less dramatic because the
+numbers of rows and columns are reduced. Going through similar calculations,
+we determined that exposing for 5 ms and 2.5 ms for 2× and 4× downsampling,
+respectively, leads to >90% temporal overlap in the worst-case vertical camera
+misalignment cases. Note that these values don’t quite scale proportionally
+between the 2× and 4× cases due to horizontal blanking periods not decreasing
+proportionally.
+S5 Impact of hardware design on height
+accuracy
+Here, we explore how hardware design choices impact the accuracy of 3D
+height estimation. We will ignore errors stemming from camera distortion,
+
+Springer Nature 2021 LATEX template
+38
+3D-RAPID
+p
+h
+wo
+wi
+wi
+wo
+xL
+xR
+ΔxL
+ΔxR
+s
+Fig. S5 Two identical cameras with effective focal length f observing a common sample
+point with height h from the focal plane. The magnification is M = wi/wo.
+aberrations, and misalignment and assume ideal paraxial imaging performance.
+Further, for simplicity, we assume two adjacent cameras spaced by p center to
+center with a common effective focal length, f, a working distance (i.e., the
+distance between the sample plane and the lens principal plane) of wo, and a
+sensor-to-lens distance of wi (Fig. S5). These latter three parameters satisfy
+the lens equation,
+1
+wo
++ 1
+wi
+= 1
+f .
+(S4)
+The magnification is thus M = wi/wo.
+Further, consider a sample point with height h positioned xL from the
+optical axis of the left camera and xR from that of the right camera. Due to
+nontelecentric optics, the apparent object-side position of this sample point is
+parallax-shifted ∆xL in the left camera and ∆xR in the right camera. These
+shifts are related to the height via Eq. 1,
+∆xL =
+hxLM
+f(M + 1) − hM ,
+∆xR =
+hxRM
+f(M + 1) − hM .
+(S5)
+We are interested in the total parallax shift between both cameras, given by
+∆x = ∆xL + ∆xR =
+hpM
+f(M + 1) − hM ,
+(S6)
+which does not depend on the lateral position of the sample point, as xL+xR =
+p. How well we can estimate ∆x depends on how accurately we can match
+and register the sample point in both camera images, which in turn depends
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+39
+on the lateral resolution of the imaging system. We consider two limits: the
+diffraction-limited regime and the pixel-size-limited regime. Let δxpixel be the
+camera pixel size, so that δxpixel/M is the object-side pixel size. Further, let
+δxdiff be the camera-side diffraction-limited spot size, so that δxdiff /M is the
+object-side diffraction-limited spot size:
+δxdiff ∝
+λ
+NA ≈ 2λwi
+w
+= 2λf(M + 1)
+w
+,
+(S7)
+where w is the lens aperture diameter and λ is the wavelength. Assum-
+ing that we can match corresponding points in the two camera images with
+an uncertainty proportional to the lateral resolution, then the corresponding
+height error can be estimated by setting ∆x (Eq. S6) equal to the object-
+side lateral spot size and solving for h. In the pixel-resolution-limited regime
+(δxpixel ≫ δxdiff ), we have that the height uncertainty is
+δhpixel ∝ fδxpixel(M + 1)
+M(δxpixel + pM),
+(S8)
+meaning that downsampling the images results in a roughly proportional
+decrease in height uncertainty. In the diffraction-limited regime, we have that
+δhdiff ∝
+2λf 2(M + 1)2
+M(2λf(M + 1) + pwM).
+(S9)
+We can see that in both cases, all else equal, decreasing f and increasing p and
+M improve the height estimation accuracy. It may appear helpful to decrease
+M to increase the amount of overlap of neighboring camera FOVs until even-
+tually non-adjacent cameras begin to overlap, resulting in larger values of p.
+However, in both pixel-limited and diffraction-limited regimes, 1/p decreases
+more slowly than the factors that include M increase as M decreases (e.g., con-
+sider p → 2p, M → M/2). Furthermore, this analysis assumes that the object
+height variation is within the depth of field of the imaging systems, within
+which the lateral resolution remains roughly constant. Thus, while designs that
+increase the lateral resolution can improve height estimation accuracy, they
+also compromise the axial FOV.
+We now consider the case where the camera FOVs are critically overlapped
+at 50%, that is when M = s/2p, where s is the sensor width. Thus, the height
+uncertainties in the pixel- and diffraction-limited regimes are, respectively,
+δhpixel ∝ 2δxpixelf(2p + s)
+s(2δxpixel + s)
+≈ 2δxpixelf(2p + s)
+s2
+,
+(S10)
+δhdiff ∝
+2λf 2(2p + s)2
+s(2λf(2p + s) + psw) ≈ 2λf 2(2p + s)2
+ps2w
+.
+(S11)
+
+Springer Nature 2021 LATEX template
+40
+3D-RAPID
+In the ideal case of p = s, so that there are no gaps in between the sensors
+and M = 1/2, we have
+δhpixel ∝ δxpixelf
+p
+,
+(S12)
+δhdiff ∝ λf 2
+pw .
+(S13)
+S6 SNR considerations
+As with all imaging systems, SNR is an important metric for 3D-RAPID.
+Specifically, the better the SNR of the photometric images, the higher the
+image registration accuracy and by extension the 3D estimation accuracy.
+There are several trade offs involving SNR with our method as it relates to
+imaging small model organisms.
+1. Numerical aperture (NA): the higher the NA, the more light collected and
+the better the shot-noise-limited SNR. The associated improved lateral reso-
+lution also improves the 3D height estimation accuracy, because the parallax
+estimation accuracy would increase (Supplementary Sec. S5). However, at
+the same time, the higher the NA, the shallower the depth of field, which
+limits the axial FOV of the 3D reconstructions. In addition, the higher the
+NA, the smaller the lateral FOV becomes in practice due to difficulties
+in correcting aberrations [22] and therefore the tighter the camera array
+packing would need to be.
+2. Behavior: while increasing the illumination power would yield higher SNR,
+care must be taken to avoid influencing the behavior of the model organisms.
+This tradeoff can be partially alleviated by using wavelengths invisible to
+the model organism’s visual system, however radiative heating from the
+illumination source can potentially still influence behavior.
+3. Speed: the higher the frame rate, the less light that is detected and therefore
+the lower the SNR per frame. Increasing illumination power can alleviate
+this tradeoff until it influences the behavior of interest.
+4. Camera type: one of the factors enabling the financial tractability of the
+3D-RAPID architecture is its use of CMOS digital image sensors that are
+currently fabricated at large scales for the cell phone camera market. While
+the sensitivities of these camera sensors have improved significantly over the
+past decade (e.g., now with very low read noise and dark current and high
+quantum efficiency, due in part to the introduction of back-side illuminated
+CMOS sensors), their performance may still generally lag behind that of
+high-end scientific CMOS and EMCCD sensors. While this latter technology
+is currently too expensive to multiplex into an array with more than several
+dozen sensors, it may become feasible in the future.
+
+Springer Nature 2021 LATEX template
+3D-RAPID
+41
+S7 Supplementary video descriptions
+1. 60-fps, 36.6-MP video of freely swimming zebrafish larvae (10 dpf) feeding
+on mostly floating AP100 food particles. The left panel is the photometric
+composite and the right panel is the 3D height map. The video zooms into
+three feeding events (or attempts) by two different fish.
+2. 230-fps, 9.1-MP video of freely swimming zebrafish larvae (10 dpf) feeding
+on mostly floating AP100 food particles. The left panel is the photometric
+composite and the right panel is the 3D height map. The video zooms in
+on three independent feeding events by three different fish. The third fish
+can be seen swallowing the food particle.
+3. 60-fps, 36.6-MP video of freely swimming zebrafish larvae (10 dpf) feeding
+on mostly floating AP100 food particles. The left panel shows the full field
+of view with the trajectories mapped out. The panels on the right each
+correspond to individual fish, uniquely identified by a 2-digit number, whose
+position and orientation are denoted with red annotations. The righthand
+panels’ border colors nonuniquely match those of the tracks in the lefthand
+panel, to assist the viewer in matching the fish to the trajectories. Righthand
+panels appear and disappear when the fish enters or exits the FOV. The
+first half of the video shows the photometric values, while the second half
+of the video shows the 3D height maps.
+4. 60-fps, 36.6-MP video of 20-dpf zebrafish larvae feeding on live brine shrimp.
+The left panel is the photometric composite and the right panel is the 3D
+height map. The video zooms in on two feeding events from two different
+fish.
+5. 230-fps, 9.1-MP video of 20-dpf zebrafish larvae feeding on live brine shrimp.
+The left panel is the photometric composite and the right panel is the 3D
+height map. The video zooms into one feeding event.
+6. 60-fps, 36.6-MP video of a large school of 5-dpf zebrafish larvae freely swim-
+ming in an open arena at high speed. The left panel is the photometric
+composite and the right panel is the 3D height map.
+7. 230-fps, 9.1-MP video of a large school of 5-dpf zebrafish larvae freely swim-
+ming in an open arena at high speed. The left panel is the photometric
+composite and the right panel is the 3D height map.
+8. 60-fps, 36.6-MP video of freely moving fruit flies. The left panel is the
+photometric composite and the right panel is the 3D height map.
+9. 230-fps, 9.1-MP video of freely moving fruit flies. The left panel is the
+photometric composite and the right panel is the 3D height map.
+10. 60-fps, 36.6-MP video of freely moving fruit flies. The left panel shows the
+full field of view with the trajectories mapped out. The panels on the right
+each correspond to individual flies, uniquely identified by a 2-digit number,
+whose position is denoted by a red circle. The righthand panels’ border
+colors nonuniquely match those of the tracks in the lefthand panel, to assist
+the viewer in matching the flies to the trajectories. Righthand panels appear
+and disappear when the fish enters or exits the FOV. The first half of the
+
+Springer Nature 2021 LATEX template
+42
+3D-RAPID
+video shows the photometric values, while the second half of the video shows
+the 3D height maps.
+11. 60-fps, 36.6-MP video of freely moving harvester ants. The left panel is the
+photometric composite and the right panel is the 3D height map.
+12. 230-fps, 9.1-MP video of freely moving harvester ants. The left panel is the
+photometric composite and the right panel is the 3D height map.
+
diff --git a/idE_T4oBgHgl3EQf4Rxl/content/tmp_files/load_file.txt b/idE_T4oBgHgl3EQf4Rxl/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be72b4a0f64089cdf2b89ad6f49afdddcc823e80
--- /dev/null
+++ b/idE_T4oBgHgl3EQf4Rxl/content/tmp_files/load_file.txt
@@ -0,0 +1,1727 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf,len=1726
+page_content='Springer Nature 2021 LATEX template  Parallelized computational 3D video  microscopy of freely moving organisms at  multiple gigapixels per second  Kevin C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Zhou1,2,6*, Mark Harfouche2, Colin L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Cooke3, Jaehee Park2, Pavan C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Konda1, Lucas  Kreiss1, Kanghyun Kim1, Joakim J¨onsson1, Jed  Doman2, Paul Reamey2, Veton Saliu2, Clare B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Cook1,2, Maxwell Zheng2, Jack P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Bechtel2, Aur´elien  B`egue2, Matthew McCarroll5, Jennifer Bagwell4, Gregor  Horstmeyer2, Michel Bagnat4 and Roarke Horstmeyer1,2,3*  1Department of Biomedical Engineering, Duke University,  Durham, NC 27708, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2Ramona Optics Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', 1000 W Main St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Durham, NC 27701, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3Department of Electrical and Computer Engineering, Duke  University, Durham, NC 27708, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  4Department of Cell Biology, Duke University, Durham, NC  27710, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5Department of Pharmaceutical Chemistry, University of  California, San Francisco, CA, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  6Current affiliation: Department of Electrical Engineering and  Computer Sciences, University of California, Berkeley, CA, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Corresponding author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' E-mail(s): kevinczhou@berkeley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  roarke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='horstmeyer@duke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Abstract  To study the behavior of freely moving model organisms such as zebrafish  (Danio rerio) and fruit flies (Drosophila) across multiple spatial scales, it  would be ideal to use a light microscope that can resolve 3D information  over a wide field of view (FOV) at high speed and high spatial resolu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' However, it is challenging to design an optical instrument to achieve  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='08351v1  [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='optics]  19 Jan 2023  Springer Nature 2021 LATEX template  2  3D-RAPID  all of these properties simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Existing techniques for large-FOV  microscopic imaging and for 3D image measurement typically require  many sequential image snapshots, thus compromising speed and through-  put.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Here, we present 3D-RAPID, a computational microscope based on  a synchronized array of 54 cameras that can capture high-speed 3D topo-  graphic videos over a 135-cm2 area, achieving up to 230 frames per second  at throughputs exceeding 5 gigapixels (GPs) per second.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3D-RAPID  features a 3D reconstruction algorithm that, for each synchronized tem-  poral snapshot, simultaneously fuses all 54 images seamlessly into a  globally-consistent composite that includes a coregistered 3D height  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The self-supervised 3D reconstruction algorithm itself trains a  spatiotemporally-compressed convolutional neural network (CNN) that  maps raw photometric images to 3D topography, using stereo overlap  redundancy and ray-propagation physics as the only supervision mecha-  nism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' As a result, our end-to-end 3D reconstruction algorithm is robust  to generalization errors and scales to arbitrarily long videos from arbi-  trarily sized camera arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The scalable hardware and software design  of 3D-RAPID addresses a longstanding problem in the field of behavioral  imaging, enabling parallelized 3D observation of large collections of freely  moving organisms at high spatiotemporal throughputs, which we demon-  strate in ants (Pogonomyrmex barbatus), fruit flies, and zebrafish larvae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Keywords: parallelized microscopy, camera array, computational microscopy,  behavioral imaging, self-supervised learning, 3D imaging  1 Introduction  Quantifying the behavior and locomotion of freely-moving model organisms,  such as the fruit fly (Drosophila) and zebrafish (Danio rerio), is essential  in a wide variety of applications, including neuroscience [1–3], developmen-  tal biology [4], disease modeling [5, 6], drug discovery [7, 8], and toxicology  [9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Particularly for high-throughput screening in these applications, it is  desirable to monitor the behaviors of tens or hundreds of organisms simulta-  neously, thus requiring high-speed imaging over large fields of view (FOVs) at  high spatial resolution, and ideally with the ability to observe behavior in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Such an imaging system would allow researchers to bridge the gap between  microscopic phenotypic expression and natural, multi-organism behavior that  manifest across more macroscopic scales, such as shoaling [11, 12], courtship  and aggression behaviors [13, 14], exploration [15, 16], and hunting [16–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Common approaches for behavioral recording utilize 2D wide-field micro-  scopes with low-magnification optics to cover as large a FOV as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  However, due to physical space-bandwidth product (SBP) limitations of con-  ventional optics [21–23], standard imaging systems are forced to accept a  tradeoff between image resolution and FOV (that is, can only record at low  resolution when observing a large FOV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Such systems are commonly used to  track the location of large populations of organisms in high-content screening  Springer Nature 2021 LATEX template  3D-RAPID  3  applications for toxicology and pharmacology [24–26], but cannot record key  morphological features and behavioral signatures that require high-resolution  capture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Techniques that enhance SBP to facilitate high-resolution imaging  over large areas, such as Fourier ptychography (FP) [27–29] and mechanical  sample translation [30, 31], often require multiple sequential measurements,  which compromises imaging speed and throughput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Approaches that perform  closed-loop mechanical tracking to record single organisms freely moving in 2D  with scanning mirrors [32] or moving cameras [16] are not scalable and thus  cannot longitudinally observe multiple organisms simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Number of overlapping cameras  cam (1,1)  cam (1,6)  cam (9,1)  cam (9,6)  a  c  0  1  2  3  4  5  6  d  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 cm  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8 cm  54-camera array  Reflection  illumination  Object  Transmission  illumination  b  ⋯  ⋯  ⋯  ⋯  ~66% Horizontal overlap  Parallax-aware stitching and 3D estimation  cam (1,1)  cam (1,2)  cam (1,6)  cam (9,1)  cam (9,5)  cam (9,6)  3D height map  height  4 mm  0 mm  Photometric composite  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='35 cm  1 cm  2 mm  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1 Overview of 3D-RAPID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a, Computational microscope setup, consisting of a 9×6  = 54 array of finite-conjugate imaging systems, jointly recording across a 135-cm2 area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  LED arrays serve as the illumination source, both in transmission and reflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' b, 9×6  array of cameras and lenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' c, Overlap map of the object plane, demonstrating roughly  66% horizontal overlap redundancy between neighboring cameras (and minimal overlap in  the vertical dimension).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Four example camera FOVs are denoted with green dotted boxes,  identified by (row,column) coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' d, The MCAM captures 54 synchronized videos at  >5-GP/sec throughputs, which are stitched to form a high-speed video sequence of globally-  consistent composites and the corresponding 3D height maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Conventional wide-field techniques also lack 3D information, which poten-  tially precludes observation of important behaviors, such as vertical displace-  ment and out-of-plane tilt changes in zebrafish larvae [20, 33, 34] and 3D  limb coordination and kinematics in various insects [35–38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Commonly used  3D microscopy techniques such as diffraction tomography [39–43], light sheet  microscopy [44–46], and optical coherence tomography (OCT) [47–50], are not  well-suited for behavioral imaging, since they often require multiple sequential  measurements for 3D estimation and inertially-limited scanners that sacrifice  speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Furthermore, while such techniques can achieve micrometer-scale spa-  tial resolutions, they typically do so over millimeter-scale FOVs rather than  Springer Nature 2021 LATEX template  4  3D-RAPID  the multi-centimeter-scale FOVs necessary for imaging freely-moving organ-  isms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, these techniques are typically limited to imaging one immobilized  organism at a time (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', embedded in agarose, tethered [37, 38], or paralyzed),  which prevents behavior studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Parallelized, camera array-based imaging systems have also been proposed  to increase imaging system SBP and overall measurement throughput [51–55];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  however, none of these prior approaches have demonstrated scalable, high-  speed, high-resolution, wide-FOV, 3D imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In particular, several of these  approaches were designed for 2D macroscopic photographic applications, which  face several challenges for miniaturization for microscopy applications, or fea-  ture a primary objective lens that limits the maximum achievable system SBP  (see Discussion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Various macroscale 3D depth imaging techniques have also  been developed, such as time-of-flight light detection and ranging (LiDAR)  [56], coherent LiDAR [57–61], structured light [62], stereo vision [63], and  active stereo vision techniques [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' However, such 3D imaging systems have  throughputs typically limited to 10s of megapixels (MPs) per second and gen-  erally have poor spatial resolutions on the order of millimeters, making them  ill-suited for behavioral imaging of small model organisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Further, active  patterned illumination techniques do not scale to high pixel counts, typically  require multiple measurements (thus compromising speed), and may directly  impact the organism’s behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Here, we present 3D Reconstruction with an Array-based Parallelized  Imaging Device (3D-RAPID), a new computational 3D microscope based on  an array of 9×6 = 54 temporally synchronized cameras, capable of acquiring  continuous high-speed video of dynamic 3D topographies over a 135-cm2 lateral  FOV at 10s of micrometer 3D spatial resolution and at spatiotemporal data  rates exceeding 5 gigapixels (GPs) per second (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We demonstrate three  operating modes of our microscope, which can be flexibly chosen depending on  whether to prioritize speed (up to 230 frames per second (fps)) or spatial SBP  (up to 146 MP/frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We also present a new scalable computational 3D recon-  struction algorithm that, for each synchronized snapshot, simultaneously forms  a globally-consistent photometric composite and a coregistered 3D height map  based on a ray-based physical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The 3D reconstruction itself trains an  underparameterized, spatiotemporally-compressed convolutional neural net-  work (CNN) that maps multi-ocular inputs to the 3D topographies, using  ray propagation physics and consistency in the overlapped regions as the  only supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, after computational reconstruction of just a few video  frames (<20), 3D-RAPID can rapidly generate photometric composites and  3D height maps for the remaining video frames non-iteratively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3D-RAPID thus solves a longstanding problem in the field of behavioral  imaging of freely moving organisms that previously only admitted low-  throughput solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To the best of our knowledge, prior to our work, there  was no imaging system that could sustainably image at such high spatiotem-  poral throughputs (>5 GP/sec) in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These new capabilities have allowed us  to capture novel 3D measurements of freely moving organism behavior, which  Springer Nature 2021 LATEX template  3D-RAPID  5  we have extensively tested in a series of experiments with three model organ-  isms: zebrafish larvae, fruit flies, and ants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In particular, the large FOV of  3D-RAPID enabled imaging of multiple freely behaving organisms in parallel,  while the dynamic 3D reconstructions and high spatial resolution and imag-  ing speeds enabled 3D tracking of fine features, such as ant leg joints during  exploration, zebrafish larva eye orientation during feeding, and fruit fly pose  while grooming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2 High-throughput 3D video with 3D-RAPID  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 3D-RAPID hardware design  The 3D-RAPID hardware is based on a multi-camera array microscope  (MCAM) architecture [55, 65], consisting of 54 synchronized micro-camera  units spaced by 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 mm and tiled in a 9×6 configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Each micro-camera  captures up to 3120 × 4208 pixels (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1-µm pitch), for a total of ∼700 megapix-  els per snapshot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The data is transmitted to computer memory via PCIe at ∼5  GB/sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Unlike conventional microscopy, 3D-RAPID is configured to acquire  multi-view videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' That is, almost every point in the synthesized ∼12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5×10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8-  cm2 is viewed from at least two perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To achieve this, we axially  positioned the lenses (Supply Chain Optics, f = 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='23 mm) to obtain a mag-  nification of M ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='11, leading to ∼66% overlap in the sample plane field  of view (FOV) between cameras adjacent along the longer camera dimension  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This overlap redundancy enables 3D estimation using stereoscopic  parallax cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The sample is illuminated in transmission or reflection using  planar arrays of white LEDs covered by diffusers (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 Tradeoff space of lateral resolution, field of view, and  frame rate  Our 3D-RAPID system has flexibility to downsample or crop the individual  sensor pixels or use fewer cameras to increase the frame rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The overall  data throughput is limited by the slower of two factors: the data transfer rate  from the sensors to the computer RAM (∼5 GB/sec) or the sensor readout  rate, which is a function of the sensor crop shape and downsample factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Streaming all 54 cameras without downsampling or cropping runs into the  data transfer rate-limited frame rate of ∼7 fps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To achieve higher frame rates,  we present results with a 1536×4096 sensor crop using either 4×, 2×, or no  downsampling, allowing us to achieve up to 230, 60, or 15 fps, respectively,  while maintaining roughly the same overall throughput of ∼5 GP/sec (Table  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' While excluding half of the sensor rows all but eliminates FOV overlap  in the vertical dimension, the benefits are two-fold: increased frame rate and  reduced rolling shutter artifacts (see Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  6  3D-RAPID  Downsample factor  1× (none)  2×  4×  Per-camera dims  1536×4096  768×2048  384×1024  Composite dims  13000×11250  6500×5625  3250×2810  Composite SBP  146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 MP  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6 MP  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 MP  Frame rate  15 fps  60 fps  230 fps  Exposure  20 ms  5 ms  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 ms  Raw pixel rate  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 GP/sec  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 GP/sec  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='9 GP/sec  Composite pixel rate  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 GP/sec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 GP/sec  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 GP/sec  Image pixel pitch  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6 µm  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 µm  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 µm  Table 1 The three imaging configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 Seamless image registration, stitching, and 3D  estimation  For each video frame, the 3D-RAPID algorithm fuses the 54 synchronously  acquired images, via gradient descent using a pixel-intensity-based loss, into  a continuous, seamless, expanded-FOV composite image, and simultaneously  estimates a coregistered 3D height map (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In fact, these two tasks  are intimately related – to form a high-quality registration, it is necessary to  account for parallax distortions induced by height deviations from a planar  sample scene that would otherwise thwart simple registration using homo-  graphic transformations (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2b) [66–68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To achieve this, the algorithm starts  with calibration of the 6-degree-of-freedom poses (x, y, z, roll, pitch, yaw),  camera distortions, and intensity variations by registering and stitching 54  images of a flat, patterned target (Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Estimating the 3D height  map of the sample of interest relative to this calibration plane is tantamount  to rendering the images registerable using homographies (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In par-  ticular, the per-pixel deformation vectors that undo the parallax shifts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=',  orthorectify the images) have magnitudes that are directly proportional to the  per-pixel heights, h(r) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', the height map), given by [68]  h(robj + rrectify) = f  ∥rrectify∥  ∥robj − rvanish∥  �  1 + 1  M  �  (1)  where f = 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='23 mm is the effective focal length of the lens, M ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='11 is  the linear magnification, robj is the apparent 2D position of the object in the  pixel (before orthorectification), rvanish is the vanishing point to which all lines  perpendicular to the sample plane appear to converge, and rrectify is the 2D  orthorectification vector pointing towards the vanishing point (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' rvanish  can be determined from the camera pose, as the point in the sample plane that  intersects with the perpendicular line that passes through the principal point  in the thin lens model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The orthorectification vectors rrectify, and therefore  the height map, for each object position robj can be determined by registering  images (via photometric pixel values) from different perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The accuracy  of the height map thus depends on the object having photometrically textured  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', not uniform) surfaces that enable unique image registration, a condition  which the model organisms we imaged satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  3D-RAPID  7  a  b  c  d  Ant anaglyph  Zebrafish anaglyph  Near focal plane  Above focal plane  2 mm  1 mm  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2 Computational 3D reconstruction and stitching algorithm for 3D-RAPID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a, The  algorithm starts with raw RGB images (only one shown for clarity), along with coregistered  images from the cameras to left and right, as CNN inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' CNN generates camera-centric  height maps, which in turn dictate orthorectification fields (see b and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Orthorecti-  ficaton fields and camera poses + distortions constitute registration parameters, dictating  where and how each image should be backprojected in the stitched photometric compos-  ite and 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The backprojection step is then reversed (reprojection) to form  forward predictions of the RGB images and camera-centric height maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Errors (photomet-  ric MSE and height MSE) guide the optimization of the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' b, The physical ray model,  intuitively showing how orthorectification facilitates stitching of non-telecentric images and  height maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' c, The patch-based joint training/stitching/3D reconstruction algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' At  each gradient descent iteration, random coordinates are chosen (red star);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' all cameras that  view a given point are isolated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' A patch is cropped out from each camera image surrounding  the randomly sampled point, along with the corresponding left/right camera images to serve  as the multi-ocular stereo inputs to the CNN to predict the patch height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These patches  undergo the procedure outlined in a to form a mini photometric and 3D height reconstruc-  tions to update the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Zeros are assigned to stereo input pixels when unavailable (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=',  at the edge of the object plane FOV), to preserve convolutionality when applying the CNN  to the entire camera images to generate the full-size reconstructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' d, Analyphs, whereby  the three stereo inputs are color-coded as RGB channels, showing the parallax that is used  to estimate 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Thus, the optimization problem is to jointly register all 54 images using  the pixel-wise photometric loss, using the orthorectification maps (which are  directly proportional to the height maps via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1) as the deformation model  on top of the fixed, pre-calibrated camera parameters, including distortions  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In practice,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' since viewpoint-dependent photometric appearance  can affect image registration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' we also employed normalized high-pass filtering  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Multi-ocular stereo input from MCAM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Left  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Right  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Camera  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Camera  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='CNN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='camera  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='camera  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='centric  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='image  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='image  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='image  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='height  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Photometric  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Registration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3D height  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Backproject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Backproject  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='composite  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='parameters  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='Orthorectification  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='fields  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='& distortions  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='RGB  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='reconstruction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='０１2345６  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='PatchMSE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='Numberofobservingcamerasrvanish  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='robj + rrectify  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='stitch  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='stitchSpringer Nature 2021 LATEX template  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3D-RAPID  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='to standardize photometric appearance (Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 and Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 Spatiotemporally-compressed 3D video via  end-to-end physics-supervised learning  Instead of optimizing the height maps directly, we reparameterized the height  maps as the output of a fully-convolutional encoder-decoder CNN that takes  the multi-view stereo images as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This reparameterization has two inter-  pretations, depending on whether we emphasize the CNN or the ray-based  physical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' On the one hand, the CNN can be thought to act entirely as a  training-data-free regularizer (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', deep image prior (DIP) [69]) that safeguards  against 3D reconstruction artifacts that may otherwise arise from practical  deviations from modeling assumptions that thwart image registration [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For  example, using the CNN as a regularizer can be useful when the sample has a  different appearance when viewed from different angles, which can be caused  by uneven illumination, angle-dependent scattering responses, or varying pixel  responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Since we wish to reconstruct hundreds to thousands of 3D video  frames, it would be prohibitively slow to independently reconstruct every indi-  vidual video frame, with or without CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, we use one shared DIP, with  each frame encoded by the raw multi-ocular stereo photometric inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  On the other hand, this leads to the second interpretation of a self-  supervised or physics-supervised learning problem, in which the image reg-  istration of the overlapped MCAM image frames, governed by a ray-based  thin lens physical model (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1), provides the physics-based supervision that  guides the CNN training (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a,c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The CNN can then be used to generalize  to other MCAM data, both spatially (other micro-cameras) and temporally  (other video frames).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  This dual interpretation of our CNN-regularized, physics-supervised learn-  ing approach reveals several advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' First, since we employ a fully-  convolutional CNN, we can optimize on arbitrarily-sized image patches (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2c) that can fit in GPU memory, and then perform non-iterative forward  inference on arbitrarily-large full-size images (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, our proposed  approach is scalable and generalizable to arbitrarily many cameras, each with  arbitrarily many pixels, for arbitrarily many video frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For implementation  details on patch-based training, see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c, and Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Second, the CNN acts as a spatiotemporally-compressed representation  of the 3D height map videos, thus avoiding the need to iteratively optimize  every single 3D video frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Third, this spatiotemporal compression offers  additional regularizing effects on top of the dataset-free, DIP-based regular-  ization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' As there are far fewer parameters in the CNN than height map pixels  across all MCAM video frames, overfitting becomes less likely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Furthermore,  the CNN implicitly enforces consistency across space and time, thus, for exam-  ple, avoiding variance induced by independent optimization runs on different  frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Fourth, our approach has an inherent fail-safe against CNN general-  ization errors, unlike other deep learning-based approaches, since the ground  Springer Nature 2021 LATEX template  3D-RAPID  9  truth is implicitly always available via the overlap redundancy of the MCAM  along with the physical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 Patch-based learning from multi-ocular stereo inputs  While Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a summarizes the ideal joint 3D reconstruction, stitching, and  training method, in practice we are constrained by GPU memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, we  train the CNN using a random patch sampling approach (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Briefly,  at each optimization iteration, we sample nbatch (batch size) random points  within the composite FOV (one shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' All cameras viewing each  point are selected, from which patches surrounding that point are extracted  from each camera view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thereafter, these nbatch groups of selected patches  independently undergo the procedure outlined in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Once CNN training  is done, the backprojection step in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a is carried out for each full temporal  frame to create the stitched RGBH 3D reconstructions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For more  implementation details, see Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  As mentioned in the previous section (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4), the CNN is supplied multi-  view inputs of the same sample scene (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a,c), whose goal is to  improve the generalizability of the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These neighboring views are stacked  along the channel input dimension in a way that preserves convolutionality, so  that patch training and full-FOV inference are consistent (Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This is beneficial because monocular stereo depth estimation is insuffi-  cient for objects whose appearances don’t change significantly as a function of  depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For example, when imaging a fruit fly or zebrafish larva, it is difficult to  distinguish between height-dependent magnification changes and natural vari-  ation in organism size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, we train our CNN to solve a multi-ocular stereo  3D estimation problem, which is better-posed, as the 3D supervision signal  itself is derived from the registration of the multi-ocular data (Supplementary  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In this paper, we use 3 stereo inputs or fewer (center, left, and right,  if available).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3 Results  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 3D-RAPID system characterization  Our 3D-RAPID system has a full-pitch lateral resolution of ∼25 µm and  DOF of ∼9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 mm, based on imaging a USAF resolution target and translat-  ing a patterned target axially (see Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We validated the  height precision and accuracy of our 3D-RAPID system by imaging precisely  machined (to within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 µm) and interferometrically characterized gauge blocks  (Mitutoyo).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' As expected, accuracy and precision of the reconstructed height  improve when imaging at higher spatial resolution, which facilitates more accu-  rate measurement of parallax shifts (see Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Specifically,  we achieved sub-20 µm accuracy and precision in the 15-fps configuration, and  ∼37 µm and ∼74 µm accuracy and precision in the 230-fps configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' See  Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1 for detailed characterization results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  10  3D-RAPID  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3 Zebrafish larvae (10 dpf) swimming in an open arena with interspersed microcap-  sulated food particles (AP100), acquired at 60 fps for 10 sec (Supplementary Videos 1-3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a,  3D height map and photometric composites of the zoomed-out FOV, projected across every  50th temporal frame (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='83 sec) to highlight dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The height map assigns an arbitrary  value to the otherwise empty background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' b, Photometric and height map frames of a single  tracked fish feeding on AP100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The first 5 frames are spaced by 500 ms while the remaining  frames are spaced by 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='7 ms (the full frame rate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' c, The same fish’s head height, elevation  angle (pitch), and eye vergence angle (illustrated in inset) throughout the 10-sec video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' d-e,  Another example of a zebrafish feeding event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Note the change in eye vergence before and  after the feeding event in both b and d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' f, A zoomed-in region of a, showing 3 individual  larvae in varying states of activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The small red tracks are the drifting and floating AP100  food particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' g Fish head height vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' elevation angle for all 40 fish over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Lines define  the approximate physical limits due to geometric fish mobility constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' h, Kernel density  estimates of the height distributions of the zebrafish and AP100 food particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Eye vergence  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' head height (i) and vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' elevation angle (j) plots are color-coded by the maximum height  the fish attained in the 10-sec video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Fixed effect components of the linear mixed-effects  regression lines are plotted (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='33 and p < 10−5) for i and j, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 Zebrafish larvae (Danio rerio)  We applied 3D-RAPID to several 10-sec videos of zebrafish larvae (Danio  rerio) freely swimming in a large 97 mm × 130 mm open arena using the  60-fps and 230-fps configurations (Table 1) across three separate experiments,  the first of which was on 10-dpf fish feeding on microcapsule food particles  (AP100) (Supplementary Videos 1 (60 fps), 2 (230 fps), and 3 (60 fps with  tracking)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3 summarizes the results for the 60-fps video of the 10-dpf fish  feeding on AP100, most of which are floating at or near the water surface (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We tracked all 40 fish using a simple particle-tracking algorithm (Methods  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Supplementary Video 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The high throughput of 3D-RAPID allowed us  to observe fine detail over a very wide FOV, capturing multiple rapid feeding  events (∼10s of ms), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3b,d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' From the photometric images,  3D height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='map  b  c  30  80  20  60  t = 500 ms  6t=16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='7ms  1 mm  eal  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2mn  Teat  30  0  2  10  1 mm  Time (s)  30  80  20  60  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  St = 167 ms  eat  t=16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='7ms  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  20  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2mm  20  eat  30  0  2  6  8  10  1mm  Time (s)  h  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  b  Fish  15  Probability  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  0  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  Height (mm)  Height (mm)  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 ,mm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  I food  60  540  40  0mm  0mm  20  1 cm  1 mm  Photometric composite  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  20  Height(mm)  Elevationangle (°)Springer Nature 2021 LATEX template  3D-RAPID  11  we can see that the larvae turn their bodies laterally so that their ventrally  positioned mouths can access the overhead floating food.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We also observe eye  convergence once the larvae identify and approach the target, as shown in  previous studies [17–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The eye angles rapidly deconverge after food capture  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3c,e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The older fish (20 dpf) exhibit similar eye behavior when feeding  on brine shrimp (Supplementary Videos 4, 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The 3D topographic information enabled by our technique reveals how the  larvae axially approach their targets from below, including their head heights  and elevation (pitch) angles during these feeding events (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3b-e) [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Note  that the larvae’s head height matches that of the targeted food particle during  ingestion (see also in Supplementary Videos 1, 2, 4, 5), offering validation of  our technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  In addition to making organism-level observations, the high throughput  of 3D-RAPID enabled us to make population-level inferences by aggregating  height and elevation angle information for all 40 individually-tracked larvae  for all in-frame time points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The results show a roughly linear trend between  height and elevation angle (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3g), which can be explained based on the  mobility constraints defined by the length of the larvae and the water depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  For example, if the head is at the bottom of the arena, then the elevation angle  must be negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Assuming a larval length of L = 4 mm and a water depth  of H = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 mm, these geometric constraints on the elevation angle, φ, for a  fish at height, h, are  φmin(h) = sin−1(h/L),  φmax(h) = sin−1((H − h)/L),  (2)  which are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This offers additional validation of the accuracy of  our 3D height maps, suggesting future applications in studying fish locomotion  dynamics [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We also estimated the probability distributions of the heights  of the larvae and the food particles (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3h), both of which are bimodal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Predominantly, the larvae dwell at the bottom of the arena, only occasionally  venturing upwards to hunt or forage for food.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Finally, we also analyzed population-level correlations between eye vergence  angle (Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4), a property observable in the photometric images, and the  fish height and elevation angle, which are derived from our 3D height maps  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3i,j), across n = 39 fish (one stationary fish excluded).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Specifically, we  used a linear mixed-effects model, where height or elevation angle is the fixed  effect and dependence among images from the same fish are accounted for as  random effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Analyses of variance suggest that while fish height is not a  statistically significant linear predictor of eye vergence angle (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='33), fish  elevation angle is (p < 10−5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This is consistent with the fact that when the  fish is swimming upwards, it is likely focusing on a food particle close to the  surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' On the other hand, the fish can still be close to the surface following  a feeding event, immediately after which the eyes deconverge (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3b-e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  With the 230-fps configuration of our system, we can trade off spatial  resolution to temporally resolve higher-speed zebrafish larval locomotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For  example, compare the beginning of Supplementary Videos 6 and 7, which  Springer Nature 2021 LATEX template  12  3D-RAPID  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4 Adult fruit flies freely moving across a flat, noise-patterned surface, acquired at 60  fps for 8 sec (Supplementary Videos 8-10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a, 3D height map and photometric composites  of the zoomed-out FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The white-outlined red lines are the trajectories the 50 flies take.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The green-circled flies are analyzed in the other figure panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' b, Select photometric and  height map frames of a single tracked fly, exhibiting several grooming behaviors (hi = hind-  leg grooming, fo = foreleg or head grooming, mi = mid leg participation, ab = abdominal  grooming).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The time points of the frames are indicated by dotted lines in the plot below,  which in turn highlights the changing heights of the head, thorax, and abdomen for the  different grooming actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' c-g, The same information for 5 additional flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' h Kernel densi-  ties of the heights of head, thorax, and abdomen for various behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Differences of head  (p < 10−7), thorax (p < 10−16), and abdomen (p < 10−62) heights across behaviors are  statistically significant (n = 43 flies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  feature rapidly swimming zebrafish larvae, captured at 60 fps and 230 fps,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Similarly, we can resolve the 4D fish dynamics as it attempts to  swallow a live brine shrimp (Supplementary Videos 4 (60 fps) and 5 (230 fps)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 Fruit flies (Drosophila hydei)  Next, we applied 3D-RAPID to image and track 50 freely exploring adult fruit  flies (Drosophila hydei) under the 60-fps (Supplementary Videos 8 and 10) and  230-fps (Supplementary Video 9) configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4 summarizes the results  for the 60-fps configuration for six individual flies exhibiting various behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Supplementary Video 10 shows tracking of all 50 flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The 3D height map  offers additional insights into such grooming behaviors, building upon works  3D height map  TO  hi/mi  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='267 s  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6  一Head  Thorax  Abdomen  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6  45678  time(s)  time(s  time(s)  e  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='767  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='267 s  3 mm  0 mm  1 cm  2  Photometric composite  5678  time (s)  time (s)  time (s)  Hindleg groom  Foreleggroom  Abdomengroom  Stand  Walk  All behavior  h  Head  nsity  Thorax  Abdomen  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  31  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  3 1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  3 1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  31  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5  Height (mm)  Height(mm)  Height (mm)  Height (mm)  Height (mm)  Height(mm)Springer Nature 2021 LATEX template  3D-RAPID  13  that study freely-moving flies in 2D [70, 71] and 3D in single tethered flies  [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In particular, we observed changes in fly height and body tilt as the flies  transition between different grooming behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4b, as an individual  fly transitions between grooming with its hindlegs and forelegs, the abdomen  moves up and down, respectively, relative to the head and thorax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' When a  middle leg joins the grooming (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4b, arrowheads), there is a subtle change  in abdomen height relative to head height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4c, our method correctly  predicts an elevated height as one fly climbs atop another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' At 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 sec, the  fly’s height drops, consistent with the straightened leg joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' A similar body  tilt trend is observed for foreleg vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' hindleg grooming in this fly, as well as  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4d, e, and f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4f, we see another instance of the fly’s leg joints  fully extended at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='767 sec, resulting in a reduced overall height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Further, we  observe that the abdomen takes on a different relative height during abdominal  grooming compared to hindleg grooming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Finally, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4g, although the fly  is grooming its forelegs throughout the video, it reduces its overall height after  1 sec, consistent with its extended leg posture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  To analyze population trends, we annotated video frames across n = 43  flies flies with one of five behaviors: hindleg grooming, foreleg/head grooming,  abdomen grooming, standing still, and walking (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Flies that exited the  FOV were excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We tested for cross-behavioral differences in heights of  the head, thorax, and abdomen using three separate linear categorical mixed-  effects models, accounting for random effects due to correlations among video  frames from the same fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Analyses of variance suggest that behavior groups  are a statistically significant predictor of the heights of the head (p < 10−7),  thorax (p < 10−16), and abdomen (p < 10−62).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 Harvester ants (Pogonomyrmex barbatus)  We also imaged freely exploring red harvester ants (Pogonomyrmex barba-  tus) under the 60-fps (Supplementary Video 11) and 230-fps (Supplementary  Video 12) configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The 60-fps results are summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' From  the static 3D height map frame, it is immediately obvious that the body is  sloped downward, from the head to the abdomen [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We used the dynamic  3D reconstructions enabled by 3D-RAPID to track the femur-tibia joints of all  six legs of an individual ant (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 5b,c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4), providing information  about the kinematics of ant locomotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The joint trajectories are plotted in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 5c, showing that the high-frequency (∼3-4 Hz) oscillations from walking  kinematics are anti-correlated (180◦ out of phase) between left and right legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  This oscillation frequency remains relatively constant throughout the ant’s  journey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Further, the forelegs and hindlegs on the same side of the body are  correlated, but anti-correlated with the mid legs on the same side of the body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  These behaviors are consistent with the well-known alternating tripod gait pat-  tern in ants [36, 72, 73], which persists even as the curvature of ant trajectory  changes in our tracked ant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  We also observe changes in lower-frequency gait patterns as the ant makes  multiple turns throughout its exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the first ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 sec, as the ant is  Springer Nature 2021 LATEX template  14  3D-RAPID  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 5 Harvester ants freely moving across a flat, noise-patterned surface, acquired at 60  fps for 10 sec (Supplementary Videos 11-12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a, Photometric composite and 3D height map  of the zoomed-out FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' One of the ants’ trajectories is color-coded by time, progressing  from blue to red over a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5-sec duration, and is analyzed in b and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' b, Temporal snapshots  of a single tracked ant along the trajectory in a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The blue and red dots are the femur-tibia  joints for the ant’s 6 legs (L = left, R = right, F = foreleg, M = middle leg, H = hindleg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' c,  The 3D positions of the femur-tibia joints over the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5-sec trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The lateral dimensions  (xy) are defined relative to the ant’s orientation, as illustrated in b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  turning right, we see a reduced oscillation amplitude in the mid and hindlegs  on the right side in both the y and z directions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' however, for the x direction,  we see the opposite trend (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 5b for the ant-centric coordinate system  definition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Between 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 and 3 sec, as the ant is turning left, we see the opposite  motions as in the first 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 sec – the oscillation amplitudes in the mid and  hindlegs on the left are reduced in both the y and z directions, while amplitude  of the right mid leg motion in the x direction is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' From 3 to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 sec, the  ant once again is turning right and we see similar trends as in the first 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Overall, this reduction in motion in y and z on the side of the ant corresponding  to the direction the ant is turning is consistent with prior knowledge [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Interestingly, the amplitudes of the foreleg oscillations on both the left and  right sides in both y and z remain relatively constant throughout the entire  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 sec, suggesting a lesser role in the biomechanics of changing directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Finally, we observe a low-frequency oscillation (with a period of ∼4 sec)  in the x direction for all 6 legs that is correlated with the curvature of the  ant’s trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Unlike the high-frequency (3-4 Hz) walking kinematics, which  are anti-correlated between left and right, these low-frequencies are correlated  between left and right legs, suggesting left-right coordination when the ant is  a  3D height map  2 mm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='100s  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='767 s  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='433 s  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='433:  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='100 s  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='767 s  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='433 s  ++x**++*  m  y (mm)  (mm  z (mm)  o  PIW  4 mm  0 mm  1 cm  2  5  0  1  2  3  4  5  0  4  2  3  4  5  Photometric composite  time (s)  time (s)  time (s)Springer Nature 2021 LATEX template  3D-RAPID  15  turning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These low-frequencies in the x direction further are correlated between  the forelegs and mid legs, but anti-correlated with the hindlegs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  4 Discussion  We have presented 3D-RAPID, a new computational microscope with a unique  capability of dynamic topographic 3D imaging at 10s-of-µm resolution and  accuracy, over >130-cm2 FOV at throughputs exceeding 5 GP/sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To handle  the large data load, we devised an efficient, end-to-end, physics-supervised,  CNN-based, joint 3D reconstruction and stitching algorithm that scales to  arbitrarily long videos and arbitrarily sized camera arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The high through-  put of 3D-RAPID enabled us to study several freely-behaving model organisms  at high speed and high resolution over a very large FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, our technique  fills a unique niche, enabling new ways for scientists to study small features of  individual organisms over a large FOV that allows unconstrained social inter-  actions of multiple organisms in parallel in 3D at high speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For example,  3D-RAPID could be applied to study dueling behavior in ants [74], sexual  behavior in fruit flies [75], and feeding decisions in fruit flies [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3D-RAPID differs from other camera array-based techniques [51–55] in  several ways, stemming from the challenge of adapting to microscopy applica-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In particular, due to the large magnification requirements, the cameras  need to be physically packed more tightly, which is a practical challenge due  to mechanical constraints and heat dissipation management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Some approaches  alleviate this challenge by using a primary objective lens to magnify the object  to an intermediate image plane, which is then imaged by a camera array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' How-  ever, this strategy limits scalability, as the primary objective’s intrinsic SBP  would limit the total imaging throughput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Instead, we solved this problem by  tiling all of the array’s CMOS sensors at the chip-scale onto a common multi-  layer PCB, which is connected to a single FPGA for unified data routing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  This allows for extremely tight packing and scalability by simply adding more  sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Finally, 3D-RAPID also differs from light field imaging, because our  cameras exhibit almost the theoretical minimum amount of overlap necessary  for 3D surface estimation – this is an important design consideration because  it allows us to maximize the SBP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In particular, to our knowledge, 3D-RAPID  is the 3D imaging system with the highest sustained throughput to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  While we have presented several convincing 3D behavioral imaging demon-  strations, there are several avenues for improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The hardware configu-  ration could be adjusted to improve the 3D height reconstruction accuracy,  which depends on how accurately parallax shifts can be detected to match  corresponding features from different cameras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S5, we  derive several equations detailing how height accuracy is impacted by hardware  design parameters, suggesting that decreasing the focal length and increas-  ing the magnification and sensor-to-sensor spacing improve height accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Furthermore, since the reconstruction algorithm is agnostic to the contrast  mechanism, it would also be possible to incorporate other optical contrast  Springer Nature 2021 LATEX template  16  3D-RAPID  mechanisms into 3D-RAPID, such as fluorescence to correlate behaviors with  molecular signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Finally, throughput could be improved beyond 5 GP/sec  by alleviating data transfer bottlenecks to the computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  In summary, we have presented a high-throughput computational 3D topo-  graphic microscope as a new platform for studying the behavior of multiple  freely-moving organisms at high speed and resolution over a very wide area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  We expect our technique to be broadly applicable to elucidate new behavioral  phenomena, not only in zebrafish, fruit flies, and ants, but also other model  organisms such as tadpoles (X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' laevis and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' tropicalis) and nematodes (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  elegans).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5 Methods  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 Temporal synchronization of the camera array  Ideally, all sensor pixels should be fully synchronized with a global shutter,  not only within each sensor, but also across sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This would ensure that  between different views of the same object, after accounting for camera poses,  the only discrepancies are due to parallax shifts and not sample motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For  example, if two camera views of a moving object with zero height were desyn-  chronized, lateral motion could be interpreted as a parallax shift, leading to  an erroneous height estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In practice, each of our sensors exhibits a rolling  shutter, whereby only a single pixel value can be read out at a given time for  a given sensor, row by row from the top-left to bottom-right corner in a raster  scan pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This means that the bottom of a given sensor is captured later  than the top of the sensor immediately below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' However, across independent  sensors, this rolling shutter readout pattern is synchronized to within 10 µs,  limited by the serial communication interface (I2C with a 100-kHz clock).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  To mitigate the rolling shutter effects, we employed two strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' First, we  cropped the sensors so that there is only significant overlap in the horizontal  dimension for stitching, in which the desynchronization is much less severe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Second, we calculated that with exposures of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 ms for 4× downsampling, 5  ms for 2× downsampling, and 20 ms for no downsampling, artifacts would be  minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For a detailed discussion and calculations, see Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 Achieving robustness to illumination variation  Since the optimization metric of our approach is the mean square per-pixel  photometric error, we would achieve optimal performance when the sample has  a camera-independent photometric appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This condition would require  not only uniform response across all pixels of all cameras, but also that the  sample is isotropically emanating light in all directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The latter property is  in practice difficult to achieve, requiring either perfectly diffuse illumination  or a diffusely scattering sample, regardless of the illumination direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In  Springer Nature 2021 LATEX template  3D-RAPID  17  addition to the regularizing effects of the CNN/DIP, we employed two addi-  tional strategies to reduce the effects of camera-dependent appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' First,  as part of the camera pose pre-calibration procedure, we also jointly optimized  per-camera second-order 2D polynomials (with cross terms) to correct the  slowly-varying image intensity variation (whether caused by uneven illumina-  tion or camera response), using the same photometric stitching loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, the  pre-calibration step not only ensures geometric consistency of the 54 images,  but also photometric continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For more details, see Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3, below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Second, for terrestrial organisms illuminated in reflection, we employed a  two-step optimization process, where we first optimize the CNN to register the  images using the RGB intensities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the second step, we continue optimizing  the CNN, except this time registering normalized high-pass-filtered versions of  the photometric images, which reduces illumination-induced differences in pho-  tometric appearance and emphasizes edges (Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This  two-step procedure effectively removes artifacts in the 3D height maps that  would otherwise result from camera-dependent photometric appearances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 Calibration of camera pose, distortion, and intensity  variation  The first step in the 3D estimation pipeline was to calibrate the cameras’  geometric and photometric properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Specifically, the geometric properties  include their 6D pose (3D position + 3D orientation) and second-order radial  distortions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', pincushion or barrel distortions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The photometric proper-  ties include the pixel intensity variations both within individual cameras and  across different cameras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These may arise due to vignetting, uneven illumi-  nation, pixel response variation, or angle-dependent scattering of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  To estimate the calibration parameters, we imaged a flat, epi-illuminated,  homogeneously-patterned calibration target with the MCAM and registered  the resulting 54 images, enforcing both geometric and photometric consistency  in the overlapped regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The calibration procedure follows the optimization procedure outlined in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a, excluding the height map-related orthorectification portion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In partic-  ular, let x0 and y0 be two vectors representing the ideal 2D spatial coordinates  of the camera pixels – that is, a 2D rectangular grid of equally-spaced points  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', 1536×4096).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Next, let Dθ{·, ·} be an image deformation operation that  maps from the ideal camera coordinates to a common global coordinate space  (the object plane), parameterized by the camera parameters, θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' See Supple-  mentary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1 of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' [68] for specific implementation details of Dθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Let θi be  the camera parameters for the ith camera, so that  xi, yi = Dθi{x0, y0}  (3)  represents the (de)warped coordinates of the ith camera in a common object  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  18  3D-RAPID  Let Ii,0 be a vector of the same length as x0 and y0, indicating the measured  photometric intensity at every pixel coordinate for the ith camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Although  the debayered images have 3 color channels, here, for simplicity, we assume  a single-channel image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Further, let Cφ,x0,y0{·} be a photometric correction  operation, parameterized by φ, so that  Ii = Cφi,x0,y0{Ii,0}  (4)  represents the photometrically-adjusted intensity values for the ith camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The dependence on x0 and y0 indicates that the photometric correction is  spatially-varying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Specifically, we used a second-order polynomial correction,  Ii = Cφi,x0,y0{Ii,0} = (ai,0 + ai,1x0 + ai,2y0 + ai,3x0 ⊙ x0+  ai,4y0 ⊙ y0 + ai,5x0 ⊙ y0) ⊙ Ii,0,  (5)  where  ⊙  represents  element-wise  multiplication  and  φi  =  {ai,0, ai,1, ai,2, ai,3, ai,4, ai,5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In sum, assuming θi and φi are optimized,  then {xi, yi, Ii,0} represents the corrected ith camera data, accounting for  distortion and photometric variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Next, let {x, y, I} be three vectors representing the flattened concatenation  of {xi, yi, Ii,0} for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We then initialize a blank matrix, R[·, ·], representing  the stitched reconstruction, into which we backproject the collection of points,  R[x, y] ← I,  (6)  with interpolation, as x and y are continuously valued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' When specific coordi-  nates are visited more than once, the values are averaged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The result of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 6 is  an estimate of the stitched composite for a given set of {θi, φi}54  i=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To update  these parameters, we form a forward prediction from R[·, ·] by reprojecting  back into the camera spaces, as follows:  Ipred = R[x, y].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  (7)  Ipred should match I when the camera images are well-registered and the cor-  rected photometric intensities match in overlapped regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, we minimize  the error metric,  MSE = ∥Ipred − I∥2,  (8)  with respect to {θi, φi}54  i=1 via gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Since the image target is  homogeneous, we also include a regularization term,  �  i  stdev(Ii),  (9)  which enforces a homogeneous reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Here, the standard deviation  (stdev) is taken across all the pixels in one image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  3D-RAPID  19  Finally, we apply the calibrated parameters, {θi, φi}54  i=1, to each frame of  the videos of the freely-moving organisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To homogenize the background in  the case of zebrafish, which uses transmission illumination instead of the epi-  illuminated calibration target, we apply a second calibration step that only  optimizes the photometric correction parameters, {φi}54  i=1, using the maximum  projection of the video across time, which eliminates all moving objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 Organism tracking and pose determination  To track the fruit flies, zebrafish larvae, and harvester ants, we first thresh-  olded the photometric composites to segment each organism and compute each  of their centroids across all video frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We then employed a simple particle-  tracking algorithm, matching the organisms by finding the closest centroid  in the subsequent video frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the case of clashing match proposals, we  assigned matches that minimized the sum of the total absolute lateral displace-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To track the ants’ 6 femur-tibia joints, we incorporated the observation  that the joint heights are local maxima in the 3D height maps for segmentation,  and employed a similar particle-tracking algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  To determine the orientation of the organisms, we performed principal  component analysis (PCA) on the thresholded pixel coordinates and took the  first principal component (PC) as the organism’s orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the case of  zebrafish, we used the height map coordinates to perform PCA in 3D, thereby  allowing us to compute the elevation angles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We resolved the sign  ambiguity of the PC either by enforcing the dot products of PCs of the tracked  organism in consecutive frames to be positive, or by computing the rela-  tive displacement between the unweighted centroid and the intensity-weighted  centroid and forcing the PC to point in the same direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The fish eye vergence angles were estimated by thresholding the green chan-  nel of the photometric intensity images to identify the eyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The orientations  of the eyes were estimated using the regionprops command in MATLAB,  which finds the angle of the major axis of the ellipse with the equivalent sec-  ond moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The vergence angle is then computed as the angle between the  two eyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 Biological samples and data acquisition  Zebrafish stocks were bred and maintained following IACUC guidelines and as  previously described [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Zebrafish were stored at 28°C with daily feeding and  water changes, and cycled through 14 hours of light and 10 hours of darkness  per day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Free swimming fish were imaged at larval stages between 5 dpf and  20 dpf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Specifically, zebrafish larvae were transferred from culture chambers  using a transfer pipette to a clear plastic imaging arena (with lateral inner  dimensions 97 mm × 130 mm), which was filled with system water a few mm  deep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The arena was then placed on the sample stage of the MCAM system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The z position of the stage was adjusted such that the zebrafish larvae were all  within the DOF of the lenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The system was left undisturbed with the LED  Springer Nature 2021 LATEX template  20  3D-RAPID  illumination panels turned on for at least 5 minutes to allow the zebrafish to  acclimate, after which multiple MCAM videos were acquired using a custom  Python script.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' After video acquisition, the arena was removed and replaced  with a flat patterned calibration target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We focused the target with the z stage  using a Laplacian-based sharpness metric and captured a single frame (all 54  cameras), which would serve to calibrate the camera poses and distortions for  all videos captured during that imaging session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The wild-type red harvester ants and fruit flies (available from various  vendors on Amazon) were maintained at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' When ready for  imaging, we positioned and focused a flat patterned calibration target, which  serves two purposes: 1) for camera calibration, just as for the zebrafish videos  described in the previous paragraph, and 2) to serve as a flat substrate for the  ants and fruit flies to walk upon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The patterned target, although not required,  serves as a global reference in the 3D height maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Alternatively, the substrate  could be monochrome/featureless or transparent (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', a glass sheet), as was the  case for the zebrafish imaging configuration, in which case the 3D height map  would assign an arbitrary height value to the background without affecting  the 3D accuracy of the organisms themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The ants or fruit flies were inserted into a Falcon tube and released onto  the center of the flat substrate, after which we immediately ran the same  custom Python script to acquire MCAM videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' If necessary, the insects were  re-collected in the tubes and re-released into the arena for repeated imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  After video acquisition, we acquired a single frame of the calibration target  alone, just as we did after zebrafish video acquisition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content=', Ding,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content=', Lin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content=', Diao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content=' Elife 5, 20713 (2016)  [76] Sareen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content=' Nature  communications 12(1), 1–13 (2021)  [77] Westerfield, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=': The zebrafish book: a guide for the laboratory use of  zebrafish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='html (2000)  [78] Abadi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Barham, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Davis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Dean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Devin,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Ghemawat, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Irving, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Isard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' : {TensorFlow}: A sys-  tem for {Large-Scale} machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In: 12th USENIX Symposium on  Operating Systems Design and Implementation (OSDI 16), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 265–283  (2016)  [79] Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', Ba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=': Adam: A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' arXiv  Springer Nature 2021 LATEX template  28  3D-RAPID  preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6980 (2014)  Acknowledgements  We would like to thank Kristin Branson, Srinivas Turaga, Timothy Dunn,  Archan Chakraborty, and Maximilian Hoffmann for their helpful feedback  on the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Research reported in this publication was supported  by the Office of Research Infrastructure Programs (ORIP),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Office Of The  Director,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' National Institutes Of Health of the National Institutes Of Health  and the National Institute Of Environmental Health Sciences (NIEHS) of  the National Institutes of Health under Award Number R44OD024879,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' the  National Cancer Institute (NCI) of the National Institutes of Health under  Award Number R44CA250877,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' the National Institute of Biomedical Imag-  ing and Bioengineering (NIBIB) of the National Institutes of Health under  Award Number R43EB030979,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' the National Science Foundation under Award  Number 2036439,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' and the Duke Coulter Translational Partnership Award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Author contributions  KCZ and RH conceived the idea and initiated the research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' KCZ developed the  algorithms and theory, with the help of CLC, JP, PCK, and RH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' KCZ wrote  the code for and performed 3D video reconstruction and stitching, animal  tracking, and data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' MH, JD, PR, VS, CBC, MZ, and RH developed  the MCAM hardware and acquisition software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' KCZ acquired and analyzed  the biological data, with the help of JPB, JB, AB, GH, and RH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' JD and KCZ  created the supplementary videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' KCZ wrote the manuscript and created the  figures, with input from all authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' RH and MB supervised the research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Disclosures  RH and MH are cofounders of Ramona Optics, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', which is commercializing  multi-camera array microscopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' MH, JP, JD, PR, VS, CBC, MZ, JPB, and  GH are or were employed by Ramona Optics, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' during the course of this  research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' KCZ is a consultant for Ramona Optics, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Data availability  Data will be available at https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='7924/r4db86b1q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Code availability  Code will be available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='com/kevinczhou/3D-RAPID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  3D-RAPID  29  Supplementary information  S1 System characterization: lateral resolution,  axial precision and accuracy, and depth of  field  We performed several experiments to characterize the performance of our com-  putational 3D imaging system, starting with imaging of a USAF resolution  target near the center and edge of the field of view (FOV) of a single cam-  era (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Our system can resolve group 5 elements 2-3, corresponding  to a bar width of 12-13 µm or a full-pitch lateral resolution of ∼25 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We  then characterized the depth of field (DOF) by axially translating the same  flat patterned target used in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 4 and 5, using a motorized stage (Zaber)  in increments of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='25 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This defines the axial FOV of our 3D reconstruc-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For each axial position, we computed a contrast metric based on the  mean image gradient magnitude (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The full width at half maximum  (FWHM) of this curve is 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='434 mm, which is similar to value obtained by  fitting the curve to the intensity of a Gaussian beam,  I(z) =  I0  1 + (z−z0)2  z2  R  + Ib,  (S1)  where I0 and Ib are the arbitrary amplitude and offset, z0 is the focal position,  and 2zR is the DOF, corresponding to when the lateral resolution degrades by  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Least-squares fitting yields 2zR = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='402 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In practice, the DOF may  be smaller if the neighboring cameras are not focused to the same plane, such  that the focus regions are offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Finally, we characterized the accuracy and precision of our 3D height maps  by imaging 6 gauge blocks (Mitutoyo), precisely machined and characterized  to be within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 µm of their nominal values: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='000, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='020, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='050, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='100, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='200,  and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='400 mm (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1d,e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We computed the accuracy as the absolute error  between the estimated and ground truth heights, aggregated across all pixels  within each gauge block, and the precision as the standard deviation of the  height estimates across each gauge block, which are summarized in Table S1  for all three configurations in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Since there is an arbitrary global height  offset, we chose the one that minimizes the MSE between the estimated and  ground truth heights [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S2 Generalization experiments  Here, we show that the multiocular stereo CNN trained on a subset of frames  can generalize well to unseen frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' As validation we compare this general-  ization performance to that of a monocular stereo CNN (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', one that only  takes in a single image as the input).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To make these comparisons, we picked  two independent subsets of the video frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In Set 1, we took about 15 frames  Springer Nature 2021 LATEX template  30  3D-RAPID  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1 System characterization experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a, b, USAF resolution test chart image near  the center and edge of the FOV of one camera without downsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' c, Image contrast of  a patterned target as a function of axial position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' d, Stitched photometric composite of 6  precisely-machined gauge blocks placed on a green patterned target (captured with the 60-  fps configuration), with their nominal thicknesses denoted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' e, The reconstructed 3D height  map of the gauge blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Accuracy and precision are quantified in Table S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Ground truth  1× downsamp  2× downsamp  4× downsamp  height  Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Prec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Prec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='9  1400  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='0  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='0  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='4  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4  mean  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='7  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='9  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3  Table S1 Accuracy (absolute error from ground truth) and precision (standard  deviation) of the height estimation of the 6 gauge blocks (and background) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S1a,b  for all three downsampling configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' All values are in µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  equally spaced temporarily across the video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In Set 2, we took another 15  equally spaced frames at half a period offset with respect to Set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For exam-  ple, if the video was 601 frames, then Set 1 would consist of frames 1, 41, 81,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 561, 601 and Set 2 would consist of frames 20, 60, 100, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='540, 580.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We then  trained two independent multiocular CNNs, one on Set 1, the other on Set 2,  and compared the 3D height map predictions on both sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The idea is that  in the absence of ground truths, the physics-supervised CNN predictions on  training set examples could serve as pseudo-truths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For comparison, we also  trained a monocular CNN on Set 1 and compared predictions on Set 1 and  Set 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S2 and S3 show the comparisons among these three CNNs for both  zebrafish and fruit flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In both organisms, the multiocular CNNs generalize  well to unseen video frames, based on comparisons between images from the  CNN trained on Set 1 and the one trained on Set 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' However, for zebrafish,  Center  Edge  a  b  Photometric composite  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='000 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='050 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='200 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='020 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='100 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='400 mm  150 μm  cm  50  3D height map  C  30  FWHM = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 mm  20  10  20  10  0  10  20  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 mm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5mm  z position (mm)Springer Nature 2021 LATEX template  3D-RAPID  31  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8 mm  0 mm  1 mm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8 mm  0 mm  1 mm  a  b  Pseudo-truth  Pseudo-truth  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S2 Generalization performance of multiocular and monocular CNNs trained on frames  from a video of freely swimming zebrafish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' a, First row shows an example from Set 1 and  3D height predictions of three different CNNs – two multiocular CNNs, trained on Set 1 and  Set 2, and one monocular CNN trained on Set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Second row shows predictions on Set 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' b,  Zoom-in of the red boxes in a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Arrowheads point out features for which the multiocular CNN  generalized well, but not the monocular CNN, as evaluated by comparing the predictions  the respective pseudo-truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  the monocular CNN (trained on Set 1) generalizes poorly (to Set 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This  is evidenced by erroneous heights of several zebrafish’s heads or tails, as it  is difficult to determine the heights of the fish based on appearance alone –  magnification-based cues are confounded by natural size variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Similarly,  the monocular CNN incorrectly estimates the heights of the sunken food par-  ticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This is likely due to the fact that the vast majority of food particles are  floating, and since the food particles have no discernible height indicators, the  monocular CNN simply uniformly assigns the floating height to all particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  While the monocular CNN performs better for the fruit flies than for zebrafish,  it still makes a few errors, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', when one fly is climbing on top of another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Photometric  Multiocular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' trained on Set 1  Multiocular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' trained on Set 2  Monocular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' trained on Set 1  Pseudo-truth  Set  Pseudo-truth  Set  Image from Photometric  Multiocular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' trained on Set 1  Multiocular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' trained on Set 2  Monocular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' trained on Set  Image from Set 1  Image from Set 2Springer Nature 2021 LATEX template  32  3D-RAPID  Such fly behavior was rare in our captured video,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' so the monocular CNN had  fewer training examples to learn the semantic cues to accurately predict the  elevated height,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' whereas the multiocular CNN was able to predict the elevated  height from the parallax cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 mm  0 mm  2 mm  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3 Generalization performance of multiocular and monocular CNNs trained on frames  from a video of fruit flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' First row shows an example from Set 1 and 3D height predictions  of three different CNNs – two multiocular CNNs, trained on Set 1 and Set 2, and one  monocular CNN trained on Set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Second row shows predictions on Set 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3 Implementation details on patch-based  training with multi-ocular stereo inputs  Here, we expand upon the explanation of our patch-based CNN training  procedure given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 Determining the observing cameras and the  coordinates  We start with the camera pose calibration based on a flat patterned target  (Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3) to generate a “visitation log”, V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' V is an nrow × ncolumn × 54  × 2 tensor look-up table specifying which of the 54 cameras view a certain spa-  tial position in the reconstruction coordinate system as well as the respective  (row,column) pixel coordinates in the camera coordinate system that map to  that position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The formation process of V is somewhat similar to the backpro-  jection step of the reconstruction (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a), but instead of backprojecting the  RGBH values, we backproject the (row, column) coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This visitation  Photometric  Multiocular, trained on Set 1  Multiocular, trained on Set 2  Monocular, trained on Set 1  Pseudo-truth  from Set  Pseudo-truth  Set  Image from :Springer Nature 2021 LATEX template  3D-RAPID  33  log facilitates rapid retrieval of the relevant cameras for each randomly sam-  pled position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Note that since we want to avoid rolling shutter artifacts that  may occur where the bottom of one camera overlaps with the top of the camera  below (Methods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1 and Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S4), we only consider horizontal  overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='2 Selecting random patches  Given this visitation log, we select nbatch random 2D coordinates in the recon-  struction frame of reference for each CNN training iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For each of these  random coordinates, we retrieve the relevant cameras and their corresponding  camera-centric coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For each camera image, we then crop out a square  patch of width wpatch centered at the sampled coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' If these coordinates  are within wpatch/2 of a camera image edge, they are shifted so that the patch  remains within the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  For each image patch, we also extract patches from the left and right cam-  eras and stack them along the channel dimension of the CNN input, which  the CNN can exploit for 3D estimation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To do this in a manner con-  sistent with both training on patches and inference on full-sized images, we  homographically transformed the left/right neighboring images into the frame  of reference of the central camera in question, as if the sample were flat (more  precisely, coincident with the pre-calibration reference plane;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3, Meth-  ods 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' If the sample were completely flat, then the transformed neighboring  images would theoretically be identical to the image captured by the camera  in question where their viewpoints overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' However, if the sample exhibits  height variation, the transformed neighboring images would exhibit parallax  shifts in proportion to the height variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' When there is no left or right  camera (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e, the first or last column of cameras), we input blank images (all  zeros).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Similarly, when either the left or right patch overlaps with the edge  of its respective camera, we assign zeros to the missing regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Note that in  this scenario, we cannot shift the left/right patch away from the edge, as we  could above, because the left/right patch must remain coaligned with the main  (central) patch so that we maintain full convolutionality for the inference step  (Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Furthermore, we do not want to exclude training  cases where the central patch is close to the edge of the camera, as these cases  appear when applied to full-size camera images during the inference step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  We note that the number of cameras observing a particular point can range  from 1 - 3, since we only consider horizontal overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' When only one camera  views a particular point (the left and right edges of the reconstruction) during  training, we reject the resulting patch as there’s nothing to register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To account  for the fact that the number of patches may vary for each batch element, we use  tensorflow’s [78] tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='RaggedTensor construct, which allows some dimensions  of a tensor to have slices with different lengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In our experiments, we used  nbatch =1, 2, and 8 for the 1×, 2×, and 4× downsampling cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  34  3D-RAPID  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='3 CNN architecture  The input to the CNN has nine channels, corresponding to three stacked RGB  inputs – the camera image whose height we wish to predict, followed by the left  and right camera views (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The output of the CNN is a single-channel  height map, obtained by summing across the channel dimension of the final  convolutional layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The encoder-decoder CNN architectures were based on one basic building  block, consisting of the following operations in sequence:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 3 × 3 convolution, k filters, stride=1, padding=‘same’,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Batch normalization,  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Leaky ReLU,  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1 × 1 convolution, k filters, stride=1, padding=‘valid’,  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Batch normalization,  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Leaky ReLU (unless final block of the CNN),  where k is a free hyperparameter, specifying the number of filters in the  convolution layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the case of an upsample block, a 2× nearest-neighbor  upsampling procedure is applied before the block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the case of a downsample  block, a 2×2 max pooling operation is applied after the block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The full, symmetric encoder-decoder CNN architecture is described by a list  of positive integers, each of which specifies the k for an upsample/downsample  block pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For example, [8, 16, 32] indicates three downsample blocks with k  = 8, 16, and 32 filters, followed by three upsample blocks with k = 32, 16,  and 8 filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In our experiments, we set k = 32 for all upsample/downsample  blocks, but varied the number of blocks between 3 and 6 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', [32, 32, 32] and  [32, 32, 32, 32, 32, 32]), depending on the sensor downsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='4 Data-dependent loss function  The data-dependent loss function is computed based on the model depicted in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a, where 2-3 image patches are used instead of 54 full-size images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Specif-  ically, the 4-channel (RGBH) image patches are backprojected onto a blank  “canvas” according to the camera poses and height map-derived orthorectifi-  cation fields (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The same coordinates are then used to reproject back  to camera-centric coordinates to obtain the forward predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The data-  dependent loss function is thus the MSE between forward predictions and the  original RGBH patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 Normalized high-pass filtering  For terrestrial samples, which were illuminated in reflection, we found that reg-  istering the RGB images sometimes led to artifacts due to camera-dependent  photometric appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This can be caused by illumination variation across  the FOV due to off-axis LED panel geometry and anisotropic, non-Lambertian  reflections, causing different amounts of light entering each camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To combat  Springer Nature 2021 LATEX template  3D-RAPID  35  these effects, we used normalized high-pass filtered versions of the images,  �Iσ(x, y) =  I(x, y) ⊛ exp  �  − x2+y2  4σ2  �  I(x, y) ⊛ exp  �  − x2+y2  2σ2  �,  (S2)  where ⊛ denotes 2D convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S2 is the ratio of two Gaussian-  blurred versions of I(x, y), the grayscale-converted RGB image, with widths  σ and  √  2σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Like high-pass filtering, applying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S2 to the images highlights  edges and attenuates DC and low-frequency features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The motivation for tak-  ing a ratio rather than subtracting (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', difference of Gaussians) is so that  the spatial fluctuations are normalized and therefore illumination-variation-  independent, thereby facilitating registration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To capture different scales, we  used three values of σ for the three image channels (σ = 1, 2, 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6 Regularization of the height maps  In addition to the CNN reparameterization (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', DIP) of the height maps as a  regularizer [43, 68, 69], we also incorporated two additive regularization terms  to the overall loss function: height map consistency regularization and support  regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The height map consistency regularization enforces agreement  in height values in overlapped regions of camera images and simply comes from  the fourth channel of the RGBH images, whose contribution can be scaled  by a hyperparameter, λheight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We observed smoothing effects with increasing  λheight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The object support regularization relies on a segmentation mask of the  background pixels, whose height values we enforce to be a particular constant  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', 0) via an L2 loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In other words,  losssupport = λsupport  �  x,y  mask background(x, y)(h(x, y) − h0)2,  (S3)  where mask background(x, y) is the segmentation mask, h(x, y) is the height map  output of the CNN, h0 is the known background height value, and λheight is  the regularization coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In this paper, we used a simple intensity-based  threshold on the green channel of the photometric images, as our backgrounds  are relatively homogeneous, although other segmentation strategies may be  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='7 Additional training details  We optimized the loss function, consisting of the aforementioned data-  dependent and regularization terms, using the Adam Optimizer [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Depend-  ing on the downsampling configuration, we used a different patch size and  number of patches per iteration: one 1024×1024 patch (no downsampling), two  768×768 patches (2× downsampling), and eight 384×384 patches (4× down-  sampling).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These patches were randomly selected from a subset of the recorded  Springer Nature 2021 LATEX template  36  3D-RAPID  video frames – for the 2× and 4× downsampling configurations, we selected  from 15-16 frames evenly distributed frames, while for the no downsampling  configuration, we used 8 frames (due to memory constraints).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  For the reflection-illuminated terrestrial samples, we performed a two-  step training procedure, where we first optimized with RGB images using  λheight = 500 (Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6) to scale the height channel (with units  of mm) and λsupport = 0 (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3) for 30k iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thereafter, we ran 70k  iterations with the normalized high-pass filtering (Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5)  and λheight = 50 and λsupport = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For aquatic samples, high-pass filtering  was not necessary because they were illuminated in transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, we  used a one-step training procedure with 70k iterations with λheight = 50 and  λsupport = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='8 Inference step - generating the full-size RGBH  videos  Once the CNN is trained to map from multi-ocular stereo inputs to a 3D height  map using the patch-based procedure, we can apply the CNN to sequences  of full-sized MCAM video streams that includes unseen frames (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Essentially, this refers to the backprojection step in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Since iterative  optimization is no longer necessary after the CNN is fully trained, generating  new 3D video frames can be done quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' For example, one application might  involve a human observer selecting a particular region of interest within the  large FOV, whose 3D height map the computer would then generate in real  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  …  …  …  …  …  …  …  Video input stream at ~5 GP/sec  Apply multi-ocular CNN  3D reconstruction  Output 3D video frames  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S4 Inference step post patch-based training (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 2c) that generates the stitched  composites and coregistered 3D height map on potentially unseen video frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  3D-RAPID  37  S4 Reducing the impact of the per-camera  rolling shutter  Each sensor exhibits a rolling shutter, whereby the pixels begin integrating  sequentially every δt = (230 MHz)−1 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='35 ns and are read out in a raster  scan pattern row by row from the top left to bottom right (with the longer  sensor dimension as the horizontal dimension).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Although the rolling shutters  are synchronized to within 10 µs across cameras, there is still significant asyn-  chrony in overlapped regions of neighboring camera FOVs, thus thwarting  accurate 3D estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Here, we consider asynchrony in 1) vertically over-  lapped FOVs and 2) horizontally overlapped FOVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The former asynchrony  is much more serious, as the bottom row of the upper sensor is not reached  until after δt × lrow × lcol, where lrow and lcol are the number of pixels per  row and column, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Using the full sensor without downsampling  (lrow = 4208, lrow = 3120), the time delay between the last row of the upper  sensor and the first row of the lower sensor is ∼57 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In practice, the delay  is even larger due to horizontal and vertical blanking (dead time between row  and column reads).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To circumvent this problem, we thus reduced the number  of rows approximately in half (3120 to 1536) to ensure the smallest overlap  between vertically adjacent cameras that still allowed for a contiguous com-  posite FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' This also has the added benefit of increasing the sensor frame  rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Asychrony in horizontally overlapped FOVs is less serious, but still an  important consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Using the full sensor without downsampling, the time  delay between corresponding rows of perfectly aligned camera FOVs is only  δt × lrow, or approximately 20 µs, which is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In practice, however,  there is a vertical offset due to slight camera misalignments, so that the time  delay is δt × lrow × lmisalign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Based on stitching a flat target, we determined  that the worst-case vertical misalignment was lmisalign = 100 rows, leading to a  2-ms delay between when the corresponding pixels in horizontally neighboring  cameras begin to expose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' To ensure significant temporal overlap (at least 90%)  in the exposure periods, we thus exposed for 2 ms/(1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='9) = 20 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  For 2× and 4× downsampling, the asynchrony is less dramatic because the  numbers of rows and columns are reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Going through similar calculations,  we determined that exposing for 5 ms and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='5 ms for 2× and 4× downsampling,  respectively, leads to >90% temporal overlap in the worst-case vertical camera  misalignment cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Note that these values don’t quite scale proportionally  between the 2× and 4× cases due to horizontal blanking periods not decreasing  proportionally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  S5 Impact of hardware design on height  accuracy  Here, we explore how hardware design choices impact the accuracy of 3D  height estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We will ignore errors stemming from camera distortion,  Springer Nature 2021 LATEX template  38  3D-RAPID  p  h  wo  wi  wi  wo  xL  xR  ΔxL  ΔxR  s  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S5 Two identical cameras with effective focal length f observing a common sample  point with height h from the focal plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The magnification is M = wi/wo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  aberrations, and misalignment and assume ideal paraxial imaging performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Further, for simplicity, we assume two adjacent cameras spaced by p center to  center with a common effective focal length, f, a working distance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', the  distance between the sample plane and the lens principal plane) of wo, and a  sensor-to-lens distance of wi (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These latter three parameters satisfy  the lens equation,  1  wo  + 1  wi  = 1  f .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  (S4)  The magnification is thus M = wi/wo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Further, consider a sample point with height h positioned xL from the  optical axis of the left camera and xR from that of the right camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Due to  nontelecentric optics, the apparent object-side position of this sample point is  parallax-shifted ∆xL in the left camera and ∆xR in the right camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' These  shifts are related to the height via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 1,  ∆xL =  hxLM  f(M + 1) − hM ,  ∆xR =  hxRM  f(M + 1) − hM .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  (S5)  We are interested in the total parallax shift between both cameras, given by  ∆x = ∆xL + ∆xR =  hpM  f(M + 1) − hM ,  (S6)  which does not depend on the lateral position of the sample point, as xL+xR =  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' How well we can estimate ∆x depends on how accurately we can match  and register the sample point in both camera images, which in turn depends  Springer Nature 2021 LATEX template  3D-RAPID  39  on the lateral resolution of the imaging system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' We consider two limits: the  diffraction-limited regime and the pixel-size-limited regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Let δxpixel be the  camera pixel size, so that δxpixel/M is the object-side pixel size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Further, let  δxdiff be the camera-side diffraction-limited spot size, so that δxdiff /M is the  object-side diffraction-limited spot size:  δxdiff ∝  λ  NA ≈ 2λwi  w  = 2λf(M + 1)  w  ,  (S7)  where w is the lens aperture diameter and λ is the wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Assum-  ing that we can match corresponding points in the two camera images with  an uncertainty proportional to the lateral resolution, then the corresponding  height error can be estimated by setting ∆x (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S6) equal to the object-  side lateral spot size and solving for h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the pixel-resolution-limited regime  (δxpixel ≫ δxdiff ), we have that the height uncertainty is  δhpixel ∝ fδxpixel(M + 1)  M(δxpixel + pM),  (S8)  meaning that downsampling the images results in a roughly proportional  decrease in height uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In the diffraction-limited regime, we have that  δhdiff ∝  2λf 2(M + 1)2  M(2λf(M + 1) + pwM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  (S9)  We can see that in both cases, all else equal, decreasing f and increasing p and  M improve the height estimation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' It may appear helpful to decrease  M to increase the amount of overlap of neighboring camera FOVs until even-  tually non-adjacent cameras begin to overlap, resulting in larger values of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  However, in both pixel-limited and diffraction-limited regimes, 1/p decreases  more slowly than the factors that include M increase as M decreases (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', con-  sider p → 2p, M → M/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Furthermore, this analysis assumes that the object  height variation is within the depth of field of the imaging systems, within  which the lateral resolution remains roughly constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, while designs that  increase the lateral resolution can improve height estimation accuracy, they  also compromise the axial FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  We now consider the case where the camera FOVs are critically overlapped  at 50%, that is when M = s/2p, where s is the sensor width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Thus, the height  uncertainties in the pixel- and diffraction-limited regimes are, respectively,  δhpixel ∝ 2δxpixelf(2p + s)  s(2δxpixel + s)  ≈ 2δxpixelf(2p + s)  s2  ,  (S10)  δhdiff ∝  2λf 2(2p + s)2  s(2λf(2p + s) + psw) ≈ 2λf 2(2p + s)2  ps2w  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  (S11)  Springer Nature 2021 LATEX template  40  3D-RAPID  In the ideal case of p = s, so that there are no gaps in between the sensors  and M = 1/2, we have  δhpixel ∝ δxpixelf  p  ,  (S12)  δhdiff ∝ λf 2  pw .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  (S13)  S6 SNR considerations  As with all imaging systems, SNR is an important metric for 3D-RAPID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Specifically, the better the SNR of the photometric images, the higher the  image registration accuracy and by extension the 3D estimation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  There are several trade offs involving SNR with our method as it relates to  imaging small model organisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Numerical aperture (NA): the higher the NA, the more light collected and  the better the shot-noise-limited SNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The associated improved lateral reso-  lution also improves the 3D height estimation accuracy, because the parallax  estimation accuracy would increase (Supplementary Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' S5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' However, at  the same time, the higher the NA, the shallower the depth of field, which  limits the axial FOV of the 3D reconstructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' In addition, the higher the  NA, the smaller the lateral FOV becomes in practice due to difficulties  in correcting aberrations [22] and therefore the tighter the camera array  packing would need to be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Behavior: while increasing the illumination power would yield higher SNR,  care must be taken to avoid influencing the behavior of the model organisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  This tradeoff can be partially alleviated by using wavelengths invisible to  the model organism’s visual system, however radiative heating from the  illumination source can potentially still influence behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Speed: the higher the frame rate, the less light that is detected and therefore  the lower the SNR per frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Increasing illumination power can alleviate  this tradeoff until it influences the behavior of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Camera type: one of the factors enabling the financial tractability of the  3D-RAPID architecture is its use of CMOS digital image sensors that are  currently fabricated at large scales for the cell phone camera market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' While  the sensitivities of these camera sensors have improved significantly over the  past decade (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=', now with very low read noise and dark current and high  quantum efficiency, due in part to the introduction of back-side illuminated  CMOS sensors), their performance may still generally lag behind that of  high-end scientific CMOS and EMCCD sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' While this latter technology  is currently too expensive to multiplex into an array with more than several  dozen sensors, it may become feasible in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  Springer Nature 2021 LATEX template  3D-RAPID  41  S7 Supplementary video descriptions  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 60-fps, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6-MP video of freely swimming zebrafish larvae (10 dpf) feeding  on mostly floating AP100 food particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel is the photometric  composite and the right panel is the 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The video zooms into  three feeding events (or attempts) by two different fish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 230-fps, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1-MP video of freely swimming zebrafish larvae (10 dpf) feeding  on mostly floating AP100 food particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel is the photometric  composite and the right panel is the 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The video zooms in  on three independent feeding events by three different fish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The third fish  can be seen swallowing the food particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 60-fps, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6-MP video of freely swimming zebrafish larvae (10 dpf) feeding  on mostly floating AP100 food particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel shows the full field  of view with the trajectories mapped out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The panels on the right each  correspond to individual fish, uniquely identified by a 2-digit number, whose  position and orientation are denoted with red annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The righthand  panels’ border colors nonuniquely match those of the tracks in the lefthand  panel, to assist the viewer in matching the fish to the trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Righthand  panels appear and disappear when the fish enters or exits the FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The  first half of the video shows the photometric values, while the second half  of the video shows the 3D height maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 60-fps, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6-MP video of 20-dpf zebrafish larvae feeding on live brine shrimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The left panel is the photometric composite and the right panel is the 3D  height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The video zooms in on two feeding events from two different  fish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 230-fps, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1-MP video of 20-dpf zebrafish larvae feeding on live brine shrimp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  The left panel is the photometric composite and the right panel is the 3D  height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The video zooms into one feeding event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 60-fps, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6-MP video of a large school of 5-dpf zebrafish larvae freely swim-  ming in an open arena at high speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel is the photometric  composite and the right panel is the 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 230-fps, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1-MP video of a large school of 5-dpf zebrafish larvae freely swim-  ming in an open arena at high speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 60-fps, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='6-MP video of freely moving fruit flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel is the  photometric composite and the right panel is the 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' 230-fps, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='1-MP video of freely moving fruit flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel is the  photometric composite and the right panel is the 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='6-MP video of freely moving fruit flies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel shows the  full field of view with the trajectories mapped out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The panels on the right  each correspond to individual flies, uniquely identified by a 2-digit number,  whose position is denoted by a red circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The righthand panels’ border  colors nonuniquely match those of the tracks in the lefthand panel, to assist  the viewer in matching the flies to the trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' Righthand panels appear  and disappear when the fish enters or exits the FOV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The first half of the  Springer Nature 2021 LATEX template  42  3D-RAPID  video shows the photometric values, while the second half of the video shows  the 3D height maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+page_content='6-MP video of freely moving harvester ants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content=' The left panel is the  photometric composite and the right panel is the 3D height map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
+page_content='  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/idE_T4oBgHgl3EQf4Rxl/content/2301.08351v1.pdf'}
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+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+1
+Hybrid Open-set Segmentation
+with Synthetic Negative Data
+Matej Grci´c, Siniˇsa ˇSegvi´c
+Abstract—Open-set segmentation is often conceived by complementing closed-set classification with anomaly detection. Existing
+dense anomaly detectors operate either through generative modelling of regular training data or by discriminating with respect to
+negative training data. These two approaches optimize different objectives and therefore exhibit different failure modes Consequently,
+we propose the first dense hybrid anomaly score that fuses generative and discriminative cues. The proposed score can be efficiently
+implemented by upgrading any semantic segmentation model with translation-equivariant estimates of data likelihood and dataset
+posterior. Our design is a remarkably good fit for efficient inference on large images due to negligible computational overhead over the
+closed-set baseline. The resulting dense hybrid open-set models require negative training images that can be sampled either from an
+auxiliary negative dataset or from a jointly trained generative model. We evaluate our contributions on benchmarks for dense anomaly
+detection and open-set segmentation of traffic scenes. The experiments reveal strong open-set performance in spite of negligible
+computational overhead.
+Index Terms—Open-set segmentation, Open-set recognition, Out-of-distribution detection, Anomaly detection, Semantic
+segmentation, Synthetic data, Normalizing flows
+!
+1
+INTRODUCTION
+H
+IGH accuracy, fast inference and small memory foot-
+print of modern neural networks [1], [2] steadily ex-
+pand the horizon of downstream applications. Many ex-
+citing applications require advanced image understanding
+functionality provided by semantic segmentation [3], [4],
+[5]. These models associate each pixel with a class from
+a predefined taxonomy [6]. They can accurately segment
+two megapixel images in real-time on low-power embedded
+hardware [7], [8], [9]. However, standard training proce-
+dures assume closed-world setup, which may raise serious
+safety issues in real-world deployments [10], [11]. For ex-
+ample, if a segmentation model missclassifies an unknown
+object (e.g. lost cargo) as road, the autonomous car may
+experience a serious accident [12]. Such hazards can be
+alleviated by complementing semantic segmentation with
+dense anomaly detection [13], [14]. The resulting open-set
+segmentation models [15] are fitter for real applications due
+to ability to decline decisions in unknown scene parts.
+Previous approaches for open-set segmentation assume
+either a generative or a discriminative perspective. Gener-
+ative approaches are based on density estimation [16] or
+image resynthesis [17], [18], [19]. Discriminative approaches
+use classification confidence [20], dataset posterior [15] or
+Bayesian inference [21]. However, the two perspectives ex-
+hibit different failure modes. Generative anomaly detectors
+inaccurately disperse the probability volume [22], [23], [24],
+[25] or face the hazards of image resynthesis [17], [18]. On
+the other hand, discriminative anomaly detectors require
+training on negative content from some general-purpose
+auxiliary dataset [15], [18], [26]. Such training may involve
+an overlap between training negatives and test set anoma-
+M. Grci´c and S. ˇSegvi´c are with University of Zagreb, Faculty of Electrical
+Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
+E-mail: {matej.grcic,sinisa.segvic}@fer.hr
+Manuscript received January 19, 2023.
+lies. Hence, the evaluation may lead to over-optimistic per-
+formance estimates and surprising failures in production.
+In this work, we combine the two perspectives by de-
+signing a hybrid anomaly detector. The proposed approach
+complements a chosen closed-set semantic segmentation
+model with unnormalized dense dataset likelihood ˆp(x) and
+dense data posterior P(din|x). Fusion of these two outputs
+yields an effective yet efficient dense anomaly detector
+which we refer to as DenseHybrid. Both components of
+our anomaly detector require training with negative data
+[15], [18], [26], [27], [28]. We present a way to relieve that
+dependence by leveraging synthetic negative data sourced
+from a generative model [28], [29], [30], [31]. Consequently,
+our experiments evaluate performance with and without
+real negative training data.
+This paper extends our preliminary conference report
+[32] by allowing our dense hybrid models to train without
+real negative data. We achieve that by generating synthetic
+negative samples with a jointly trained normalizing flow.
+Different from previous work [31], the normalizing flow
+does not receive the gradients from the training objectives
+for anomaly detection. Such design ensures correct con-
+vergence of the normalziing flow in view of a complex
+formulation of the anomaly score, and provides a stronger
+learning signal to the dataset posterior head. Our new
+experiments explore open-set performance without training
+on real negative data and compare our unnormalized den-
+sity estimator with respect to a general-purpose generative
+module. Finally, we substantially revise our presentation by
+supplying a more comprehensive review of the related work
+and improved descriptions of our method.
+Our consolidated work brings forth the following contri-
+butions. First, we propose the first hybrid anomaly detector
+that allows end-to-end training, translational equivariance,
+and pixel-level predictions. The proposed DenseHybrid
+arXiv:2301.08555v1  [cs.CV]  19 Jan 2023
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+2
+SMIYC-ObstacleTrack
+LostAndFound
+Fishyscapes Static
+StreetHazards
+Road Anomaly
+Fig. 1. Qualitative performance of the proposed DenseHybrid approach on standard datasets. Top: input images. Bottom: dense maps of the
+proposed anomaly score. Unknown pixels are assigned with higher anomaly scores designated in yellow. Such a highly accurate anomaly detector
+enables us to derive the open-set segmentation model.
+method combines unnormalized density and discriminative
+dataset posterior. Both of these two components involve
+minimal computational overhead and require training on
+negative data. Second, we extend our approach by allowing
+it to learn only on inlier images. This configuration lever-
+ages synthetic negative data that correspond to generated
+samples at the boundary of the inlier distribution. Third, we
+propose open-mIoU as a novel performance metric for open-
+set segmentation in safety-critical applications. The main
+strength of the novel metric is exact quantification of the
+gap between closed-set and open-set setups. Fourth, our
+DenseHybrid anomaly detector can be easily attached to
+any closed-set segmentation approach. The resulting open-
+set segmentation algorithm delivers very competitive per-
+formance on standard benchmarks in road-driving scenes
+with and without training on real negative data.
+2
+RELATED WORK
+The related work considers anomaly detection (Sec. 2.1 and
+Sec. 2.2), open-set recognition (Sec. 2.3), training open-set
+recognition on synthetic data (Sec. 2.4), as well as progres-
+sion towards open-world recognition (Sec. 2.5).
+2.1
+Image-wide Anomaly Detection
+Detecting samples which deviate from the generative pro-
+cess of the training data is a decades old problem [33].
+In the machine learning community, this task is also
+known as anomaly detection, novelty detection and out-of-
+distribution (OOD) detection [13], [34]. Early image-wide
+approaches utilize max-softmax probability [34], input per-
+turbations [35] ensembling [36] or Bayesian uncertainty [21].
+More encouraging performance has been attained through
+discriminative training against real negative data [15], [27],
+[37], [38], adversarial attacks [39] or samples from appro-
+priate generative models [28], [29], [31], [40]. Another line
+of work detects anomalies by estimating the likelihood.
+Surprisingly, this research reveals that anomalies may give
+rise to higher likelihood than inliers [22], [23], [25]. Gener-
+ative models can mitigate this problem by sharing features
+with the primary discriminative model [41] and training on
+negative data [27].
+2.2
+Pixel-wise Anomaly Detection
+Image-wide anomaly detection can be adapted for dense
+prediction with variable success. Some of the existing
+image-wide approaches [41] are not applicable in dense
+prediction context, while others do not perform well [35]
+or involve excessive computational complexity [35], [36].
+On the other hand, concepts such as discriminative train-
+ing with negative data [27], [37], [42] are easily ported to
+dense prediction. Hence, several dense anomaly detectors
+are trained on mixed-content images obtained by pasting
+negatives (e.g. ImageNet, COCO, ADE20k) over regular
+training images [15], [18], [26]. Dataset posterior can be
+recovered by a dedicated head that shares features with the
+standard semantic segmentation head [15].
+Anomalies can also be recognized in feature space [16].
+However, this approach complicates detection of small ob-
+jects due to subsampling and feature collapse [24]. Orthog-
+onally, anomaly detector can be implemented according to
+learned dissimilarity between the input and the resynthe-
+sised image [17], [18], [19], [43]. The resynthesis is per-
+formed by a generative model conditioned on the predicted
+labels. However, this approach is suitable only for uniform
+backgrounds such as roads [17], and offline applications
+due to significant computational overhead. Besides dense
+anomaly detection in road driving scenes, some approaches
+consider applications in industrial facilities [44]. However,
+these setups are less relevant for our open-set algorithms
+since they do not involve the primary discriminative task.
+Different than all previous work, we propose the first
+hybrid anomaly detector for dense prediction models. In
+comparison with previous approaches that build on dataset
+posterior [15], [27], [37], our method introduces synergy
+with likelihood evaluation. In comparison with approaches
+that recover dense likelihood [10], our method introduces
+joint hybrid training and efficient joint inference together
+with standard semantic segmentation. Our method is also
+related to joint energy-based models [45], since we also
+reinterpret logits as unnormalized joint likelihood. How-
+ever, their method has to backprop through the intractable
+normalization constant and is therefore unsuitable for large
+resolutions and dense prediction. Our method completely
+avoids sampling by recovering unnormalized likelihood
+and training on negative data. Concurrent approaches [46],
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+3
+[47] consider only the generative component of our hybrid
+anomaly detector.
+2.3
+Open-set recognition
+Open-set recognition assumes presence of test examples that
+transcend the training taxonomy. Such examples are also
+known as semantic anomalies [13]. During inference, the
+model has to recognize semantic anomalies and withhold
+(or reject) the decision [48]. The rejection mechanism can
+be implemented by restricting the shape of the decision
+boundary [49], [50]. This can be carried out by thresholding
+the distance from learned class centers in the embedding
+space [49], [51]. Recognition performance can be further
+improved through employing a stronger classifier [52], [53].
+Alternatively, the rejection mechanism can emerge by com-
+plementing the classifier with an anomaly detector [14], [34],
+[35]. The anomaly detector then detects samples which do
+not belong to the known classes. We direct the reader to [54]
+for a comprehensive overview of open-set approaches.
+Most open-set approaches quantify performance by sep-
+arate evaluation of closed-set recognition and anomaly de-
+tection [10], [34], [55], [56]. However, such practice does
+not reveal degradation of discriminative predictions due
+to errors in anomaly detection [57], [58]. This is especially
+pertinent to dense prediction models where we can observe
+inlier and outlier pixels in the same image. Recent work
+proposes a solution for the related problem of semantic
+segmentation in adverse conditions [59]. Their uncertainty-
+aware UIoU metric takes into account prediction confidence
+as measured by the probability of the winning class. How-
+ever, UIoU assumes that each pixel belongs to one of the
+K known classes, which makes it inapplicable for open-set
+recognition. Different than all previous work, our anomaly-
+aware open-IoU metric specializes for evaluation of open-set
+segmentation in presence of outliers. It takes into account
+both false positive semantic predictions at outliers as well
+as false negative semantic predictions due to false positive
+anomaly detection. Furthermore, the difference between
+mIoU and open-mIoU reveals the performance gap due to
+presence of outliers in the test set.
+2.4
+Synthetic data in open-set recognition
+Recent seminal approaches train open-set recognition mod-
+els on synthetic negative data produced by a jointly trained
+generative adversarial network (GAN) [28], [29]. The GAN
+is trained to generate inlier data that give rise to low
+recognition scores for each known class [28]. However,
+GANs are biased towards limited distribution coverage [24].
+Consequently, they are unlikely to span the whole space
+of possible outliers. Thus, more promising results were
+achieved by mixing real and synthetic negative samples [40].
+Alternatively, GANs can be replaced with generative
+models that optimize likelihood in order to improve dis-
+tributional coverage [24]. This task calls for efficient ap-
+proaches that support fast sampling since joint training
+requires sample generation on the fly. This puts at disad-
+vantage many interesting generative models such as au-
+toregressive PixelCNN and energy-based models. Normal-
+izing flows are a great candidate for this role due to fast
+training and capability to quickly generate samples with
+different resolutions [31]. Instead of targeting negative data,
+a generative model can also target negative features [40].
+This can be carried out by modelling inlier features and
+sampling synthetic anomalies from low-likelihood regions
+of feature space [60]. Negative data have also been crafted
+by leveraging adversarial perturbations [39].
+2.5
+Beyond open-set recognition
+Anomalous images or pixels can be clustered into new se-
+mantic classes. This can be done in incremental [61], [62] or
+zero/one/few-shot [63] setting. However, these approaches
+are still unable to compete with supervised learning on
+standard datasets. We direct reader to [64] for better analysis
+of pros and cons of low-shot learning.
+3
+HYBRID SCORE FOR ANOMALY DETECTION
+We propose a dense hybrid anomaly score that improves
+upon discriminative and generative anomaly detection (Sec.
+3.1). The new hybrid anomaly score can be efficiently fused
+with a semantic classifier (Sec. 3.2).
+We represent the input images with a random variable x.
+Variable yij denotes the corresponding label at the location
+(i, j), while binary random variable dij models whether a
+given pixel belongs to the inliers or outliers. We write dij
+in
+for inliers and dij
+out for outliers. We denote a realization of a
+random variable without the underline. Thus, P(yij|x) is a
+shortcut for P(yij = yij|x = x). For brevity, we often omit
+spatial locations.
+3.1
+Hybrid Anomaly Detection for Dense Prediction
+Generative and discriminative approaches to anomaly de-
+tection exhibit different failure modes. Fig. 2 illustrates the
+shortcomings of both approaches on a toy problem. Blue
+dots designate inlier data. Green triangles designate the neg-
+ative data used for training. Red squares denote anomalous
+test data. Discriminative detectors model dataset posterior
+P(dout|x). They fail if the negative training data does not
+cover the entire negative manifold (left) [27]. On the other
+hand, generative detectors which model p(x) tend to in-
+accurately distribute probability volume over the sample
+space [22], [23], [24] (center). We fuse discriminative and
+generative approaches into a hybrid detector that alleviates
+the aforementioned limitations (right).
+We build our hybrid anomaly detector upon the discrim-
+inative dataset posterior P(din|x) and the generative data
+likelihood p(x). We express a novel hybrid anomaly score
+as log-ratio between P(dout|x) = 1 − P(din|x) and p(x):
+s(x) := ln P(dout|x)
+p(x)
+= ln P(dout|x) − ln p(x).
+(1)
+We will further show that this formulation is especially
+suitable for dense predictions atop the dense classifier. There
+may be other effective formulations of s(x), which is an
+interesting direction for future work.
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+4
+Discriminative P(dout|x)
+Generative p(x)
+Hybrid P(dout|x)/p(x)
+Inlier data
+Negative training data
+Outlier test data
+FPR=11.0%
+FPR=24.0%
+FPR=9.5%
+Fig. 2. Anomaly detection on a toy dataset. The discriminative approach (left) models the dataset posterior. It fails if the negative training dataset
+fails to cover all modes of the test anomalies. The generative approach (middle) models the data likelihood. It may assign high likelihoods to test
+anomalies [22] due to over-generalization [24]. The hybrid approach attains a synergy between discriminative and generative modelling.
+3.2
+Efficient Implementation Atop Semantic Classifier
+Standard semantic classification can be viewed as a two-step
+procedure. Given an input image x, a deep feature extractor
+fθ1 computes an abstract representation z also known as
+pre-logits. The computed pre-logits are projected into logits
+s, and activated by softmax. The softmax output is defined
+as class posterior probability P(y|x):
+P(y|x) := softmax(s)y, where s = fθ2(z), z = fθ1(x). (2)
+In practice, fθ1 is an encoder-decoder architecture common
+for semantic segmentation and fθ2 is a simple projection by
+means of 1x1 convolution. We extend this framework with
+dense data likelihood and discriminative dataset posterior.
+Dense data likelihood can be conveniently derived atop
+dense classifier by re-interpreting logits as unnormalized
+joint probability of input and label [45]:
+p(y, x) = 1
+Z ˆp(y, x) := 1
+Z exp sy, where
+s = fθ2(z).
+(3)
+Z denotes the corresponding normalization constant depen-
+dent only on model parameters. As usual, Z is finite but in-
+tractable, since it requires computing the unnormalized dis-
+tribution for all realizations of y and x: Z = �
+x
+�
+y exp sy.
+Throughout this work, we conveniently eschew the evalua-
+tion of Z in order to enable efficient training and inference.
+We express the dense likelihood p(x) by marginalizing
+out y:
+p(x) =
+�
+y
+p(y, x) = 1
+Z
+�
+y
+ˆp(y, x) = 1
+Z
+�
+y
+exp sy.
+(4)
+Standard discriminative predictions are easily recovered
+through Bayes rule p(y, x)/p(x):
+P(y|x) =
+p(y, x)
+�
+y′ p(y′, x) =
+exp sy
+�
+y′ exp sy′ = softmax(s)y. (5)
+The normalization constant Z appears both in the numer-
+ator and denominator, and hence can be cancelled out.
+Reinterpretation of logits as unnormalized joint probability
+enables likelihood estimation atop a discriminative classifier
+task and even exploiting pretrained classifiers. Note that
+adding a constant value to the logits does not affect the
+standard classification but affects our framework since the
+value of p(x) changes. Hence, we use the extra degree of
+freedom in logits to express the data likelihood [45]. The
+same extra degree of freedom has been used to model a
+discriminator network in semi-supervised learning [65].
+We define the dataset posterior P(din|x) as a non-linear
+transformation based on pre-logits z [15]:
+P(din|x) := σ(gγ(z)).
+(6)
+In our case, the function g is BN-ReLU-Conv1x1 of pre-
+logits, followed by a sigmoid non-linearity.
+We can now compute the proposed dense hybrid
+anomaly score (1) atop the classifier as:
+s(x) := ln P(dout|x) − ln ˆp(x) + ln Z
+(7)
+∼= ln P(dout|x) − ln ˆp(x).
+(8)
+We can neglect Z since ranking performance [34] is invariant
+to monotonic transformations such as taking a logarithm
+or adding a constant. Note that the logarithmic function
+re-scales the unnormalized ˆp(x) and P(dout|x) on approx-
+imately the same scale, equalizing the influence of both
+components in the final decision. The resulting formulation
+(7) is especially well suited for dense prediction due to
+minimal overhead and translation equivariance.
+Figure 3 illustrates dense inference with the proposed
+hybrid open-set setup. RGB input is fed to a hybrid dense
+model which produces pre-logit activations z and logits s.
+We activate the closed-set class posterior P(y|x) with soft-
+max and the unnormalized data log-likelihood ln ˆp(x) via
+log-sum-exp operator (designated in green). A distinct head
+g transforms pre-logits z into the dataset posterior P(dout|x)
+(designated in yellow). The anomaly score s(x) is a log ratio
+between the latter two outputs. The resulting anomaly map
+is thresholded and fused with the discriminative output into
+the final dense open-set recognition map.
+4
+OPEN-SET TRAINING WITH DENSEHYBRID
+Our open-set approach complements an arbitrary closed-
+set segmentation model with the DenseHybrid anomaly
+detector. We propose a novel training setup that eschews the
+intractable normalization constant by introducing negative
+data to the generative learning objective (Sec. 4.1). The same
+negative data are used to train the dataset posterior. We
+relax dependence on real negatives by sampling a suitably
+trained normalizing flow (Sec. 4.2).
+
+PR=95%JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+5
+Threshold
+Fuse
+P(y|x)
+Input
+Open-set 
+segmentation
+Dense anomaly score
+DenseHybrid
+s(x) = 
+-
+Projection
+z
+Feature
+extractor
+Log-sum-exp
+BN-ReLU-Conv
+ln p(x)
+P(din|z)
+s
+Softmax
+σ
+Feature
+extractor
+Fig. 3. The proposed open-set segmentation approach. Our anomaly
+score is the log-ratio of dense data likelihood and discriminative dataset
+posterior. Both outputs are derived from the standard dense classifier.
+We formulate open-set segmentation by complementing the closed-set
+segmentation map with the thresholded anomaly score.
+4.1
+Open-set training with real negative data
+The multi-task model from Fig. 3 requires joint fine-tuning
+of three dense prediction heads: i) closed-set class posterior
+P(y|x), ii) unnormalized data likelihood ˆp(x) [45], and iii)
+dataset posterior P(din|x) [15]. The class-posterior head
+requires a discriminative loss over the inlier dataset Din:
+Lcls(θ) = Ex,y∈Din[− ln P(y|x)]
+(9)
+= − Ex,y∈Din[sy − ln
+�
+y′
+exp sy′].
+(10)
+Training unnormalized likelihood is a daunting task
+since backpropagation through p(x) involves intractable
+integration over all possible images [66], [67]. Previous
+solutions are based on MCMC sampling [45], however, this
+is not feasible in our setup due to high-resolution inputs and
+dense prediction. We eschew the normalization constant by
+optimizing the likelihood both in inlier and outlier pixels:
+Lx(θ) = Ex∈Din[− ln p(x)] − Ex∈Dout[− ln p(x)]
+(11)
+= −Ex∈Din[ln ˆp(x)] − ln Z + Ex∈Dout[ln ˆp(x)] + ln Z
+(12)
+= − EDin
+�
+ln
+�
+i
+exp(si)
+�
++ EDout
+�
+ln
+�
+i
+exp(si)
+�
+(13)
+As before, s stands for logits computed by fθ. Note that the
+normalization constant Z cancels out due to training on out-
+liers. In practice, we use a simplified loss that corresponds
+to an upper bound of the above expression (LUB
+x
+≥ Lx):
+LUB
+x (θ) = − Ex,y∈Din[sy] + Ex∈Dout[ln
+�
+i
+exp(si)].
+(14)
+Proof can be easily derived by recalling that log-sum-exp is
+a smooth upper bound of the max function. Thus, our upper
+bound LUB
+x
+leverages the following inequalities:
+ln
+�
+i
+exp si ≥ max
+i
+si ≥ sy.
+(15)
+Comparison of the discriminative loss (9) and the gen-
+erative upper bound (14) reveals that the standard clas-
+sification loss is well aligned with the upper bound in
+inlier pixels. Recall that training data likelihood only on
+inliers [45], [66] would require MCMC sampling, which is
+infeasible in our context. Unnormalized likelihood could
+also be trained through score matching [67]. However, this
+would preclude hybrid modelling due to having to train
+on noisy inputs. Consequently, it appears that the proposed
+training approach is a method of choice in our context.
+The dataset-posterior head P(din|x) requires a discrimi-
+native loss that distinguishes the inlier dataset Din from the
+outlier dataset Dout [15]:
+Ld(θ, γ) = −Ex∈Din[ln P(din|x)]
+− Ex∈Dout[ln(1 − P(din|x))].
+(16)
+Our final compound loss aggregates Lcls, LUB
+x
+and Ld:
+L(θ, γ) = −Ex,y∈Din[ln P(y|x) + ln P(din|x)]
+− β · Ex∈Dout[ln(1 − P(din|x)) − ln ˆp(x)].
+(17)
+Hyperparameter β controls the impact of negative data to
+the primary classification task. Note that we omit the first
+term from LUB
+x
+(14) in inlier pixels since this is implicitly
+enforced through optimization of Lcls (9).
+Figure 4 illustrates the described procedure for training
+open-set segmentation models. We prepare mixed-content
+training images x′ by pasting negative patches x− into
+regular training images x+:
+x′ = (1 − s) · x+ + pad(x−, m),
+x− ∈ Dout.
+(18)
+Note that here we leverage real negative images x− ∈ Dout.
+We consider synthetic negatives in the subsequent subsec-
+tion. The binary mask m identifies negative pixels within
+the mixed-content image x′. Negative pixels are labelled as
+dout while positive pixels are labelled as din. Semantic labels
+of negative pixels are set to void.
+The resulting mixed-content image x′ is fed to the de-
+sired semantic segmentation model that produces pre-logits
+z and logits s. We recover the class posterior P(y|x) by
+activating logits with softmax. We recover the unnormalized
+log-likelihood ln ˆp(x) by processing logits with log-sum-
+exp. We recover dataset posterior P(d + in|x) by processing
+pre-logit activations with the standard BN-ReLU-Conv1 × 1
+unit. The compound training loss L(θ, γ) (17) aggregates
+class-discriminative loss Lcls (9), generative loss LUB
+x
+(14)
+and dataset-discriminative loss Ld (16).
+4.2
+Open-set training with synthetic negative data
+Anomaly detectors can avoid biased predictions by replac-
+ing real negative training data with samples of a suitable
+generative model [28], [30], [31], [68]. The generative model
+has to be trained to generate synthetic samples that encom-
+pass the border of the inlier distribution [28]. The required
+learning signal can be derived from discriminative predic-
+tions [28], [30], [31] or provided by an adversarial module
+[39]. Hence, replacing real negative data with synthetic
+counterparts requires joint training of the generative model.
+We choose a normalizing flow [69] for this task due to
+exceptional distributional coverage and ability to quickly
+generate samples of varying spatial dimensions [70]. We
+train the normalizing flow pζ according to a weighted sum
+of two loss terms: Lmle and Ljsd.
+The data term Lmle
+corresponds to negative log-
+likelihood of random crops from inlier images x+:
+Lmle(ζ) = −Ex+∈Din[ln pζ(crop(x+))].
+(19)
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+6
+Sample
+instance
+Input image
+Synthetic
+negative
+Paste
+Mixed content image
+Ground truth
+Traffic
+Scenes
+z ~ N(0, I)
+Normalizing
+Flow (hζ)
+Random
+crop
+Lmle
+L(ζ)
+Ljsd
+L(ζ)
+Shared weights
+x-
+x+
+x’
+Soft
+Max
+BN
+ReLU
+Conv
+Sum
+Exp
+Lcls
+Lx
+Ld
+L(Θ,Ɣ)
+t
+s
+z
+Projection
+Feature
+extractor
+Normalizing
+Flow (h-1
+ζ)
+Auxiliary
+Dataset
+OR
+Synthetic negatives
+Real negatives
+crop(x+)
+Fig. 4. The two training procedures for the proposed open-set training with DenseHybrid. We construct mixed-content images by pasting negatives
+into inlier images. The negative training data can be sampled either from an auxiliary real dataset (Sec. 4.1) or from a jointly trained normalizing flow
+(Sec. 4.2). Mixed-content images are fed to the open-set model with three dense outputs: closed-set class posterior, unnormalized likelihood, and
+dataset posterior. Outputs are optimized according to the compound loss (17). In the case of synthetic negatives, the normalizing flow optimizes
+the loss (20).
+The crop notation mirrors the pad notation from (18). Ran-
+dom crops vary in spatial resolution. This term aligns the
+generative distribution with the distribution of the training
+data. It encourages coverage of the entire inlier distribution
+under the condition that the generative model has sufficient
+capacity.
+The boundary-attraction term Ljsd [70] corresponds to
+negative Jensen-Shannon divergence between the class-
+posterior and the uniform distribution at all generated pix-
+els. This term pushes the generative distribution towards the
+periphery of the inlier distribution where the class posterior
+should be unclear. Note that gradients of this term must
+propagate through the entire semantic model in order to
+reach the normalizing flow. Hence, the flow is penalized
+when the generated sample yields high softmax confidence.
+This signal pushes the generative distribution away from
+high-density regions of the input space [28].
+The total loss of the normalizing flow modulates the
+contribution of the boundary term with the hyperparameter
+λ:
+L(ζ) = Lmle(ζ) + λ · Ljsd(ζ; θ)
+(20)
+Optimization of this loss enforces the generative distribution
+to encompass all modes of inlier distribution. Note that our
+normalizing flow can never match the diversity of images
+from a real dataset such as COCO or ADE20k. It would
+be unreasonable to expect a generative model to draw a
+sofa after training on Cityscapes. Still, if the flow suc-
+ceeded to learn well the boundary of the inlier distribution,
+then DenseHybrid would be inclined to recognize all off-
+distribution samples as anomalies [28].
+Details of the training procedure are again illustrated in
+Figure 4. We sample the normalizing flow by i) selecting a
+random spatial resolution (H,W) from a predefined interval,
+ii) sampling a random latent representation z ∼ N(0, IHW ),
+and iii) feeding z to the flow so that x− = h−1
+ζ (z). We again
+craft a mixed-content image x′ by pasting the synthesized
+negative patch x− into the regular training image x+ ac-
+cording to (18). We perform the forward pass, determine
+Lcls, Ld, Lx, and Ljsd, and recover the training gradients by
+backpropagation. Of course, gradient of Ljsd is propagated
+all the way to the normalizing flow. We now take the deleted
+inlier patch x+
+s , perform inference with the normalizing
+flow (z = hζ(x+
+s )) and accumulate gradients of Lmle before
+performing a model-wide parameter update.
+5
+EXPERIMENTAL SETUP
+We describe benchmarks and datasets used for the evalua-
+tion of DenseHybrid in dense anomaly detection and open-
+set segmentation experiments (Sec. 5.1). We propose a new
+metric to adequately quantify the gap between the open-set
+and closed-set performance (Sec. 5.2). Also, we present the
+main implementation details of our solution (Sec. 5.3).
+5.1
+Benchmarks and Datasets
+We evaluate performance on standard benchmarks for
+dense
+anomaly
+detection
+and
+open-set
+segmentation.
+Fishyscapes [10] considers urban scenarios on a subset of
+LostAndFound [12] and on Cityscapes validation images
+with pasted anomalies (FS Static). SegmentMeIfYouCan
+(SMIYC) [56] collects carefully selected images from the real
+world and groups them with respect to the anomaly size
+into AnomalyTrack (large) and ObstacleTrack (small). More-
+over, the benchmark includes a selection of images of the
+LostAndFound dataset [12] in which the lost objects do not
+correspond to the Cityscapes taxonomy. Unfortunately, both
+benchmarks supply only binary labels, which makes them
+inappropriate for evaluating open-set performance. Hence,
+we report only anomaly detection performance on these
+benchmarks. We also validate performance on Cityscapes
+while reinterpreting a subset of ignore classes as the un-
+known class [40].
+StreetHazards [71] is a synthetic dataset created with
+CARLA virtual environment. The simulated environment
+enables smooth anomaly injection and low-cost label extrac-
+tion. Consequently, the dataset contains K+1 labels, making
+it suitable for measuring open-set recognition performance.
+5.2
+Measuring open-set performance
+Previous work evaluates open-set segmentation through
+anomaly detection [12], [56] and closed-set segmentation
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+7
+[10]. The reported drop in closed-set performance is usu-
+ally negligible and is explained by the allocation of model
+capacity for anomaly detection. However, we will show that
+the impact of anomalies onto segmentation performance can
+be clearly characterized only in the open-set setup. More
+precisely, we shall take into account false positive semantic
+predictions at anomalies as well as false negative semantic
+predictions due to false anomaly detections.
+We propose a novel evaluation procedure for open-set
+segmentation. Our procedure starts by thresholding the
+anomaly score so that it yields 95% TPR anomaly detection
+on held-out data. This is equivalent to the 5th percentile
+of inlier scores. Then, we override the classification in pixels
+which score higher than the threshold. This yields a recogni-
+tion map with K+1 labels. We assess open-set segmentation
+performance according to a novel metric that we term open-
+mIoU. We compute open-IoU for the k-th class as follows:
+open-IoUk =
+TPk
+TPk + FPos
+k + FNos
+k
+,
+where
+(21)
+FPos
+k =
+K+1
+�
+i=1,i̸=k
+FPi
+k,
+FNos
+k =
+K+1
+�
+i=1,i̸=k
+FNi
+k.
+(22)
+Different that the standard IoU formulation, open-IoU takes
+into account false positives and false negatives caused by
+applying imperfect anomaly detectors at open-set pixels. In
+particular, a prediction of class k at an outlier pixel (false
+negative anomaly detection) counts as a false positive for
+class k. Furthermore, a prediction of class K+1 at a pixel
+labelled as class k (false positive anomaly detection) counts
+as a false negative for class k. Note that we still average
+open-IoU over K inlier classes. Thus, a recognition model
+with perfect anomaly detection gets assigned the same
+performance as in the closed world. Note that this property
+would not be preserved if we averaged open-IoU over K+1
+classes. Hence, a comparison between closed-set mIoU and
+open-set open-mIoU quantifies the gap between the open
+and closed-set performance. Some experiments report F1
+score averaged over K+1 classes [40], [57]. However, mF1
+can not be used to quantify the performance gap.
+Figure 5 compares the closed-set (left) and open-set
+(right) evaluation protocols. Imperfect anomaly detection
+impacts recognition performance through increased false
+positive semantics (designated in yellow) and false nega-
+tive semantics (designated in red). The difference between
+closed-set mIoU and open-mIoU reveals the performance
+drop due to inaccurate anomaly detection.
+Measuring performance according to open-mIoU re-
+quires datasets with K+1 labels. Collecting and annotating a
+dataset with such taxonomy requires substantial resources.
+Currently, only StreetHazards [71] offers this opportunity.
+5.3
+Implementation Details
+The proposed approach can be easily applied to any pre-
+trained semantic segmentation baseline: the only require-
+ment is access to pre-logit features and dense logits. We
+append an additional branch gγ which is in our case
+BN-ReLU-Conv1x1, to compute the discriminative dataset
+posterior. We obtain unnormalized likelihood as the sum
+1
+2
+3
+k
+K
+K+1
+1
+2
+3
+k
+K
+K+1
+TPA FPA
+FNA TNA
+1
+0
+1
+0
+TPRA = 
+TPA
+TPA + FNA
+Σ
+i = 1
+i ≠ k
+K+1
+FNos
+k=
+FNi
+k
+open-IoUk = 
+TPk
+TPk + FPos
+k + FNos
+k
+A
+A
+Closed-set segmentation
+Anomaly detection
+Open-set segmentation
+...
+...
+...
+...
+FN2
+k
+FN3
+k
+FP1
+k FP2
+k FP3
+k
+FPK
+k FPA
+k
+FNK
+k
+FNA
+k
+FN1
+k
+TPk
+1
+2
+3
+k
+K
+1
+2
+3
+k
+K
+...
+...
+...
+...
+FN2
+k
+FN3
+k
+FP1
+k FP2
+k FP3
+k
+FPK
+k
+FNK
+k
+FN1
+k
+TPk
+...
+...
+...
+...
+...
+...
+...
+...
+A
+A
+Σ
+i = 1
+i ≠ k
+K+1
+FPos
+k=
+FPi
+k
+Σ
+i = 1
+i ≠ k
+K
+FNk=
+FNi
+k
+IoUk = 
+TPk
+TPk + FPk + FNk
+Σ
+i = 1
+i ≠ k
+K
+FPk=
+FPi
+k
+Fig. 5.
+We extend closed-set performance evaluation (left) with a
+novel open-set metric (right). Open-IoU takes into account false positive
+semantics at anomalies as well as false negative semantics due to
+false anomaly detections. The proposed open-mIoU metric quantifies
+recognition performance in presence of anomalies.
+of exponentiated logits. We fine-tune the resulting open-
+set models on mixed-content images with pasted negative
+ADE20k instances (4.1) or synthetic negative patches (4.2).
+In the case of SMIYC, we fine-tune LDN-121 [75] for 10
+epochs on images from Cityscapes [76], Vistas [77] and Wild-
+dash2 [55]. In the case of Fishyscapes, we use DeepLabV3+
+with WideResNet38 [78]. We fine-tune the model for 10
+epochs on Cityscapes. In the case of StreetHazards, we train
+LDN-121 for 120 epochs in the closed-world setting and then
+fine-tune the open-set model on mixed-content images.
+Configurations that do not rely on real negative data
+leverage synthetic data of varying resolution as generated
+by DenseFlow-45-6 [69]. All such experiments pre-train
+DenseFlow with the standard MLE loss on 64 × 64 crops
+from road-driving images prior to joint learning. Our fine-
+tuning experiments last less than 24h on RTX A5000 GPU.
+Our source code is publicly available [79].
+6
+EXPERIMENTAL RESULTS
+We evaluate DenseHybrid performance in dense anomaly
+detection (Sec. 6.1) and open-set segmentation (Sec. 6.2)
+experiments, after training with and without real negative
+data. We also ablate the design choices (Sec. 6.3), explore
+the influence of distance (Sec. 6.4), and present the compu-
+tational requirements of the proposed module (Sec. 6.5).
+6.1
+Dense Anomaly Detection in Open-set Setups
+Table 1 presents dense anomaly detection performance on
+SMIYC [56] and Fishyscapes [16]. We include our model
+trained on real negative data (DenseHybrid) as well as
+our model trained on synthetic negatives (SynDenseHy-
+brid). DenseHybrid outperforms contemporary approaches
+on both AnomalyTrack and ObstacleTrack by a wide mar-
+gin. Also, it achieves the best FPR95 on LostAndFound-
+noKnown. Similarly, it delivers the best performance on
+Fishyscapes LostAndFound and the best FPR95 on Static.
+DenseHybridSyn outperforms all previous methods that
+do not train on real negative data on ObstacleTrack and
+LostAndFound-noKnown. In the case of AnomalyTrack, it
+is outperformed only by image resynthesis [17] that requires
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+8
+TABLE 1
+Anomaly detection performance on SegmentMeIfYouCan [56] and Fishyscapes [16]. Aux data denotes training on real negatives, while Img rsyn.
+denotes image resynthesis.
+Method
+SegmentMeIfYouCan [56]
+Fishyscapes [10]
+Aux
+Img
+AnomalyTrack
+ObstacleTrack
+LAF-noKnown
+FS LAF
+FS Static
+CS val
+data
+rsyn.
+AP
+FPR95
+AP
+FPR95
+AP
+FPR95
+AP
+FPR95
+AP
+FPR95
+IoU
+Image Resyn. [17]
+
+
+52.3
+25.9
+37.7
+4.7
+57.1
+8.8
+5.7
+48.1
+29.6
+27.1
+81.4
+Road Inpaint. [72]
+
+
+-
+-
+54.1
+47.1
+82.9
+35.8
+-
+-
+-
+-
+-
+Max softmax [34]
+
+
+28.0
+72.1
+15.7
+16.6
+30.1
+33.2
+1.8
+44.9
+12.9
+39.8
+80.3
+MC Dropout [21]
+
+
+28.9
+69.5
+4.9
+50.3
+36.8
+35.6
+-
+-
+-
+-
+-
+ODIN [35]
+
+
+33.1
+71.7
+22.1
+15.3
+52.9
+30.0
+-
+-
+-
+-
+-
+SML [73]
+
+
+-
+-
+-
+-
+-
+-
+31.7
+21.9
+52.1
+20.5
+-
+Embed. Dens. [10]
+
+
+37.5
+70.8
+0.8
+46.4
+61.7
+10.4
+4.3
+47.2
+62.1
+17.4
+80.3
+JSRNet [19]
+
+
+33.6
+43.9
+28.1
+28.9
+74.2
+6.6
+-
+-
+-
+-
+-
+SynDenseHybrid (ours)
+
+
+51.5
+33.2
+64.0
+0.6
+78.8
+1.1
+51.8
+11.5
+54.7
+15.5
+79.9
+SynBoost [18]
+
+
+56.4
+61.9
+71.3
+3.2
+81.7
+4.6
+43.2
+15.8
+72.6
+18.8
+81.4
+Prior Entropy [74]
+
+
+-
+-
+-
+-
+-
+-
+34.3
+47.4
+31.3
+84.6
+70.5
+OOD Head [42]
+
+
+-
+-
+-
+-
+-
+-
+31.3
+19.0
+96.8
+0.3
+79.6
+Void Classifier [10]
+
+
+36.6
+63.5
+10.4
+41.5
+4.8
+47.0
+10.3
+22.1
+45.0
+19.4
+70.4
+Dirichlet prior [74]
+
+
+-
+-
+-
+-
+-
+-
+34.3
+47.4
+84.6
+30.0
+70.5
+DenseHybrid (ours)
+
+
+78.0
+9.8
+87.1
+0.2
+78.7
+2.1
+43.9
+6.2
+72.3
+5.5
+81.0
+significant computational overhead. Also, DenseHybridSyn
+achieves the best performance on all but one metric of
+Fishyscapes and the second-best AP on Fishyscapes Static.
+As in the case of training on real negative data, the hy-
+brid anomaly detector achieves the best performance on
+Fishyscapes with exception of AP on Static. Note that the
+presented performance evaluation uses standard perfor-
+mance metrics of the particular datasets. Our performance
+metrics on Fishyscapes LostAndFound would increase if we
+considered only the road pixels as in [19]. The rightmost
+column of the table indicates that our fine-tuning protocol
+exerts a negligible impact on closed-set performance. How-
+ever, the next section will show that the impact of anomaly
+detection on final recognition performance is more signifi-
+cant than what can be measured with closed-set metrics.
+Figure 6 shows synthetic negatives produced by the
+training setup from Sec. 4.2. Samples vary in spatial resolu-
+tion and lack meaningful visual concepts. Yet, training our
+open-set model on such samples yields only slightly worse
+performance than when training on real negative data.
+Fig. 6. Synthetic negatives produced by a normalizing flow trained as
+described in Sec. 4.2. These samples are pasted into training crops
+instead of real negative images (instances from ADE20k). We sample
+the normalizing flow at different resolutions in order to mimic real-world
+anomalies which vary in size.
+Table 2 presents performance on Road Anomaly [17]
+and on validation subsets of Fishyscapes. The top section
+presents methods which do not train on real negative data.
+The bottom section presents methods which train on real
+negative data. Our method performs competitively with
+respect to the previous works in both setups.
+TABLE 2
+Performance of DenseHybrid on Road Anomaly and Fishyscapes val.
+DenseHybrid delivers strong performance when trained with and
+without real negative images.
+Model
+RA
+FS L&F
+FS Static
+AP
+FPR
+AP
+FPR
+AP
+FPR
+MSP [34]
+15.7
+71.4
+4.6
+40.6
+19.1
+24.0
+ML [71]
+19.0
+70.5
+14.6
+42.2
+38.6
+18.3
+SML [73]
+25.8
+49.7
+36.6
+14.5
+48.7
+16.8
+SynthCP [43]
+24.9
+64.7
+6.5
+46.0
+23.2
+34.0
+Density [10]
+-
+-
+4.1
+22.3
+-
+-
+SynDenseHybrid
+35.1
+37.2
+59.5
+10.4
+49.0
+10.3
+SynBoost [18]
+38.2
+64.8
+60.6
+31.0
+66.4
+25.6
+OOD head [15]
+-
+-
+45.7
+24.0
+-
+-
+Energy [38]
+19.5
+70.2
+16.1
+41.8
+41.7
+17.8
+DenseHybrid
+63.9
+43.2
+60.5
+6.0
+63.1
+4.2
+We validate our method by considering a subset of
+Cityscapes void classes as the unknown class [40]. More
+precisely, we consider all void classes except ’unlabeled’,
+’ego vehicle’, ’rectification border’, ’out of roi’ and ’license
+plate’ as unknowns during validation. Table 3 compares
+performance according to the AUROC (AUC) metric. Syn-
+DenseHybrid outperforms all previous works. Most notably,
+it outperforms the previous state of the art [40] by three per-
+centage points. To offer fair comparison with previous work,
+we do not report results when training on real negative data
+since such data was not used in related work [40], [80].
+TABLE 3
+Open-set segmentation performance on Cityscapes val. Following [40],
+we consider a subset of ignored classes as unknowns.
+Method
+AUC
+Method
+AUC
+MSP [34]
+72.1
+GDM [81]
+74.3
+Entropy [82]
+69.7
+GMM [68]
+76.5
+OpenMax [50]
+75.1
+K+1 classifier
+75.5
+C2AE [80]
+72.7
+OpenGAN-O [40]
+70.9
+ODIN [35]
+75.5
+OpenGAN [40]
+88.5
+MC dropout [21]
+76.7
+SynDenseHybrid (ours)
+91.7
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+9
+6.2
+Open-set Segmentation
+We recover open-set segmentation by fusing a closed-set
+segmentation with properly thresholded dense anomaly
+detection (Fig. 3). Such model detects anomalous regions,
+while also correctly classifying inlier parts of the scene.
+We measure open-set performance on the StreetHazards
+dataset according to mean F1 (F1) score and the proposed
+open-mIoU (oIoU) metric. We partition the test subset into
+two folds which correspond to the two test cities - t5 and
+t6. We set the anomaly score threshold in order to obtain
+95% TPR on t5, and measure open-mIoU on t6. Subse-
+quently, we switch the folds and measure open-mIoU on
+t5. We compute the overall open-mIoU by weighting these
+two measurements according to the number of images in
+the two folds. Table 4 presents performance evaluation on
+StreetHazards. The left part of the table considers anomaly
+detection while the right part of the table considers closed-
+set and open-set segmentation performance. Our method
+outperforms contemporary approaches in anomaly detec-
+tion both with and without training on real negative data.
+Furthermore, our method achieves the best open-set per-
+formance (columns oIoU and F1) despite lower closed-set
+segmentation score (IoU column). The performance drop
+between closed-set and open-set can be quantified as the
+difference between IoU and oIoU (”Gap” column). Our
+method achieves the least performance gap of around 18
+perventage points. Nevertheless, an ideal anomaly detector
+would achieve equal open-set and closed-set metrics. Hence,
+we conclude that even the state-of-the-art anomaly detectors
+are still insufficient for delivering closed-set performance
+in open-set setups. Researchers should strive to further
+close this gap in order to improve the safety of recognition
+systems in the real world. We implemented [38], [84] into
+TABLE 4
+Performance evaluation on StreetHazards [71]. We evaluate anomaly
+detection (Anomaly), closed-set segmentation (Cls.), open-set
+segmentation (Open-set), and the open-set gap (Gap). Our
+DenseHybrid delivers competitive open-set performance.
+Method
+Anomaly
+Cls.
+Open-set
+Gap
+AP
+FPR
+AUC
+IoU
+F1
+oIoU
+SynthCP [43]
+9.3
+28.4
+88.5
+-
+-
+-
+-
+Dropout [21]
+7.5
+79.4
+69.9
+-
+-
+-
+-
+TRADI [83]
+7.2
+25.3
+89.2
+-
+-
+-
+-
+SO+H [31]
+12.7
+25.2
+91.7
+59.7
+-
+-
+-
+DML [51]
+14.7
+17.3
+93.7
+-
+-
+-
+-
+MSP [34]
+7.5
+27.9
+90.1
+65.0
+46.4
+35.1
+29.9
+ODIN [35]
+7.0
+28.7
+90.0
+65.0
+41.6
+28.8
+36.2
+ReAct [84]
+10.9
+21.2
+92.3
+62.7
+46.4
+34.0
+28.7
+SynDnsHyb
+19.7
+17.4
+93.9
+61.3
+50.6
+37.3
+24.0
+Energy [38]
+12.9
+18.2
+93.0
+63.3
+50.4
+42.7
+29.9
+OE [27]
+14.6
+17.7
+94.0
+61.7
+56.1
+43.8
+17.9
+OH [42]
+19.7
+56.2
+88.8
+66.6
+-
+33.9
+32.7
+OH*MSP [15]
+18.8
+30.9
+89.7
+66.6
+-
+43.6
+23.0
+DenseHybrid
+30.2
+13.0
+95.6
+63.0
+59.7
+45.8
+17.2
+our code base by following publicly available implemen-
+tations. For the energy fine-tuning [38], we found that the
+optimal hyperparameters for dense setup are min = −15
+and mout = −5. ReAct [84] delivers the best results when
+the method-specific hyperparameter c = 0.99. Note that [39]
+also reports performance on StreetHazards, however, they
+aim to detect classification errors instead of anomalies.
+Figure 7 visualises qualitative open-set segmentation
+performance on StreetHazards test. Our hybrid anomaly de-
+tector accurately combines dense anomaly detection (second
+row) with closed-set segmentation and delivers open-set
+segmentation (third row). We also show the energy-based
+approach [38] which yields more false positives (fourth
+row).
+DH Anomaly 
+Score
+DH Open-set 
+Segmentation
+Input
+Energy
+Ground
+Truth
+Fig. 7. Qualitative open-set segmentation performance on StreetHaz-
+ards. DenseHybrid (rows 2 and 3) has more accurate open-set perfor-
+mance compared to the energy-based approach [38](row 4), as denoted
+with red rectangles. Zoom in for a better view.
+6.3
+Ablating Components of our Hybrid Detector
+Table 5 validates components of our hybrid anomaly de-
+tection approach on Fishyscapes val. The top two sections
+compare our hybrid anomaly detector (7) with its generative
+and discriminative components – ˆp(x) and P(din|x) when
+training on real and synthetic negative data, respectively. We
+observe that the hybrid detector outperforms unnormalized
+density which outperforms dataset posterior. We observe
+the same qualitative behaviour when training on real and
+synthetic negative data. Interestingly, the synergistic effect
+of compound hybrid detection is larger in the case of
+synthetic negatives. This finding suggests that our hybrid
+formulation can compensate for incomplete coverage of the
+out-of-distribution manifold in test images.
+Bottom section replaces our unnormalized likelihood
+with likelihood of pre-logits as estimated by a normalizing
+flow. The flow is applied point-wise to obtain dense like-
+lihood, similar to embeding density [10]. This can also be
+viewed as a generalization of a previous image-wide open-
+set approach [41] on dense predictions. We still train on
+negative data in an end-to-end fashion in order to make
+the two generative components comparable. The resulting
+model behaves simlarly to embedding density [10] — good
+performance on FS Static and somewhat poorer perfor-
+mance on FS LostAndFound. Formulating dense likelihood
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+10
+with unnormalized density (4) delivers more consistent
+performance than a point-wise normalizing flow on top of
+latent representation.
+TABLE 5
+Validation of hybrid anomaly detection on Fishyscapes val. Hybrid
+anomaly detection outperforms its generative and discriminative
+components. This behaviour is consistent in models trained on real and
+synthetic negative data, as well as for different generative components.
+Anomaly detector
+Neg.
+FS L&F
+FS Static
+data
+AP
+FPR
+AP
+FPR
+Disc. (1 − P(din|x))
+46.5
+38.3
+53.5
+30.9
+Gen. ˆp(x)
+Real
+58.2
+7.3
+58.0
+5.3
+Hyb. (1 − P(din|x))/ˆp(x)
+60.5
+6.0
+63.1
+4.2
+Disc. (1 − P(din|x))
+30.9
+61.0
+29.4
+71.5
+Gen. ˆp(x)
+Syn.
+52.8
+13.1
+35.8
+11.1
+Hyb. (1 − P(din|x))/ˆp(x)
+59.5
+10.4
+49.0
+10.3
+Gen. p(z)
+Real
+5.7
+58.9
+61.7
+7.6
+Hyb. (1 − P(din|x))/p(z)
+6.5
+46.1
+65.1
+6.5
+6.4
+Impact of the Depth to the Detection Performance
+Road driving scenes typically involve a wide range of depth.
+Hence, we explore the anomaly detection performance at
+different ranges from the camera in order to gain a better
+insight into the performance of different methods. We per-
+form these experiments on LostAndFound test [12] since it
+allows us to compute the depth in each ground pixel. Due
+to errors in the provided disparity maps, we perform our
+analysis up to 50 meters from the camera. Table 6 indicates
+that DenseHybrid achieves accurate results even at large
+distances from the vehicle. We observe that SynBoost [18] is
+better than our approach at the shortest range. However, the
+computational complexity of image resynthesis precludes
+real-time deployment of such approaches [17], [18], [43] on
+present hardware as we show next.
+TABLE 6
+Anomaly detection performance at different distances from camera.
+Range
+MSP [34]
+ML [71]
+SynBoost [18]
+DH (ours)
+AP
+FPR
+AP
+FPR
+AP
+FPR
+AP
+FPR
+5-10
+28.7
+16.4
+76.1
+5.4
+93.7
+0.2
+90.7
+0.3
+10-15
+28.8
+29.7
+73.9
+16.2
+78.7
+17.7
+89.8
+1.1
+15-20
+26.0
+28.8
+78.2
+5.9
+76.9
+25.0
+92.9
+0.6
+20-25
+25.1
+44.2
+69.6
+12.8
+70.0
+23.3
+89.1
+1.4
+25-30
+29.0
+41.3
+72.6
+9.5
+65.6
+18.8
+89.5
+1.4
+30-35
+26.2
+47.8
+70.2
+10.0
+58.5
+27.4
+87.7
+2.5
+35-40
+29.6
+44.7
+71.0
+9.8
+59.8
+25.4
+85.0
+3.7
+40-45
+31.7
+43.2
+74.0
+9.8
+60.0
+25.8
+85.6
+4.7
+45-50
+33.7
+45.3
+73.9
+11.0
+53.3
+29.9
+82.1
+6.3
+6.5
+Inference speed
+Table 7 compares computational overheads of prominent
+anomaly detectors on two-megapixel images. All measure-
+ments are averaged over 200 runs on RTX3090. Dense-
+Hybrid involves a negligible computational overhead of
+0.1 GFLOPs and 2.8ms. These experiments indicate that
+image resynthesis is not applicable for real-time inference
+on present hardware.
+TABLE 7
+Computational overhead of prominent anomaly detectors over the
+baseline semantic segmentation model when inferring on
+two-megapixel images. The inference time is in milliseconds.
+Method
+Resynth.
+Inf. time
+FPS
+GFLOPs
+SynBoost [18]
+
+1055.5
+<1
+-
+SynthCP [43]
+
+146.9
+<1
+4551.1
+LDN-121 [75]
+
+60.9
+16.4
+202.3
+LDN-121 + SML [73]
+
+75.4
+13.3
+202.6
+LDN-121 + DH (ours)
+
+63.7
+15.7
+202.4
+7
+CONCLUSION
+Discriminative and generative approaches to anomaly de-
+tection assume different failure modes. We propose to
+achieve synergy between these two approaches by fusing
+the dataset posterior with unnormalized data likelihood. We
+refer to the resulting method as DenseHybrid since its low
+computational overhead and translational equivariance are
+especially well suited for dense prediction context. Dense-
+Hybrid eschews the evaluation of the intractable normal-
+ization constant by leveraging negative training data. It can
+be trained either on real negative data sourced from some
+general-purpose dataset, or on synthetic negative data gen-
+erated by a jointly trained normalizing flow. Finally, it can
+be easily attached to any closed-set segmentation approach
+in order to attain open-set competence. DenseHybrid yields
+competitive performance on the standard benchmarks for
+dense anomaly detection and open-set segmentation. We
+evaluate open-set segmentation performance according to
+a novel open-mIoU metric that quantifies the performance
+gap between closed-set and open-set conditions. Ablation
+experiments confirm the contributions of both components
+of hybrid anomaly detection. Suitable directions for future
+work include extending DenseHybrid towards open-set
+panoptics as well as towards further reduction of the per-
+formance gap between the closed-set and open-set setups.
+8
+LIMITATIONS
+It may seem that our method may generate samples due
+to likelihood evaluation being a standard feature of gener-
+ative models (except GANs). However, sample generation
+with unnormalized distributions requires MCMC sampling
+which can not be performed at large resolutions and dense
+loss, at least not with known techniques. Still, our hy-
+brid open-set model delivers competitive performance even
+without the ability to generate samples. Also, variety and
+quality of synthetic samples are limited by the capacity
+of the generative model, which will be mitigated with
+advances in GPU design.
+ACKNOWLEDGMENTS
+This work has been supported by Croatian Science Foun-
+dation grant IP-2020-02-5851 ADEPT, by NVIDIA Academic
+Hardware Grant Program, as well as by European Regional
+Development Fund grants KK.01.1.1.01.0009 DATACROSS
+and KK.01.2.1.02.0119 A-Unit.
+
+JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015
+11
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+Matej Grci´c received a M.Sc. degree from the
+Faculty of Electrical Engineering and Computing
+in Zagreb. He finished the master study program
+in Computer Science in 2020. He is pursuing his
+Ph.D. degree at University of Zagreb, FER. His
+research interests include generative modeling
+and open-world recognition.
+Siniˇsa ˇSegvi´c received a Ph.D. degree in com-
+puter science from the University of Zagreb,
+Croatia. He was a post-doctoral researcher at
+IRISA Rennes and also at TU Graz. He is cur-
+rently a full professor at Uni-ZG FER. His re-
+search interests focus on deep convolutional ar-
+chitectures for classification and dense predic-
+tion.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf,len=1587
+page_content='JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  1  Hybrid Open-set Segmentation  with Synthetic Negative Data  Matej Grci´c, Siniˇsa ˇSegvi´c  Abstract—Open-set segmentation is often conceived by complementing closed-set classification with anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Existing  dense anomaly detectors operate either through generative modelling of regular training data or by discriminating with respect to  negative training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' These two approaches optimize different objectives and therefore exhibit different failure modes Consequently,  we propose the first dense hybrid anomaly score that fuses generative and discriminative cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The proposed score can be efficiently  implemented by upgrading any semantic segmentation model with translation-equivariant estimates of data likelihood and dataset  posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our design is a remarkably good fit for efficient inference on large images due to negligible computational overhead over the  closed-set baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resulting dense hybrid open-set models require negative training images that can be sampled either from an  auxiliary negative dataset or from a jointly trained generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We evaluate our contributions on benchmarks for dense anomaly  detection and open-set segmentation of traffic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The experiments reveal strong open-set performance in spite of negligible  computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Index Terms—Open-set segmentation, Open-set recognition, Out-of-distribution detection, Anomaly detection, Semantic  segmentation, Synthetic data, Normalizing flows  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  1  INTRODUCTION  H  IGH accuracy, fast inference and small memory foot-  print of modern neural networks [1], [2] steadily ex-  pand the horizon of downstream applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Many ex-  citing applications require advanced image understanding  functionality provided by semantic segmentation [3], [4],  [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' These models associate each pixel with a class from  a predefined taxonomy [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' They can accurately segment  two megapixel images in real-time on low-power embedded  hardware [7], [8], [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, standard training proce-  dures assume closed-world setup, which may raise serious  safety issues in real-world deployments [10], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' For ex-  ample, if a segmentation model missclassifies an unknown  object (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' lost cargo) as road, the autonomous car may  experience a serious accident [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Such hazards can be  alleviated by complementing semantic segmentation with  dense anomaly detection [13], [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resulting open-set  segmentation models [15] are fitter for real applications due  to ability to decline decisions in unknown scene parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Previous approaches for open-set segmentation assume  either a generative or a discriminative perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Gener-  ative approaches are based on density estimation [16] or  image resynthesis [17], [18], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Discriminative approaches  use classification confidence [20], dataset posterior [15] or  Bayesian inference [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, the two perspectives ex-  hibit different failure modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Generative anomaly detectors  inaccurately disperse the probability volume [22], [23], [24],  [25] or face the hazards of image resynthesis [17], [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' On  the other hand, discriminative anomaly detectors require  training on negative content from some general-purpose  auxiliary dataset [15], [18], [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Such training may involve  an overlap between training negatives and test set anoma-  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Grci´c and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' ˇSegvi´c are with University of Zagreb, Faculty of Electrical  Engineering and Computing, Unska 3, 10000 Zagreb, Croatia  E-mail: {matej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='grcic,sinisa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='segvic}@fer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='hr  Manuscript received January 19, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  lies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence, the evaluation may lead to over-optimistic per-  formance estimates and surprising failures in production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  In this work, we combine the two perspectives by de-  signing a hybrid anomaly detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The proposed approach  complements a chosen closed-set semantic segmentation  model with unnormalized dense dataset likelihood ˆp(x) and  dense data posterior P(din|x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Fusion of these two outputs  yields an effective yet efficient dense anomaly detector  which we refer to as DenseHybrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Both components of  our anomaly detector require training with negative data  [15], [18], [26], [27], [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We present a way to relieve that  dependence by leveraging synthetic negative data sourced  from a generative model [28], [29], [30], [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Consequently,  our experiments evaluate performance with and without  real negative training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  This paper extends our preliminary conference report  [32] by allowing our dense hybrid models to train without  real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We achieve that by generating synthetic  negative samples with a jointly trained normalizing flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Different from previous work [31], the normalizing flow  does not receive the gradients from the training objectives  for anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Such design ensures correct con-  vergence of the normalziing flow in view of a complex  formulation of the anomaly score, and provides a stronger  learning signal to the dataset posterior head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our new  experiments explore open-set performance without training  on real negative data and compare our unnormalized den-  sity estimator with respect to a general-purpose generative  module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Finally, we substantially revise our presentation by  supplying a more comprehensive review of the related work  and improved descriptions of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Our consolidated work brings forth the following contri-  butions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' First, we propose the first hybrid anomaly detector  that allows end-to-end training, translational equivariance,  and pixel-level predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The proposed DenseHybrid  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='08555v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='CV]  19 Jan 2023  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  2  SMIYC-ObstacleTrack  LostAndFound  Fishyscapes Static  StreetHazards  Road Anomaly  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Qualitative performance of the proposed DenseHybrid approach on standard datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Top: input images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Bottom: dense maps of the  proposed anomaly score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Unknown pixels are assigned with higher anomaly scores designated in yellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Such a highly accurate anomaly detector  enables us to derive the open-set segmentation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  method combines unnormalized density and discriminative  dataset posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Both of these two components involve  minimal computational overhead and require training on  negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Second, we extend our approach by allowing  it to learn only on inlier images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This configuration lever-  ages synthetic negative data that correspond to generated  samples at the boundary of the inlier distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Third, we  propose open-mIoU as a novel performance metric for open-  set segmentation in safety-critical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The main  strength of the novel metric is exact quantification of the  gap between closed-set and open-set setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Fourth, our  DenseHybrid anomaly detector can be easily attached to  any closed-set segmentation approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resulting open-  set segmentation algorithm delivers very competitive per-  formance on standard benchmarks in road-driving scenes  with and without training on real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  2  RELATED WORK  The related work considers anomaly detection (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1 and  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2), open-set recognition (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3), training open-set  recognition on synthetic data (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4), as well as progres-  sion towards open-world recognition (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  Image-wide Anomaly Detection  Detecting samples which deviate from the generative pro-  cess of the training data is a decades old problem [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  In the machine learning community, this task is also  known as anomaly detection, novelty detection and out-of-  distribution (OOD) detection [13], [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Early image-wide  approaches utilize max-softmax probability [34], input per-  turbations [35] ensembling [36] or Bayesian uncertainty [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  More encouraging performance has been attained through  discriminative training against real negative data [15], [27],  [37], [38], adversarial attacks [39] or samples from appro-  priate generative models [28], [29], [31], [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Another line  of work detects anomalies by estimating the likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Surprisingly, this research reveals that anomalies may give  rise to higher likelihood than inliers [22], [23], [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Gener-  ative models can mitigate this problem by sharing features  with the primary discriminative model [41] and training on  negative data [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  Pixel-wise Anomaly Detection  Image-wide anomaly detection can be adapted for dense  prediction with variable success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Some of the existing  image-wide approaches [41] are not applicable in dense  prediction context, while others do not perform well [35]  or involve excessive computational complexity [35], [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  On the other hand, concepts such as discriminative train-  ing with negative data [27], [37], [42] are easily ported to  dense prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence, several dense anomaly detectors  are trained on mixed-content images obtained by pasting  negatives (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' ImageNet, COCO, ADE20k) over regular  training images [15], [18], [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Dataset posterior can be  recovered by a dedicated head that shares features with the  standard semantic segmentation head [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Anomalies can also be recognized in feature space [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  However, this approach complicates detection of small ob-  jects due to subsampling and feature collapse [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Orthog-  onally, anomaly detector can be implemented according to  learned dissimilarity between the input and the resynthe-  sised image [17], [18], [19], [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resynthesis is per-  formed by a generative model conditioned on the predicted  labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, this approach is suitable only for uniform  backgrounds such as roads [17], and offline applications  due to significant computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Besides dense  anomaly detection in road driving scenes, some approaches  consider applications in industrial facilities [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However,  these setups are less relevant for our open-set algorithms  since they do not involve the primary discriminative task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Different than all previous work, we propose the first  hybrid anomaly detector for dense prediction models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In  comparison with previous approaches that build on dataset  posterior [15], [27], [37], our method introduces synergy  with likelihood evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In comparison with approaches  that recover dense likelihood [10], our method introduces  joint hybrid training and efficient joint inference together  with standard semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our method is also  related to joint energy-based models [45], since we also  reinterpret logits as unnormalized joint likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' How-  ever, their method has to backprop through the intractable  normalization constant and is therefore unsuitable for large  resolutions and dense prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our method completely  avoids sampling by recovering unnormalized likelihood  and training on negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Concurrent approaches [46],  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  3  [47] consider only the generative component of our hybrid  anomaly detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  Open-set recognition  Open-set recognition assumes presence of test examples that  transcend the training taxonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Such examples are also  known as semantic anomalies [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' During inference, the  model has to recognize semantic anomalies and withhold  (or reject) the decision [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The rejection mechanism can  be implemented by restricting the shape of the decision  boundary [49], [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This can be carried out by thresholding  the distance from learned class centers in the embedding  space [49], [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Recognition performance can be further  improved through employing a stronger classifier [52], [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Alternatively, the rejection mechanism can emerge by com-  plementing the classifier with an anomaly detector [14], [34],  [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The anomaly detector then detects samples which do  not belong to the known classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We direct the reader to [54]  for a comprehensive overview of open-set approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Most open-set approaches quantify performance by sep-  arate evaluation of closed-set recognition and anomaly de-  tection [10], [34], [55], [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, such practice does  not reveal degradation of discriminative predictions due  to errors in anomaly detection [57], [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This is especially  pertinent to dense prediction models where we can observe  inlier and outlier pixels in the same image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Recent work  proposes a solution for the related problem of semantic  segmentation in adverse conditions [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Their uncertainty-  aware UIoU metric takes into account prediction confidence  as measured by the probability of the winning class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' How-  ever, UIoU assumes that each pixel belongs to one of the  K known classes, which makes it inapplicable for open-set  recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Different than all previous work, our anomaly-  aware open-IoU metric specializes for evaluation of open-set  segmentation in presence of outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' It takes into account  both false positive semantic predictions at outliers as well  as false negative semantic predictions due to false positive  anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Furthermore, the difference between  mIoU and open-mIoU reveals the performance gap due to  presence of outliers in the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  Synthetic data in open-set recognition  Recent seminal approaches train open-set recognition mod-  els on synthetic negative data produced by a jointly trained  generative adversarial network (GAN) [28], [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The GAN  is trained to generate inlier data that give rise to low  recognition scores for each known class [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However,  GANs are biased towards limited distribution coverage [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Consequently, they are unlikely to span the whole space  of possible outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Thus, more promising results were  achieved by mixing real and synthetic negative samples [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Alternatively, GANs can be replaced with generative  models that optimize likelihood in order to improve dis-  tributional coverage [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This task calls for efficient ap-  proaches that support fast sampling since joint training  requires sample generation on the fly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This puts at disad-  vantage many interesting generative models such as au-  toregressive PixelCNN and energy-based models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Normal-  izing flows are a great candidate for this role due to fast  training and capability to quickly generate samples with  different resolutions [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Instead of targeting negative data,  a generative model can also target negative features [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  This can be carried out by modelling inlier features and  sampling synthetic anomalies from low-likelihood regions  of feature space [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Negative data have also been crafted  by leveraging adversarial perturbations [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  Beyond open-set recognition  Anomalous images or pixels can be clustered into new se-  mantic classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This can be done in incremental [61], [62] or  zero/one/few-shot [63] setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, these approaches  are still unable to compete with supervised learning on  standard datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We direct reader to [64] for better analysis  of pros and cons of low-shot learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  3  HYBRID SCORE FOR ANOMALY DETECTION  We propose a dense hybrid anomaly score that improves  upon discriminative and generative anomaly detection (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The new hybrid anomaly score can be efficiently fused  with a semantic classifier (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We represent the input images with a random variable x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Variable yij denotes the corresponding label at the location  (i, j), while binary random variable dij models whether a  given pixel belongs to the inliers or outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We write dij  in  for inliers and dij  out for outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We denote a realization of a  random variable without the underline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Thus, P(yij|x) is a  shortcut for P(yij = yij|x = x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' For brevity, we often omit  spatial locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  Hybrid Anomaly Detection for Dense Prediction  Generative and discriminative approaches to anomaly de-  tection exhibit different failure modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2 illustrates the  shortcomings of both approaches on a toy problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Blue  dots designate inlier data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Green triangles designate the neg-  ative data used for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Red squares denote anomalous  test data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Discriminative detectors model dataset posterior  P(dout|x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' They fail if the negative training data does not  cover the entire negative manifold (left) [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' On the other  hand, generative detectors which model p(x) tend to in-  accurately distribute probability volume over the sample  space [22], [23], [24] (center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We fuse discriminative and  generative approaches into a hybrid detector that alleviates  the aforementioned limitations (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We build our hybrid anomaly detector upon the discrim-  inative dataset posterior P(din|x) and the generative data  likelihood p(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We express a novel hybrid anomaly score  as log-ratio between P(dout|x) = 1 − P(din|x) and p(x):  s(x) := ln P(dout|x)  p(x)  = ln P(dout|x) − ln p(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (1)  We will further show that this formulation is especially  suitable for dense predictions atop the dense classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' There  may be other effective formulations of s(x), which is an  interesting direction for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  4  Discriminative P(dout|x)  Generative p(x)  Hybrid P(dout|x)/p(x)  Inlier data  Negative training data  Outlier test data  FPR=11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0%  FPR=24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0%  FPR=9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5%  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Anomaly detection on a toy dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The discriminative approach (left) models the dataset posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' It fails if the negative training dataset  fails to cover all modes of the test anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The generative approach (middle) models the data likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' It may assign high likelihoods to test  anomalies [22] due to over-generalization [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The hybrid approach attains a synergy between discriminative and generative modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  Efficient Implementation Atop Semantic Classifier  Standard semantic classification can be viewed as a two-step  procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Given an input image x, a deep feature extractor  fθ1 computes an abstract representation z also known as  pre-logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The computed pre-logits are projected into logits  s, and activated by softmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The softmax output is defined  as class posterior probability P(y|x):  P(y|x) := softmax(s)y, where s = fθ2(z), z = fθ1(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (2)  In practice, fθ1 is an encoder-decoder architecture common  for semantic segmentation and fθ2 is a simple projection by  means of 1x1 convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We extend this framework with  dense data likelihood and discriminative dataset posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Dense data likelihood can be conveniently derived atop  dense classifier by re-interpreting logits as unnormalized  joint probability of input and label [45]:  p(y, x) = 1  Z ˆp(y, x) := 1  Z exp sy, where  s = fθ2(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (3)  Z denotes the corresponding normalization constant depen-  dent only on model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' As usual, Z is finite but in-  tractable, since it requires computing the unnormalized dis-  tribution for all realizations of y and x: Z = �  x  �  y exp sy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Throughout this work, we conveniently eschew the evalua-  tion of Z in order to enable efficient training and inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We express the dense likelihood p(x) by marginalizing  out y:  p(x) =  �  y  p(y, x) = 1  Z  �  y  ˆp(y, x) = 1  Z  �  y  exp sy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (4)  Standard discriminative predictions are easily recovered  through Bayes rule p(y, x)/p(x):  P(y|x) =  p(y, x)  �  y′ p(y′, x) =  exp sy  �  y′ exp sy′ = softmax(s)y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (5)  The normalization constant Z appears both in the numer-  ator and denominator, and hence can be cancelled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Reinterpretation of logits as unnormalized joint probability  enables likelihood estimation atop a discriminative classifier  task and even exploiting pretrained classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that  adding a constant value to the logits does not affect the  standard classification but affects our framework since the  value of p(x) changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence, we use the extra degree of  freedom in logits to express the data likelihood [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The  same extra degree of freedom has been used to model a  discriminator network in semi-supervised learning [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We define the dataset posterior P(din|x) as a non-linear  transformation based on pre-logits z [15]:  P(din|x) := σ(gγ(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (6)  In our case, the function g is BN-ReLU-Conv1x1 of pre-  logits, followed by a sigmoid non-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We can now compute the proposed dense hybrid  anomaly score (1) atop the classifier as:  s(x) := ln P(dout|x) − ln ˆp(x) + ln Z  (7)  ∼= ln P(dout|x) − ln ˆp(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (8)  We can neglect Z since ranking performance [34] is invariant  to monotonic transformations such as taking a logarithm  or adding a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that the logarithmic function  re-scales the unnormalized ˆp(x) and P(dout|x) on approx-  imately the same scale, equalizing the influence of both  components in the final decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resulting formulation  (7) is especially well suited for dense prediction due to  minimal overhead and translation equivariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Figure 3 illustrates dense inference with the proposed  hybrid open-set setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' RGB input is fed to a hybrid dense  model which produces pre-logit activations z and logits s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We activate the closed-set class posterior P(y|x) with soft-  max and the unnormalized data log-likelihood ln ˆp(x) via  log-sum-exp operator (designated in green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' A distinct head  g transforms pre-logits z into the dataset posterior P(dout|x)  (designated in yellow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The anomaly score s(x) is a log ratio  between the latter two outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resulting anomaly map  is thresholded and fused with the discriminative output into  the final dense open-set recognition map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  4  OPEN-SET TRAINING WITH DENSEHYBRID  Our open-set approach complements an arbitrary closed-  set segmentation model with the DenseHybrid anomaly  detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We propose a novel training setup that eschews the  intractable normalization constant by introducing negative  data to the generative learning objective (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The same  negative data are used to train the dataset posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We  relax dependence on real negatives by sampling a suitably  trained normalizing flow (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  PR=95%JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  5  Threshold  Fuse  P(y|x)  Input  Open-set  segmentation  Dense anomaly score  DenseHybrid  s(x) = Projection  z  Feature  extractor  Log-sum-exp  BN-ReLU-Conv  ln p(x)  P(din|z)  s  Softmax  σ  Feature  extractor  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The proposed open-set segmentation approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our anomaly  score is the log-ratio of dense data likelihood and discriminative dataset  posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Both outputs are derived from the standard dense classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We formulate open-set segmentation by complementing the closed-set  segmentation map with the thresholded anomaly score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  Open-set training with real negative data  The multi-task model from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 3 requires joint fine-tuning  of three dense prediction heads: i) closed-set class posterior  P(y|x), ii) unnormalized data likelihood ˆp(x) [45], and iii)  dataset posterior P(din|x) [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The class-posterior head  requires a discriminative loss over the inlier dataset Din:  Lcls(θ) = Ex,y∈Din[− ln P(y|x)]  (9)  = − Ex,y∈Din[sy − ln  �  y′  exp sy′].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (10)  Training unnormalized likelihood is a daunting task  since backpropagation through p(x) involves intractable  integration over all possible images [66], [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Previous  solutions are based on MCMC sampling [45], however, this  is not feasible in our setup due to high-resolution inputs and  dense prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We eschew the normalization constant by  optimizing the likelihood both in inlier and outlier pixels:  Lx(θ) = Ex∈Din[− ln p(x)] − Ex∈Dout[− ln p(x)]  (11)  = −Ex∈Din[ln ˆp(x)] − ln Z + Ex∈Dout[ln ˆp(x)] + ln Z  (12)  = − EDin  �  ln  �  i  exp(si)  �  + EDout  �  ln  �  i  exp(si)  �  (13)  As before, s stands for logits computed by fθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that the  normalization constant Z cancels out due to training on out-  liers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In practice, we use a simplified loss that corresponds  to an upper bound of the above expression (LUB  x  ≥ Lx):  LUB  x (θ) = − Ex,y∈Din[sy] + Ex∈Dout[ln  �  i  exp(si)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (14)  Proof can be easily derived by recalling that log-sum-exp is  a smooth upper bound of the max function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Thus, our upper  bound LUB  x  leverages the following inequalities:  ln  �  i  exp si ≥ max  i  si ≥ sy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (15)  Comparison of the discriminative loss (9) and the gen-  erative upper bound (14) reveals that the standard clas-  sification loss is well aligned with the upper bound in  inlier pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Recall that training data likelihood only on  inliers [45], [66] would require MCMC sampling, which is  infeasible in our context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Unnormalized likelihood could  also be trained through score matching [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, this  would preclude hybrid modelling due to having to train  on noisy inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Consequently, it appears that the proposed  training approach is a method of choice in our context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The dataset-posterior head P(din|x) requires a discrimi-  native loss that distinguishes the inlier dataset Din from the  outlier dataset Dout [15]:  Ld(θ, γ) = −Ex∈Din[ln P(din|x)]  − Ex∈Dout[ln(1 − P(din|x))].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (16)  Our final compound loss aggregates Lcls, LUB  x  and Ld:  L(θ, γ) = −Ex,y∈Din[ln P(y|x) + ln P(din|x)]  − β · Ex∈Dout[ln(1 − P(din|x)) − ln ˆp(x)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (17)  Hyperparameter β controls the impact of negative data to  the primary classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that we omit the first  term from LUB  x  (14) in inlier pixels since this is implicitly  enforced through optimization of Lcls (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Figure 4 illustrates the described procedure for training  open-set segmentation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We prepare mixed-content  training images x′ by pasting negative patches x− into  regular training images x+:  x′ = (1 − s) · x+ + pad(x−, m),  x− ∈ Dout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (18)  Note that here we leverage real negative images x− ∈ Dout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We consider synthetic negatives in the subsequent subsec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The binary mask m identifies negative pixels within  the mixed-content image x′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Negative pixels are labelled as  dout while positive pixels are labelled as din.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Semantic labels  of negative pixels are set to void.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The resulting mixed-content image x′ is fed to the de-  sired semantic segmentation model that produces pre-logits  z and logits s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We recover the class posterior P(y|x) by  activating logits with softmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We recover the unnormalized  log-likelihood ln ˆp(x) by processing logits with log-sum-  exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We recover dataset posterior P(d + in|x) by processing  pre-logit activations with the standard BN-ReLU-Conv1 × 1  unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The compound training loss L(θ, γ) (17) aggregates  class-discriminative loss Lcls (9), generative loss LUB  x  (14)  and dataset-discriminative loss Ld (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  Open-set training with synthetic negative data  Anomaly detectors can avoid biased predictions by replac-  ing real negative training data with samples of a suitable  generative model [28], [30], [31], [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The generative model  has to be trained to generate synthetic samples that encom-  pass the border of the inlier distribution [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The required  learning signal can be derived from discriminative predic-  tions [28], [30], [31] or provided by an adversarial module  [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence, replacing real negative data with synthetic  counterparts requires joint training of the generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We choose a normalizing flow [69] for this task due to  exceptional distributional coverage and ability to quickly  generate samples of varying spatial dimensions [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We  train the normalizing flow pζ according to a weighted sum  of two loss terms: Lmle and Ljsd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The data term Lmle  corresponds to negative log-  likelihood of random crops from inlier images x+:  Lmle(ζ) = −Ex+∈Din[ln pζ(crop(x+))].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (19)  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  6  Sample  instance  Input image  Synthetic  negative  Paste  Mixed content image  Ground truth  Traffic  Scenes  z ~ N(0, I)  Normalizing  Flow (hζ)  Random  crop  Lmle  L(ζ)  Ljsd  L(ζ)  Shared weights  x-  x+  x’  Soft  Max  BN  ReLU  Conv  Sum  Exp  Lcls  Lx  Ld  L(Θ,Ɣ)  t  s  z  Projection  Feature  extractor  Normalizing  Flow (h-1  ζ)  Auxiliary  Dataset  OR  Synthetic negatives  Real negatives  crop(x+)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The two training procedures for the proposed open-set training with DenseHybrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We construct mixed-content images by pasting negatives  into inlier images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The negative training data can be sampled either from an auxiliary real dataset (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1) or from a jointly trained normalizing flow  (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Mixed-content images are fed to the open-set model with three dense outputs: closed-set class posterior, unnormalized likelihood, and  dataset posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Outputs are optimized according to the compound loss (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In the case of synthetic negatives, the normalizing flow optimizes  the loss (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The crop notation mirrors the pad notation from (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Ran-  dom crops vary in spatial resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This term aligns the  generative distribution with the distribution of the training  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' It encourages coverage of the entire inlier distribution  under the condition that the generative model has sufficient  capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The boundary-attraction term Ljsd [70] corresponds to  negative Jensen-Shannon divergence between the class-  posterior and the uniform distribution at all generated pix-  els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This term pushes the generative distribution towards the  periphery of the inlier distribution where the class posterior  should be unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that gradients of this term must  propagate through the entire semantic model in order to  reach the normalizing flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence, the flow is penalized  when the generated sample yields high softmax confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  This signal pushes the generative distribution away from  high-density regions of the input space [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The total loss of the normalizing flow modulates the  contribution of the boundary term with the hyperparameter  λ:  L(ζ) = Lmle(ζ) + λ · Ljsd(ζ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' θ)  (20)  Optimization of this loss enforces the generative distribution  to encompass all modes of inlier distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that our  normalizing flow can never match the diversity of images  from a real dataset such as COCO or ADE20k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' It would  be unreasonable to expect a generative model to draw a  sofa after training on Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Still, if the flow suc-  ceeded to learn well the boundary of the inlier distribution,  then DenseHybrid would be inclined to recognize all off-  distribution samples as anomalies [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Details of the training procedure are again illustrated in  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We sample the normalizing flow by i) selecting a  random spatial resolution (H,W) from a predefined interval,  ii) sampling a random latent representation z ∼ N(0, IHW ),  and iii) feeding z to the flow so that x− = h−1  ζ (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We again  craft a mixed-content image x′ by pasting the synthesized  negative patch x− into the regular training image x+ ac-  cording to (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We perform the forward pass, determine  Lcls, Ld, Lx, and Ljsd, and recover the training gradients by  backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Of course, gradient of Ljsd is propagated  all the way to the normalizing flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We now take the deleted  inlier patch x+  s , perform inference with the normalizing  flow (z = hζ(x+  s )) and accumulate gradients of Lmle before  performing a model-wide parameter update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  5  EXPERIMENTAL SETUP  We describe benchmarks and datasets used for the evalua-  tion of DenseHybrid in dense anomaly detection and open-  set segmentation experiments (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We propose a new  metric to adequately quantify the gap between the open-set  and closed-set performance (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Also, we present the  main implementation details of our solution (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  Benchmarks and Datasets  We evaluate performance on standard benchmarks for  dense  anomaly  detection  and  open-set  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Fishyscapes [10] considers urban scenarios on a subset of  LostAndFound [12] and on Cityscapes validation images  with pasted anomalies (FS Static).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' SegmentMeIfYouCan  (SMIYC) [56] collects carefully selected images from the real  world and groups them with respect to the anomaly size  into AnomalyTrack (large) and ObstacleTrack (small).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' More-  over, the benchmark includes a selection of images of the  LostAndFound dataset [12] in which the lost objects do not  correspond to the Cityscapes taxonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Unfortunately, both  benchmarks supply only binary labels, which makes them  inappropriate for evaluating open-set performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence,  we report only anomaly detection performance on these  benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We also validate performance on Cityscapes  while reinterpreting a subset of ignore classes as the un-  known class [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  StreetHazards [71] is a synthetic dataset created with  CARLA virtual environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The simulated environment  enables smooth anomaly injection and low-cost label extrac-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Consequently, the dataset contains K+1 labels, making  it suitable for measuring open-set recognition performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  Measuring open-set performance  Previous work evaluates open-set segmentation through  anomaly detection [12], [56] and closed-set segmentation  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  7  [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The reported drop in closed-set performance is usu-  ally negligible and is explained by the allocation of model  capacity for anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, we will show that  the impact of anomalies onto segmentation performance can  be clearly characterized only in the open-set setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' More  precisely, we shall take into account false positive semantic  predictions at anomalies as well as false negative semantic  predictions due to false anomaly detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We propose a novel evaluation procedure for open-set  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our procedure starts by thresholding the  anomaly score so that it yields 95% TPR anomaly detection  on held-out data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This is equivalent to the 5th percentile  of inlier scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Then, we override the classification in pixels  which score higher than the threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This yields a recogni-  tion map with K+1 labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We assess open-set segmentation  performance according to a novel metric that we term open-  mIoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We compute open-IoU for the k-th class as follows:  open-IoUk =  TPk  TPk + FPos  k + FNos  k  ,  where  (21)  FPos  k =  K+1  �  i=1,i̸=k  FPi  k,  FNos  k =  K+1  �  i=1,i̸=k  FNi  k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  (22)  Different that the standard IoU formulation, open-IoU takes  into account false positives and false negatives caused by  applying imperfect anomaly detectors at open-set pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In  particular, a prediction of class k at an outlier pixel (false  negative anomaly detection) counts as a false positive for  class k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Furthermore, a prediction of class K+1 at a pixel  labelled as class k (false positive anomaly detection) counts  as a false negative for class k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that we still average  open-IoU over K inlier classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Thus, a recognition model  with perfect anomaly detection gets assigned the same  performance as in the closed world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that this property  would not be preserved if we averaged open-IoU over K+1  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence, a comparison between closed-set mIoU and  open-set open-mIoU quantifies the gap between the open  and closed-set performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Some experiments report F1  score averaged over K+1 classes [40], [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, mF1  can not be used to quantify the performance gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Figure 5 compares the closed-set (left) and open-set  (right) evaluation protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Imperfect anomaly detection  impacts recognition performance through increased false  positive semantics (designated in yellow) and false nega-  tive semantics (designated in red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The difference between  closed-set mIoU and open-mIoU reveals the performance  drop due to inaccurate anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Measuring performance according to open-mIoU re-  quires datasets with K+1 labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Collecting and annotating a  dataset with such taxonomy requires substantial resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Currently, only StreetHazards [71] offers this opportunity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  Implementation Details  The proposed approach can be easily applied to any pre-  trained semantic segmentation baseline: the only require-  ment is access to pre-logit features and dense logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We  append an additional branch gγ which is in our case  BN-ReLU-Conv1x1, to compute the discriminative dataset  posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We obtain unnormalized likelihood as the sum  1  2  3  k  K  K+1  1  2  3  k  K  K+1  TPA FPA  FNA TNA  1  0  1  0  TPRA =  TPA  TPA + FNA  Σ  i = 1  i ≠ k  K+1  FNos  k=  FNi  k  open-IoUk =  TPk  TPk + FPos  k + FNos  k  A  A  Closed-set segmentation  Anomaly detection  Open-set segmentation  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  FN2  k  FN3  k  FP1  k FP2  k FP3  k  FPK  k FPA  k  FNK  k  FNA  k  FN1  k  TPk  1  2  3  k  K  1  2  3  k  K  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  FN2  k  FN3  k  FP1  k FP2  k FP3  k  FPK  k  FNK  k  FN1  k  TPk  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  A  A  Σ  i = 1  i ≠ k  K+1  FPos  k=  FPi  k  Σ  i = 1  i ≠ k  K  FNk=  FNi  k  IoUk =  TPk  TPk + FPk + FNk  Σ  i = 1  i ≠ k  K  FPk=  FPi  k  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We extend closed-set performance evaluation (left) with a  novel open-set metric (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Open-IoU takes into account false positive  semantics at anomalies as well as false negative semantics due to  false anomaly detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The proposed open-mIoU metric quantifies  recognition performance in presence of anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  of exponentiated logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We fine-tune the resulting open-  set models on mixed-content images with pasted negative  ADE20k instances (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1) or synthetic negative patches (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  In the case of SMIYC, we fine-tune LDN-121 [75] for 10  epochs on images from Cityscapes [76], Vistas [77] and Wild-  dash2 [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In the case of Fishyscapes, we use DeepLabV3+  with WideResNet38 [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We fine-tune the model for 10  epochs on Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In the case of StreetHazards, we train  LDN-121 for 120 epochs in the closed-world setting and then  fine-tune the open-set model on mixed-content images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Configurations that do not rely on real negative data  leverage synthetic data of varying resolution as generated  by DenseFlow-45-6 [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' All such experiments pre-train  DenseFlow with the standard MLE loss on 64 × 64 crops  from road-driving images prior to joint learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our fine-  tuning experiments last less than 24h on RTX A5000 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Our source code is publicly available [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  6  EXPERIMENTAL RESULTS  We evaluate DenseHybrid performance in dense anomaly  detection (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1) and open-set segmentation (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2)  experiments, after training with and without real negative  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We also ablate the design choices (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3), explore  the influence of distance (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4), and present the compu-  tational requirements of the proposed module (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  Dense Anomaly Detection in Open-set Setups  Table 1 presents dense anomaly detection performance on  SMIYC [56] and Fishyscapes [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We include our model  trained on real negative data (DenseHybrid) as well as  our model trained on synthetic negatives (SynDenseHy-  brid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' DenseHybrid outperforms contemporary approaches  on both AnomalyTrack and ObstacleTrack by a wide mar-  gin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Also, it achieves the best FPR95 on LostAndFound-  noKnown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Similarly, it delivers the best performance on  Fishyscapes LostAndFound and the best FPR95 on Static.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  DenseHybridSyn outperforms all previous methods that  do not train on real negative data on ObstacleTrack and  LostAndFound-noKnown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' In the case of AnomalyTrack, it  is outperformed only by image resynthesis [17] that requires  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  8  TABLE 1  Anomaly detection performance on SegmentMeIfYouCan [56] and Fishyscapes [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Aux data denotes training on real negatives, while Img rsyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  denotes image resynthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Method  SegmentMeIfYouCan [56]  Fishyscapes [10]  Aux  Img  AnomalyTrack  ObstacleTrack  LAF-noKnown  FS LAF  FS Static  CS val  data  rsyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  AP  FPR95  AP  FPR95  AP  FPR95  AP  FPR95  AP  FPR95  IoU  Image Resyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' [17]  \x17  \x13  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  Road Inpaint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' [72]  \x17  \x13 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8 Max softmax [34]  \x17  \x17  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  MC Dropout [21]  \x17  \x17  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6 ODIN [35]  \x17  \x17  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0 SML [73]  \x17  \x17 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5 Embed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Dens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' [10]  \x17  \x17  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
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+page_content='4  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  JSRNet [19]  \x17  \x17  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6 SynDenseHybrid (ours)  \x17  \x17  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  SynBoost [18]  \x13  \x13  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  Prior Entropy [74]  \x13  \x17 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  OOD Head [42]  \x13  \x17 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  Void Classifier [10]  \x13  \x17  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  Dirichlet prior [74]  \x13  \x17 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  DenseHybrid (ours)  \x13  \x17  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  significant computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Also, DenseHybridSyn  achieves the best performance on all but one metric of  Fishyscapes and the second-best AP on Fishyscapes Static.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  As in the case of training on real negative data, the hy-  brid anomaly detector achieves the best performance on  Fishyscapes with exception of AP on Static.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that the  presented performance evaluation uses standard perfor-  mance metrics of the particular datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our performance  metrics on Fishyscapes LostAndFound would increase if we  considered only the road pixels as in [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The rightmost  column of the table indicates that our fine-tuning protocol  exerts a negligible impact on closed-set performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' How-  ever, the next section will show that the impact of anomaly  detection on final recognition performance is more signifi-  cant than what can be measured with closed-set metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Figure 6 shows synthetic negatives produced by the  training setup from Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Samples vary in spatial resolu-  tion and lack meaningful visual concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Yet, training our  open-set model on such samples yields only slightly worse  performance than when training on real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Synthetic negatives produced by a normalizing flow trained as  described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' These samples are pasted into training crops  instead of real negative images (instances from ADE20k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We sample  the normalizing flow at different resolutions in order to mimic real-world  anomalies which vary in size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Table 2 presents performance on Road Anomaly [17]  and on validation subsets of Fishyscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The top section  presents methods which do not train on real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  The bottom section presents methods which train on real  negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our method performs competitively with  respect to the previous works in both setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  TABLE 2  Performance of DenseHybrid on Road Anomaly and Fishyscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  DenseHybrid delivers strong performance when trained with and  without real negative images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Model  RA  FS L&F  FS Static  AP  FPR  AP  FPR  AP  FPR  MSP [34]  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  ML [71]  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  SML [73]  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  SynthCP [43]  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  Density [10] 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3 SynDenseHybrid  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  SynBoost [18]  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  OOD head [15] 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0 Energy [38]  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  DenseHybrid  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  We validate our method by considering a subset of  Cityscapes void classes as the unknown class [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' More  precisely, we consider all void classes except ’unlabeled’,  ’ego vehicle’, ’rectification border’, ’out of roi’ and ’license  plate’ as unknowns during validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Table 3 compares  performance according to the AUROC (AUC) metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Syn-  DenseHybrid outperforms all previous works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Most notably,  it outperforms the previous state of the art [40] by three per-  centage points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' To offer fair comparison with previous work,  we do not report results when training on real negative data  since such data was not used in related work [40], [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  TABLE 3  Open-set segmentation performance on Cityscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Following [40],  we consider a subset of ignored classes as unknowns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Method  AUC  Method  AUC  MSP [34]  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  GDM [81]  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  Entropy [82]  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  GMM [68]  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  OpenMax [50]  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  K+1 classifier  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  C2AE [80]  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  OpenGAN-O [40]  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  ODIN [35]  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  OpenGAN [40]  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  MC dropout [21]  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  SynDenseHybrid (ours)  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  Open-set Segmentation  We recover open-set segmentation by fusing a closed-set  segmentation with properly thresholded dense anomaly  detection (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Such model detects anomalous regions,  while also correctly classifying inlier parts of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  We measure open-set performance on the StreetHazards  dataset according to mean F1 (F1) score and the proposed  open-mIoU (oIoU) metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We partition the test subset into  two folds which correspond to the two test cities - t5 and  t6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We set the anomaly score threshold in order to obtain  95% TPR on t5, and measure open-mIoU on t6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Subse-  quently, we switch the folds and measure open-mIoU on  t5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We compute the overall open-mIoU by weighting these  two measurements according to the number of images in  the two folds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Table 4 presents performance evaluation on  StreetHazards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The left part of the table considers anomaly  detection while the right part of the table considers closed-  set and open-set segmentation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our method  outperforms contemporary approaches in anomaly detec-  tion both with and without training on real negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Furthermore, our method achieves the best open-set per-  formance (columns oIoU and F1) despite lower closed-set  segmentation score (IoU column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The performance drop  between closed-set and open-set can be quantified as the  difference between IoU and oIoU (”Gap” column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our  method achieves the least performance gap of around 18  perventage points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Nevertheless, an ideal anomaly detector  would achieve equal open-set and closed-set metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hence,  we conclude that even the state-of-the-art anomaly detectors  are still insufficient for delivering closed-set performance  in open-set setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Researchers should strive to further  close this gap in order to improve the safety of recognition  systems in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We implemented [38], [84] into  TABLE 4  Performance evaluation on StreetHazards [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We evaluate anomaly  detection (Anomaly), closed-set segmentation (Cls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' ), open-set  segmentation (Open-set), and the open-set gap (Gap).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our  DenseHybrid delivers competitive open-set performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Method  Anomaly  Cls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Open-set  Gap  AP  FPR  AUC  IoU  F1  oIoU  SynthCP [43]  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5 Dropout [21]  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9 TRADI [83]  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
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+page_content='6  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  our code base by following publicly available implemen-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' For the energy fine-tuning [38], we found that the  optimal hyperparameters for dense setup are min = −15  and mout = −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' ReAct [84] delivers the best results when  the method-specific hyperparameter c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Note that [39]  also reports performance on StreetHazards, however, they  aim to detect classification errors instead of anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Figure 7 visualises qualitative open-set segmentation  performance on StreetHazards test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Our hybrid anomaly de-  tector accurately combines dense anomaly detection (second  row) with closed-set segmentation and delivers open-set  segmentation (third row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We also show the energy-based  approach [38] which yields more false positives (fourth  row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  DH Anomaly  Score  DH Open-set  Segmentation  Input  Energy  Ground  Truth  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Qualitative open-set segmentation performance on StreetHaz-  ards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' DenseHybrid (rows 2 and 3) has more accurate open-set perfor-  mance compared to the energy-based approach [38](row 4), as denoted  with red rectangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Zoom in for a better view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  Ablating Components of our Hybrid Detector  Table 5 validates components of our hybrid anomaly de-  tection approach on Fishyscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The top two sections  compare our hybrid anomaly detector (7) with its generative  and discriminative components – ˆp(x) and P(din|x) when  training on real and synthetic negative data, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We  observe that the hybrid detector outperforms unnormalized  density which outperforms dataset posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We observe  the same qualitative behaviour when training on real and  synthetic negative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Interestingly, the synergistic effect  of compound hybrid detection is larger in the case of  synthetic negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This finding suggests that our hybrid  formulation can compensate for incomplete coverage of the  out-of-distribution manifold in test images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Bottom section replaces our unnormalized likelihood  with likelihood of pre-logits as estimated by a normalizing  flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The flow is applied point-wise to obtain dense like-  lihood, similar to embeding density [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This can also be  viewed as a generalization of a previous image-wide open-  set approach [41] on dense predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We still train on  negative data in an end-to-end fashion in order to make  the two generative components comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The resulting  model behaves simlarly to embedding density [10] — good  performance on FS Static and somewhat poorer perfor-  mance on FS LostAndFound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Formulating dense likelihood  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  10  with unnormalized density (4) delivers more consistent  performance than a point-wise normalizing flow on top of  latent representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  TABLE 5  Validation of hybrid anomaly detection on Fishyscapes val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hybrid  anomaly detection outperforms its generative and discriminative  components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' This behaviour is consistent in models trained on real and  synthetic negative data, as well as for different generative components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Anomaly detector  Neg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  FS L&F  FS Static  data  AP  FPR  AP  FPR  Disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (1 − P(din|x))  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' ˆp(x)  Real  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  Hyb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (1 − P(din|x))/ˆp(x)  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  Disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (1 − P(din|x))  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' ˆp(x)  Syn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  Hyb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (1 − P(din|x))/ˆp(x)  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' p(z)  Real  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  Hyb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' (1 − P(din|x))/p(z)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  Impact of the Depth to the Detection Performance  Road driving scenes typically involve a wide range of depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Hence, we explore the anomaly detection performance at  different ranges from the camera in order to gain a better  insight into the performance of different methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We per-  form these experiments on LostAndFound test [12] since it  allows us to compute the depth in each ground pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Due  to errors in the provided disparity maps, we perform our  analysis up to 50 meters from the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Table 6 indicates  that DenseHybrid achieves accurate results even at large  distances from the vehicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We observe that SynBoost [18] is  better than our approach at the shortest range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, the  computational complexity of image resynthesis precludes  real-time deployment of such approaches [17], [18], [43] on  present hardware as we show next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  TABLE 6  Anomaly detection performance at different distances from camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Range  MSP [34]  ML [71]  SynBoost [18]  DH (ours)  AP  FPR  AP  FPR  AP  FPR  AP  FPR  5-10  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  10-15  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  15-20  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  20-25  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
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+page_content='1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  Inference speed  Table 7 compares computational overheads of prominent  anomaly detectors on two-megapixel images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' All measure-  ments are averaged over 200 runs on RTX3090.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Dense-  Hybrid involves a negligible computational overhead of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1 GFLOPs and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='8ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' These experiments indicate that  image resynthesis is not applicable for real-time inference  on present hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  TABLE 7  Computational overhead of prominent anomaly detectors over the  baseline semantic segmentation model when inferring on  two-megapixel images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' The inference time is in milliseconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Method  Resynth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' time  FPS  GFLOPs  SynBoost [18]  \x13  1055.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='5  <1 SynthCP [43]  \x13  146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  <1  4551.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1  LDN-121 [75]  \x17  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='9  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  LDN-121 + SML [73]  \x17  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='3  202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='6  LDN-121 + DH (ours)  \x17  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='7  202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='4  7  CONCLUSION  Discriminative and generative approaches to anomaly de-  tection assume different failure modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We propose to  achieve synergy between these two approaches by fusing  the dataset posterior with unnormalized data likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We  refer to the resulting method as DenseHybrid since its low  computational overhead and translational equivariance are  especially well suited for dense prediction context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Dense-  Hybrid eschews the evaluation of the intractable normal-  ization constant by leveraging negative training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' It can  be trained either on real negative data sourced from some  general-purpose dataset, or on synthetic negative data gen-  erated by a jointly trained normalizing flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Finally, it can  be easily attached to any closed-set segmentation approach  in order to attain open-set competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' DenseHybrid yields  competitive performance on the standard benchmarks for  dense anomaly detection and open-set segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' We  evaluate open-set segmentation performance according to  a novel open-mIoU metric that quantifies the performance  gap between closed-set and open-set conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Ablation  experiments confirm the contributions of both components  of hybrid anomaly detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Suitable directions for future  work include extending DenseHybrid towards open-set  panoptics as well as towards further reduction of the per-  formance gap between the closed-set and open-set setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  8  LIMITATIONS  It may seem that our method may generate samples due  to likelihood evaluation being a standard feature of gener-  ative models (except GANs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' However, sample generation  with unnormalized distributions requires MCMC sampling  which can not be performed at large resolutions and dense  loss, at least not with known techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Still, our hy-  brid open-set model delivers competitive performance even  without the ability to generate samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Also, variety and  quality of synthetic samples are limited by the capacity  of the generative model, which will be mitigated with  advances in GPU design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This work has been supported by Croatian Science Foun-  dation grant IP-2020-02-5851 ADEPT, by NVIDIA Academic  Hardware Grant Program, as well as by European Regional  Development Fund grants KK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0009 DATACROSS  and KK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='0119 A-Unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  JOURNAL OF LATEX CLASS FILES, VOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 14, NO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 8, AUGUST 2015  11  REFERENCES  [1]  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Sun, “Deep residual learning for  image recognition,” in 2016 IEEE Conference on Computer Vision and  Pattern Recognition, CVPR 2016, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 770–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  [2]  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Wei, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Lin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Guo,  “Swin transformer: Hierarchical vision transformer using shifted  windows,” in 2021 IEEE/CVF International Conference on Computer  Vision, ICCV 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' 9992–10 002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
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+page_content='  [83] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Franchi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Bursuc, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Aldea, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Dubuisson, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Bloch,  “TRADI: tracking deep neural network weight distributions,” in  16th European Conference on Computer Vision, ECCV, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  [84] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Sun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Guo, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' Li, “React: Out-of-distribution detection  with rectified activations,” in NeurIPS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Matej Grci´c received a M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' degree from the  Faculty of Electrical Engineering and Computing  in Zagreb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' He finished the master study program  in Computer Science in 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' He is pursuing his  Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' degree at University of Zagreb, FER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' His  research interests include generative modeling  and open-world recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='  Siniˇsa ˇSegvi´c received a Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' degree in com-  puter science from the University of Zagreb,  Croatia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' He was a post-doctoral researcher at  IRISA Rennes and also at TU Graz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' He is cur-  rently a full professor at Uni-ZG FER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
+page_content=' His re-  search interests focus on deep convolutional ar-  chitectures for classification and dense predic-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdFAT4oBgHgl3EQfbB3C/content/2301.08555v1.pdf'}
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+Predictive World Models from Real-World Partial
+Observations
+1st Robin Karlsson
+Graduate School of Informatics
+Nagoya University
+Nagoya, Japan
+karlsson.robin@g.sp.m.is.nagoya-u.ac.jp
+2nd Alexander Carballo
+Department of Electrical, Electronic and Computer Engineering
+Gifu University
+Gifu, Japan
+alex@gifu-u.ac.jp
+3rd Keisuke Fujii
+Graduate School of Informatics
+Nagoya University
+Nagoya, Japan
+fujii@i.nagoya-u.ac.jp
+4th Kento Ohtani
+Graduate School of Informatics
+Nagoya University
+Nagoya, Japan
+ohtani.kento@g.sp.m.is.nagoya-u.ac.jp
+5th Kazuya Takeda
+Graduate School of Informatics
+Nagoya University, TIER IV
+Nagoya, Japan
+kazuya.takeda@nagoya-u.jp
+Abstract—Cognitive scientists believe adaptable intelligent
+agents like humans perform reasoning through learned causal
+mental simulations of agents and environments. The problem of
+learning such simulations is called predictive world modeling.
+Recently, reinforcement learning (RL) agents leveraging world
+models have achieved SOTA performance in game environments.
+However, understanding how to apply the world modeling ap-
+proach in complex real-world environments relevant to mobile
+robots remains an open question. In this paper, we present a
+framework for learning a probabilistic predictive world model
+for real-world road environments. We implement the model using
+a hierarchical VAE (HVAE) capable of predicting a diverse set of
+fully observed plausible worlds from accumulated sensor obser-
+vations. While prior HVAE methods require complete states as
+ground truth for learning, we present a novel sequential training
+method to allow HVAEs to learn to predict complete states from
+partially observed states only. We experimentally demonstrate
+accurate spatial structure prediction of deterministic regions
+achieving 96.21 IoU, and close the gap to perfect prediction
+by 62 % for stochastic regions using the best prediction. By
+extending HVAEs to cases where complete ground truth states do
+not exist, we facilitate continual learning of spatial prediction as a
+step towards realizing explainable and comprehensive predictive
+world models for real-world mobile robotics applications. Code
+released after publication.
+Index Terms—World model, generative model, partial observ-
+ability, BEV generation, autonomous vehicles, self-supervised
+learning
+I. INTRODUCTION
+Cognitive scientists believe cognition in adaptable intel-
+ligent agents like humans is founded on a small number
+of foundational components for representing the world in
+terms of inanimate objects, goal-directed agents, number sys-
+tems and sets, social partners and groups, and geometry of
+environments [1]. These cognitive abilities allow intelligent
+agents to perform common-sense physical reasoning to facil-
+itate accomplishment of tasks [2]. One ability is to predict
+multiple plausible long-tail outcomes of a sequence of actions,
+and perform counterfactual reasoning [3]–[5] through causal
+Fig. 1. The framework integrates observations into a common vector space
+representing the partially observed world state. A predictive world model
+samples a set of diverse plausible complete world states. The model improves
+through continual learning from experience by predicting future observations.
+1
+arXiv:2301.04783v1  [cs.CV]  12 Jan 2023
+
+Sensor observations
+BEV projections
+p(road)
+Intensity
+Accumulation
+in vector space
+个
+Sampled plausible worlds
+Probabilistic
+integration
+Predictive
+world model
+Improve model
+Accumulated future partial observations
+Self-supervised
+learningmental simulations of the world. Another ability is to imagine
+different plausible spatial configurations of unobserved regions
+of the world based on past experience. The problem of
+learning such simulations is called predictive world modeling
+in machine learning [6], [7], [12].
+The explicit world modeling approach provides several
+potential advantages over implicit predictive models learned
+as part of the task; data efficiency as policies can be opti-
+mized through simulation, long-tail planning and reasoning by
+search, explicit representation of agent’s knowledge and state
+space coverage, explainable sequential decision processes, and
+improved domain generalization by enabling planning over
+abstract latent structures decoupled from particular observable
+appearance (i.e. pixels). The advantage of world models is
+demonstrated by recent model-based reinforcement learning
+(RL) methods like Dreamer V2 [8] demonstrating better per-
+formance than SOTA model-free RL methods like IQN [9] and
+Rainbow [10] on Atari environments [11] when compared by
+the same amount of compute and wall-clock time. However,
+understanding how to learn and apply the world modeling
+approach in visually complex real-world environments relevant
+to autonomous vehicles (AV) and other mobile robots remains
+an open question. Learning world models of real-world envi-
+ronments is associated with challenges. Agent observations are
+perceptually complex, making it difficult to decompose obser-
+vations into consistent and distinct semantic objects, in turn
+making relationship learning infeasible. Percepts are generally
+agent-centric, partial observations due to occlusion and limited
+sensor observation reach, meaning explicitly inferring the
+complete world state is difficult if not impossible. World state
+transition dynamics resulting from multi-agent interactions
+are generally stochastic and complex. Tasks are generally
+specified vaguely and lack rich reward signals. In contrast to
+game environments, experience gathering is radically limited
+in real-world environments, as failure may have unacceptable
+consequences and generally prohibit learning world states
+primarily by exploration.
+Mobile robots like AVs typically perform motion plan-
+ning on the assumption that the spatial environment is fully
+known [13], [14]. This assumption is conventionally satisfied
+through localizing the agent within point cloud maps encoded
+with layers of human annotated HD map information about the
+environment [15]. However, solely relying on a priori maps
+has demerits [16]. Map generation proves difficult to scale,
+as creating maps require labor-intensive human annotation
+and regular updating as environments change. Dependence
+on maps for navigation renders the agent inoperable in case
+of loading or localization failure, as well as in unmapped
+environments. Additionally, changes in the environment not
+reflected in the map may result in unsafe behavior.
+This work proposes a framework for learning probabilistic
+predictive world models for real-world spatial environments
+from self-supervised learning using sensor observations. We
+implement the world model based on the recent SOTA hier-
+archical VAE (HVAE) model Very Deep VAE (VDVAE) [17]
+capable of representing and sampling general and spatially
+large real-world environments by a compact latent code while
+preserving fine detail. We introduce two novel components
+to overcome the fact that the original VDVAE model cannot
+learn to predict complete states from partially observed states
+only. First, we demonstrate how to generate pseudo-complete
+states using a combination of latent variable predictive and
+an adversarial modeling. Secondly, we present an approach to
+enable HVAEs to predict a diverse set of complete states from
+single partial state by learning to match the latent variable
+distributions between the partial and pseudo-complete states.
+By enabling learning from partial observations generated
+by sensor information, our predictive world model becomes
+capable of improving from new experiences obtained during
+operation akin to continual learning [18]–[20]. The model can
+avoid catastrophic forgetting by retaining a replay buffer of
+past experiences [21].
+We consider a structured state description of the spa-
+tial world as a discrete, agent-centric, 2.5D homogeneous
+gridmap to represent probabilistic spatiosemantic informa-
+tion of the environment as observed and predicted by the
+agent. The gridmap is considered a well-established and ade-
+quate approach for representing spatial information in mobile
+robotics [23] and compatible with potent generative image
+modeling approaches in machine learning.
+We propose several useful mobile robotics applications; ro-
+bust and safe planning by taking into account diverse sampled
+structures for unobserved regions; improve localization match-
+ing success through densifying observations and predicting
+plausible structure of unobserved regions; and verify map
+consistency with the actual perceived environment.
+The contributions of our paper are fourfold:
+• A new conceptual approach to predict a diverse set of
+plausible, fully observed, real-world spatial environments
+by a predictive world model and sensor observations.
+• A novel method to train a HVAE to predict complete
+states from partially observed states only.
+• A holistic mobile robotics framework tying together real-
+world sensor observations and world modeling as a self-
+supervised learning problem.
+• Demonstrate accurately spatial structure prediction of
+deterministic regions achieving 96.21 % IoU with 1
+sample, and close the gap to perfect prediction by 62 %
+for stochastic regions using the best prediction out of 32
+samples.
+II. RELATED WORK
+A. Arbitrary conditional density estimation
+The problem of arbitrary conditional density estimation
+[24]–[26] is about estimating the probability distributions
+p(xu|xo), where the random variables x are expected to be
+partitioned into arbitrary plausible subsets of observed xo
+and unobserved xu random variables. In this section we
+present methods incorporating different application-specific
+presumptions on how x is partitioned into xo and xu.
+Image inpainting methods predict unobserved pixels xu
+from observed pixels xo. The problem formulation is similar
+2
+
+to the problem of predicting complete world states from
+partially observed states. The prototypical solution is to use an
+autoencoder (AE) [27] to compress partially observed images
+xo into constrained latent codes z encoding similar visual
+patterns as learned from reconstructing complete images x by
+matching global contextual clues.
+However, optimizing models simply by pixel-wise recon-
+struction is afflicted by the marginalization problem, resulting
+in blurry outputs as missing regions can be filled by many
+plausible pixel configurations. The Context encoder [28] at-
+tempts to address the blurriness problem by introducing an
+adversarial objective. Furthermore, GLCIG [29] introduces a
+course-to-fine generation scheme with diluted convolutions
+and two adversarial objectives. The global objective ensures
+the image remains coherent as a whole, while the local
+objective improves detail. Yeh et al. [30] finds the closest
+sample in an image database and use its latent code for
+prediction. Contextual attention [31] adds an attention mecha-
+nism for long-distance information crossover. Our framework
+similarly applies and adversarial objective for learning to
+predict texture-like content such as lidar reflectance intensity
+from road surface (henceforth, road surface intensity).
+Other approaches focus on learning mask-aware convolu-
+tional filters. Liu et al. [32] introduces a special convolution
+filter and a observed element mask update rule for propagating
+information about which elements provide information. Yu et
+al. [33] introduces gated convolutions for learned mask updat-
+ing. While we add an observed element mask to the model
+input following the missing data VAE approach, explicitly
+convoluting over masks is an interesting future direction.
+Another line of image inpainting works focus on pluralis-
+tic stochastic state completion methods based on generative
+models. GAN-based methods [34], [35] generates multiple
+plausible completions by conditioning on a random vector.
+VAE-based methods [36] replaces the deterministic latent
+code generated by the AE to allow stochastic sampling
+of multiple plausible predictions. Previous methods improve
+training stability by constraining the latent distribution of
+partially observed images by matching the distribution for fully
+observed images. PIC-Net [37] trains separate encoders for
+observable and unobservable image regions, and matches the
+distributions between the two. UCTGAN [38] adds a cross
+attention module to mix latent representations of partially and
+fully observed images. DSI-VQVAE [39] applies VQVAE to
+stabilize training. Concurrently to our work, Posterior Match-
+ing [22] presents arbitrary conditioning based on HVAEs by
+optimizing a secondary partially observed encoder to match
+the latent distributions of a fully observed encoder. We extend
+prior VAE work by introducing a two-stage training paradigm
+to allow learning to predict complete images from partially
+observed images only.
+Another approach frames predicting unobserved state vari-
+ables from observed variables as the missing data VAE prob-
+lem. HI-VAE [40] derives an evidence lower bound (ELBO)
+for missing data by masking out contributions from unob-
+served data. EDDI [41] introduces an alternative Partial VAE
+model which processes observable data only by encoding ele-
+ments by a positional encoding and processed by permutation
+invariant operations similarly to PointNet [42]. VAEM [43] is
+a hierarchical VAE that operates on heterogeneous data by
+first transforming all input variables into a common latent
+space by a type-specific transformation. HH-VAEM [44] is a
+recent hierarchical VAE demonstrating effective sampling us-
+ing the Hamiltonian Monte Carlo algorithm. Collier et al. [45]
+demonstrate results on high-dimensional image data. Our work
+extends prior missing data VAE approaches by learning to
+model p(xu|xo) for high-dimensional representations without
+requiring fully observed ground truth samples for training.
+Video prediction methods aims to model a stochastic state
+transition process where a sequence of future images xu are
+predicted conditioned on a sequence of past fully observed
+images xo. Babaeizadeh [46] presents a sequential stochastic
+variational video prediction model based on predicting a
+latent code explaining away the stochasticity of the sequence.
+Denton [47] presents a end-to-end framework to explain away
+stochasticity by a frame-to-frame latent code and a learned
+prior to improve training robustness. Our work reformulates
+the stochastic latent variable video prediction approach of
+Denton to the problem of predicting complete world states
+from partially observed world states only.
+B. Bird’s-eye-view generation
+Mobile robotics, and in particular AVs, pursue the problem
+of generating top-down bird’s-eye-view (BEV) representations
+from perception inputs as a substitute or complement to human
+annotated maps [16].
+Camera-based methods receive much attention because of
+affordability and motivation by human vision. However, lift-
+ing 2D perspective images to 3D is fundamentally an ill-
+posed problem. Inverse perspective mapping (IPM) [48]–[50]
+propose to overcome the problem by assuming the ground
+plane is flat. However, the flat plane assumption is generally
+not true. Stereo cameras propose to solve the lifting problem
+by inferring depth maps based on physics. However, the
+resulting depth maps tend to be noisy for far-away objects,
+object borders, and objects covered with non-distinct textures.
+Learning-based methods are proposed to overcome the weak-
+nesses of stereo based depth map estimation. Cam2BEV [51]
+presents an approach that projects semantic features using
+IPM and corrects the projection by a spatial transformer
+module learned from synthetic ground truth BEVs. Many
+works are based on using monocular depth estimation [52]–
+[57] to lift images to a 3D point cloud before projection
+to a top-down 2D grid. Schulter et al. [58] proposes an
+adversarial objective relying on ground truth maps to refine
+the resulting BEV representation. MonoLayout [59] learns the
+view transformation from self-supervised targets by integrating
+projected observations while still relying on ground truth maps
+for BEV refinement. Later works introduce probabilistic depth
+projection [60], categorical depth distribution network [61],
+and multi-task learning [62]. VED [63] is a variational en-
+coder trained from stereo vision to predict low-dimensional
+3
+
+(64x64 px) semantic BEV representations from forward view
+monocular images. Other methods lift images using multilayer
+perceptrons (MLP) trained on ground truth maps [64]–[66].
+Recently, cross-attention based transformer modules [67], [68]
+and Transformers modules [69] are applied to model view
+transformations motivated by the global attention mechanism
+not being limited to process neighboring pixel information like
+CNNs. However, due to lacking inductive biases attention-
+based models tend to require more data, effort, and compute to
+train as well as for inference. While our framework in principle
+is compatible with depth estimation, we choose to leverage
+lidar for substantial improvements in representation accuracy
+and observation integration performance. Additionally, our
+generative model can generate diverse plausible predictions,
+unlike view transformation models which typically are deter-
+ministic functions.
+Lidar-based BEV generation methods have a significant
+advantage from explicitly measuring distance though deemed
+prohibitively expensive for mass deployment by some. Fishing
+Net [66] utilizes lidar information to improve spatial accuracy
+of BEVs generated by sensor fusion. MP3 [70] uses a learned
+module for generating map elements from lidar observations
+and ground truth map supervision. HDMapNet [71] also
+include image information. In contrast to these methods, our
+framework does not rely on preexisting ground truth maps for
+supervised training. Our method is also generative and can
+provide diverse predictions, which is fundamentally necessary
+as the correct prediction for occluded regions are generally
+indeterminable.
+C. Spatial AI
+Simultaneous localization and mapping (SLAM) [72]–[74]
+is the conventional robotics approach to map 3D spatial
+environments. SLAM works by computing the translation and
+rotation transformation to optimally match sequential point
+clouds. Knowing the transformation allows accumulation of
+point clouds in a common reference frame or vector space.
+Our framework integrates sensor observations using the same
+principle. Another component of SLAM is loop closure op-
+timization when previously traversed spaces are revisited.
+Our framework can be considered as adding a predictive
+component to SLAM.
+Neural Radiance Fields (NeRF) [75] is a recent approach
+to represent 3D objects [76], [78] and environments [77], [79]
+by neural networks. While NeRFs can interpolate between
+observations they do not extrapolate beyond what is observed
+like our framework.
+D. World models
+The idea of learning a predictive model of the world in
+machine learning was first introduced by Schmidhuber [6], [7],
+[12]. A common approach is to learn latent state representa-
+tions from images using a VAE [80]–[82], and use the learned
+latent code as a compact representation of the world state
+for planning actions. Other works use adversarial learning to
+optimize the latent code [83], [84], or contrastive learning with
+latent variables to model stochastic transition processes [85].
+Another line of work focus on inferring a set of object
+encodings from images. Watters et al. [86] uses a variational
+encoder to infer a fixed set of latent object encoding vectors
+from a sequence images. Later works apply a VAEs to learn
+semantically richer object embeddings [87], [88]. MONet [89]
+is a prominent model for learning to extract a variable amount
+of semantic object encodings using a recurrent attention
+module. Recent works leveraging MONet demonstrate the
+merits of explicit object discovery for future state prediction
+using compositional reasoning [90], and for reinforcement
+learning [8], [91] surpassing the performance of SOTA model-
+free RL models [9], [10].
+Our work approaches the world modeling problem of
+learning to predict a 2D spatiosemantic representation from
+agent-centric partial observations. We hope our method will
+contribute towards bridging recent SOTA world modeling
+approaches from game environments to partially observed real-
+world mobile robotics environments.
+III. GENERATING PARTIAL WORLD STATES
+This section describes the process of turning a sequence
+of sensor observations into partially observed world states.
+We conceptualize our approach as the most elementary and
+general way of achieving spatiosemantic cognition based on
+projecting and integrating observations into a common metric
+vector space. See Fig. 2 for a visual overview.
+A. Sensor observation processing
+Perception sensor configurations for mobile robots are
+primarily composed of two types of physical light sensing
+mechanism with complementary strengths and weaknesses.
+First, active sensing lidars to accurately represent metric space
+using point clouds. Secondly, passive sensing cameras for
+representing rich semantic information of the environment.
+Sensor fusion approaches aim at leveraging the complimentary
+strengths of both vision modalities [66].
+Semantic point clouds is the natural data structure for repre-
+senting both spatial and semantic information. Image content
+can be projected to a 3D point cloud if pixel-wise depth and
+camera calibration parameters are known [92]. In principle
+monocular [55], [93], [131], [132] or stereo vision [94]–[97]
+can provide depth maps and enable a vision-only perception
+configuration equivalent to biological vision systems [98].
+However, we opted for a sensor fusion approach as current
+depth estimation methods result in excessively noisy estimates
+compared with lidar measurements.
+Our framework processes observations as follows. First, the
+agent is instantiated within an unknown metric vector space.
+Next, sensor observations are projected onto a common vector
+space by known intrinsic and extrinsic calibration parameters
+of each sensor with respect to the agent [99]. For simplicity we
+assume all sensor observations are synchronized into discrete
+timesteps. We first infer semantics from images using a pre-
+trained semantic segmentation model [100] that partitions the
+4
+
+Fig. 2. Perception pipeline for transforming synchronized sensor observations into BEVs by projection into a common vector space. A semantic segmentation
+model interprets images. The inferred semantics are attached to the point clouds. Multiple semantic point clouds are temporally integrated into an ego-centric
+reference frame. BEVs are generated by projecting and probabilistically integrating all semantic points into a 2D discretized grid.
+Fig. 3.
+Temporal accumulation turns sparse observations (i.e. present) into
+dense representations (i.e. past and future). Partitioning the accumulated
+semantic point cloud in past and future observation subsets provide a natural
+self-supervised learning signal. Left figures show “road” (yellow) and “not-
+road” (purple) semantics. Right figures show height information.
+Fig. 4. Examples of geometrically diverse set of training samples generated
+from a single set of real observations using data augmentation.
+image into distinct semantic regions. The 3D point cloud is
+projected onto the image frame resulting in a one-to-many
+mapping between semantic pixels and 3D points. The semantic
+information is appended to all respective points. Points without
+semantic information are discarded.
+The set of all encounterable object semantics cannot be
+defined a priori in the open-world assumption. However, it
+is always possible to infer whether or not any new novel
+object possesses a known semantic. Following this principle,
+we semantically partition the static environment into “road”
+and “not-road” observations. Dynamic objects are not part of
+the static environment and should be ignored. For simplicity
+we infer all dynamic objects as “not-road” observations and
+generally rely on temporal observation integration to filter
+out the resulting noise. The noise resulting from cars is
+problematic, as cars are large, abundant, and often parked on
+the road. For this reason we infer “car” semantics as a special
+case for filtering out excessive noise. Alternatively dynamic
+objects can be removed by applying a filtering method [101],
+[102].
+The resulting representation is an agent-centric 3D semantic
+point cloud as visualized in the top row of Fig. 3.
+B. Temporal observation accumulation
+The agent collects a sequence of temporally ordered se-
+mantic point clouds during operation. The goal is to integrate
+all observations into a single vector space centered on the
+agent. The least assumptions approach to estimate motion
+is by computing the transformation optimally matching two
+sequential observations by point cloud registration also known
+as scan matching [23]. We found that the iterative closest point
+(ICP) algorithm [103] on unfiltered point clouds results in
+a simple but sufficiently accurate and robust implementation
+for accumulating observations covering 80 × 80 m2 suburban
+road environments without revisitation. The agent trajectory is
+computed from the sequence of transformations.
+ICP takes the previous and latest point cloud and computes
+the transformation aligning the previous point cloud p(t) to
+the latest one p(t+1). This transformation matrix Tt→t+1
+correspond to the agent motion during the time difference
+between the two observations as shown in (1). We update the
+relative position of all previously accumulated point clouds
+P (t) to ˜P (t+1) every time step recursively by applying the
+transformation as a matrix multiplication as in (2). Finally
+we add the new observations p(t+1) to the transformed ac-
+cumulated observations
+˜P (t+1), resulting in a new set of
+accumulated observations P (t+1) as in (3)
+5
+
+Sensor observations
+Semantic segmentation
+Present
+Past
+Future
+Semantics
+Intensity
+Semantic point
+[BEV projection
+cloud
+Accumulation
+(BEV projection)
+in vector spacePresent
+轮车
+Past
+FutureTt→t+1 = ICP(p(t), p(t+1))
+(1)
+˜P (t+1) = Tt→t+1P (t)
+(2)
+P (t+1) = concatenate( ˜P (t+1), p(t+1)).
+(3)
+Fig. 2 show the agent trajectory from lidar odometry as a
+line. See Fig. 3 for a visual demonstration of accumulated
+semantic point clouds.
+C. Partial world state representation
+Accumulated observations are projected onto homogeneous
+probabilistic grids representing world states. In contrast to 3D
+point clouds, 2D discrete grids can be processed by convolu-
+tional neural networks (CNN) [104] forming the backbone of
+recent potent generative models for images [17], [105]–[107].
+The projection is performed as follows. First, we initialize a
+2D grid x(c) spanning (I, J) elements covering a rectangular
+spatial region with lengths (H, W) for each semantic class or
+value c ∈ (1, . . . , C). Next, the accumulated semantic point
+cloud P is projected onto the grids.
+We represent semantic information by beta distributions
+p(x(c)
+i,j = True) modeling the Bayesian probability of element
+(i, j) represent a semantic c. This formulation allows a single
+element to represent several semantics. The beta distribution
+is computed by counting the number of semantic points that
+confirm or refutes the semantic within each grid element [108].
+Note that probability distributions allows representing igno-
+rance or lack of knowledge. For example, if a grid element
+have no observations, the distribution p(x(road)
+i,j
+) is uniform,
+indicating unknown uncertainty. Value information, like road
+surface lidar intensity measurements, are expressed as Gaus-
+sian distributions representing the mean and standard deviation
+of all observations encompassed by the grid element. Finally,
+we concatenate all probabilistic and scalar 2D grids into a 3D
+tensor representation x. See Fig. 2 and Fig. 4 for partial world
+state representation visualizations.
+IV. PREDICTIVE WORLD MODEL
+The predictive world model samples diverse and plausible
+complete worlds conditioned on partially observed worlds
+as illustrated in Fig. 1. We implement the world model as
+an arbitrary conditioning generative model. The model is
+trained by self-supervised learning to predict future observa-
+tions from present observations akin to the predictive coding
+problem [109]–[111].
+Note that our method does not assume that integrating the
+future observations necessarily result in complete observations.
+In early experiments we found that learning a model to predict
+complete world states from partially observed world states
+is not a trivial problem. One challenge is conditioning by
+high-resolution dense partial observations. Another challenge
+is the lack of a complete ground truth learning signal, as
+typically learning to predicting empty structure (i.e. predicting
+“nothing”) is an easier solution than predicting plausible struc-
+ture when lacking a target. Both issues rule out modeling by
+Fig. 5.
+Overview of all modules in our framework. The goal is to predict
+complete worlds ˆx conditioned on partially observed worlds xpast (bottom).
+We train the predictive world model (purple) by first training an auxiliary
+module (green) providing pseudo ground-truth world states x∗
+full (top).
+GANs [34], [35] but naturally lends themselves to VAEs [37]–
+[39].
+We present a novel solution extending the capability of
+hierarchical VAEs to learn to predict complete states from
+partial states only. Our method is formulated as a two-stage
+training process as illustrated in Fig. 5.
+In the first stage, we train two auxiliary models to generate
+a single complete plausible state by filling in the remaining
+unobserved elements after having integrated both past and
+future observations xfull. The first auxiliary model is a masked
+stochastic latent variable model that predicts structure (i.e. road
+region). The second auxiliary model is an adversarial model
+that generate texture (i.e. road surface intensity) for predicted
+structure elements. In the second stage, we use the complete
+plausible world states as pseudo ground truth states in order to
+train a more expressive HVAE capable of predicting complete
+states ˆx from past observations xpast only.
+We implement the predictive world model by the recent
+SOTA hierarchical VAE model VDVAE by Child [17]. The
+VDVAE model is capable of learning a rich hierarchical
+distribution of latent variables for high-resolution images, and
+achieves higher likelihoods than SOTA autoregressive models
+like PixelCNN [105] while using fewer paramters and generate
+samples thousands of magnitudes quicker [17].
+6
+
+Observation
+World
+C full
+accumulation
+Plausible state
+completion
+Training
+past
+full
+Predictive world
+model
+[]
+(c, C full)
+Observation
+World
+accumulation
+Inference
+past
+Predictive world
+modelFig. 6.
+Overview of the plausible state completion module. The stochastic
+latent variable predictive model learns to predict missing structure ˜xpast from
+future observations xfull. The trained module is used to predict missing
+structure never observed, structurally completing the full observation ˜xfull.
+The adversarial predictive model learns to fill in texture-like content in the
+predicted structure resulting in the pseudo ground-truth world state x∗
+full.
+A. Plausible complete state prediction
+The pseudo ground truth states are generated by a sequential
+process illustrated in Fig. 6. The first auxiliary model in the
+process takes the partially observed world state xfull and
+predicts a new completed world state ˜xfull which includes the
+environment structure for unobserved regions. By structure we
+mean regions corresponding to navigable space and possessing
+semantic and scalar information. The second auxiliary model
+predicts a completed representation x∗
+full which includes
+texture-like content such as road intensity values for the newly
+predicted regions. In the rest of this section we explain each
+auxiliary model in detail. Note that this process does not
+substitute the predictive world model as the process leverages
+future observations not available at inference time.
+We perform data augmentation on the original partially
+observed world representations when training the predic-
+tive world model. Augmentations include random rotation,
+translation, and warping operations applied identically on all
+tensor layers. Geometric data augmentation is essential for
+the predictive model to learn geometric invariance for top-
+down spatial representations [136]. Additionally, we perform
+a random sequence of sharpening, blurring, and value scaling
+operations to reduce overfitting to particular observed road
+intensity patterns. A set of training samples generated by
+augmenting a single sample is shown in Fig. 4.
+1) Predicting structure by a stochastic latent variable pre-
+dictive model: The model is structured as a dual path latent
+variable encoder-decoder model. When training the model, the
+first encoder takes the full state xfull and predicts a latent
+variable distribution Zfull. The second encoder takes the past
+Fig. 7.
+Stochastic latent variable predictive model. An encoder-decoder
+is trained to predict the future observations xfull from past observations
+xpast. A secondary encoder learns to encapsulate the inherent stochasticity
+by encoding the future observations as a latent code zfull. A learned prior
+is trained to predict the distribution for zpast matching the distribution of
+zfull. During inference only the learned prior is used.
+Fig. 8. Adversarial predictive model. An inpainting module is trained to fill
+in texture-like content indistinguishable from real observations. An element-
+wise discriminator module is trained to predict which regions are real and
+generated. During inference only the inpainting module is used.
+state xpast and predicts a latent variable distribution Zpast. The
+distributions Zfull and Zpast are optimized to be similar. Next,
+a latent variable zfull is sampled from Zfull and appended
+to the encoding hpast and feed to a decoder generating a
+new predicted complete state ˆx. The model is optimized by
+computing the ℓ2 loss between ˆx and observed elements in
+xfull
+Lstruct =
+1
+Nstruct
+Mfull ⊙ (ˆx − xfull)2
+(4)
+where Nstruct is the number of structure elements, Mfull is
+a binary mask indicating observed elements in xfull used to
+7
+
+Observation
+World
+accumulation
+Plausible state
+completion
+C full
+Cpast
+Stochastic latent variable
+predictive model
+c full
+past → Lstruct(εpast,  full)
+Adversarial
+predictive model
+Lteature(c full, & full)
+fullTraining
+NN1
+mf←(In)
+Enc1
+C full
+Lstr
+& full,
+DKL
+Learned prior
+Enc2
+NN2
+Cpast
+Dec
+→
+Z full
+Inference
+NN2
+past
+past
+Enc2
+Dec
+→ε
+Zpast.Training
+Inpainter
+Discriminator
+Enci
+Deci
+Encd
+Decd
+full
+m
+Observed element
+m
+mask
+Inference
+Inpainter
+Enci
+Deci
+full
+ulllimit the loss to observed elements as is common in masked
+VAE methods [40], [41], [43]–[45].
+The intuiting is that the learned distribution Zfull contains
+the information required to reconstruct xfull, and the second
+encoder learns to estimate this distribution from xpast. In other
+words, knowing Zfull explains away the stochasticity involved
+in reconstructing xfull from xpast. At inference time zfull is
+not known, but the second encoder has learned to predict Zpast
+that is close to Zfull, effectively acting as a learned prior that
+explains away the stochasticity by a latent variable.
+2) Predicting texture by an adversarial predictive model:
+Non-hierarchical reconstruction-based VAEs are ill-suited for
+generating fine-grained details [17], [112]. We therefore use
+an adversarial predictive model to generate pixel-like content
+such as road intensity for newly predicted structure. The model
+design is shown in Fig. 8. The model consists of an encoder-
+decoder inpainting module that takes the world state ˜xfull
+with completed structure, and generates a new world state
+x∗
+full also with completed content. The inpainting module
+is optimized by the minimax adversarial loss [28], [113] to
+make observed and generated content indistinguishable, while
+an element-wise discriminator module [114] is optimized to
+discriminate elements. The adversarial loss is computed using
+the binary cross entropy (BCE) objective
+Ltexture = −
+1
+Nstruct
+�
+(i,j)
+BCE(m(i,j), ˆm(i,j))
+(5)
+where m is the real observed element binary mask, ˆm is the
+predicted mask by the discriminator, and (i, j) are indices
+of structure elements. At inference time only the inpanting
+module is used to generate the completed world state x∗
+full.
+B. World model training
+We train a model to predict a set of plausible worlds
+conditioned on partially observed worlds as depicted in Fig. 9.
+First, we optimize a regular HVAE model [115], [116] param-
+eterized by qθ(z|x) and pθ(x|z) to encode and reconstruct
+pseudo ground-truth world states x∗
+full generated by the plau-
+sible state completion module (see Sec. IV-A). The learned
+hierarchical latent variable prior pθ(z) and posterior qθ(z|x)
+distributions [17] can be factorized as
+pθ(z) = pθ(z1|z2) . . . pθ(zK−1|zK)pθ(zK)
+(6)
+qφ(z|x) = qφ(z1|z2, x) . . . qφ(zK−1|zK, x)qφ(zK|x)
+(7)
+where each random variable is modeled by Normal distri-
+butions N(z|µ, σ). Deeper or more abstract codes (i.e. zK)
+encodes the global structure, while shallow codes (i.e. z1)
+encode the visual appearance of elements in x∗
+full. We train
+the HVAE by maximizing the hierarchical ELBO
+log pθ ≥
+E
+qφ(z|x∗
+full)
+�
+log pθ(x∗
+full|z)
+�
+−DKL(qθ(z|x∗
+full)||pθ(z))
+(8)
+where log pθ(x∗
+full|z) is the likelihood of the reconstructed
+state, and a KL divergence term that measures the divergence
+between the distributions
+DKL(qθ(z|x∗
+full)||pθ(z)) =
+K
+�
+k=2
+E
+qθ(z≥k|x∗
+full)
+�
+DKL(qθ(zk−1|zk, x∗
+full)||pθ(zk−1|zk))
+�
++DKL
+�
+qθ(zK|x∗
+full)||pθ(zK)
+�
+.
+(9)
+We simultaneously train a secondary partially observed
+encoder qφ(z|xpast) to predict a latent distribution similar
+to qθ(z|x∗
+full) based on the original partially observed world
+states xpast. The second encoder is optimized by minimizing
+DKL(qφ(z|x∗
+full)||qψ(z|xpast)) =
+K
+�
+k=1
+E
+q(z>k|x)
+�
+DKL(qφ(zk|z>k, x∗
+full)||qψ(zk|z>k, xpast))
+�
+.
+(10)
+At inference time the model uses the partially observed
+encoder to generate a latent distribution qφ(z|xpast) that can
+be decoded by pθ(x|z) into a completely observed world state
+ˆx similar to a pseudo ground-truth world state x∗
+full without
+the need to observe the future.
+We developed the approach of optimizing hierarchical latent
+distribution similarity as an extension of the single layer
+latent variable model described in Sec. IV-A1 inspired by
+the stochastic video prediction model by Denton [47]. A
+similar approach named Posterior Matching by Strauss [22]
+was very recently published concurrently to our work. Our
+method extends their method by allowing HVAEs to learn to
+predict complete states from partial states only. This property
+is important in continual learning real-world mobile robotics
+problems where the existence of a priori complete ground truth
+states cannot be presumed.
+V. EXPERIMENTS
+We conduct three sets of experiments to verify the feasibility
+of each part of our framework in real-world environments.
+First, we evaluate the expected performance of pretrained
+vision-based semantic segmentation models used to inter-
+pretate sensor observations. Secondly, we demonstrate the
+quality of generated partially observed world states. Finaly,
+we evaluate the trained world model in terms of predictive
+accuracy and structural diversity.
+Our self-supervised learning framework does not depend
+on human annotations and instead leverages a pretrained
+vision-based semantic segmentation models to infer semantic
+information from image observations. The first experiment set
+quantifies the expected domain generalization performance of
+models trained on one or several annotated public datasets
+and evaluated on our application target domain dataset. The
+training datasets are Apolloscape, BDD100K, Cityscapes, and
+Mapillary Vistas [117]–[120] providing 49287, 8000, 3475,
+and 20000 training samples, respectively. Our target domain
+8
+
+Fig. 9.
+Predictive world model. We train a hierarchical latent variable
+generative model to reconstruct pseudo ground-truth world states x∗
+full.
+Simultaneously, we train a secondary encoder to predict similar latent dis-
+tributions from the original partially observed world states xpast to predict
+complete world states ˆx at inference time.
+dataset is KITTI-360 [121] providing 12054 annotated samples
+across all sequences. All experiments are listed in Table I. All
+datasets provide Cityscapes-like labels and are thus easy to
+concatenate into a larger multi-domain dataset. We use the
+SOTA semantic segmentation model DeepLabV3+ [100] and
+evaluate performance using different ResNet backbones [122]
+and number of training iterations. We leverage the MMSeg-
+mentation framework [123] to train and evaluate models.
+The second experiment set demonstrates how our framework
+generates BEV world state representations by integrating se-
+quences of sensor observations. We found that leveraging 360
+degree sensor observations result in a more useful temporal
+self-supervision learning signal than forward view observa-
+tions only. As observations are not spatially and temporally
+biased in the driving direction, future observations are less
+obvious to predict, and thus improve extrapolation to to all
+unobserved regions. While KITTI-360 provides 360 degree
+vision from two fisheye cameras, it is not trivial to make
+use of these images. First, availability of annotated fisheye
+image datasets is low. Secondly, camera calibration parameters
+for projecting the point cloud into the fisheye images are
+not specified. We choose to qualitatively demonstrate the full
+perception pipeline on NuScenes [124] as it provides 360
+degree camera views and point clouds. We also quantitatively
+estimate semantic accuracy of the generated BEV representa-
+tions on KITTI-360 by comparing the single forward facing
+camera results and the corresponding ground truth point cloud
+semantics. We use the “RN 101 320K cm” model variant (see
+Table I) for segmenting images on both datasets.
+TABLE I
+SEMANTIC SEGMENTATION DOMAIN GENERALIZATION PERFORMANCE.
+Model
+Iters
+Datasets∗
+mIoU
+road IoU
+car IoU
+RN 18
+80K
+••cm
+51.91
+90.02
+88.36
+160K
+••cm
+53.52
+92.30
+89.45
+320K
+••cm
+54.31
+92.12
+89.20
+RN 50
+80K
+•••m
+55.30
+92.84
+89.90
+••cm
+55.78
+89.71
+90.30
+abcm
+48.70
+85.97
+88.85
+160K
+•••m
+54.98
+92.92
+89.90
+••cm
+56.67
+91.70
+90.45
+abcm
+50.15
+86.82
+89.34
+320K
+•••m
+56.04
+93.67
+89.43
+••cm
+56.65
+93.56
+90.26
+abcm
+53.27
+90.76
+89.11
+RN 101
+80K
+•••m
+56.96
+93.44
+90.23
+••cm
+56.00
+93.23
+89.74
+•bcm
+54.98
+93.12
+89.27
+abcm
+51.81
+88.74
+88.67
+160K
+•••m
+55.57
+93.30
+90.29
+••cm
+58.00
+94.23
+90.48
+•bcm
+55.85
+93.39
+90.23
+abcm
+51.71
+90.20
+89.55
+320K
+••cm
+58.72
+94.24
+90.55
+∗a: Apolloscape, b: BDD100K, c: Cityscapes, m: Mapillary V., •: Filler
+TABLE II
+BEV SEMANTIC SEGMENTATION PERFORMANCE ON KITTI-360
+road IoU
+Evaluate all regions
+92.31
+Evaluate unobserved regions only
+90.97
+TABLE III
+MEAN AND BEST WORLD MODEL PREDICTION ON THE TEST SEQUENCE.
+road IoU
+#samples
+1
+2
+4
+8
+16
+32
+Mean (all regions)
+97.94
+97.94
+97.96
+97.94
+97.94
+97.94
+Best (all regions)
+97.94
+98.18
+98.38
+98.52
+98.63
+98.73
+Mean (unob. only)
+96.21
+96.22
+96.23
+96.21
+96.21
+96.21
+Best (unob. only)
+96.21
+96.53
+96.81
+97.01
+97.16
+97.31
+The third experiment set evaluates the performance of our
+predictive world model. We evaluate our model on the KITTI-
+360 dataset as it contains long driving sequences with high-
+frequency image and point cloud observations as expected in
+a real system. Long sequences improves learning to model
+large 80x80 m representations. High-frequency observations
+increase the element density of partially observed world states.
+We evaluate our model on sequence #6 containing both subur-
+ban and urban road scenes. We use the remaining 8 sequences
+for training. We use the ground truth point cloud semantics in
+the predictive world modeling experiments due to KITTI-360
+lacking usable 360 degree vision coverage.
+VI. RESULTS
+Semantic segmentation performance We present our exper-
+iment results in Table I. The consistently best training dataset
+combination is Cityscapes and Mapillary Vistas, and saturating
+the training data with a large set of regionally and camera-wise
+9
+
+Training
+Enc
+ZK
+Dec
+Observation
+DKL
+accumulation
+Z1
+. ZK-1
+Zk = N(Zkluk, Ok
+个
+Observation
+Inference
+accumulation
+EnCpo
+Dec
+α
+ZK
+Z1unsimilar samples, like Apolloscape, is detrimental for domain
+generalization performance on KITTI-360. Our hypothesis
+is that data regionally similar to the application domain,
+like Cityscapes, and diverse dataset capturing many regions
+and varying cameras, like Mapillary Vistas, are beneficial
+learning domain invariant features. For backbone size we find
+that domain generalization performance improves with larger
+backbone sizes and additional training iterations.
+The high IoU values in Table I indicate that leveraging
+a pretrained semantic segmentation model is an adequate
+solution to infer relatively unambigous semantic classes like
+“road” and “car” from image data. See Fig. 10-12 for a visual
+demonstration of performance obtained on both NuScenes and
+KITTI 360.
+Low IoU score samples are overrepresented by ambiguous
+classification of what is and is not “road”. We conclude that the
+remaining performance gap is primarily a matter of semantic
+definition instead of a modeling problem. See Fig. 12 for a
+visual demonstration of vauge semantics.
+Generation and integration of semantic point clouds We
+confirm that our framework is able to generate and temporally
+integrate semantic point clouds. In Fig. 10 we show qualitative
+results on NuScenes based on the full 360 degree perception
+pipeline presented in Sec. III. Fig. 11 shows results on KITTI-
+360 with a forward facing camera only. In Table II we present
+quantitative results comparing the “road” BEV generated by
+the pretrained semantic segmentation model and ground truth
+point cloud semantics. We present results evaluated for unob-
+served regions only (i.e. future) and also including previously
+observed regions (i.e. past + future). The results show that
+the BEV IoU score is comparable to that of the original
+perspective image IoU.
+Our method lacks obvious comparative baselines. To the
+best of our knowledge, no prior work uses lidar observations
+and generative modeling to stochastically predict spatial en-
+vironments without relying on ground truth map data. Prior
+image-based methods are generally non-generative models and
+are trained and evaluated on the same ground truth data
+domain. A reasonably fair comparison is between a recent
+SOTA image-based monocular model [67] reporting 68.34
+road IoU on the full KITTI Raw dataset [137], and our model
+achieving 92.31 road IoU on the KITTI-360 dataset. Note that
+our results indicate the true expected domain generalization
+performance as the model is not trained on the same dataset
+domain, unlike the image-based model result. The degree of
+performance difference demonstrate the inherent advantage of
+using lidar observations for spatial prediction as presented by
+our method.
+We observe an issue in open rural environments where
+incoming trucks may cause the ICP algorithm to lose point
+cloud correspondence. We believe a more robust probabilistic
+filtering approach [125]–[127] would remedy this problem.
+Another issue is that very large structures, such as express-
+way intersections, are never comprehensively observed due to
+limited effective lidar observation range and thus difficult to
+learn to predict. We believe longer range lidars [128], [129]
+Fig. 10. BEVs generated from our perception pipeline applied on NuScenes
+providing 360 degree camera setup and lidar. The top row show semantics.
+The bottom rows shows semantic segmentation output.
+Fig. 11. BEVs generated from our perception pipeline applied on KITTI-360
+using one camera and lidar. The top row show semantics. The middle row
+show intensity. The bottom row shows semantic segmentation output.
+and incorporating vision-based depth estimation methods [97],
+[132] may provide the necessary sensory range.
+Predictive world model performance Table III presents
+quantitative results showing the best IoU match among N sam-
+pled complete world predictions and the actual future observed
+world. We find that in most situations the future observations
+are deterministically predictable, meaning a single prediction
+gives a reasonable estimation of the true world. However, when
+the future observations are not deterministically predictable,
+sampling more worlds increases the likelihood of some pre-
+diction matching the future observations.
+The relation between sampling and predictive performance
+is seen in Table III by how increasing the number of samples
+results in the best sample matching the future observations
+better (i.e. “Best”) while the mean over all samples remain
+unchanged. The best prediction among 32 samples reaching
+98.73 % IoU, closing the gap to perfect prediction by 61.7 %
+10
+
+Past
+Future
+FullPast
+Future
+FullFig. 12. Visual comparisons of world samples generated from semantic segmentation and ground truth annotation. The human annotated “road” semantics
+can be ambiguous as seen in the right example.
+on average, when evaluating over both past and future obser-
+vations. See Fig. 13 for examples of sampled worlds.
+VII. CONCLUSIONS
+We present a framework to generate partially observed
+world representations from sensor observations, and a self-
+supervised predictive world model for generating a diverse
+set of plausible complete world states trained from partially
+observed states only. We introduce a plausible complete state
+module for generating pseudo ground-truth world states for
+training the HVAE implementing the world model, and a latent
+distribution similarity optimization approach for processing
+partially observed world states.
+ACKNOWLEDGMENT
+This work was financially supported by JST SPRING,
+Grant Number JPMJSP2125. The authors would like to take
+this opportunity to thank the “Interdisciplinary Frontier Next-
+Generation Researcher Program of the Tokai Higher Education
+and Research System”.
+The computation was carried out through the “General
+Projects” program on the supercomputer “Flow” at the In-
+formation Technology Center, Nagoya University.
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+15
+
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+page_content='Predictive World Models from Real-World Partial  Observations  1st Robin Karlsson  Graduate School of Informatics  Nagoya University  Nagoya, Japan  karlsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='jp  2nd Alexander Carballo  Department of Electrical, Electronic and Computer Engineering  Gifu University  Gifu, Japan  alex@gifu-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='jp  3rd Keisuke Fujii  Graduate School of Informatics  Nagoya University  Nagoya, Japan  fujii@i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='jp  4th Kento Ohtani  Graduate School of Informatics  Nagoya University  Nagoya, Japan  ohtani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='nagoya-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='jp  5th Kazuya Takeda  Graduate School of Informatics  Nagoya University, TIER IV  Nagoya, Japan  kazuya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='takeda@nagoya-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='jp  Abstract—Cognitive scientists believe adaptable intelligent  agents like humans perform reasoning through learned causal  mental simulations of agents and environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The problem of  learning such simulations is called predictive world modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Recently, reinforcement learning (RL) agents leveraging world  models have achieved SOTA performance in game environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  However, understanding how to apply the world modeling ap-  proach in complex real-world environments relevant to mobile  robots remains an open question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In this paper, we present a  framework for learning a probabilistic predictive world model  for real-world road environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We implement the model using  a hierarchical VAE (HVAE) capable of predicting a diverse set of  fully observed plausible worlds from accumulated sensor obser-  vations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' While prior HVAE methods require complete states as  ground truth for learning, we present a novel sequential training  method to allow HVAEs to learn to predict complete states from  partially observed states only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We experimentally demonstrate  accurate spatial structure prediction of deterministic regions  achieving 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='21 IoU, and close the gap to perfect prediction  by 62 % for stochastic regions using the best prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' By  extending HVAEs to cases where complete ground truth states do  not exist, we facilitate continual learning of spatial prediction as a  step towards realizing explainable and comprehensive predictive  world models for real-world mobile robotics applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Code  released after publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Index Terms—World model, generative model, partial observ-  ability, BEV generation, autonomous vehicles, self-supervised  learning  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' INTRODUCTION  Cognitive scientists believe cognition in adaptable intel-  ligent agents like humans is founded on a small number  of foundational components for representing the world in  terms of inanimate objects, goal-directed agents, number sys-  tems and sets, social partners and groups, and geometry of  environments [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' These cognitive abilities allow intelligent  agents to perform common-sense physical reasoning to facil-  itate accomplishment of tasks [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' One ability is to predict  multiple plausible long-tail outcomes of a sequence of actions,  and perform counterfactual reasoning [3]–[5] through causal  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The framework integrates observations into a common vector space  representing the partially observed world state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A predictive world model  samples a set of diverse plausible complete world states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The model improves  through continual learning from experience by predicting future observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='04783v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='CV]  12 Jan 2023  Sensor observations  BEV projections  p(road)  Intensity  Accumulation  in vector space  个  Sampled plausible worlds  Probabilistic  integration  Predictive  world model  Improve model  Accumulated future partial observations  Self-supervised  learningmental simulations of the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Another ability is to imagine  different plausible spatial configurations of unobserved regions  of the world based on past experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The problem of  learning such simulations is called predictive world modeling  in machine learning [6], [7], [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The explicit world modeling approach provides several  potential advantages over implicit predictive models learned  as part of the task;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' data efficiency as policies can be opti-  mized through simulation, long-tail planning and reasoning by  search, explicit representation of agent’s knowledge and state  space coverage, explainable sequential decision processes, and  improved domain generalization by enabling planning over  abstract latent structures decoupled from particular observable  appearance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' pixels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The advantage of world models is  demonstrated by recent model-based reinforcement learning  (RL) methods like Dreamer V2 [8] demonstrating better per-  formance than SOTA model-free RL methods like IQN [9] and  Rainbow [10] on Atari environments [11] when compared by  the same amount of compute and wall-clock time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However,  understanding how to learn and apply the world modeling  approach in visually complex real-world environments relevant  to autonomous vehicles (AV) and other mobile robots remains  an open question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Learning world models of real-world envi-  ronments is associated with challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Agent observations are  perceptually complex, making it difficult to decompose obser-  vations into consistent and distinct semantic objects, in turn  making relationship learning infeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Percepts are generally  agent-centric, partial observations due to occlusion and limited  sensor observation reach, meaning explicitly inferring the  complete world state is difficult if not impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' World state  transition dynamics resulting from multi-agent interactions  are generally stochastic and complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Tasks are generally  specified vaguely and lack rich reward signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In contrast to  game environments, experience gathering is radically limited  in real-world environments, as failure may have unacceptable  consequences and generally prohibit learning world states  primarily by exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Mobile robots like AVs typically perform motion plan-  ning on the assumption that the spatial environment is fully  known [13], [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' This assumption is conventionally satisfied  through localizing the agent within point cloud maps encoded  with layers of human annotated HD map information about the  environment [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, solely relying on a priori maps  has demerits [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Map generation proves difficult to scale,  as creating maps require labor-intensive human annotation  and regular updating as environments change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Dependence  on maps for navigation renders the agent inoperable in case  of loading or localization failure, as well as in unmapped  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Additionally, changes in the environment not  reflected in the map may result in unsafe behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  This work proposes a framework for learning probabilistic  predictive world models for real-world spatial environments  from self-supervised learning using sensor observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We  implement the world model based on the recent SOTA hier-  archical VAE (HVAE) model Very Deep VAE (VDVAE) [17]  capable of representing and sampling general and spatially  large real-world environments by a compact latent code while  preserving fine detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We introduce two novel components  to overcome the fact that the original VDVAE model cannot  learn to predict complete states from partially observed states  only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' First, we demonstrate how to generate pseudo-complete  states using a combination of latent variable predictive and  an adversarial modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Secondly, we present an approach to  enable HVAEs to predict a diverse set of complete states from  single partial state by learning to match the latent variable  distributions between the partial and pseudo-complete states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  By enabling learning from partial observations generated  by sensor information, our predictive world model becomes  capable of improving from new experiences obtained during  operation akin to continual learning [18]–[20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The model can  avoid catastrophic forgetting by retaining a replay buffer of  past experiences [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We consider a structured state description of the spa-  tial world as a discrete, agent-centric, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='5D homogeneous  gridmap to represent probabilistic spatiosemantic informa-  tion of the environment as observed and predicted by the  agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The gridmap is considered a well-established and ade-  quate approach for representing spatial information in mobile  robotics [23] and compatible with potent generative image  modeling approaches in machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We propose several useful mobile robotics applications;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' ro-  bust and safe planning by taking into account diverse sampled  structures for unobserved regions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' improve localization match-  ing success through densifying observations and predicting  plausible structure of unobserved regions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' and verify map  consistency with the actual perceived environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The contributions of our paper are fourfold:  A new conceptual approach to predict a diverse set of  plausible, fully observed, real-world spatial environments  by a predictive world model and sensor observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  A novel method to train a HVAE to predict complete  states from partially observed states only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  A holistic mobile robotics framework tying together real-  world sensor observations and world modeling as a self-  supervised learning problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Demonstrate accurately spatial structure prediction of  deterministic regions achieving 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='21 % IoU with 1  sample, and close the gap to perfect prediction by 62 %  for stochastic regions using the best prediction out of 32  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' RELATED WORK  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Arbitrary conditional density estimation  The problem of arbitrary conditional density estimation  [24]–[26] is about estimating the probability distributions  p(xu|xo), where the random variables x are expected to be  partitioned into arbitrary plausible subsets of observed xo  and unobserved xu random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In this section we  present methods incorporating different application-specific  presumptions on how x is partitioned into xo and xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Image inpainting methods predict unobserved pixels xu  from observed pixels xo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The problem formulation is similar  2  to the problem of predicting complete world states from  partially observed states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The prototypical solution is to use an  autoencoder (AE) [27] to compress partially observed images  xo into constrained latent codes z encoding similar visual  patterns as learned from reconstructing complete images x by  matching global contextual clues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  However, optimizing models simply by pixel-wise recon-  struction is afflicted by the marginalization problem, resulting  in blurry outputs as missing regions can be filled by many  plausible pixel configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The Context encoder [28] at-  tempts to address the blurriness problem by introducing an  adversarial objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Furthermore, GLCIG [29] introduces a  course-to-fine generation scheme with diluted convolutions  and two adversarial objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The global objective ensures  the image remains coherent as a whole, while the local  objective improves detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Yeh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' [30] finds the closest  sample in an image database and use its latent code for  prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Contextual attention [31] adds an attention mecha-  nism for long-distance information crossover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our framework  similarly applies and adversarial objective for learning to  predict texture-like content such as lidar reflectance intensity  from road surface (henceforth, road surface intensity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Other approaches focus on learning mask-aware convolu-  tional filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' [32] introduces a special convolution  filter and a observed element mask update rule for propagating  information about which elements provide information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Yu et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' [33] introduces gated convolutions for learned mask updat-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' While we add an observed element mask to the model  input following the missing data VAE approach, explicitly  convoluting over masks is an interesting future direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Another line of image inpainting works focus on pluralis-  tic stochastic state completion methods based on generative  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' GAN-based methods [34], [35] generates multiple  plausible completions by conditioning on a random vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  VAE-based methods [36] replaces the deterministic latent  code generated by the AE to allow stochastic sampling  of multiple plausible predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Previous methods improve  training stability by constraining the latent distribution of  partially observed images by matching the distribution for fully  observed images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' PIC-Net [37] trains separate encoders for  observable and unobservable image regions, and matches the  distributions between the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' UCTGAN [38] adds a cross  attention module to mix latent representations of partially and  fully observed images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' DSI-VQVAE [39] applies VQVAE to  stabilize training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Concurrently to our work, Posterior Match-  ing [22] presents arbitrary conditioning based on HVAEs by  optimizing a secondary partially observed encoder to match  the latent distributions of a fully observed encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We extend  prior VAE work by introducing a two-stage training paradigm  to allow learning to predict complete images from partially  observed images only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Another approach frames predicting unobserved state vari-  ables from observed variables as the missing data VAE prob-  lem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' HI-VAE [40] derives an evidence lower bound (ELBO)  for missing data by masking out contributions from unob-  served data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' EDDI [41] introduces an alternative Partial VAE  model which processes observable data only by encoding ele-  ments by a positional encoding and processed by permutation  invariant operations similarly to PointNet [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' VAEM [43] is  a hierarchical VAE that operates on heterogeneous data by  first transforming all input variables into a common latent  space by a type-specific transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' HH-VAEM [44] is a  recent hierarchical VAE demonstrating effective sampling us-  ing the Hamiltonian Monte Carlo algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Collier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' [45]  demonstrate results on high-dimensional image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our work  extends prior missing data VAE approaches by learning to  model p(xu|xo) for high-dimensional representations without  requiring fully observed ground truth samples for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Video prediction methods aims to model a stochastic state  transition process where a sequence of future images xu are  predicted conditioned on a sequence of past fully observed  images xo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Babaeizadeh [46] presents a sequential stochastic  variational video prediction model based on predicting a  latent code explaining away the stochasticity of the sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Denton [47] presents a end-to-end framework to explain away  stochasticity by a frame-to-frame latent code and a learned  prior to improve training robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our work reformulates  the stochastic latent variable video prediction approach of  Denton to the problem of predicting complete world states  from partially observed world states only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Bird’s-eye-view generation  Mobile robotics, and in particular AVs, pursue the problem  of generating top-down bird’s-eye-view (BEV) representations  from perception inputs as a substitute or complement to human  annotated maps [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Camera-based methods receive much attention because of  affordability and motivation by human vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, lift-  ing 2D perspective images to 3D is fundamentally an ill-  posed problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Inverse perspective mapping (IPM) [48]–[50]  propose to overcome the problem by assuming the ground  plane is flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, the flat plane assumption is generally  not true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Stereo cameras propose to solve the lifting problem  by inferring depth maps based on physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, the  resulting depth maps tend to be noisy for far-away objects,  object borders, and objects covered with non-distinct textures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Learning-based methods are proposed to overcome the weak-  nesses of stereo based depth map estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Cam2BEV [51]  presents an approach that projects semantic features using  IPM and corrects the projection by a spatial transformer  module learned from synthetic ground truth BEVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Many  works are based on using monocular depth estimation [52]–  [57] to lift images to a 3D point cloud before projection  to a top-down 2D grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Schulter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' [58] proposes an  adversarial objective relying on ground truth maps to refine  the resulting BEV representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' MonoLayout [59] learns the  view transformation from self-supervised targets by integrating  projected observations while still relying on ground truth maps  for BEV refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Later works introduce probabilistic depth  projection [60], categorical depth distribution network [61],  and multi-task learning [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' VED [63] is a variational en-  coder trained from stereo vision to predict low-dimensional  3  (64x64 px) semantic BEV representations from forward view  monocular images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Other methods lift images using multilayer  perceptrons (MLP) trained on ground truth maps [64]–[66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Recently, cross-attention based transformer modules [67], [68]  and Transformers modules [69] are applied to model view  transformations motivated by the global attention mechanism  not being limited to process neighboring pixel information like  CNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, due to lacking inductive biases attention-  based models tend to require more data, effort, and compute to  train as well as for inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' While our framework in principle  is compatible with depth estimation, we choose to leverage  lidar for substantial improvements in representation accuracy  and observation integration performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Additionally, our  generative model can generate diverse plausible predictions,  unlike view transformation models which typically are deter-  ministic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Lidar-based BEV generation methods have a significant  advantage from explicitly measuring distance though deemed  prohibitively expensive for mass deployment by some.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Fishing  Net [66] utilizes lidar information to improve spatial accuracy  of BEVs generated by sensor fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' MP3 [70] uses a learned  module for generating map elements from lidar observations  and ground truth map supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' HDMapNet [71] also  include image information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In contrast to these methods, our  framework does not rely on preexisting ground truth maps for  supervised training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our method is also generative and can  provide diverse predictions, which is fundamentally necessary  as the correct prediction for occluded regions are generally  indeterminable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Spatial AI  Simultaneous localization and mapping (SLAM) [72]–[74]  is the conventional robotics approach to map 3D spatial  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' SLAM works by computing the translation and  rotation transformation to optimally match sequential point  clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Knowing the transformation allows accumulation of  point clouds in a common reference frame or vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Our framework integrates sensor observations using the same  principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Another component of SLAM is loop closure op-  timization when previously traversed spaces are revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Our framework can be considered as adding a predictive  component to SLAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Neural Radiance Fields (NeRF) [75] is a recent approach  to represent 3D objects [76], [78] and environments [77], [79]  by neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' While NeRFs can interpolate between  observations they do not extrapolate beyond what is observed  like our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' World models  The idea of learning a predictive model of the world in  machine learning was first introduced by Schmidhuber [6], [7],  [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A common approach is to learn latent state representa-  tions from images using a VAE [80]–[82], and use the learned  latent code as a compact representation of the world state  for planning actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Other works use adversarial learning to  optimize the latent code [83], [84], or contrastive learning with  latent variables to model stochastic transition processes [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Another line of work focus on inferring a set of object  encodings from images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Watters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' [86] uses a variational  encoder to infer a fixed set of latent object encoding vectors  from a sequence images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Later works apply a VAEs to learn  semantically richer object embeddings [87], [88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' MONet [89]  is a prominent model for learning to extract a variable amount  of semantic object encodings using a recurrent attention  module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Recent works leveraging MONet demonstrate the  merits of explicit object discovery for future state prediction  using compositional reasoning [90], and for reinforcement  learning [8], [91] surpassing the performance of SOTA model-  free RL models [9], [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Our work approaches the world modeling problem of  learning to predict a 2D spatiosemantic representation from  agent-centric partial observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We hope our method will  contribute towards bridging recent SOTA world modeling  approaches from game environments to partially observed real-  world mobile robotics environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' GENERATING PARTIAL WORLD STATES  This section describes the process of turning a sequence  of sensor observations into partially observed world states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We conceptualize our approach as the most elementary and  general way of achieving spatiosemantic cognition based on  projecting and integrating observations into a common metric  vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 2 for a visual overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Sensor observation processing  Perception sensor configurations for mobile robots are  primarily composed of two types of physical light sensing  mechanism with complementary strengths and weaknesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  First, active sensing lidars to accurately represent metric space  using point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Secondly, passive sensing cameras for  representing rich semantic information of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Sensor fusion approaches aim at leveraging the complimentary  strengths of both vision modalities [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Semantic point clouds is the natural data structure for repre-  senting both spatial and semantic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Image content  can be projected to a 3D point cloud if pixel-wise depth and  camera calibration parameters are known [92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In principle  monocular [55], [93], [131], [132] or stereo vision [94]–[97]  can provide depth maps and enable a vision-only perception  configuration equivalent to biological vision systems [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  However, we opted for a sensor fusion approach as current  depth estimation methods result in excessively noisy estimates  compared with lidar measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Our framework processes observations as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' First, the  agent is instantiated within an unknown metric vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Next, sensor observations are projected onto a common vector  space by known intrinsic and extrinsic calibration parameters  of each sensor with respect to the agent [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' For simplicity we  assume all sensor observations are synchronized into discrete  timesteps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We first infer semantics from images using a pre-  trained semantic segmentation model [100] that partitions the  4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Perception pipeline for transforming synchronized sensor observations into BEVs by projection into a common vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A semantic segmentation  model interprets images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The inferred semantics are attached to the point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Multiple semantic point clouds are temporally integrated into an ego-centric  reference frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' BEVs are generated by projecting and probabilistically integrating all semantic points into a 2D discretized grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Temporal accumulation turns sparse observations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' present) into  dense representations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' past and future).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Partitioning the accumulated  semantic point cloud in past and future observation subsets provide a natural  self-supervised learning signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Left figures show “road” (yellow) and “not-  road” (purple) semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Right figures show height information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Examples of geometrically diverse set of training samples generated  from a single set of real observations using data augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  image into distinct semantic regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The 3D point cloud is  projected onto the image frame resulting in a one-to-many  mapping between semantic pixels and 3D points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The semantic  information is appended to all respective points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Points without  semantic information are discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The set of all encounterable object semantics cannot be  defined a priori in the open-world assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, it  is always possible to infer whether or not any new novel  object possesses a known semantic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Following this principle,  we semantically partition the static environment into “road”  and “not-road” observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Dynamic objects are not part of  the static environment and should be ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' For simplicity  we infer all dynamic objects as “not-road” observations and  generally rely on temporal observation integration to filter  out the resulting noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The noise resulting from cars is  problematic, as cars are large, abundant, and often parked on  the road.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' For this reason we infer “car” semantics as a special  case for filtering out excessive noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Alternatively dynamic  objects can be removed by applying a filtering method [101],  [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The resulting representation is an agent-centric 3D semantic  point cloud as visualized in the top row of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Temporal observation accumulation  The agent collects a sequence of temporally ordered se-  mantic point clouds during operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The goal is to integrate  all observations into a single vector space centered on the  agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The least assumptions approach to estimate motion  is by computing the transformation optimally matching two  sequential observations by point cloud registration also known  as scan matching [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We found that the iterative closest point  (ICP) algorithm [103] on unfiltered point clouds results in  a simple but sufficiently accurate and robust implementation  for accumulating observations covering 80 × 80 m2 suburban  road environments without revisitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The agent trajectory is  computed from the sequence of transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  ICP takes the previous and latest point cloud and computes  the transformation aligning the previous point cloud p(t) to  the latest one p(t+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' This transformation matrix Tt→t+1  correspond to the agent motion during the time difference  between the two observations as shown in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We update the  relative position of all previously accumulated point clouds  P (t) to ˜P (t+1) every time step recursively by applying the  transformation as a matrix multiplication as in (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Finally  we add the new observations p(t+1) to the transformed ac-  cumulated observations  ˜P (t+1), resulting in a new set of  accumulated observations P (t+1) as in (3)  5  Sensor observations  Semantic segmentation  Present  Past  Future  Semantics  Intensity  Semantic point  [BEV projection  cloud  Accumulation  (BEV projection)  in vector spacePresent  轮车  Past  FutureTt→t+1 = ICP(p(t), p(t+1))  (1)  ˜P (t+1) = Tt→t+1P (t)  (2)  P (t+1) = concatenate( ˜P (t+1), p(t+1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  (3)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 2 show the agent trajectory from lidar odometry as a  line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 3 for a visual demonstration of accumulated  semantic point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Partial world state representation  Accumulated observations are projected onto homogeneous  probabilistic grids representing world states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In contrast to 3D  point clouds, 2D discrete grids can be processed by convolu-  tional neural networks (CNN) [104] forming the backbone of  recent potent generative models for images [17], [105]–[107].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The projection is performed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' First, we initialize a  2D grid x(c) spanning (I, J) elements covering a rectangular  spatial region with lengths (H, W) for each semantic class or  value c ∈ (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' , C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Next, the accumulated semantic point  cloud P is projected onto the grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We represent semantic information by beta distributions  p(x(c)  i,j = True) modeling the Bayesian probability of element  (i, j) represent a semantic c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' This formulation allows a single  element to represent several semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The beta distribution  is computed by counting the number of semantic points that  confirm or refutes the semantic within each grid element [108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Note that probability distributions allows representing igno-  rance or lack of knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' For example, if a grid element  have no observations, the distribution p(x(road)  i,j  ) is uniform,  indicating unknown uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Value information, like road  surface lidar intensity measurements, are expressed as Gaus-  sian distributions representing the mean and standard deviation  of all observations encompassed by the grid element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Finally,  we concatenate all probabilistic and scalar 2D grids into a 3D  tensor representation x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 2 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 4 for partial world  state representation visualizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' PREDICTIVE WORLD MODEL  The predictive world model samples diverse and plausible  complete worlds conditioned on partially observed worlds  as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We implement the world model as  an arbitrary conditioning generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The model is  trained by self-supervised learning to predict future observa-  tions from present observations akin to the predictive coding  problem [109]–[111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Note that our method does not assume that integrating the  future observations necessarily result in complete observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  In early experiments we found that learning a model to predict  complete world states from partially observed world states  is not a trivial problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' One challenge is conditioning by  high-resolution dense partial observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Another challenge  is the lack of a complete ground truth learning signal, as  typically learning to predicting empty structure (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' predicting  “nothing”) is an easier solution than predicting plausible struc-  ture when lacking a target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Both issues rule out modeling by  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Overview of all modules in our framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The goal is to predict  complete worlds ˆx conditioned on partially observed worlds xpast (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We train the predictive world model (purple) by first training an auxiliary  module (green) providing pseudo ground-truth world states x∗  full (top).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  GANs [34], [35] but naturally lends themselves to VAEs [37]–  [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We present a novel solution extending the capability of  hierarchical VAEs to learn to predict complete states from  partial states only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our method is formulated as a two-stage  training process as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  In the first stage, we train two auxiliary models to generate  a single complete plausible state by filling in the remaining  unobserved elements after having integrated both past and  future observations xfull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The first auxiliary model is a masked  stochastic latent variable model that predicts structure (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' road  region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The second auxiliary model is an adversarial model  that generate texture (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' road surface intensity) for predicted  structure elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In the second stage, we use the complete  plausible world states as pseudo ground truth states in order to  train a more expressive HVAE capable of predicting complete  states ˆx from past observations xpast only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We implement the predictive world model by the recent  SOTA hierarchical VAE model VDVAE by Child [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The  VDVAE model is capable of learning a rich hierarchical  distribution of latent variables for high-resolution images, and  achieves higher likelihoods than SOTA autoregressive models  like PixelCNN [105] while using fewer paramters and generate  samples thousands of magnitudes quicker [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  6  Observation  World  C full  accumulation  Plausible state  completion  Training  past  full  Predictive world  model  []  (c, C full)  Observation  World  accumulation  Inference  past  Predictive world  modelFig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Overview of the plausible state completion module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The stochastic  latent variable predictive model learns to predict missing structure ˜xpast from  future observations xfull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The trained module is used to predict missing  structure never observed, structurally completing the full observation ˜xfull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The adversarial predictive model learns to fill in texture-like content in the  predicted structure resulting in the pseudo ground-truth world state x∗  full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Plausible complete state prediction  The pseudo ground truth states are generated by a sequential  process illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The first auxiliary model in the  process takes the partially observed world state xfull and  predicts a new completed world state ˜xfull which includes the  environment structure for unobserved regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' By structure we  mean regions corresponding to navigable space and possessing  semantic and scalar information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The second auxiliary model  predicts a completed representation x∗  full which includes  texture-like content such as road intensity values for the newly  predicted regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In the rest of this section we explain each  auxiliary model in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Note that this process does not  substitute the predictive world model as the process leverages  future observations not available at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We perform data augmentation on the original partially  observed world representations when training the predic-  tive world model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Augmentations include random rotation,  translation, and warping operations applied identically on all  tensor layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Geometric data augmentation is essential for  the predictive model to learn geometric invariance for top-  down spatial representations [136].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Additionally, we perform  a random sequence of sharpening, blurring, and value scaling  operations to reduce overfitting to particular observed road  intensity patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A set of training samples generated by  augmenting a single sample is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  1) Predicting structure by a stochastic latent variable pre-  dictive model: The model is structured as a dual path latent  variable encoder-decoder model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' When training the model, the  first encoder takes the full state xfull and predicts a latent  variable distribution Zfull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The second encoder takes the past  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Stochastic latent variable predictive model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' An encoder-decoder  is trained to predict the future observations xfull from past observations  xpast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A secondary encoder learns to encapsulate the inherent stochasticity  by encoding the future observations as a latent code zfull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A learned prior  is trained to predict the distribution for zpast matching the distribution of  zfull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' During inference only the learned prior is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Adversarial predictive model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' An inpainting module is trained to fill  in texture-like content indistinguishable from real observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' An element-  wise discriminator module is trained to predict which regions are real and  generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' During inference only the inpainting module is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  state xpast and predicts a latent variable distribution Zpast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The  distributions Zfull and Zpast are optimized to be similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Next,  a latent variable zfull is sampled from Zfull and appended  to the encoding hpast and feed to a decoder generating a  new predicted complete state ˆx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The model is optimized by  computing the ℓ2 loss between ˆx and observed elements in  xfull  Lstruct =  1  Nstruct  Mfull ⊙ (ˆx − xfull)2  (4)  where Nstruct is the number of structure elements,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Mfull is  a binary mask indicating observed elements in xfull used to  7  Observation  World  accumulation  Plausible state  completion  C full  Cpast  Stochastic latent variable  predictive model  c full  past → Lstruct(εpast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  full)  Adversarial  predictive model  Lteature(c full,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' & full)  fullTraining  NN1  mf←(In)  Enc1  C full  Lstr  & full,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  DKL  Learned prior  Enc2  NN2  Cpast  Dec  →  Z full  Inference  NN2  past  past  Enc2  Dec  →ε  Zpast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='Training  Inpainter  Discriminator  Enci  Deci  Encd  Decd  full  m  Observed element  m  mask  Inference  Inpainter  Enci  Deci  full  ulllimit the loss to observed elements as is common in masked  VAE methods [40], [41], [43]–[45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The intuiting is that the learned distribution Zfull contains  the information required to reconstruct xfull, and the second  encoder learns to estimate this distribution from xpast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In other  words, knowing Zfull explains away the stochasticity involved  in reconstructing xfull from xpast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' At inference time zfull is  not known, but the second encoder has learned to predict Zpast  that is close to Zfull, effectively acting as a learned prior that  explains away the stochasticity by a latent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  2) Predicting texture by an adversarial predictive model:  Non-hierarchical reconstruction-based VAEs are ill-suited for  generating fine-grained details [17], [112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We therefore use  an adversarial predictive model to generate pixel-like content  such as road intensity for newly predicted structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The model  design is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The model consists of an encoder-  decoder inpainting module that takes the world state ˜xfull  with completed structure, and generates a new world state  x∗  full also with completed content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The inpainting module  is optimized by the minimax adversarial loss [28], [113] to  make observed and generated content indistinguishable, while  an element-wise discriminator module [114] is optimized to  discriminate elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The adversarial loss is computed using  the binary cross entropy (BCE) objective  Ltexture = −  1  Nstruct  �  (i,j)  BCE(m(i,j), ˆm(i,j))  (5)  where m is the real observed element binary mask, ˆm is the  predicted mask by the discriminator, and (i, j) are indices  of structure elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' At inference time only the inpanting  module is used to generate the completed world state x∗  full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' World model training  We train a model to predict a set of plausible worlds  conditioned on partially observed worlds as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  First, we optimize a regular HVAE model [115], [116] param-  eterized by qθ(z|x) and pθ(x|z) to encode and reconstruct  pseudo ground-truth world states x∗  full generated by the plau-  sible state completion module (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' IV-A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The learned  hierarchical latent variable prior pθ(z) and posterior qθ(z|x)  distributions [17] can be factorized as  pθ(z) = pθ(z1|z2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' pθ(zK−1|zK)pθ(zK)  (6)  qφ(z|x) = qφ(z1|z2, x) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' qφ(zK−1|zK, x)qφ(zK|x)  (7)  where each random variable is modeled by Normal distri-  butions N(z|µ, σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Deeper or more abstract codes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' zK)  encodes the global structure, while shallow codes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' z1)  encode the visual appearance of elements in x∗  full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We train  the HVAE by maximizing the hierarchical ELBO  log pθ ≥  E  qφ(z|x∗  full)  �  log pθ(x∗  full|z)  �  −DKL(qθ(z|x∗  full)||pθ(z))  (8)  where log pθ(x∗  full|z) is the likelihood of the reconstructed  state, and a KL divergence term that measures the divergence  between the distributions  DKL(qθ(z|x∗  full)||pθ(z)) =  K  �  k=2  E  qθ(z≥k|x∗  full)  �  DKL(qθ(zk−1|zk, x∗  full)||pθ(zk−1|zk))  �  +DKL  �  qθ(zK|x∗  full)||pθ(zK)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  (9)  We simultaneously train a secondary partially observed  encoder qφ(z|xpast) to predict a latent distribution similar  to qθ(z|x∗  full) based on the original partially observed world  states xpast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The second encoder is optimized by minimizing  DKL(qφ(z|x∗  full)||qψ(z|xpast)) =  K  �  k=1  E  q(z>k|x)  �  DKL(qφ(zk|z>k, x∗  full)||qψ(zk|z>k, xpast))  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  (10)  At inference time the model uses the partially observed  encoder to generate a latent distribution qφ(z|xpast) that can  be decoded by pθ(x|z) into a completely observed world state  ˆx similar to a pseudo ground-truth world state x∗  full without  the need to observe the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We developed the approach of optimizing hierarchical latent  distribution similarity as an extension of the single layer  latent variable model described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' IV-A1 inspired by  the stochastic video prediction model by Denton [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A  similar approach named Posterior Matching by Strauss [22]  was very recently published concurrently to our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our  method extends their method by allowing HVAEs to learn to  predict complete states from partial states only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' This property  is important in continual learning real-world mobile robotics  problems where the existence of a priori complete ground truth  states cannot be presumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' EXPERIMENTS  We conduct three sets of experiments to verify the feasibility  of each part of our framework in real-world environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  First, we evaluate the expected performance of pretrained  vision-based semantic segmentation models used to inter-  pretate sensor observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Secondly, we demonstrate the  quality of generated partially observed world states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Finaly,  we evaluate the trained world model in terms of predictive  accuracy and structural diversity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Our self-supervised learning framework does not depend  on human annotations and instead leverages a pretrained  vision-based semantic segmentation models to infer semantic  information from image observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The first experiment set  quantifies the expected domain generalization performance of  models trained on one or several annotated public datasets  and evaluated on our application target domain dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The  training datasets are Apolloscape, BDD100K, Cityscapes, and  Mapillary Vistas [117]–[120] providing 49287, 8000, 3475,  and 20000 training samples, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our target domain  8  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Predictive world model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We train a hierarchical latent variable  generative model to reconstruct pseudo ground-truth world states x∗  full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Simultaneously, we train a secondary encoder to predict similar latent dis-  tributions from the original partially observed world states xpast to predict  complete world states ˆx at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  dataset is KITTI-360 [121] providing 12054 annotated samples  across all sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' All experiments are listed in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' All  datasets provide Cityscapes-like labels and are thus easy to  concatenate into a larger multi-domain dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We use the  SOTA semantic segmentation model DeepLabV3+ [100] and  evaluate performance using different ResNet backbones [122]  and number of training iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We leverage the MMSeg-  mentation framework [123] to train and evaluate models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The second experiment set demonstrates how our framework  generates BEV world state representations by integrating se-  quences of sensor observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We found that leveraging 360  degree sensor observations result in a more useful temporal  self-supervision learning signal than forward view observa-  tions only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' As observations are not spatially and temporally  biased in the driving direction, future observations are less  obvious to predict, and thus improve extrapolation to to all  unobserved regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' While KITTI-360 provides 360 degree  vision from two fisheye cameras, it is not trivial to make  use of these images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' First, availability of annotated fisheye  image datasets is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Secondly, camera calibration parameters  for projecting the point cloud into the fisheye images are  not specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We choose to qualitatively demonstrate the full  perception pipeline on NuScenes [124] as it provides 360  degree camera views and point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We also quantitatively  estimate semantic accuracy of the generated BEV representa-  tions on KITTI-360 by comparing the single forward facing  camera results and the corresponding ground truth point cloud  semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We use the “RN 101 320K cm” model variant (see  Table I) for segmenting images on both datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  TABLE I  SEMANTIC SEGMENTATION DOMAIN GENERALIZATION PERFORMANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Model  Iters  Datasets∗  mIoU  road IoU  car IoU  RN 18  80K  ••cm  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='91  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='02  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='36  160K  ••cm  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='52  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='30  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='45  320K  ••cm  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='31  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='12  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='20  RN 50  80K  •••m  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='30  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='84  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='90  ••cm  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='78  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='71  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='30  abcm  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='70  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='97  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='85  160K  •••m  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='98  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='92  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='90  ••cm  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='67  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='70  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='45  abcm  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='15  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='82  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='34  320K  •••m  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='04  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='67  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='43  ••cm  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='65  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='56  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='26  abcm  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='27  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='76  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='11  RN 101  80K  •••m  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='96  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='44  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='23  ••cm  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='00  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='23  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='74  bcm  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='98  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='12  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='27  abcm  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='81  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='74  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='67  160K  •••m  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='57  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='30  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='29  ••cm  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='00  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='23  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='48  bcm  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='85  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='39  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='23  abcm  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='71  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='20  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='55  320K  ••cm  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='72  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='24  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='55  ∗a: Apolloscape, b: BDD100K, c: Cityscapes, m: Mapillary V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=', •: Filler  TABLE II  BEV SEMANTIC SEGMENTATION PERFORMANCE ON KITTI-360  road IoU  Evaluate all regions  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='31  Evaluate unobserved regions only  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='97  TABLE III  MEAN AND BEST WORLD MODEL PREDICTION ON THE TEST SEQUENCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  road IoU  #samples  1  2  4  8  16  32  Mean (all regions)  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='94  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='94  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='96  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='94  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='94  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='94  Best (all regions)  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='94  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='52  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='73  Mean (unob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' only)  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='21  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+page_content='21  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='21  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='21  Best (unob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' only)  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='21  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='53  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='81  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='01  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='16  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='31  The third experiment set evaluates the performance of our  predictive world model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We evaluate our model on the KITTI-  360 dataset as it contains long driving sequences with high-  frequency image and point cloud observations as expected in  a real system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Long sequences improves learning to model  large 80x80 m representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' High-frequency observations  increase the element density of partially observed world states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We evaluate our model on sequence #6 containing both subur-  ban and urban road scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We use the remaining 8 sequences  for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We use the ground truth point cloud semantics in  the predictive world modeling experiments due to KITTI-360  lacking usable 360 degree vision coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' RESULTS  Semantic segmentation performance We present our exper-  iment results in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The consistently best training dataset  combination is Cityscapes and Mapillary Vistas, and saturating  the training data with a large set of regionally and camera-wise  9  Training  Enc  ZK  Dec  Observation  DKL  accumulation  Z1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' ZK-1  Zk = N(Zkluk, Ok  个  Observation  Inference  accumulation  EnCpo  Dec  α  ZK  Z1unsimilar samples, like Apolloscape, is detrimental for domain  generalization performance on KITTI-360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Our hypothesis  is that data regionally similar to the application domain,  like Cityscapes, and diverse dataset capturing many regions  and varying cameras, like Mapillary Vistas, are beneficial  learning domain invariant features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' For backbone size we find  that domain generalization performance improves with larger  backbone sizes and additional training iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The high IoU values in Table I indicate that leveraging  a pretrained semantic segmentation model is an adequate  solution to infer relatively unambigous semantic classes like  “road” and “car” from image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 10-12 for a visual  demonstration of performance obtained on both NuScenes and  KITTI 360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Low IoU score samples are overrepresented by ambiguous  classification of what is and is not “road”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We conclude that the  remaining performance gap is primarily a matter of semantic  definition instead of a modeling problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 12 for a  visual demonstration of vauge semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Generation and integration of semantic point clouds We  confirm that our framework is able to generate and temporally  integrate semantic point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 10 we show qualitative  results on NuScenes based on the full 360 degree perception  pipeline presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 11 shows results on KITTI-  360 with a forward facing camera only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' In Table II we present  quantitative results comparing the “road” BEV generated by  the pretrained semantic segmentation model and ground truth  point cloud semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We present results evaluated for unob-  served regions only (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' future) and also including previously  observed regions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' past + future).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The results show that  the BEV IoU score is comparable to that of the original  perspective image IoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Our method lacks obvious comparative baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' To the  best of our knowledge, no prior work uses lidar observations  and generative modeling to stochastically predict spatial en-  vironments without relying on ground truth map data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Prior  image-based methods are generally non-generative models and  are trained and evaluated on the same ground truth data  domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' A reasonably fair comparison is between a recent  SOTA image-based monocular model [67] reporting 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='34  road IoU on the full KITTI Raw dataset [137], and our model  achieving 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='31 road IoU on the KITTI-360 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Note that  our results indicate the true expected domain generalization  performance as the model is not trained on the same dataset  domain, unlike the image-based model result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The degree of  performance difference demonstrate the inherent advantage of  using lidar observations for spatial prediction as presented by  our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  We observe an issue in open rural environments where  incoming trucks may cause the ICP algorithm to lose point  cloud correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We believe a more robust probabilistic  filtering approach [125]–[127] would remedy this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Another issue is that very large structures, such as express-  way intersections, are never comprehensively observed due to  limited effective lidar observation range and thus difficult to  learn to predict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We believe longer range lidars [128], [129]  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' BEVs generated from our perception pipeline applied on NuScenes  providing 360 degree camera setup and lidar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The top row show semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The bottom rows shows semantic segmentation output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' BEVs generated from our perception pipeline applied on KITTI-360  using one camera and lidar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The top row show semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The middle row  show intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The bottom row shows semantic segmentation output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  and incorporating vision-based depth estimation methods [97],  [132] may provide the necessary sensory range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  Predictive world model performance Table III presents  quantitative results showing the best IoU match among N sam-  pled complete world predictions and the actual future observed  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We find that in most situations the future observations  are deterministically predictable, meaning a single prediction  gives a reasonable estimation of the true world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' However, when  the future observations are not deterministically predictable,  sampling more worlds increases the likelihood of some pre-  diction matching the future observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The relation between sampling and predictive performance  is seen in Table III by how increasing the number of samples  results in the best sample matching the future observations  better (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' “Best”) while the mean over all samples remain  unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The best prediction among 32 samples reaching  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='73 % IoU, closing the gap to perfect prediction by 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='7 %  10  Past  Future  FullPast  Future  FullFig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' Visual comparisons of world samples generated from semantic segmentation and ground truth annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The human annotated “road” semantics  can be ambiguous as seen in the right example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  on average, when evaluating over both past and future obser-  vations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' 13 for examples of sampled worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' CONCLUSIONS  We present a framework to generate partially observed  world representations from sensor observations, and a self-  supervised predictive world model for generating a diverse  set of plausible complete world states trained from partially  observed states only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' We introduce a plausible complete state  module for generating pseudo ground-truth world states for  training the HVAE implementing the world model, and a latent  distribution similarity optimization approach for processing  partially observed world states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  ACKNOWLEDGMENT  This work was financially supported by JST SPRING,  Grant Number JPMJSP2125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content=' The authors would like to take  this opportunity to thank the “Interdisciplinary Frontier Next-  Generation Researcher Program of the Tokai Higher Education  and Research System”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
+page_content='  The computation was carried out through the “General  Projects” program on the supercomputer “Flow” at the In-  formation Technology Center, Nagoya University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ktE3T4oBgHgl3EQf5wsL/content/2301.04783v1.pdf'}
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+ASEAN’s Portfolio Investment in a Gravity Model∗
+Tomoo Kikuchia and Satoshi Tobeb
+aGraduate School of Asia-Pacific Studies, Waseda University
+bSchool of Policy Studies, Kwansei Gakuin University
+January 16, 2023
+Abstract
+We investigate the elasticity of portfolio investment to geographical distance in a
+gravity model utilizing a bilateral panel of 86 reporting and 241 counterparty coun-
+tries/territories for 2007-2017. We find that the elasticity is more negative for ASEAN
+than OECD members. The difference is larger if we exclude Singapore. This indicates
+that Singapore’s behavior is very different from other ASEAN members. While Sin-
+gapore tends to invest in faraway OECD countries, other ASEAN members tend to
+invest in nearby countries. Our study also shows the emergence of China as a significant
+investment destination for ASEAN members.
+Keywords: portfolio investment; ASEAN; gravity model; Poisson Pseudo Maximum
+Likelihood
+JEL Classification: F21; F34; O16
+∗We would like to thank Benedict Tiu and Yupeng Wang for their excellent research assistance. We
+would like to thank Mariel Monica R. Sauler and Junko Koeda for helpful comments that helped us revise
+the paper. This research was funded by Sumitomo Mitsui Banking Corporation Foundation for Interna-
+tional Cooperation. Corresponding author: Tomoo Kikuchi. Nishi-Waseda Bldg.7F, 1-21-1 Nishi-Waseda,
+Shinjyuku-ku, Tokyo 169-0051 Japan. Email: tomookikuchi@waseda.jp.
+1
+arXiv:2301.05443v1  [econ.GN]  13 Jan 2023
+
+1
+Introduction
+Net portfolio investment of ASEAN started to become positive for the period after the Asian
+Financial Crisis in 1997 (see Figure 1). This means that ASEAN invests in securities in the
+rest of the world more than the rest of the world invests in securities in ASEAN. On the
+other hand, the opposite is true for OECD after 2000, which is the period of our interest in
+this paper.
+Figure 1: Net portfolio investment of ASEAN and OECD (% of GDP, 5-year moving average
+across countries)
+Source: IMF Balance of Payments. Note: From 1970 to 2020, ASEAN members increased from 5 to 10 and
+OECD members from 22 to 37. There are also missing data for some years. The net portfolio investment of
+OECD fell from -76 billion USD in 2001 to -500 billion USD in 2002. This is mainly caused by the US and
+the UK, whose net portfolio investment fell from -325 billion USD to -425 billion USD and from 183 billion
+USD to -64 billion USD respectively accounting jointly for 48% of the drop in the net portfolio investment
+of OECD.
+Since 2001 ASEAN’s portfolio investment asset in OECD has increased much more in OECD
+than ASEAN (see Figure 2(a)). This suggests that ASEAN’s capital markets are less inte-
+grated than its goods markets, which have seen a steady growth in inter-regional trade in
+past years (compare Figure 2(c) and 2(d)). In contrast, OECD-OECD portfolio investment
+and trade have both grown over time (see Figure 2(b) and 2(d)). This tendency of ASEAN
+to invest in securities outside more than inside the region seems to go against regional fi-
+nancial integration that has been promoted after the Asian Financial Crisis in 1997. Indeed,
+comparing 2(a) and 2(b) we can see that around 80 percent of OECD’s portfolio assets are
+in OECD while only 7 percent of ASEAN’s portfolio assets are in ASEAN (60 percent in
+2
+
+4%
+2%
+0%
+2%
+ASEAN
+-4%
+OECD
+6%
+8%
+10%
+1960
+1964
+1966
+1968
+1970
+1972
+1974
+1976
+1978
+1980
+1988
+2010
+2012
+2014
+1962
+1982
+1984
+1986
+1990
+1992
+1994
+1996
+1998
+2002
+2004
+2006
+2008
+2016
+2000
+2018
+2020OECD) as of 2020. This concentration of portfolio investment in OECD also contributes to
+economic growth in OECD as shown in ?.
+(a) Porfolio investment of ASEAN
+(b) Portfolio investment of OECD
+(c) Trade of ASEAN
+(d) Trade of OECD
+Figure 2: Portfolio investment and trade of ASEAN and OECD (USD billion)
+Source: Portfolio investment data are from IMF CPIS including 5 ASEAN countries and 34 OECD countries.
+Trade data are from UN Comtrade including 10 ASEAN countries and 34 OECD countries.
+The purpose of this paper is to investigate the property of ASEAN’s portfolio investment
+in comparison with OECD’s. Unless otherwise stated, we refer to Indonesia, Malaysia, the
+Philippines, Singapore and Thailand, the so-called ASEAN-5, for which data are widely
+available as ASEAN. Since regional economic integration entails free movement of produc-
+tion factors within a geographical space, we employ a gravity model approach using a bi-
+lateral portfolio investment asset dataset to examine the elasticity of portfolio investment
+to geographical distance. Our bilateral panel includes 86 reporting and 241 counterparty
+countries/territories for the period 2007-2017. The coordinated portfolio investment survey
+(CPIS) by the International Monetary Fund (IMF) reports the bilateral gross stock of port-
+folio investment in each year based on the residency of investors and issuers. The series can
+be divided into two sub-categories: the equity instrument (investment) and the debt instru-
+ment (investment). In this paper we also make use of the data provided by Coppola et al.
+3
+
+1,600
+1,400
+1,200
+1,000
+800
+600
+400
+200
+ASEAN-ASEANPortfolio
+ASEAN-OECDPortfolio
+ASEAN-Row Portfolio$60,000
+$50,000
+$40,000
+$30,000
+$20.000
+$10.000
+$o
+2002
+2003
+2004
+2005
+2006
+2007
+2008
+2009
+2010
+2012
+2013
+2014
+2015
+2016
+001
+2011
+2017
+2018
+2019
+2020
+OECD-OECD Portfolio
+OECD-ASEAN Portfolio
+OECD-RoW Portfolio$3,000
+$2,500
+$2,000
+$1,500
+$1,000
+$500
+$o
+800
+2009
+2010
+2013
+2014
+2016
+2018
+2020
+00
+00
+.00
+201
+01
+ASEAN-ASEAN Trade All
+ASEAN-OECD Trade Al
+ASEAN-RoW Trade All$25,000
+$20.000
+$15,000
+S10,000
+$5,000
+$o
+2020
+二
+L
+L
+OECD-OECD Trade All
+OECD-ASEAN Trade All
+OECD-RoW Trade All(2021) who complied a restatement of the CPIS portfolio investment data from a residency
+to nationality basis, which is available for the period 2007-2017. By comparing the results
+of residency and nationality-based data we can reveal the role of tax havens for portfolio
+investment allocation of ASEAN.
+Our main results are:
+1. For 2007-2017 the elasticity of both debt and equity investment to distance is more
+negative for ASEAN than for OECD. This means that the tendency to invest in se-
+curities issued in nearby countries is stronger for ASEAN than OECD. This tendency
+is even stronger for ASEAN excluding Singapore. This suggests that Singapore’s be-
+havior is different from other ASEAN members. While Singapore tends to invest in
+faraway countries, other ASEAN members tend to invest in nearby countries.
+2. Relative to 2007 the elasticity of debt investment to distance has become more positive
+in the recent years for ASEAN while it has become more negative for OECD. ASEAN
+excluding Singapore follows a similar trend as OECD. This is consistent with a dramatic
+increase in Singapore’s debt investment in the US over the past decade (Singapore is
+far away from New York relative to other investment destinations).
+3. Relative to 2007 there is no significant change in the elasticity of equity investment to
+distance in the recent years for both ASEAN and OECD except that it has become
+positive on a residency basis in the original CPIS data for ASEAN and on a residency
+basis in the data by Coppola et al. (2021) for OECD in recent years. The deviating
+results are due to different coverage of countries in each data set and suggest that
+China for ASEAN and tax havens for OECD in recent years have become significant
+equity investment destinations. ASEAN excluding Singapore follows a similar trend
+as OECD.
+The results highlight the role of Singapore as a platform for both inward investment from
+other ASEAN members and outward investment to distant OECD members. In fact, Sin-
+gapore is ASEAN’s largest host for multinational companies attracting portfolio investment
+from other ASEAN members as well as ASEAN’s largest investor in the US and China. In
+other words, the contrasting investment behaviors of Singapore and other ASEAN mem-
+bers are not just caused by Singapore’s investment behavior but also by Singapore being a
+major destination for portfolio investment of other ASEAN members. Therefore, ASEAN’s
+financial integration would inevitably require a higher exposure of Singapore to securities in
+ASEAN.
+4
+
+Gravity model estimation is widely applied to analysis using bilateral trade flow data but also
+international asset allocation data (for a theoretical background see Okawa and Van Win-
+coop, 2012) such as foreign direct investment (FDI) in Head and Ries (2008) and De Sousa
+and Lochard (2011), cross-sectional bilateral portfolio equity flows in Lane and Milesi-Ferretti
+(2008), equity flows using panel data covering 1989 to 1996 in Portes and Rey (2005), and US
+bilateral asset holdings data in Chit¸u et al. (2014). There are several features of our paper
+that should be highlighted in relation to the literature. First, we employ a structural gravity
+model estimation combining the Poissson Pseudo Maximum Likelihood (PPML) approach
+with a set of various fixed-effects. The structural gravity model can solve concerns on omit-
+ted variable bias, heteroskedasticity and zero observations, which are well known challenges
+in estimating gravity models (see Anderson and Van Wincoop, 2003; Silva and Tenreyro,
+2006). Second, we provide a comparison between residency and nationality-based data to
+reflect the significance of tax havens in international financial markets in recent years. Third,
+we use a comprehensive dataset covering a wide range of investor and issuer countries from
+2007 to 2017 and contrast general patterns of asset allocation of ASEAN and OECD.
+The rest of the paper is organized as follows. Section 2 introduces the dataset. Section 3
+introduces our baseline specification and presents our main results. Section 4 discusses the
+portfolio investment of Singapore and other ASEAN members. Section 5 concludes.
+2
+Bilateral panel data
+This paper uses a bilateral panel data covering 86 reporting and 241 counterparty coun-
+tries/territories from 2007 to 2017. The country lists are provided in Table A.1 and A.2.
+The original bilateral portfolio investment asset data are from the CPIS by the IMF. We also
+make use of the data provided by Coppola et al. (2021) who complied a restatement of the
+CPIS portfolio investment data from a residency to nationality basis. The restatement from
+a residency to nationality basis is particularly important for tax havens such as the Cayman
+Island, Hong Kong or Singapore that attract large investment to companies that have in
+most cases other nationality but reside in the tax havens. For example, consider Alibaba
+Group Holding Ltd., which is a Chinese multinational technology company incorporated in
+the Cayman Islands, and listed in the New York Stock Exchange (NYSE) as well as in the
+Stock Exchange of Hong Kong (SEHK). When investors buy shares of the company listed
+either in NYSE or SEHK, it is recorded as equity investment in the Cayman Islands on a
+residency basis. On a nationality basis, however, the same investment is recorded as equity
+5
+
+investment in China as its main base of operation is in China.
+Unfortunately, the CPIS data contain only total portfolio investment but not the decompo-
+sition into debt and equity investment in China. The nationality- and residency-based data
+by Coppola et al. (2021) contain both debt and equity investments in China but their cov-
+erage is less comprehensive compared to the original CPIS data. For example, the data do
+not include 28 reporting countries, of which 15 are OECD countries. Therefore, we present
+results using all three datasets: 1) the residency-based data by Coppola et al. (2021), 2)
+the nationality-based restatement data by Coppola et al. (2021), and 3) the residency-based
+original CPIS data. The geographical distance is calculated using the latitudes and longitude
+of the single largest cities in countries provided by the CEPII database. In the following
+analysis the distance is expected to capture costs associated with investing in a remote
+country. Unlike in international trade where geographical distance matters as goods need
+to be transported, we might think that distance matters less for global capital allocation.
+Nevertheless, to the extend that investment is related to other economic activities such as
+international trade, we believe that the geographical distance should matter for portfolio
+investment too.
+Figure 3 highlights the geographical asset allocation of ASEAN. We divide issuer countries
+into 10 groups based on the geographical distance from investor countries (i.e., ASEAN
+members). Each bin in horizontal axis covers 2000 kilometers from the investors. The first
+bin includes countries located from 0 to 2000 kilometers away from the investor countries,
+the second bin from 2000 to 4000 kilometers away and so on.1 The figure underscores a weak
+tendency of ASEAN to invest in a nearby country and that the US has over the past two
+decades become a dominant destination for both debt and equity investments of ASEAN. In
+addition, the figure shows that China has become a significant equity investment destination
+for ASEAN.
+In contrast to ASEAN, Figure 4 shows that OECD has a strong tendency to invest in nearby
+countries. The US is a significant destination of both debt and equity investments for OECD
+but unlike for ASEAN it is in different bins for different members. In addition, we can see
+that China has become a significant equity investment destination for OECD, which is also
+located in different bins for different members. Note that the US is 14000-16000km away
+from most of ASEAN members while it is in varying distance away for different OECD
+1The figures are created by dividing the bilateral distance measures between the single largest cities from
+the CEPII GeoDist Database by 2000km in order to create a histogram with 10 bins. Counterpart countries
+are then divided by color into ASEAN, US, and Non-ASEAN Non-US categories.
+6
+
+(a) Debt in 2007
+(b) Debt in 2017
+(c) Equity in 2007
+(d) Equity in 2017
+Figure 3: Portfolio investment (nationality basis) of ASEAN in 10 distance groups (2000km
+per bin, USD billion)
+Source: Restated Bilateral External Portfolios - “Tax Haven Only” data are based on the work by Coppola
+et al. (2021) and were taken from www.globalcapitalallocation.com. Note: 5 ASEAN source countries
+(Indonesia, Malaysia, Philippines, Singapore, Thailand) and 144 destination countries.
+members. China is 4000-6000km away from most of ASEAN members while it is too in
+varying distance away for different OECD members. This suggests that the tendency of
+ASEAN members to invest in faraway countries can largely be attributed to the dominance
+of the US as a destination for both debt and equity investments of ASEAN members. In
+addition, the significance of China as a destination for equity investment of ASEAN members
+should contribute to weaken the trend of ASEAN members to invest in equities issued in
+faraway countries.
+3
+Gravity in portfolio investment
+Section 2 shows that ASEAN as a whole has a tendency to invest in faraway countries while
+OECD has a tendency to invest in nearby countries. This section examines the elasticity of
+portfolio investment to geographical distance for ASEAN and shows that Singapore behaves
+differently from other ASEAN members in allocating its portfolio investment.
+7
+
+$90
+$80
+$70
+$60
+$50
+$40
+$30
+$20
+$10
+$o
+ASEAN
+Rest of World
+USA
+CHN$250
+$200
+$150
+$100
+$50
+$o
+Y
+5
+6
+8
+ASEAN
+Rest of Worlc
+USA
+CHN$90
+$80
+$70
+$60
+$50
+$40
+$30
+$20
+$10
+$o
+5
+ASEAN
+Rest of Worlc
+VSA
+CHN$250
+$200
+$150
+$100
+$50
+$O
+n
+6
+ASEAN
+Rest of Worlc
+USA
+CHN(a) Debt in 2001
+(b) Debt in 2017
+(c) Equity in 2007
+(d) Equity in 2017
+Figure 4: Portfolio investment of OECD in 10 distance groups (2000km per bin, USD billion)
+Source:
+Distance is taken from CEPII GeoDist Database.
+Restated Bilateral External Portfolios -
+“Tax Haven Only” data are based on the work by Coppola et al. (2021) and were taken from www.
+globalcapitalallocation.com. Note: 19 OECD source countries and 196 destination countries.
+3.1
+Baseline analysis
+This subsection presents the baseline results. To investigate the elasticity of portfolio in-
+vestment to distance for both ASEAN and OECD as well as the rest of the world (ROW),
+we estimate a gravity model using the PPML estimation method that can reduce concerns
+such as heteroscedasticity and zero observations. In particular, zero observation is a serious
+issue in our application because almost one half of our observations are zeros.2 Our baseline
+specification is
+Portfoliok
+i,j,t = exp
+�
+βASEAN(ln Distancei,j × DASEAN)
++ βOECD(ln Distancei,j × DOECD) + βROW(ln Distancei,j × DROW) + δi,t + θi,t
+�
+εi,j,t,
+(1)
+where Portfoliok
+i,j,t represents the gross stock of portfolio investment asset, and superscript
+k corresponds to the types of portfolio investment: debt or equity instrument; Distancei,j
+2Silva and Tenreyro (2006) shows that the method performs well when the proportion of zeros is large
+by Monte Carlo simulations.
+8
+
+$1,800
+$1,600
+$1,400
+$1,200
+$1,000
+$800
+$600
+$400
+$200
+$O
+OECD Non-US
+Rest of Worlo
+USA
+CHN$2,000
+$1,800
+$1,600
+$1,400
+$1,200
+$1,000
+$800
+$600
+$400
+$200
+$o
+OECD Non-US
+Rest of Worla
+USA
+CHN$2,500
+$2,000
+$1,500
+$1,000
+$500
+$o
+OECD Non-US
+Rest ot Worlo
+USA
+CHN$4,000
+$3,500
+$3,000
+$2,500
+$2,000
+$1,500
+$1,000
+$500
+$O
+OECD Non-US
+Rest of Worlc
+USA
+CHNrepresents the geographical distance between the single largest cities in a particular pair
+country; DASEAN, DOECD and DROW are dummy variables that take a value of one if a
+reporting country is in ASEAN, OECD or ROW and zero otherwise; δi,t and θj,t are reporting
+country-time specific fixed effects and counterparty country-time specific fixed effects. εi,j,t
+is the error term.
+Reporting and counterparty country-time fixed effects control country-specific time varying
+factors. For example, they can control the sizes of GDP of investor and issuer countries in
+each year, both of which are often included in traditional plain-vanilla gravity models as
+well as geographical distance. In addition to the two types of fixed effects, structural gravity
+models often include country-pair fixed effects (Anderson and Van Wincoop (2003)). The
+pair-fixed effects can control time-invariant country-pair specific factors, such as geographical
+distance, common official language, contiguous borders, and presence of colonial ties between
+investor and issuer countries. In this baseline analysis, however, specification excludes the
+country pair-fixed effects to focus on average elasticity of the distance throughout sampled
+period.
+Inclusion of both the pair-fixed effects and geographical distance causes perfect
+collinearity, because they are time-invariant country-pair specific variables indexed by (i,
+j)-level. We show the estimation results based on the specification with country pair-fixed
+effects in the next subsection. We use the gross stock of portfolio investment asset as netting
+of gross asset and liability may overlook key information on asset allocation of domestic
+and foreign investors.3 The coefficients of our interest are βASEAN, βOECD and βROW that
+capture the relative elasticity to distance of each country group.
+Figure 5 plots the coefficients of distance for each country group with 95 percent confidence
+intervals.
+Panel (a) shows that the elasticity of distance to portfolio debt investment is
+negative and statistically significant for all country groups and datasets, which is consistent
+with the typical behavior observed in gravity model estimations using bilateral trade flows.
+The result suggests that the investors prefer debt securities issued in a nearby country.
+However, the size of the coefficients is different across the groups. They are more negative in
+ASEAN and ROW compared to OECD. Panel (b) shows similar results for equity investment.
+These results indicate that ASEAN and ROW investors in equities are more sensitive to
+distance than OECD investors. One might think that these results contradict our observation
+of ASEAN’s portfolio investment in Section 2. In the following we will solve those seemingly
+contradicting observations.
+Each ASEAN member differs in terms of level of economic development, depth of domestic
+3Standard gravity estimations for trade uses gross export or import too.
+9
+
+(a) Debt investment
+(b) Equity investment
+Figure 5: Baseline analysis
+Note:
+The figures plot the coefficients of interaction terms of geographical distance (logged) and
+ASEAN/OECD dummy with 95 percent confidence intervals based on standard error clustering at country-
+pair level. The circle, diamond, and square markers represent the results using residency-based, nationality-
+based, and CPIS residency-based data. We omit the coefficients of ROW to focus on the ASEAN-OECD
+comparison. The full results are available on request.
+(a) Debt investment
+(b) Equity investment
+Figure 6: Baseline analysis (ASEAN ex-SGP dummy)
+Note: The figures plot the coefficients of interaction terms of geographical distance (logged) and ASEAN
+ex-SGP/OECD/ROW dummy with 95 percent confidence intervals based on standard error clustering at
+country-pair level. The circle, diamond, and square markers represent the results using residency-based,
+nationality-based, and CPIS residency-based data. We omit the coefficients of ROW to focus on the ASEAN-
+OECD comparison. The full results are available on request.
+10
+
+Coefficient of geographical distance
+OECD
+ASEAN
+Residency
+Nationality
+Residency (CPISCoefficient of geographical distance
+OECD
+ASEAN
+Residency
+Nationality
+Residency (CPISCoefficient of geographical distance
+OECD
+ex-SGP ASEAN
+Residency
+Nationality
+Residency (CPIS)Coefficient of geographical distance
+OECD
+ex-SGP ASEAN
+Residency
+Nationality
+Residency (CPIS)financial market, and preference of investors. Especially, Singapore being an international
+financial center plays a special role in the group. Figure 6 presents the results when the
+specification uses ASEAN ex-Singapore dummy (i.e., ASEAN4-member dummy) instead of
+ASEAN5-member dummy. Panel (a) shows the results for debt investment. The coefficients
+of ex-SGP ASEAN become more negative compared to those of ASEAN presented in Figure
+5(a). The size of the coefficients are around -1.3 for ASEAN ex-SGP, while they are around
+-1.0 for ASEAN. Comparing Figures 6(b) and 5(b) the coefficients for equity investment of
+ASEAN ex-SGP are also slightly more negative than those of ASEAN. The results indicate
+that Singapore investors are less sensitive to distance than other ASEAN investors. There-
+fore, we obtain contrasting results when we treat ASEAN as a whole and when we treat them
+separately. This is particularly the case because of Singapore’s dominant position both as
+investor and investment destination in ASEAN as we will discuss in Section 4.
+3.2
+Time-series change in portfolio investment
+This subsection investigates the change in the elasticity of portfolio investment to distance
+over time. The specification is
+Portfoliok
+i,j,t = exp
+� 2017
+�
+t=2008
+βASEAN
+t
+(ln Distancei,j × γt × DASEAN)
++
+2017
+�
+t=2008
+βOECD
+t
+(ln Distancei,j × γt × DOECD) + δi,t + θi,t + µi,j
+�
+εi,j,t.
+(2)
+The setting follows the baseline analysis described in the previous section, except for includ-
+ing the interaction terms of geographical distance (ln Distancei,j), time-fixed effects (γt), and
+ASEAN/OECD dummy (DASEAN and DOECD) as well as country-pair fixed effects (µj,i).
+Interacting the distance and time-fixed effects enables us to include country pair-fixed ef-
+fects. The interaction terms are country-pair-time-specific variables indexed by (i, j, t)-level,
+so we can avoid multicollinearity with country-pair fixed effects indexed by (i, j)-level. Spec-
+ification with full set of fixed effects (i.e., reporting/counterparty country-time fixed effects
+and country-pair fixed effects) is the standard setting in structural gravity literature (e.g.,
+Anderson and Van Wincoop (2003)), which can reduce the concern on possible estimation
+bias.4 The coefficients of our interest are βASEAN
+t
+and βOECD
+t
+that capture the relative elas-
+4We confirm that the specification additionally including the interaction term of geographical distance,
+time-fixed effects, and ROW dummy delivers similar results. Including reporting country-time fixed effects,
+11
+
+ticity to distance in each year and country group compared to a specific base year. We set
+the first year of the sample, i.e., 2007, as the base year. Thus, the sequences of βASEAN
+t
+and
+βOECD
+t
+capture the time variation of the elasticity from 2008 to 2017 in each country group.
+Figure 7 plots the time variation of the coefficients of debt investment to distance with 95
+percent confidence intervals. The blue and red markers represent the results of the residency-
+and nationality-based data provided by Coppola et al. (2021) and the green markers represent
+the results of the residency-based CPIS data. Panels (a) and (b) report the results of ASEAN
+and OECD.
+(a) ASEAN
+(b) OECD
+Figure 7: Debt investment
+Note: The figures plot the coefficients of interaction terms of geographical distance (logged), time-fixed
+effects, and ASEAN/OECD dummy with 95 percent confidence intervals based on standard error clustering
+at country-pair level. The circle and diamond markers represent the results using residency- and nationality-
+based data.
+Panel (a) shows that the coefficients of ASEAN get larger and significant since the mid-
+2010, while they are small and insignificant in the 2000s. All three datasets follow a similar
+pattern. The positive elasticity indicates that ASEAN tends to invest in bonds issued in
+a faraway country compared to the base year 2007. This is consistent with the fact that
+ASEAN has increased its portfolio investment to faraway OECD countries (see Figure 2(a))
+and in particular in the US in the past decade (see Figure 3(a) and 3(b)).
+Panel (b) shows the result for OECD. The elasticity presents a contrasting pattern to that
+of ASEAN and gets more negative and significant after the late-2000s indicating that OECD
+counterparty country-time fixed effects, and country-pair fixed efects is the first best choice in estimating a
+structural gravity model (Anderson and Van Wincoop (2003) and Silva and Tenreyro (2006)).
+12
+
+Coefficient of interaction terms of
+6
+2
+2008
+2009
+2010
+2011
+2012
+2013
+2014 
+5
+2016
+2017
+201
+Residency
+Nationality
+Residency (CPIS)5
+Coefficient of interaction terms of
+-.05
+5
+2008
+2009
+2010
+2011
+2012
+2013
+2014 
+5
+2016
+2017
+2015
+Residency
+Nationality
+Residency (CPIS)tends to invest in bonds issued in a nearby country compared to the base year 2007. The
+three datasets largely deliver similar results.
+The result is consistent with the fact that
+OECD members have increased investment in bonds issued by other OECD members (see
+Figure 2(b)) who are in close proximity relative to the distance between ASEAN and OECD
+members (see Figure 4(a) and 4(b)).5
+(a) ASEAN
+(b) OECD
+Figure 8: Equity investment
+Note: The figures plot the coefficients of interaction terms of geographical distance (logged), time-fixed
+effects, and ASEAN/OECD dummy with 95 percent confidence intervals based on standard error clustering
+at country-pair level. The circle and diamond markers represent the results using residency- and nationality-
+based data.
+Figure 8 reports the results for equity investment. The results show qualitatively similar
+patterns for ASEAN and OECD especially for nationality-based data. The coefficients are
+not statistically different from zero throughout the sample period. The results indicate that
+there is little change in the geographical allocation of equity investment for ASEAN and
+OECD. This is consistent with our earlier observations for ASEAN (compare Figure 3(c)
+and 3(d)) and OECD (compare Figure 4(c) and 4(d)). Note that the points of the original
+residency-based data deviate from the other two data points based on Coppola et al. (2021)
+in Figure 8(a) because the original residency-based data do not provide data for equity
+investment in China, which is 4000-6000km away from most of ASEAN members (see Figure
+3(c) and 3(d)).
+We confirmed that the coefficients estimated by the three dataset (i.e.,
+Coppola et al. (2021)’s data on a residency-basis and a nationality-basis, and the CPIS data
+on a residency-basis) are similar if we use the same sample countries. This suggests the
+5In the literature on bilateral trade flows, the negative coefficients of distance is known as “distance
+puzzle”, where estimated negative impact of distance on trade flows has remained persistently large across
+major different settings and samples (e.g., (Disdier and Head, 2008; Yotov, 2012)).
+13
+
+Coefficient of interaction terms of
+2008
+2009
+2010
+2011
+2
+3
+2014
+5
+2016
+2017
+2012
+2013
+201
+Residency
+Nationality
+Residency (CPIS)Coefficient of interaction terms of
+2008
+2009
+2010
+2011
+2012
+2013
+2014
+5
+2016
+2017
+2015
+Residency
+Nationality
+Residency (CPIS)difference between the three dataset comes from the coverage of the countries rather than
+the restatement from residency- to nationality-basis.
+(a) Debt investment
+(b) Equity investment
+Figure 9: Portfolio investment of ASEAN ex SGP
+Note: The figures plot the coefficients of interaction terms of geographical distance (logged), time-fixed
+effects, and ASEAN ex-Singapore dummy with 95 percent confidence intervals based on the standard error
+clustering at the country-pair level. The circle and diamond markers represent the results using residency-
+and nationality-based data.
+Figure 9 presents the results when the specification uses ASEAN ex-SGP. Figure 9(a) shows
+the results for debt investment. The elasticity gets negative and largely significant after
+the late-2000s, which is similar to the results for OECD presented in Figure 7(b). Figure
+9(b) shows that the result for equity investment is similar to that for OECD too. These re-
+sults indicate that investors in ASEAN except Singapore have not significantly changed their
+behavior in allocating portfolio investment across countries since the base year 2007. There-
+fore, the positive trend in the elasticity of ASEAN’s debt investment to distance observed
+in Figure 7(a) must be driven by Singapore.
+4
+Discussions
+Section 3 shows that the elasticity of portfolio investment to distance is more negative for
+ASEAN than OECD. However, the difference is less significant when we exclude Singapore
+from the ASEAN sample. This suggests that Singapore’s investment behavior is very differ-
+ent from other ASEAN members. Therefore, this section will examine the role of Singapore
+for portfolio investment of ASEAN as a whole.
+14
+
+Coefficient of interaction terms of
+5
+2008
+2009
+2010
+2011
+2012
+2013
+2014
+5
+2016
+2017
+2015
+Residency
+Nationality
+Residency (CPIS)Coefficient of interaction terms of
+2
+2008
+2009
+2010
+2011
+2012
+2013
+2014
+2015
+2016
+2017
+Residency
+Nationality
+Residency (CPIS)4.1
+Portfolio investment of Singapore and other ASEAN members
+Table 1 shows debt investment of ASEAN members in OECD, ASEAN and the rest of the
+world. Singapore allocates above 70 percent of its debt investment to OECD in 2007 and
+2017.
+Besides Singapore and Indonesia other ASEAN members increased the allocation
+of their debt investment to ASEAN but decreased the allocation to OECD from 2007 to
+2017. This is consistent with our result that the elasticity of debt investment to distance
+is more negative for ASEAN ex-SGP than for ASEAN, and indicates that Singapore is the
+global debt investor in ASEAN. Figure 10 shows a network chart indicating the relative
+Table 1: Debt investment (nationality basis) allocation of ASEAN members
+Note: ASEAN 5 countries and 144 destination countries. Restated Bilateral External Portfolios - “Tax Haven
+Only” data based on the work by Coppola et al. (2021) and obtained from www.globalcapitalallocation.
+com.
+investment size of ASEAN countries in top 10 countries in 2007 and 2017.6 The figure shows
+that Singapore is absolutely ASEAN’s largest investor in foreign debt and the US grew to
+become the dominant destination of its debt investment from 2007 to 2017. Indeed, the US
+alone accounts for 43 percent of ASEAN’s debt investment in 2017.7 Notably, emerging as
+the number two destination China accounts for 13 percent of ASEAN’s debt investment in
+2017. This largely explains the positive trend in the elasticity of ASEAN’s debt investment
+shown in Figure 7(a).
+Table 2 shows that Singapore’s allocation of equity investment is largely similar to that of
+other ASEAN members from 2007 to 2017 as seen in Figure 8(a) and 9(b). Both Singapore
+and other ASEAN members’ allocation has decreased from 67 to 63 percent to OECD, has
+increased from 25 to 30-32 percent to the rest of the world, and has decreased from 8-9
+6The size of each “thread” denotes a relative size for each graph (year), so we can not compare the
+investment size across graphs (years). The network charts are created using the replication code available
+at https://github.com/global-capital-allocation-project/redrawing-the-map.
+7Malaysia and Indonesia feature within ASEAN’s top 10 debt investment destinations. However, the
+amount is dwarfed by Singapore’s investment in the US and China.
+15
+
+(a) 2007
+(b) 2017
+Figure 10: Debt investment (nationality basis) of ASEAN members in top 10 countries
+Note: 144 destination countries. Restated Bilateral External Portfolios - “Tax Haven Only” data based on
+the work by Coppola et al. (2021) and obtained from www.globalcapitalallocation.com.
+Table 2: Equity investment (nationality basis) allocation of ASEAN members
+Note:
+Note:
+ASEAN 5 countries and 144 destination countries.
+Restated Bilateral External Portfo-
+lios - “Tax Haven Only” data based on the work by Coppola et al. (2021) and obtained from www.
+globalcapitalallocation.com.
+to 5-8 percent to ASEAN. Figure 11 shows that Singapore is absolutely the largest equity
+investor among ASEAN members too. The US and China have grown to become the most
+dominant destinations accounting for 31 and 21 percent of ASEAN’s equity investment in
+2017, most of which is Singapore’s investment. The figure also shows that the large equity
+investment of Singapore in ASEAN in 2007 is in Malaysia, which has since then fallen out of
+top 10 equity investment destinations of ASEAN members. On the other hand, Singapore
+features as a top 10 destination of ASEAN’s equity investment. Note that the US is 14000-
+16000km away and China is 4000-6000km away from most ASEAN members. The presence
+16
+
+Malaysia
+Indonesia
+UnitedStates
+United Kingdom
+Australia
+Singapore
+Germany
+Korea, Rep. of
+Japan
+France
+ Thailand
+Italy
+Philippines
+Others
+Malaysia
+IndonesiaMalaysia
+Indonesia
+UnitedStates
+China
+Singapore
+Germany
+United Kingdon
+Australia
+India
+Korea, Rep. of
+Thailand
+Canada
+Malaysia
+Philippines
+Others
+Indonesia(a) 2007
+(b) 2017
+Figure 11: Equity investment (nationality basis) of ASEAN countries in top 10 countries
+Note: Note: 144 destination countries. Restated Bilateral External Portfolios - “Tax Haven Only” data
+based on the work by Coppola et al. (2021) and obtained from www.globalcapitalallocation.com.
+of China as a destination for ASEAN’s equity investment explains why the elasticity of equity
+investment to distance is less negative than that of debt investment for ASEAN given the
+relative proximity of China to ASEAN members (see Figure 5 and 6).
+4.2
+Singapore’s role in ASEAN
+Section 4.1 showed the dominant role of Singapore for ASEAN’s portfolio investment. Con-
+sidering its size of GDP relative to other ASEAN members, Singapore’s portfolio investment
+is disproportionately large. On the other hand, Singapore is also a major destination of
+ASEAN’s portfolio investment. Figures 12 shows the time series of portfolio investment of
+ASEAN members on a nationality basis from 2007 to 2017 sorted according to different des-
+tinations. We can see that Singapore is a major destination for both debt investment (see
+Figure 12(a)) and equity investment (see Figure 12(b)) on a nationality basis for Malaysia.
+Given the relatively large investment size of Malaysia we can say that Singapore attracts
+most of ASEAN’s portfolio investment.
+We now examine the changes in data the restatement (i.e., from a residency to nationality
+basis) makes to ASEAN’s portfolio investment. The changes highlight 1) ASEAN’s invest-
+ment in multinational companies residing in Singapore and 2) Singapore’s investment in
+17
+
+Malaysia
+UnitedStates
+China
+United Kingdom
+Japan
+Singapore
+India
+Korea, Rep. of
+Australia
+France
+HongKong
+Malaysia
+Thailand
+Others
+Indonesia
+PhilippinesSingapore
+UnitedStates
+China
+Singapore
+Japan
+India
+United Kingdon
+Korea, Rep. of
+Luxembourg
+Malaysia
+Australia
+Hong Kong
+Thailand
+Indonesia
+Others
+Philippines(a) Debt
+(b) Equity
+Figure 12: Portfolio investment (nationality basis) of ASEAN countries from 2007 to 2017
+(USD billion)
+Note: Note: 144 destination countries. Restated Bilateral External Portfolios - “Tax Haven Only” data
+based on the work by Coppola et al. (2021) and obtained from www.globalcapitalallocation.com.
+multinational companies in other tax havens such as the Cayman Island.8
+Figure 13(a) shows the top 10 changes in each ASEAN member’s investment after the re-
+statement (ASEAN members are highlighted in blue). We can see that Singapore records by
+far the largest changes but for all ASEAN countries the restatement increases investment in
+China and the US and decreases investment in tax-haves such as the Cayman Island, Singa-
+pore, Hong Kong, and the Netherlands. This suggests that there is a significant amount of
+investment from ASEAN in Chinese and American companies located in those tax-havens
+outside China and the US such as Singapore’s investment in Chinese companies in the Cay-
+man Island and Hong Kong (e.g. Alibaba Group Holding Ltd. and Tencent Holdings Ltd.).
+We estimate that roughly 50 billion USD out of Singapore’s portfolio investment of 70 billion
+USD on a residency basis in the Cayman Islands and Hong Kong is in Chinese companies.9
+Next to Singapore, Malaysia records the largest changes. Malaysia’s investment after the
+8The database provided by Coppola et al. (2021) identifies the identity of the issuer of debt or equity
+but not of the investor. Therefore, it can not tell us the nationality of multinational companies who reside
+in Singapore and invest outside Singapore.
+9If we assume that the entire drop in Singapore’s investment in Hong Kong (20 billion USD) and in the
+Cayman Islands (30 billion USD) is due to investment in Chinese companies, we get roughly 50 billion USD.
+18
+
+Indonesia
+7.5
+OECD
+Row
+5.0
+ASEANex-Singapore
+Singapore
+2.5
+0.0
+Malaysia
+25.0
+20.0
+15.0
+10.0
+5.0
+0.0
+Philippines
+9.0
+6.0
+3.0
+0.0
+Thailand
+20.0
+10.0
+0.0
+2007
+2008
+2009
+2010
+2011
+2012
+2013201420152016
+2017Indonesia
+6.0
+OECD
+Row
+4.0
+ASEAN ex-Singapore
+Singapore
+2.0
+0.0
+Malaysia
+40.0
+20.0
+0.0
+Philippines
+1.0
+0.5
+0.0
+Thanand
+20.0
+10.0
+0.0
+2007
+2008
+2009
+2010
+2011
+2012
+20132014
+2015
+2016
+2017(a) Investment from ASEAN
+(b) Investment into ASEAN
+Figure 13: Portfolio investment from and into ASEAN: Top 10 changes (nationality - resi-
+dency) in 2017 (USD million)
+Note: 144 destination countries. Restated Bilateral External Portfolios - “Tax Haven Only” data based on
+the work by Coppola et al. (2021) and obtained from www.globalcapitalallocation.com.
+restatement falls the largest in Singapore (see Malaysia in Figure 13(a)). This shows that
+Singapore is the largest host of Malaysia’s investment in multinational companies outside
+their home countries. On the other hand, Malaysia’s investment after the restatement rises
+the largest in China (see Malaysia in Figure 13(a)) suggesting that Malaysia invests a sig-
+nificant amount in Chinese companies residing in Singapore (see Figure 14). We estimate
+that roughly 2 billion USD out of Malaysia’s total portfolio investment of 25 billion USD on
+19
+
+Singapore
+40.00
+20.00
+0.00
+20.00
+Indonesia
+1.00
+0.00
+-1.00
+-2.00
+6.00
+Malaysia
+4.00
+2.00-
+0.00
+-2.00
+Philippines
+0.50
+0.25-
+0.00
+-0.25
+Thailand
+4.00
+2.00
+S
+0.00
+2.00Singapore
+8.0
+4.0
+0.0
+Indonesia
+3.0
+2.0
+1.0
+0.0 -
+Malaysia
+8.0
+6.0 -
+4.0
+2.0
+0.0 -
+Philippines
+0.6 
+0.4
+0.2
+0.0-
+Thailand
+4.0
+3.0
+2.0
+1.0
+NOR
+KOR
+3
+9
+0.0 -a residency basis in Singapore in 2017 is in Chinese companies.10
+Figure 14: Malaysia’s investment in Singapore
+Figure 13(b) shows the top 10 changes in investment into ASEAN members after the re-
+statement (ASEAN members are highlighted in blue). We can see that Singapore records
+the largest changes but the difference to other ASEAN members is not as large as in Figure
+13(a) when we compare ASEAN members as investors. The largest rise in investment in
+all ASEAN members after the restatement is from the US and Japan showing that the two
+countries invest in ASEAN companies outside their homes more than in multinational com-
+panies in each of ASEAN members. Notably, Malaysia records the largest fall for investment
+in Singapore (see Singapore in Figure 13(b)). Therefore, Singapore is not only the largest
+host of Malaysia’s investment in multinational companies outside their home country as seen
+in Figure 13(a) but Malaysia is the largest international investor in such multinational com-
+panies in Singapore. These examples show that Singapore is a platform for multinational
+(e.g. Chinese) companies to raise capital attracting inward portfolio investment from other
+ASEAN members.
+To summarize, Singapore’s investments in tax havens such as the Cayman Island and Hong
+Kong, which are largely investments in Chinese and American companies, are by an order
+of a magnitude larger than other ASEAN member’s investments in those tax havens. On
+the other hand, ASEAN members (Malaysia in particular) invest in multinational (Chinese
+in particular) companies residing in Singapore. Note that those investment in multinational
+(non-Singaporean) companies in Singapore as well as Singapore’s investments in multina-
+tional companies in tax havens only highlight Singapore’s role as a platform for both inward
+10If we assume that Malaysia invests in Chinese companies in Hong Kong, the Caymand Islands and
+Singapore and that most of the drop in Malaysia’s investment in Hong Kong (2.5 billion USD) and two
+thirds of the drop in the Cayman Islands (1 billion USD) is due to investment in Chinese companies, we get
+roughly 2 billion USD (5.5 − 2.5 − 1 = 2).
+20
+
+and outward investments in multinational companies (whose nationality is different from res-
+idency) but are only a part of Singapore’s overall outward investments as well as investments
+of other ASEAN members in Singapore.
+5
+Conclusion
+It is often argued that ASEAN as a whole tend to invest in securities outside more than
+inside the region. We estimate a gravity model using the PPML estimation method utilizing
+a bilateral panel of 86 reporting and 241 counterparty countries/territories for the period
+2007-2017. We find that the elasticity of both debt and equity investments to geographi-
+cal distance is actually more negative for ASEAN than for OECD. However, we find that
+the ASEAN-OECD difference in elasticity gets smaller when we exclude Singapore from the
+ASEAN sample. This indicates that Singapore’s investment behavior is very different from
+that of other ASEAN members. Singapore tends to invest in faraway countries predomi-
+nantly in the US while other ASEAN members tend to invest in nearby countries. Since
+Singapore’s investment is disproportionately large, its behavior drives the investment of
+ASEAN as a whole. Indeed, Singapore facilitates both inward investment from ASEAN and
+outward investment to OECD. Multinational companies in Singapore attract investment
+from ASEAN, in particular, Malaysia. On the other hand, Singapore is by far ASEAN’s
+largest investor in American and Chinese companies residing tax haves such as the Cayman
+Island and Hong Kong. Lastly, the elasticity of equity investment is less negative than that
+of debt investment for ASEAN reflecting the increasing presence of China as a destination
+for equity investment.
+Our analysis shows that geographical distance inhibit ASEAN’s portfolio investment more
+than OECD’s but Singapore defies gravity and invests in faraway OECD countries. There-
+fore, ASEAN’s financial integration would inevitably require a higher exposure of Singapore’s
+investment to ASEAN. Is it the high level of financial development that facilitate portfolio
+investment among OECD members who happen to be relatively close to each other? It
+might be that having a developed financial market Singapore invests in the US and other
+OECD countries because the developed financial markets are better connected. Our gravity
+model uses only distance and fixed effects to estimate portfolio investment. It remains as a
+future research to investigate the determinants in reporting and counterparty countries that
+can explain our results and hold the key for financial integration.
+21
+
+A
+Appendix
+Table A.1: List of reporting countries
+Note: Data availability of reporting country as of 2017. †Reporting countries Coppola et al. (2021)’s data
+do not cover.
+22
+
+Albania
+Denmark
+Korea, Rep. of
+Poland, Rep. of
+Argentina
+Egypt, Arab Rep. of
+Kosovo, Rep. of
+Portugal
+Aruba
+Estonia, Rep. of
+Kuwait
+Romania
+Australia
+Finland
+Latvia
+Russian Federation
+Austria
+France
+Lebanon
+Saudi Arabia
+Bahrain, Kingdom of
+Germany
+Lithuania
+ Singapore
+Bangladesh
+Gibraltar
+Luxembourg
+Slovak Rep.
+Belarus, Rep. of
+Greece
+Macao
+Slovenia, Rep. of
+Belgium
+Guernsey
+Malaysia
+South Africa
+Bermuda
+Honduras
+Malta
+Spain
+Boliviat
+Hong Kong
+Mauritius
+Sweden
+Brazil
+Hungary
+Mexico
+Switzerland
+Bulgaria
+Iceland
+Mongolia
+Thailand
+Canada
+India
+Netherlands, The
+Turkey
+Cayman Islands
+Indonesia
+New Zealand
+Ukrainet
+Chile
+Ireland
+North Macedonia, Rep. of
+United Kingdom
+China
+Isle of Man
+Norway
+United States
+Colombia
+Israel
+Pakistan
+Uruguay
+Costa Rica
+Italy
+Palau, Rep. of
+Venezuela, Rep.t
+Curacao and Sint Maarten
+Japan
+Panama
+West Bank and Gaza
+Cyprus
+Jersey
+Peru
+Czech Rep.
+Kazakhstan, Rep. of
+PhilippinesTable A.2: List of counterparty countries
+Note: Data availability of counterparty countries as of 2017.
+23
+
+Afghanistan, Islamic Rep. of
+Dominican Rep.
+Leb anon
+Samoa
+Albania
+Ecuador
+Lesotho, Kingdom of
+San Marino, Rep. of
+Algeria
+Egypt, Arab Rep. of
+Liberia
+Sao Tome and Principe, Dem. Rep. of
+American Samoa
+Ei Salvador
+Libya
+Saudi Arabia
+Andotra
+Equatorial Guinea Rep. of
+Liechtenstein
+Senegal
+Angola
+Eritrea, The State of
+Lithuania
+Serbia Rep. of
+Anguilla
+Estonia, Rep. of
+Luxembourg
+Seychelles
+Antigua and Barbuda
+Eswatini, Kingdom of
+Macao
+Sierra Leone
+Argentina
+Ethiopia
+Madagascar, Rep. of
+Singapore
+Armenia, Rep. of
+Falkland Islands (Malvinas)
+Malawi
+Sint Maarten
+Aruba
+Faroe Islands
+Malaysia
+Slovak Rep.
+Australia
+Fiji
+ Maldives
+Slovenia, Rep. of
+Austria
+Finland
+Mali
+Solomon Islands
+Azerbaijan, Rep. of
+France
+Malta
+Somalia
+Bahamas, The
+French Polynesia
+Marshall Islands, Rep. of the
+South Afica
+Bahrain, Kingdom of
+French Southern Territories
+Martirique
+South Sudan, Rep. of
+Bangladesh
+Gabon
+Mauritania, Islamic Rep. of
+Spain
+Barb ados
+Gambia, The
+Mauritius
+Sri Lanka
+Belarus, Rep. of
+Georgia
+Mayotte
+St. Kitts and Nevis
+Belgum
+Germany
+Mexico
+St. Lucia
+Belize
+Ghana
+Micronesia, Federated States of
+St. Vincent and the Grenadines
+Benin
+Gibraltar
+Moldova Rep. of
+Sudan
+Bemuda
+Greece
+Monaco
+Suriname
+Bhutan
+Greenland
+Mongolia
+Sweden
+Bolivia
+Grenada
+Montenegro
+Switzerland
+Bonaire, St. Eustatius and Saba
+Guadeloupe
+Montserrat
+Syrian Arab Rep.
+Bosnia and Herzegovina
+Guam
+Morocco
+Taiwan
+Botswana
+Guatemala
+Mozambique, Rep. of
+Tajikistan, Rep. of
+Brazil
+Guernsey
+Tanzania, United Rep. of
+British Indian Ocean Teritory
+Guiana, French
+Namibia
+Thailand
+British Virgin Islands
+Guinea
+Nauru, Rep. of
+Timor-Leste, Dem Rep. of
+Brunei Darussalam
+Guinea-Bissaul
+ Nepal
+Togo
+Bulgaria
+Guyana
+Netherlands, The
+Tokelau
+Burkina Faso
+Haiti
+New Caledonia
+Tonga
+Burundi
+Holy See
+New Zealand
+Trinidad and Tobago
+Cabo Verde
+Honduras
+Nicaragua
+Tunisia
+Cambo dia
+ Hong Kong
+Niger
+Turkey
+Cameroon
+Hungary
+Nigeria
+Turkmenistan
+Canada
+ Iceland
+Niue
+Turks and Caicos Islands
+Cayman Islands
+India
+Norfolk Island
+Tuvalu
+Central Afican Rep.
+Indonesia
+North Macedonia, Republic of
+Uganda
+Chad
+Iran, Islamic Rep. of
+ Norway
+Ukraine
+Chile
+Iraq
+Oman
+United Arab Emirates
+China
+Ireland
+Pakistan
+United Kingdom
+Christmas Island
+Isle of Man
+Palau, Rep. of
+United States
+Cocos (Keeling) Islands
+Israel
+Panama
+United States Virgin Islands
+Colombia
+Italy
+Papua New Guinea
+Uruguay
+Comoros, Union of the
+ Jamaica
+Paraguay
+US Pacific Islands
+Congo, Dem. Rep. of the
+Jap an
+Peru
+Uzbekistan, Rep. of
+Congo, Rep. of
+Jersey
+Philippines
+Vamatu
+Cook Islands
+Jordan
+Pitcairn Islands
+Venezuela, Rep. Bolivariana de
+Costa Rica
+Kazakhstan Rep. of
+Poland, Rep. of
+Vietnam
+Cote d'lvoire
+Kenya
+Portugal
+Wallis and Futuna Islands
+Croatia, Rep. of
+Kirib ati
+Puerto Rico
+West Bank and Gaza
+Cuba
+Korea, Dem People's Rep. of
+Qatar
+Westem Sahara
+Curaao, Kingdom of the Netherlands Korea, Rep. of
+Reunion
+Yemen Rep. of
+Cyprus
+Kosovo, Rep. of
+Romania
+Zambia
+Czech Rep.
+Kuwait
+Russian Federation
+Zimbabwe
+Denmark
+Kyrgyz Rep.
+Rwanda
+Djib outi
+Lao People's Dem Rep.
+Saint Helena
+Dominica
+Latvia
+Saint Piere and MiquelonReferences
+Anderson, J. E. and E. Van Wincoop (2003): “Gravity with gravitas: A solution to
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+Chit¸u, L., B. Eichengreen, and A. Mehl (2014): “History, gravity and international
+finance,” Journal of international Money and Finance, 46, 104–129.
+Coppola, A., M. Maggiori, B. Neiman, and J. Schreger (2021): “Redrawing the
+map of global capital flows: The role of cross-border financing and tax havens,” The
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+De Sousa, J. and J. Lochard (2011): “Does the single currency affect foreign direct
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+Disdier, A.-C. and K. Head (2008): “The puzzling persistence of the distance effect on
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+Head, K. and J. Ries (2008): “FDI as an outcome of the market for corporate control:
+Theory and evidence,” Journal of International Economics, 74, 2–20.
+Lane, P. R. and G. M. Milesi-Ferretti (2008): “International investment patterns,”
+The Review of Economics and Statistics, 90, 538–549.
+Okawa, Y. and E. Van Wincoop (2012): “Gravity in international finance,” Journal of
+international Economics, 87, 205–215.
+Portes, R. and H. Rey (2005): “The determinants of cross-border equity flows,” Journal
+of international Economics, 65, 269–296.
+Silva, J. S. and S. Tenreyro (2006): “The log of gravity,” The Review of Economics
+and statistics, 88, 641–658.
+Yotov, Y. V. (2012): “A simple solution to the distance puzzle in international trade,”
+Economics Letters, 117, 794–798.
+24
+
diff --git a/m9E5T4oBgHgl3EQfHw6d/content/tmp_files/load_file.txt b/m9E5T4oBgHgl3EQfHw6d/content/tmp_files/load_file.txt
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@@ -0,0 +1,577 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf,len=576
+page_content='ASEAN’s Portfolio Investment in a Gravity Model∗  Tomoo Kikuchia and Satoshi Tobeb  aGraduate School of Asia-Pacific Studies, Waseda University  bSchool of Policy Studies, Kwansei Gakuin University  January 16, 2023  Abstract  We investigate the elasticity of portfolio investment to geographical distance in a  gravity model utilizing a bilateral panel of 86 reporting and 241 counterparty coun-  tries/territories for 2007-2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We find that the elasticity is more negative for ASEAN  than OECD members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The difference is larger if we exclude Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This indicates  that Singapore’s behavior is very different from other ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' While Sin-  gapore tends to invest in faraway OECD countries, other ASEAN members tend to  invest in nearby countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Our study also shows the emergence of China as a significant  investment destination for ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Keywords: portfolio investment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' ASEAN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' gravity model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Poisson Pseudo Maximum  Likelihood  JEL Classification: F21;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' F34;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' O16  ∗We would like to thank Benedict Tiu and Yupeng Wang for their excellent research assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We  would like to thank Mariel Monica R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Sauler and Junko Koeda for helpful comments that helped us revise  the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This research was funded by Sumitomo Mitsui Banking Corporation Foundation for Interna-  tional Cooperation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Corresponding author: Tomoo Kikuchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Nishi-Waseda Bldg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='7F, 1-21-1 Nishi-Waseda,  Shinjyuku-ku, Tokyo 169-0051 Japan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Email: tomookikuchi@waseda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='jp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='05443v1  [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='GN]  13 Jan 2023  1  Introduction  Net portfolio investment of ASEAN started to become positive for the period after the Asian  Financial Crisis in 1997 (see Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This means that ASEAN invests in securities in the  rest of the world more than the rest of the world invests in securities in ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On the  other hand, the opposite is true for OECD after 2000, which is the period of our interest in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Figure 1: Net portfolio investment of ASEAN and OECD (% of GDP, 5-year moving average  across countries)  Source: IMF Balance of Payments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note: From 1970 to 2020, ASEAN members increased from 5 to 10 and  OECD members from 22 to 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' There are also missing data for some years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The net portfolio investment of  OECD fell from -76 billion USD in 2001 to -500 billion USD in 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This is mainly caused by the US and  the UK, whose net portfolio investment fell from -325 billion USD to -425 billion USD and from 183 billion  USD to -64 billion USD respectively accounting jointly for 48% of the drop in the net portfolio investment  of OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Since 2001 ASEAN’s portfolio investment asset in OECD has increased much more in OECD  than ASEAN (see Figure 2(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This suggests that ASEAN’s capital markets are less inte-  grated than its goods markets, which have seen a steady growth in inter-regional trade in  past years (compare Figure 2(c) and 2(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In contrast, OECD-OECD portfolio investment  and trade have both grown over time (see Figure 2(b) and 2(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This tendency of ASEAN  to invest in securities outside more than inside the region seems to go against regional fi-  nancial integration that has been promoted after the Asian Financial Crisis in 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Indeed,  comparing 2(a) and 2(b) we can see that around 80 percent of OECD’s portfolio assets are  in OECD while only 7 percent of ASEAN’s portfolio assets are in ASEAN (60 percent in  2  4%  2%  0%  2%  ASEAN  4%  OECD  6%  8%  10%  1960  1964  1966  1968  1970  1972  1974  1976  1978  1980  1988  2010  2012  2014  1962  1982  1984  1986  1990  1992  1994  1996  1998  2002  2004  2006  2008  2016  2000  2018  2020OECD) as of 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This concentration of portfolio investment in OECD also contributes to  economic growth in OECD as shown in ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='.  (a) Porfolio investment of ASEAN  (b) Portfolio investment of OECD  (c) Trade of ASEAN  (d) Trade of OECD  Figure 2: Portfolio investment and trade of ASEAN and OECD (USD billion)  Source: Portfolio investment data are from IMF CPIS including 5 ASEAN countries and 34 OECD countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Trade data are from UN Comtrade including 10 ASEAN countries and 34 OECD countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  The purpose of this paper is to investigate the property of ASEAN’s portfolio investment  in comparison with OECD’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Unless otherwise stated, we refer to Indonesia, Malaysia, the  Philippines, Singapore and Thailand, the so-called ASEAN-5, for which data are widely  available as ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Since regional economic integration entails free movement of produc-  tion factors within a geographical space, we employ a gravity model approach using a bi-  lateral portfolio investment asset dataset to examine the elasticity of portfolio investment  to geographical distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Our bilateral panel includes 86 reporting and 241 counterparty  countries/territories for the period 2007-2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The coordinated portfolio investment survey  (CPIS) by the International Monetary Fund (IMF) reports the bilateral gross stock of port-  folio investment in each year based on the residency of investors and issuers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The series can  be divided into two sub-categories: the equity instrument (investment) and the debt instru-  ment (investment).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In this paper we also make use of the data provided by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  3  1,600  1,400  1,200  1,000  800  600  400  200  ASEAN-ASEANPortfolio  ASEAN-OECDPortfolio  ASEAN-Row Portfolio$60,000  $50,000  $40,000  $30,000  $20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $o  2002  2003  2004  2005  2006  2007  2008  2009  2010  2012  2013  2014  2015  2016  001  2011  2017  2018  2019  2020  OECD-OECD Portfolio  OECD-ASEAN Portfolio  OECD-RoW Portfolio$3,000  $2,500  $2,000  $1,500  $1,000  $500  $o  800  2009  2010  2013  2014  2016  2018  2020  00  00  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  201  01  ASEAN-ASEAN Trade All  ASEAN-OECD Trade Al  ASEAN-RoW Trade All$25,000  $20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $15,000  S10,000  $5,000  $o  2020  二  L  L  OECD-OECD Trade All  OECD-ASEAN Trade All  OECD-RoW Trade All(2021) who complied a restatement of the CPIS portfolio investment data from a residency  to nationality basis, which is available for the period 2007-2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' By comparing the results  of residency and nationality-based data we can reveal the role of tax havens for portfolio  investment allocation of ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Our main results are:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' For 2007-2017 the elasticity of both debt and equity investment to distance is more  negative for ASEAN than for OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This means that the tendency to invest in se-  curities issued in nearby countries is stronger for ASEAN than OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This tendency  is even stronger for ASEAN excluding Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This suggests that Singapore’s be-  havior is different from other ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' While Singapore tends to invest in  faraway countries, other ASEAN members tend to invest in nearby countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Relative to 2007 the elasticity of debt investment to distance has become more positive  in the recent years for ASEAN while it has become more negative for OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' ASEAN  excluding Singapore follows a similar trend as OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This is consistent with a dramatic  increase in Singapore’s debt investment in the US over the past decade (Singapore is  far away from New York relative to other investment destinations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Relative to 2007 there is no significant change in the elasticity of equity investment to  distance in the recent years for both ASEAN and OECD except that it has become  positive on a residency basis in the original CPIS data for ASEAN and on a residency  basis in the data by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) for OECD in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The deviating  results are due to different coverage of countries in each data set and suggest that  China for ASEAN and tax havens for OECD in recent years have become significant  equity investment destinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' ASEAN excluding Singapore follows a similar trend  as OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  The results highlight the role of Singapore as a platform for both inward investment from  other ASEAN members and outward investment to distant OECD members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In fact, Sin-  gapore is ASEAN’s largest host for multinational companies attracting portfolio investment  from other ASEAN members as well as ASEAN’s largest investor in the US and China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In  other words, the contrasting investment behaviors of Singapore and other ASEAN mem-  bers are not just caused by Singapore’s investment behavior but also by Singapore being a  major destination for portfolio investment of other ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Therefore, ASEAN’s  financial integration would inevitably require a higher exposure of Singapore to securities in  ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  4  Gravity model estimation is widely applied to analysis using bilateral trade flow data but also  international asset allocation data (for a theoretical background see Okawa and Van Win-  coop,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' 2012) such as foreign direct investment (FDI) in Head and Ries (2008) and De Sousa  and Lochard (2011),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' cross-sectional bilateral portfolio equity flows in Lane and Milesi-Ferretti  (2008),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' equity flows using panel data covering 1989 to 1996 in Portes and Rey (2005),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' and US  bilateral asset holdings data in Chit¸u et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' There are several features of our paper  that should be highlighted in relation to the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' First, we employ a structural gravity  model estimation combining the Poissson Pseudo Maximum Likelihood (PPML) approach  with a set of various fixed-effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The structural gravity model can solve concerns on omit-  ted variable bias, heteroskedasticity and zero observations, which are well known challenges  in estimating gravity models (see Anderson and Van Wincoop, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Silva and Tenreyro,  2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Second, we provide a comparison between residency and nationality-based data to  reflect the significance of tax havens in international financial markets in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Third,  we use a comprehensive dataset covering a wide range of investor and issuer countries from  2007 to 2017 and contrast general patterns of asset allocation of ASEAN and OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Section 2 introduces the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Section 3  introduces our baseline specification and presents our main results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Section 4 discusses the  portfolio investment of Singapore and other ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Section 5 concludes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  2  Bilateral panel data  This paper uses a bilateral panel data covering 86 reporting and 241 counterparty coun-  tries/territories from 2007 to 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The country lists are provided in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='1 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  The original bilateral portfolio investment asset data are from the CPIS by the IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We also  make use of the data provided by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) who complied a restatement of the  CPIS portfolio investment data from a residency to nationality basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The restatement from  a residency to nationality basis is particularly important for tax havens such as the Cayman  Island, Hong Kong or Singapore that attract large investment to companies that have in  most cases other nationality but reside in the tax havens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' For example, consider Alibaba  Group Holding Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', which is a Chinese multinational technology company incorporated in  the Cayman Islands, and listed in the New York Stock Exchange (NYSE) as well as in the  Stock Exchange of Hong Kong (SEHK).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' When investors buy shares of the company listed  either in NYSE or SEHK, it is recorded as equity investment in the Cayman Islands on a  residency basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On a nationality basis, however, the same investment is recorded as equity  5  investment in China as its main base of operation is in China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Unfortunately, the CPIS data contain only total portfolio investment but not the decompo-  sition into debt and equity investment in China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The nationality- and residency-based data  by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) contain both debt and equity investments in China but their cov-  erage is less comprehensive compared to the original CPIS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' For example, the data do  not include 28 reporting countries, of which 15 are OECD countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Therefore, we present  results using all three datasets: 1) the residency-based data by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021), 2)  the nationality-based restatement data by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021), and 3) the residency-based  original CPIS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The geographical distance is calculated using the latitudes and longitude  of the single largest cities in countries provided by the CEPII database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In the following  analysis the distance is expected to capture costs associated with investing in a remote  country.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Unlike in international trade where geographical distance matters as goods need  to be transported, we might think that distance matters less for global capital allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Nevertheless, to the extend that investment is related to other economic activities such as  international trade, we believe that the geographical distance should matter for portfolio  investment too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Figure 3 highlights the geographical asset allocation of ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We divide issuer countries  into 10 groups based on the geographical distance from investor countries (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', ASEAN  members).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Each bin in horizontal axis covers 2000 kilometers from the investors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The first  bin includes countries located from 0 to 2000 kilometers away from the investor countries,  the second bin from 2000 to 4000 kilometers away and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='1 The figure underscores a weak  tendency of ASEAN to invest in a nearby country and that the US has over the past two  decades become a dominant destination for both debt and equity investments of ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In  addition, the figure shows that China has become a significant equity investment destination  for ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  In contrast to ASEAN, Figure 4 shows that OECD has a strong tendency to invest in nearby  countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The US is a significant destination of both debt and equity investments for OECD  but unlike for ASEAN it is in different bins for different members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In addition, we can see  that China has become a significant equity investment destination for OECD, which is also  located in different bins for different members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note that the US is 14000-16000km away  from most of ASEAN members while it is in varying distance away for different OECD  1The figures are created by dividing the bilateral distance measures between the single largest cities from  the CEPII GeoDist Database by 2000km in order to create a histogram with 10 bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Counterpart countries  are then divided by color into ASEAN, US, and Non-ASEAN Non-US categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  6  (a) Debt in 2007  (b) Debt in 2017  (c) Equity in 2007  (d) Equity in 2017  Figure 3: Portfolio investment (nationality basis) of ASEAN in 10 distance groups (2000km  per bin, USD billion)  Source: Restated Bilateral External Portfolios - “Tax Haven Only” data are based on the work by Coppola  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and were taken from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note: 5 ASEAN source countries  (Indonesia, Malaysia, Philippines, Singapore, Thailand) and 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' China is 4000-6000km away from most of ASEAN members while it is too in  varying distance away for different OECD members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This suggests that the tendency of  ASEAN members to invest in faraway countries can largely be attributed to the dominance  of the US as a destination for both debt and equity investments of ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In  addition, the significance of China as a destination for equity investment of ASEAN members  should contribute to weaken the trend of ASEAN members to invest in equities issued in  faraway countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  3  Gravity in portfolio investment  Section 2 shows that ASEAN as a whole has a tendency to invest in faraway countries while  OECD has a tendency to invest in nearby countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This section examines the elasticity of  portfolio investment to geographical distance for ASEAN and shows that Singapore behaves  differently from other ASEAN members in allocating its portfolio investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  7  $90  $80  $70  $60  $50  $40  $30  $20  $10  $o  ASEAN  Rest of World  USA  CHN$250  $200  $150  $100  $50  $o  Y  5  6  8  ASEAN  Rest of Worlc  USA  CHN$90  $80  $70  $60  $50  $40  $30  $20  $10  $o  5  ASEAN  Rest of Worlc  VSA  CHN$250  $200  $150  $100  $50  $O  n  6  ASEAN  Rest of Worlc  USA  CHN(a) Debt in 2001  (b) Debt in 2017  (c) Equity in 2007  (d) Equity in 2017  Figure 4: Portfolio investment of OECD in 10 distance groups (2000km per bin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' USD billion)  Source:  Distance is taken from CEPII GeoDist Database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Restated Bilateral External Portfolios -  “Tax Haven Only” data are based on the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and were taken from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note: 19 OECD source countries and 196 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='1  Baseline analysis  This subsection presents the baseline results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' To investigate the elasticity of portfolio in-  vestment to distance for both ASEAN and OECD as well as the rest of the world (ROW),  we estimate a gravity model using the PPML estimation method that can reduce concerns  such as heteroscedasticity and zero observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In particular, zero observation is a serious  issue in our application because almost one half of our observations are zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='2 Our baseline  specification is  Portfoliok  i,j,t = exp  �  βASEAN(ln Distancei,j × DASEAN)  + βOECD(ln Distancei,j × DOECD) + βROW(ln Distancei,j × DROW) + δi,t + θi,t  �  εi,j,t,  (1)  where Portfoliok  i,j,t represents the gross stock of portfolio investment asset, and superscript  k corresponds to the types of portfolio investment: debt or equity instrument;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Distancei,j  2Silva and Tenreyro (2006) shows that the method performs well when the proportion of zeros is large  by Monte Carlo simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  8  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='800  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='600  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='400  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='200  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $800  $600  $400  $200  $O  OECD Non-US  Rest of Worlo  USA  CHN$2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='800  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='600  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='400  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='200  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $800  $600  $400  $200  $o  OECD Non-US  Rest of Worla  USA  CHN$2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='500  $2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='500  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $500  $o  OECD Non-US  Rest ot Worlo  USA  CHN$4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='500  $3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='500  $2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='500  $1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='000  $500  $O  OECD Non-US  Rest of Worlc  USA  CHNrepresents the geographical distance between the single largest cities in a particular pair  country;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' DASEAN, DOECD and DROW are dummy variables that take a value of one if a  reporting country is in ASEAN, OECD or ROW and zero otherwise;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' δi,t and θj,t are reporting  country-time specific fixed effects and counterparty country-time specific fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' εi,j,t  is the error term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Reporting and counterparty country-time fixed effects control country-specific time varying  factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' For example, they can control the sizes of GDP of investor and issuer countries in  each year, both of which are often included in traditional plain-vanilla gravity models as  well as geographical distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In addition to the two types of fixed effects, structural gravity  models often include country-pair fixed effects (Anderson and Van Wincoop (2003)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The  pair-fixed effects can control time-invariant country-pair specific factors, such as geographical  distance, common official language, contiguous borders, and presence of colonial ties between  investor and issuer countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In this baseline analysis, however, specification excludes the  country pair-fixed effects to focus on average elasticity of the distance throughout sampled  period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Inclusion of both the pair-fixed effects and geographical distance causes perfect  collinearity, because they are time-invariant country-pair specific variables indexed by (i,  j)-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We show the estimation results based on the specification with country pair-fixed  effects in the next subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We use the gross stock of portfolio investment asset as netting  of gross asset and liability may overlook key information on asset allocation of domestic  and foreign investors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='3 The coefficients of our interest are βASEAN, βOECD and βROW that  capture the relative elasticity to distance of each country group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Figure 5 plots the coefficients of distance for each country group with 95 percent confidence  intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Panel (a) shows that the elasticity of distance to portfolio debt investment is  negative and statistically significant for all country groups and datasets, which is consistent  with the typical behavior observed in gravity model estimations using bilateral trade flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  The result suggests that the investors prefer debt securities issued in a nearby country.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  However, the size of the coefficients is different across the groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' They are more negative in  ASEAN and ROW compared to OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Panel (b) shows similar results for equity investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  These results indicate that ASEAN and ROW investors in equities are more sensitive to  distance than OECD investors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' One might think that these results contradict our observation  of ASEAN’s portfolio investment in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' In the following we will solve those seemingly  contradicting observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Each ASEAN member differs in terms of level of economic development, depth of domestic  3Standard gravity estimations for trade uses gross export or import too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  9  (a) Debt investment  (b) Equity investment  Figure 5: Baseline analysis  Note:  The figures plot the coefficients of interaction terms of geographical distance (logged) and  ASEAN/OECD dummy with 95 percent confidence intervals based on standard error clustering at country-  pair level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The circle, diamond, and square markers represent the results using residency-based, nationality-  based, and CPIS residency-based data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We omit the coefficients of ROW to focus on the ASEAN-OECD  comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The full results are available on request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  (a) Debt investment  (b) Equity investment  Figure 6: Baseline analysis (ASEAN ex-SGP dummy)  Note: The figures plot the coefficients of interaction terms of geographical distance (logged) and ASEAN  ex-SGP/OECD/ROW dummy with 95 percent confidence intervals based on standard error clustering at  country-pair level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The circle, diamond, and square markers represent the results using residency-based,  nationality-based, and CPIS residency-based data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We omit the coefficients of ROW to focus on the ASEAN-  OECD comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The full results are available on request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  10  Coefficient of geographical distance  OECD  ASEAN  Residency  Nationality  Residency (CPISCoefficient of geographical distance  OECD  ASEAN  Residency  Nationality  Residency (CPISCoefficient of geographical distance  OECD  ex-SGP ASEAN  Residency  Nationality  Residency (CPIS)Coefficient of geographical distance  OECD  ex-SGP ASEAN  Residency  Nationality  Residency (CPIS)financial market, and preference of investors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Especially, Singapore being an international  financial center plays a special role in the group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Figure 6 presents the results when the  specification uses ASEAN ex-Singapore dummy (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', ASEAN4-member dummy) instead of  ASEAN5-member dummy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Panel (a) shows the results for debt investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The coefficients  of ex-SGP ASEAN become more negative compared to those of ASEAN presented in Figure  5(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The size of the coefficients are around -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='3 for ASEAN ex-SGP, while they are around  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0 for ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Comparing Figures 6(b) and 5(b) the coefficients for equity investment of  ASEAN ex-SGP are also slightly more negative than those of ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The results indicate  that Singapore investors are less sensitive to distance than other ASEAN investors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' There-  fore, we obtain contrasting results when we treat ASEAN as a whole and when we treat them  separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This is particularly the case because of Singapore’s dominant position both as  investor and investment destination in ASEAN as we will discuss in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='2  Time-series change in portfolio investment  This subsection investigates the change in the elasticity of portfolio investment to distance  over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The specification is  Portfoliok  i,j,t = exp  � 2017  �  t=2008  βASEAN  t  (ln Distancei,j × γt × DASEAN)  +  2017  �  t=2008  βOECD  t  (ln Distancei,j × γt × DOECD) + δi,t + θi,t + µi,j  �  εi,j,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  (2)  The setting follows the baseline analysis described in the previous section, except for includ-  ing the interaction terms of geographical distance (ln Distancei,j), time-fixed effects (γt), and  ASEAN/OECD dummy (DASEAN and DOECD) as well as country-pair fixed effects (µj,i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Interacting the distance and time-fixed effects enables us to include country pair-fixed ef-  fects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The interaction terms are country-pair-time-specific variables indexed by (i, j, t)-level,  so we can avoid multicollinearity with country-pair fixed effects indexed by (i, j)-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Spec-  ification with full set of fixed effects (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', reporting/counterparty country-time fixed effects  and country-pair fixed effects) is the standard setting in structural gravity literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=',  Anderson and Van Wincoop (2003)), which can reduce the concern on possible estimation  bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='4 The coefficients of our interest are βASEAN  t  and βOECD  t  that capture the relative elas-  4We confirm that the specification additionally including the interaction term of geographical distance,  time-fixed effects, and ROW dummy delivers similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Including reporting country-time fixed effects,  11  ticity to distance in each year and country group compared to a specific base year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We set  the first year of the sample, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', 2007, as the base year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Thus, the sequences of βASEAN  t  and  βOECD  t  capture the time variation of the elasticity from 2008 to 2017 in each country group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Figure 7 plots the time variation of the coefficients of debt investment to distance with 95  percent confidence intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The blue and red markers represent the results of the residency-  and nationality-based data provided by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and the green markers represent  the results of the residency-based CPIS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Panels (a) and (b) report the results of ASEAN  and OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  (a) ASEAN  (b) OECD  Figure 7: Debt investment  Note: The figures plot the coefficients of interaction terms of geographical distance (logged), time-fixed  effects, and ASEAN/OECD dummy with 95 percent confidence intervals based on standard error clustering  at country-pair level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The circle and diamond markers represent the results using residency- and nationality-  based data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Panel (a) shows that the coefficients of ASEAN get larger and significant since the mid-  2010, while they are small and insignificant in the 2000s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' All three datasets follow a similar  pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The positive elasticity indicates that ASEAN tends to invest in bonds issued in  a faraway country compared to the base year 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This is consistent with the fact that  ASEAN has increased its portfolio investment to faraway OECD countries (see Figure 2(a))  and in particular in the US in the past decade (see Figure 3(a) and 3(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Panel (b) shows the result for OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The elasticity presents a contrasting pattern to that  of ASEAN and gets more negative and significant after the late-2000s indicating that OECD  counterparty country-time fixed effects, and country-pair fixed efects is the first best choice in estimating a  structural gravity model (Anderson and Van Wincoop (2003) and Silva and Tenreyro (2006)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  12  Coefficient of interaction terms of  6  2  2008  2009  2010  2011  2012  2013  2014  5  2016  2017  201  Residency  Nationality  Residency (CPIS)5  Coefficient of interaction terms of  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='05  5  2008  2009  2010  2011  2012  2013  2014  5  2016  2017  2015  Residency  Nationality  Residency (CPIS)tends to invest in bonds issued in a nearby country compared to the base year 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The  three datasets largely deliver similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  The result is consistent with the fact that  OECD members have increased investment in bonds issued by other OECD members (see  Figure 2(b)) who are in close proximity relative to the distance between ASEAN and OECD  members (see Figure 4(a) and 4(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5  (a) ASEAN  (b) OECD  Figure 8: Equity investment  Note: The figures plot the coefficients of interaction terms of geographical distance (logged), time-fixed  effects, and ASEAN/OECD dummy with 95 percent confidence intervals based on standard error clustering  at country-pair level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The circle and diamond markers represent the results using residency- and nationality-  based data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Figure 8 reports the results for equity investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The results show qualitatively similar  patterns for ASEAN and OECD especially for nationality-based data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The coefficients are  not statistically different from zero throughout the sample period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The results indicate that  there is little change in the geographical allocation of equity investment for ASEAN and  OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This is consistent with our earlier observations for ASEAN (compare Figure 3(c)  and 3(d)) and OECD (compare Figure 4(c) and 4(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note that the points of the original  residency-based data deviate from the other two data points based on Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021)  in Figure 8(a) because the original residency-based data do not provide data for equity  investment in China, which is 4000-6000km away from most of ASEAN members (see Figure  3(c) and 3(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  We confirmed that the coefficients estimated by the three dataset (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=',  Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021)’s data on a residency-basis and a nationality-basis, and the CPIS data  on a residency-basis) are similar if we use the same sample countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This suggests the  5In the literature on bilateral trade flows, the negative coefficients of distance is known as “distance  puzzle”, where estimated negative impact of distance on trade flows has remained persistently large across  major different settings and samples (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', (Disdier and Head, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Yotov, 2012)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  13  Coefficient of interaction terms of  2008  2009  2010  2011  2  3  2014  5  2016  2017  2012  2013  201  Residency  Nationality  Residency (CPIS)Coefficient of interaction terms of  2008  2009  2010  2011  2012  2013  2014  5  2016  2017  2015  Residency  Nationality  Residency (CPIS)difference between the three dataset comes from the coverage of the countries rather than  the restatement from residency- to nationality-basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  (a) Debt investment  (b) Equity investment  Figure 9: Portfolio investment of ASEAN ex SGP  Note: The figures plot the coefficients of interaction terms of geographical distance (logged), time-fixed  effects, and ASEAN ex-Singapore dummy with 95 percent confidence intervals based on the standard error  clustering at the country-pair level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The circle and diamond markers represent the results using residency-  and nationality-based data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Figure 9 presents the results when the specification uses ASEAN ex-SGP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Figure 9(a) shows  the results for debt investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The elasticity gets negative and largely significant after  the late-2000s, which is similar to the results for OECD presented in Figure 7(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Figure  9(b) shows that the result for equity investment is similar to that for OECD too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' These re-  sults indicate that investors in ASEAN except Singapore have not significantly changed their  behavior in allocating portfolio investment across countries since the base year 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' There-  fore, the positive trend in the elasticity of ASEAN’s debt investment to distance observed  in Figure 7(a) must be driven by Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  4  Discussions  Section 3 shows that the elasticity of portfolio investment to distance is more negative for  ASEAN than OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' However, the difference is less significant when we exclude Singapore  from the ASEAN sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This suggests that Singapore’s investment behavior is very differ-  ent from other ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Therefore, this section will examine the role of Singapore  for portfolio investment of ASEAN as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  14  Coefficient of interaction terms of  5  2008  2009  2010  2011  2012  2013  2014  5  2016  2017  2015  Residency  Nationality  Residency (CPIS)Coefficient of interaction terms of  2  2008  2009  2010  2011  2012  2013  2014  2015  2016  2017  Residency  Nationality  Residency (CPIS)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='1  Portfolio investment of Singapore and other ASEAN members  Table 1 shows debt investment of ASEAN members in OECD, ASEAN and the rest of the  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Singapore allocates above 70 percent of its debt investment to OECD in 2007 and  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Besides Singapore and Indonesia other ASEAN members increased the allocation  of their debt investment to ASEAN but decreased the allocation to OECD from 2007 to  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This is consistent with our result that the elasticity of debt investment to distance  is more negative for ASEAN ex-SGP than for ASEAN, and indicates that Singapore is the  global debt investor in ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Figure 10 shows a network chart indicating the relative  Table 1: Debt investment (nationality basis) allocation of ASEAN members  Note: ASEAN 5 countries and 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Restated Bilateral External Portfolios - “Tax Haven  Only” data based on the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and obtained from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  investment size of ASEAN countries in top 10 countries in 2007 and 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='6 The figure shows  that Singapore is absolutely ASEAN’s largest investor in foreign debt and the US grew to  become the dominant destination of its debt investment from 2007 to 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Indeed, the US  alone accounts for 43 percent of ASEAN’s debt investment in 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='7 Notably, emerging as  the number two destination China accounts for 13 percent of ASEAN’s debt investment in  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This largely explains the positive trend in the elasticity of ASEAN’s debt investment  shown in Figure 7(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Table 2 shows that Singapore’s allocation of equity investment is largely similar to that of  other ASEAN members from 2007 to 2017 as seen in Figure 8(a) and 9(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Both Singapore  and other ASEAN members’ allocation has decreased from 67 to 63 percent to OECD, has  increased from 25 to 30-32 percent to the rest of the world, and has decreased from 8-9  6The size of each “thread” denotes a relative size for each graph (year), so we can not compare the  investment size across graphs (years).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The network charts are created using the replication code available  at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com/global-capital-allocation-project/redrawing-the-map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  7Malaysia and Indonesia feature within ASEAN’s top 10 debt investment destinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' However, the  amount is dwarfed by Singapore’s investment in the US and China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  15  (a) 2007  (b) 2017  Figure 10: Debt investment (nationality basis) of ASEAN members in top 10 countries  Note: 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Restated Bilateral External Portfolios - “Tax Haven Only” data based on  the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and obtained from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Table 2: Equity investment (nationality basis) allocation of ASEAN members  Note:  Note:  ASEAN 5 countries and 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Restated Bilateral External Portfo-  lios - “Tax Haven Only” data based on the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and obtained from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  to 5-8 percent to ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Figure 11 shows that Singapore is absolutely the largest equity  investor among ASEAN members too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The US and China have grown to become the most  dominant destinations accounting for 31 and 21 percent of ASEAN’s equity investment in  2017, most of which is Singapore’s investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The figure also shows that the large equity  investment of Singapore in ASEAN in 2007 is in Malaysia, which has since then fallen out of  top 10 equity investment destinations of ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On the other hand, Singapore  features as a top 10 destination of ASEAN’s equity investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note that the US is 14000-  16000km away and China is 4000-6000km away from most ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The presence  16  Malaysia  Indonesia  UnitedStates  United Kingdom  Australia  Singapore  Germany  Korea, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Japan  France  Thailand  Italy  Philippines  Others  Malaysia  IndonesiaMalaysia  Indonesia  UnitedStates  China  Singapore  Germany  United Kingdon  Australia  India  Korea, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Thailand  Canada  Malaysia  Philippines  Others  Indonesia(a) 2007  (b) 2017  Figure 11: Equity investment (nationality basis) of ASEAN countries in top 10 countries  Note: Note: 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Restated Bilateral External Portfolios - “Tax Haven Only” data  based on the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and obtained from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  of China as a destination for ASEAN’s equity investment explains why the elasticity of equity  investment to distance is less negative than that of debt investment for ASEAN given the  relative proximity of China to ASEAN members (see Figure 5 and 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='2  Singapore’s role in ASEAN  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='1 showed the dominant role of Singapore for ASEAN’s portfolio investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Con-  sidering its size of GDP relative to other ASEAN members, Singapore’s portfolio investment  is disproportionately large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On the other hand, Singapore is also a major destination of  ASEAN’s portfolio investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Figures 12 shows the time series of portfolio investment of  ASEAN members on a nationality basis from 2007 to 2017 sorted according to different des-  tinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We can see that Singapore is a major destination for both debt investment (see  Figure 12(a)) and equity investment (see Figure 12(b)) on a nationality basis for Malaysia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Given the relatively large investment size of Malaysia we can say that Singapore attracts  most of ASEAN’s portfolio investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  We now examine the changes in data the restatement (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=', from a residency to nationality  basis) makes to ASEAN’s portfolio investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The changes highlight 1) ASEAN’s invest-  ment in multinational companies residing in Singapore and 2) Singapore’s investment in  17  Malaysia  UnitedStates  China  United Kingdom  Japan  Singapore  India  Korea, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Australia  France  HongKong  Malaysia  Thailand  Others  Indonesia  PhilippinesSingapore  UnitedStates  China  Singapore  Japan  India  United Kingdon  Korea, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Luxembourg  Malaysia  Australia  Hong Kong  Thailand  Indonesia  Others  Philippines(a) Debt  (b) Equity  Figure 12: Portfolio investment (nationality basis) of ASEAN countries from 2007 to 2017  (USD billion)  Note: Note: 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Restated Bilateral External Portfolios - “Tax Haven Only” data  based on the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and obtained from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  multinational companies in other tax havens such as the Cayman Island.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='8  Figure 13(a) shows the top 10 changes in each ASEAN member’s investment after the re-  statement (ASEAN members are highlighted in blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We can see that Singapore records by  far the largest changes but for all ASEAN countries the restatement increases investment in  China and the US and decreases investment in tax-haves such as the Cayman Island, Singa-  pore, Hong Kong, and the Netherlands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This suggests that there is a significant amount of  investment from ASEAN in Chinese and American companies located in those tax-havens  outside China and the US such as Singapore’s investment in Chinese companies in the Cay-  man Island and Hong Kong (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Alibaba Group Holding Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' and Tencent Holdings Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  We estimate that roughly 50 billion USD out of Singapore’s portfolio investment of 70 billion  USD on a residency basis in the Cayman Islands and Hong Kong is in Chinese companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='9  Next to Singapore, Malaysia records the largest changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Malaysia’s investment after the  8The database provided by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) identifies the identity of the issuer of debt or equity  but not of the investor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Therefore, it can not tell us the nationality of multinational companies who reside  in Singapore and invest outside Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  9If we assume that the entire drop in Singapore’s investment in Hong Kong (20 billion USD) and in the  Cayman Islands (30 billion USD) is due to investment in Chinese companies, we get roughly 50 billion USD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  18  Indonesia  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5  OECD  Row  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  ASEANex-Singapore  Singapore  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Malaysia  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Philippines  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Thailand  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  2007  2008  2009  2010  2011  2012  2013201420152016  2017Indonesia  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  OECD  Row  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  ASEAN ex-Singapore  Singapore  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Malaysia  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Philippines  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Thanand  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  2007  2008  2009  2010  2011  2012  20132014  2015  2016  2017(a) Investment from ASEAN  (b) Investment into ASEAN  Figure 13: Portfolio investment from and into ASEAN: Top 10 changes (nationality - resi-  dency) in 2017 (USD million)  Note: 144 destination countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Restated Bilateral External Portfolios - “Tax Haven Only” data based on  the work by Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021) and obtained from www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='globalcapitalallocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  restatement falls the largest in Singapore (see Malaysia in Figure 13(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This shows that  Singapore is the largest host of Malaysia’s investment in multinational companies outside  their home countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On the other hand, Malaysia’s investment after the restatement rises  the largest in China (see Malaysia in Figure 13(a)) suggesting that Malaysia invests a sig-  nificant amount in Chinese companies residing in Singapore (see Figure 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We estimate  that roughly 2 billion USD out of Malaysia’s total portfolio investment of 25 billion USD on  19  Singapore  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  Indonesia  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  Malaysia  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  Philippines  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='25-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='25  Thailand  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='00Singapore  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  Indonesia  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0 -  Malaysia  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0 -  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0 -  Philippines  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0-  Thailand  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0  NOR  KOR  3  9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='0 -a residency basis in Singapore in 2017 is in Chinese companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='10  Figure 14: Malaysia’s investment in Singapore  Figure 13(b) shows the top 10 changes in investment into ASEAN members after the re-  statement (ASEAN members are highlighted in blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We can see that Singapore records  the largest changes but the difference to other ASEAN members is not as large as in Figure  13(a) when we compare ASEAN members as investors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' The largest rise in investment in  all ASEAN members after the restatement is from the US and Japan showing that the two  countries invest in ASEAN companies outside their homes more than in multinational com-  panies in each of ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Notably, Malaysia records the largest fall for investment  in Singapore (see Singapore in Figure 13(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Therefore, Singapore is not only the largest  host of Malaysia’s investment in multinational companies outside their home country as seen  in Figure 13(a) but Malaysia is the largest international investor in such multinational com-  panies in Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' These examples show that Singapore is a platform for multinational  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Chinese) companies to raise capital attracting inward portfolio investment from other  ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  To summarize, Singapore’s investments in tax havens such as the Cayman Island and Hong  Kong, which are largely investments in Chinese and American companies, are by an order  of a magnitude larger than other ASEAN member’s investments in those tax havens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On  the other hand, ASEAN members (Malaysia in particular) invest in multinational (Chinese  in particular) companies residing in Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Note that those investment in multinational  (non-Singaporean) companies in Singapore as well as Singapore’s investments in multina-  tional companies in tax havens only highlight Singapore’s role as a platform for both inward  10If we assume that Malaysia invests in Chinese companies in Hong Kong, the Caymand Islands and  Singapore and that most of the drop in Malaysia’s investment in Hong Kong (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5 billion USD) and two  thirds of the drop in the Cayman Islands (1 billion USD) is due to investment in Chinese companies, we get  roughly 2 billion USD (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='5 − 1 = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  20  and outward investments in multinational companies (whose nationality is different from res-  idency) but are only a part of Singapore’s overall outward investments as well as investments  of other ASEAN members in Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  5  Conclusion  It is often argued that ASEAN as a whole tend to invest in securities outside more than  inside the region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We estimate a gravity model using the PPML estimation method utilizing  a bilateral panel of 86 reporting and 241 counterparty countries/territories for the period  2007-2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' We find that the elasticity of both debt and equity investments to geographi-  cal distance is actually more negative for ASEAN than for OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' However, we find that  the ASEAN-OECD difference in elasticity gets smaller when we exclude Singapore from the  ASEAN sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' This indicates that Singapore’s investment behavior is very different from  that of other ASEAN members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Singapore tends to invest in faraway countries predomi-  nantly in the US while other ASEAN members tend to invest in nearby countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Since  Singapore’s investment is disproportionately large, its behavior drives the investment of  ASEAN as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Indeed, Singapore facilitates both inward investment from ASEAN and  outward investment to OECD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Multinational companies in Singapore attract investment  from ASEAN, in particular, Malaysia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' On the other hand, Singapore is by far ASEAN’s  largest investor in American and Chinese companies residing tax haves such as the Cayman  Island and Hong Kong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Lastly, the elasticity of equity investment is less negative than that  of debt investment for ASEAN reflecting the increasing presence of China as a destination  for equity investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Our analysis shows that geographical distance inhibit ASEAN’s portfolio investment more  than OECD’s but Singapore defies gravity and invests in faraway OECD countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' There-  fore, ASEAN’s financial integration would inevitably require a higher exposure of Singapore’s  investment to ASEAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Is it the high level of financial development that facilitate portfolio  investment among OECD members who happen to be relatively close to each other?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' It  might be that having a developed financial market Singapore invests in the US and other  OECD countries because the developed financial markets are better connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Our gravity  model uses only distance and fixed effects to estimate portfolio investment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' It remains as a  future research to investigate the determinants in reporting and counterparty countries that  can explain our results and hold the key for financial integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  21  A  Appendix  Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='1: List of reporting countries  Note: Data availability of reporting country as of 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' †Reporting countries Coppola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' (2021)’s data  do not cover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  22  Albania  Denmark  Korea, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Poland, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Argentina  Egypt, Arab Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Kosovo, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Portugal  Aruba  Estonia, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Kuwait  Romania  Australia  Finland  Latvia  Russian Federation  Austria  France  Lebanon  Saudi Arabia  Bahrain, Kingdom of  Germany  Lithuania  Singapore  Bangladesh  Gibraltar  Luxembourg  Slovak Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Belarus, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Greece  Macao  Slovenia, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Belgium  Guernsey  Malaysia  South Africa  Bermuda  Honduras  Malta  Spain  Boliviat  Hong Kong  Mauritius  Sweden  Brazil  Hungary  Mexico  Switzerland  Bulgaria  Iceland  Mongolia  Thailand  Canada  India  Netherlands, The  Turkey  Cayman Islands  Indonesia  New Zealand  Ukrainet  Chile  Ireland  North Macedonia, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  United Kingdom  China  Isle of Man  Norway  United States  Colombia  Israel  Pakistan  Uruguay  Costa Rica  Italy  Palau, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Venezuela, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='t  Curacao and Sint Maarten  Japan  Panama  West Bank and Gaza  Cyprus  Jersey  Peru  Czech Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Kazakhstan, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  PhilippinesTable A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='2: List of counterparty countries  Note: Data availability of counterparty countries as of 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  23  Afghanistan, Islamic Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Dominican Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Leb anon  Samoa  Albania  Ecuador  Lesotho, Kingdom of  San Marino, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Algeria  Egypt, Arab Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Liberia  Sao Tome and Principe, Dem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  American Samoa  Ei Salvador  Libya  Saudi Arabia  Andotra  Equatorial Guinea Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Liechtenstein  Senegal  Angola  Eritrea, The State of  Lithuania  Serbia Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Anguilla  Estonia, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Luxembourg  Seychelles  Antigua and Barbuda  Eswatini, Kingdom of  Macao  Sierra Leone  Argentina  Ethiopia  Madagascar, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Singapore  Armenia, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Falkland Islands (Malvinas)  Malawi  Sint Maarten  Aruba  Faroe Islands  Malaysia  Slovak Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content='  Australia  Fiji  Maldives  Slovenia, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Austria  Finland  Mali  Solomon Islands  Azerbaijan, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  France  Malta  Somalia  Bahamas, The  French Polynesia  Marshall Islands, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of the  South Afica  Bahrain, Kingdom of  French Southern Territories  Martirique  South Sudan, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content=' of  Bangladesh  Gabon  Mauritania, Islamic Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
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+page_content='  Kuwait  Russian Federation  Zimbabwe  Denmark  Kyrgyz Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
+page_content="  Rwanda  Djib outi  Lao People's Dem Rep." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9E5T4oBgHgl3EQfHw6d/content/2301.05443v1.pdf'}
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+DRAFT VERSION JANUARY 10, 2023
+Typeset using LATEX twocolumn style in AASTeX631
+JWST/NIRSpec Balmer-line Measurements of Star Formation and Dust Attenuation at z ∼ 3−6
+ALICE E. SHAPLEY,1 RYAN L. SANDERS,2, ∗ NAVEEN A. REDDY,3 MICHAEL W. TOPPING,4 AND GABRIEL B. BRAMMER5, 6
+1Department of Physics & Astronomy, University of California, Los Angeles, 430 Portola Plaza, Los Angeles, CA 90095, USA
+2Department of Physics and Astronomy, University of California, Davis, One Shields Ave, Davis, CA 95616, USA
+3Department of Physics & Astronomy, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA
+4Steward Observatory, University of Arizona, 933 N Cherry Avenue, Tucson, AZ 85721, USA
+5Cosmic Dawn Center (DAWN), Denmark
+6Niels Bohr Institute, University of Copenhagen, Lyngbyvej 2, DK2100 Copenhagen Ø, Denmark
+ABSTRACT
+We present an analysis of the star-formation rates (SFRs) and dust attenuation properties of star-forming
+galaxies at 2.7 ≤ z < 6.5 drawn from the Cosmic Evolution Early Release Science (CEERS) Survey. Our analy-
+sis is based on JWST/NIRSpec Micro-Shutter Assembly (MSA) R ∼ 1000 spectroscopic observations covering
+approximately 1−5µm. Our primary rest-frame optical spectroscopic measurements are Hα/Hβ Balmer decre-
+ments, which we use as an indicator of nebular dust attenuation. In turn, we use Balmer decrements to obtain
+dust-corrected Hα-based SFRs (i.e., SFR(Hα)). We construct the relationship between SFR(Hα) and stellar
+mass (M∗) in three bins of redshift (2.7 ≤ z < 4.0, 4.0 ≤ z < 5.0, and 5.0 ≤ z < 6.5), which represents the first
+time the star-forming main sequence has been traced at these redshifts using direct spectroscopic measurements
+of Balmer emission as a proxy for SFR. In tracing the relationship between SFR(Hα) and M∗ back to such
+early times (z > 3), it is essential to use a conversion factor between Hα and SFR that accounts for the subsolar
+metallicity prevalent among distant galaxies. We also use measured Balmer decrements to investigate the re-
+lationship between dust attenuation and stellar mass out to z ∼ 6. The lack of significant redshift evolution in
+attenuation at fixed stellar mass, previously confirmed using Balmer decrements out to z ∼ 2.3, appears to hold
+out to z ∼ 6.5. Given the rapidly evolving gas, dust, and metal content of star-forming galaxies at fixed mass,
+this lack of significant evolution in attenuation provides an ongoing challenge to explain.
+1. INTRODUCTION
+Hydrogen Balmer-line emission from H II regions has long
+been recognized as one of the most robust probes of star
+formation and dust extinction in star-forming galaxies. The
+Balmer decrement based on the Hα/Hβ flux ratio can be used
+to infer the amount of nebular attenuation, and, in turn, the
+dust-corrected, instantaneous star-formation rate (SFR) (e.g.,
+Kennicutt 1998). The flux of a Balmer line, in combination
+with the UV continuum flux density, can also be used to in-
+fer the efficiency of ionizing photon production (e.g., Shiv-
+aei et al. 2018), and search for evidence of bursty past star-
+formation histories (e.g., Domínguez et al. 2015; Guo et al.
+2016; Emami et al. 2019; Atek et al. 2022).
+Vast samples of galaxies with multiple Balmer emission
+line measurements exist in the local universe, from surveys
+such as the Sloan Digital Sky Survey (SDSS; Abazajian et al.
+aes@astro.ucla.edu
+∗ NHFP Hubble Fellow
+2009), and including both integrated spectra and spatially-
+resolved emission-line maps (e.g., Belfiore et al. 2018; Elli-
+son et al. 2018). Large samples of Balmer decrements and
+dust-corrected Hα SFRs (SFR(Hα)) were assembled for the
+first time at z > 1 with the advent of the HST/WFC3 IR grism
+(Domínguez et al. 2013; Price et al. 2014) as well as multi-
+object near-IR spectrographs on 8–10-meter class ground-
+based telescopes (Reddy et al. 2015). These measurements
+were used to trace the so-called “main sequence" of galaxy
+formation during the epoch of peak SFR density in the uni-
+verse (Shivaei et al. 2015), constrain the nature of nebular
+dust attenuation and ISM geometry (Reddy et al. 2015, 2020;
+Shivaei et al. 2020), describe the spatially-resolved growth of
+galaxy disks (Nelson et al. 2016), and investigate the relation-
+ship between dust attenuation and stellar mass (Shapley et al.
+2022).
+Until recently, it was impossible to perform such funda-
+mental measures of the star-forming galaxy population past
+z ∼ 3, because of both Earth’s atmosphere and a lack of the
+required instrumentation. Indeed, Hα shifts past the red edge
+of the near-IR K band (2.4µm) beyond a redshift of z = 2.65.
+arXiv:2301.03241v1  [astro-ph.GA]  9 Jan 2023
+
+2
+SHAPLEY ET AL.
+The launch of JWST and the capabilities of its NIRSpec in-
+strument (Ferruit et al. 2022) have transformed the ability
+to detect both Hα and Hβ, respectively, out to z ∼ 6.5 and
+z ∼ 9.3. Recent NIRSpec observations from the Cosmic Evo-
+lution Early Release (CEERS) program (Finkelstein et al.
+2022b,a) showcase this ability beautifully, for the first time
+enabling Balmer decrement measurements based on Hα and
+Hβ fluxes for a large sample of galaxies at z ∼ 3 − 6. Here
+we report on these Balmer decrements, as well as their im-
+plications for the star-formation rates (SFR(Hα)) and dust
+attenuation in typical star-forming galaxies extending from
+“cosmic noon" back into the reionization epoch.
+In §2, we describe our observations, data reduction, mea-
+surements, and sample.
+In §3, we present results on the
+observed relationships between SFR(Hα) and stellar mass,
+and Balmer decrement and stellar mass, measured for the
+first time at z ∼ 3 − 6.
+In §4, we consider the implica-
+tions of these new measurements and consider future di-
+rections.
+Throughout, we adopt cosmological parameters
+of H0 = 70 km s−1 Mpc−1, Ωm = 0.30, and ΩΛ = 0.7, and a
+Chabrier (2003) IMF.
+2. OBSERVATIONS AND SAMPLE
+2.1. The CEERS NIRSpec Program
+We use publicly available medium-resolution NIRSpec
+Micro-Shutter Assembly (MSA) data from the CEERS pro-
+gram (Program ID:1345 Finkelstein et al. 2022b,a).
+The
+CEERS NIRSpec observations we analyzed consist of 6
+pointings in the AEGIS field, all of which utilized the grat-
+ing/filter combination of G140M/F100LP, G235M/F170LP,
+and G395M/F290LP, which provide a spectral resolution of
+R ∼ 1000 over the wavelength range approximately 1−5µm.
+For each pointing, each grating/filter combination was ob-
+served for a total of 3107 sec, broken down into three expo-
+sures of 14 groups, and adopting the NRSIRS2 readout mode.
+A 3-point nod pattern was adopted for each observation, and
+each MSA “slit" consisted of 3 microshutters. Each of the
+6 pointings contained between 52 and 55 targets, for a total
+sample of 321 slits and 318 distinct targets (3 galaxies were
+observed on two pointings).
+2.2. Data Reduction
+We followed the same two-dimensional (2D) reduction
+procedures to reduce data for all three NIRSpec gratings.
+We began by passing individual uncalibrated detector im-
+ages through the JWST calwebb_detector1 pipeline 1.
+In this step, we masked all saturated pixels, subtracted the
+bias and dark current, and masked “snowballs" and “show-
+ers" associated with high-energy cosmic ray events. Images
+1 https://jwst-pipeline.readthedocs.io/en/latest/index.html
+were then corrected for striping by estimating and subtract-
+ing the 1/ f noise in each image. We then cut out the 2D
+spectrum for each MSA slit, and applied a flat-field correc-
+tion, background subtraction using dithered exposures as the
+background, photometric calibration, and a wavelength solu-
+tion based on the up-to-date calibration reference data system
+(CRDS) context (jwst_1027.pmap). Each slitlet was rec-
+tified and interpolated onto a common wavelength grid based
+on its grating and filter combination. Finally, individual cal-
+ibrated 2D spectra exposures were combined following the
+defined three-shutter dither pattern, while excluding pixels
+that had been previously masked. The 2D error spectra rep-
+resent a combination of the variance from Poisson noise, read
+noise, flat-fielding, and variance between exposures, summed
+in quadrature. This stage of the reduction yielded 310 targets
+with 2D spectra covering all three gratings, reflecting a neg-
+ligible sample of 8 initial targets that did not result in a viable
+2D reduction.
+One-dimensional (1D) science and error spectra were op-
+timally extracted from the rectified 2D spectra (Horne 1986).
+The spatial profile in each grating was obtained by manually
+identifying wavelength ranges in the 2D spectrum contain-
+ing high-S/N emission lines when present or detected contin-
+uum otherwise and summing the corresponding columns of
+the 2D spectrum. For targets with detected lines or contin-
+uum in at least one grating, a blind extraction was applied to
+any remaining grating lacking such information. Out of 310
+CEERS targets with the full set of 2D spectra, we extracted
+1D spectra for 252.
+As described in detail in Reddy et al. (2023a, in prep.),
+wavelength-dependent slit-loss corrections were estimated
+for each target based on its intrinsic morphology and posi-
+tion in the NIRSpec slit, as well as the wavelength-dependent
+JWST PSF. Intrinsic morphologies were estimated from
+JWST/NIRCam F115W imaging if available, or a Sérsic fit
+to HST/F160W imaging if not. In the absence of NIRCam
+F115W imaging or a robust Sérsic fit, a point source was as-
+sumed.
+The final flux calibration was achieved by scaling 1D
+science spectra to match the photometric SEDs. Slit-loss-
+corrected NIRSpec spectra were passed through the avail-
+able photometric filter transmission for each target to pro-
+duce synthetic photometric flux densities and errors. The ra-
+tio of the image-based and synthetic flux densities was calcu-
+lated for each filter in which both types of measurements had
+S/N>5. If the number of filters meeting this requirement was
+≥ 3, 1D spectra and error spectra in all three gratings were
+scaled by the median of the individual ratios to achieve the fi-
+nal flux calibration. For the 109 targets that did not meet this
+criterion, no scale factor was applied. For the remaining 143
+targets, the median scale factor was 0.997 with a standard
+deviation of 0.23 dex.
+
+BALMER LINES AT z ∼ 3−6
+3
+Figure 1. Left: Redshift distribution of all 113 CEERS galaxies at 2.7 ≤ z ≤ 6.5, from which the sample of star-forming galaxies we analyze
+is drawn. The three redshift bins we delineate are indicated in green (2.7 ≤ z < 4.0), blue (4.0 ≤ z < 5.0), and magenta (5.0 ≤ z < 6.5).
+Right: Stellar mass distributions for the three redshift samples indicated in the left-hand panel, using the same color coding. For each redshift
+distribution, the median stellar mass is marked with a vertical dotted line. These median stellar mass values are log(M∗/M⊙) =9.59, 9.38, and
+8.38, respectively, for the 2.7 ≤ z < 4.0, 4.0 ≤ z < 5.0, and 5.0 ≤ z < 6.5 redshift samples.
+2.3. Measurements
+Redshifts and emission-line fluxes were measured from the
+1D spectra for which we were able to robustly identify emis-
+sion lines. Reported redshifts for 231 galaxies are based on
+the best-fit centroid from a single Gaussian fit to the line with
+the highest signal-to-noise ratio, usually [OIII]λ5007 (57%)
+or Hα (36%).
+As described in more detail in Sanders et
+al. 2023 (in prep.), to estimate line fluxes, we used single
+Gaussian fits for widely-separated lines, adjacent lines such
+as [NII]λ6548, Hα, and [NII]λ6583 are simultaneously with
+multiple Gaussians, and closely spaced lines that are blended
+and unresolved at R ∼ 1000 are fit with a single Gaussian.
+The continuum model is taken to be the best-fit SED model
+(described below), where the only free parameter is an addi-
+tive offset. Using the best-fit SED model as the continuum
+has the advantage of self-consistently accounting for stellar
+absorption such that the measured hydrogen recombination
+line fluxes are robust.
+The same emission line was measured in two adjacent
+gratings for many targets. These overlapping measurements
+showed good agreement, with a median offset of 0.02 dex
+and an intrinsic scatter of 0.08 dex, suggesting that the rel-
+ative flux calibration between grating configurations is ro-
+bust on average. In these cases of overlapping spectra, we
+adopted the inverse-variance weighted mean of the two avail-
+able fluxes as our reported measurement.
+We used existing multi-wavelength catalogs to derive best-
+fit SED models from which we infer stellar masses (M∗)
+and other stellar population parameters.
+Specifically, for
+the 99 CEERS NIRSpec targets with coverage, we used
+the publicly available catalog constructed by G. Brammer2,
+which includes 7 HST bands (F435W, F606W, F814W,
+F105W, F125W, F140W, and F160W), and 7 JWST/NIRCam
+bands F115W, F150W, F200W, F277W, F356W, F410M, and
+F444W) from the initial CEERS NIRcam observations in
+June 2022. For an additional 185 objects we used the spec-
+tral energy distributions in the AEGIS field cataloged by the
+3D-HST team (Momcheva et al. 2016; Skelton et al. 2014),
+which include ground-based and HST optical and near-IR
+photometry, and measurements from Spitzer/IRAC at 3.6–
+8.0µm. There were 35 CEERS NIRSpec targets not covered
+by the Brammer HST+NIRCam catalog, and lacking a robust
+multi-wavelength SED in the 3D-HST catalog. Restricted
+to the sample of 231 galaxies with NIRSpec spectroscopic
+redshifts, we found robust SED information for 210. When
+restricted to the sample of 109 star-forming galaxies spectro-
+scopically confirmed at 2.7 ≤ z ≤ 6.5, which forms the basis
+of the current analysis, we have robust SEDs for 94 (86%).
+For SED modeling, we used the FAST program (Kriek
+et al. 2009), assuming the stellar population synthesis mod-
+2 https://s3.amazonaws.com/grizli-v2/JwstMosaics/v4/index.html
+
+4
+SHAPLEY ET AL.
+els of Conroy et al. (2009), and a Chabrier (2003) IMF.
+Following Reddy et al. (2018a), we adopted two combina-
+tions of metallicity and extinction curves for SED model-
+ing. These include 1.4 solar metallicity (Z⊙ = 0.014) cou-
+pled with the Calzetti et al. (2000) attenuation curve (here-
+after “1.4 Z⊙+Calzetti"), and 0.27 solar models with the
+SMC extinction curve (hereafter “0.27 Z⊙+SMC"). We as-
+sumed delayed-τ star-formation histories, where SFR(t) ∝
+t × exp(−t/τ). Here, t is the time since the onset of star for-
+mation and τ is the characteristic star-formation timescale.
+The adoption of 1.4 Z⊙+Calzetti or 0.27 Z⊙+SMC was de-
+termined for each galaxy on the basis of its redshift and
+mass. Following Du et al. (2018) and guided by the evolving
+galaxy mass-metallicity relation (e.g., Sanders et al. 2021),
+at z ≤ 1.4 we adopted 1.4 Z⊙+Calzetti. At 1.4 < z ≤ 2.7
+(2.7 < z ≤ 3.4), we adopted 1.4 Z⊙+Calzetti for galax-
+ies above log(M∗,1.4Z⊙+Calzetti/M⊙) = 10.45 (10.66) and 0.27
+Z⊙+SMC for those at lower masses. At z > 3.4, we adopted
+0.27 Z⊙+SMC models (Reddy et al. 2018a). We note that
+all relevant photometric bands were corrected for the contri-
+butions from strong nebular emission lines using the method
+described in Sanders et al. (2021), and Balmer emission-line
+fluxes were corrected for the underlying stellar absorption
+implied by the best-fit stellar population model.
+Finally, SFR(Hα) was estimated from dust-corrected Hα
+luminosities. Reddy et al. (2020) showed that the Milky Way
+dust law of Cardelli et al. (1989) provides a good match to
+the wavelength dependence of nebular attenuation in z ∼ 2.3
+star-forming galaxies. Accordingly, we used the measured
+Hα/Hβ ratio, along with an assumption of the Cardelli et al.
+(1989) dust extinction curve, to infer E(B−V)neb, the nebular
+extinction. Then the dust-corrected Hα luminosity was mul-
+tiplied by a conversion factor depending on the metallicity
+of the best-fit SED model. Following the analysis of Reddy
+et al. (2018a), for galaxies with 1.4 Z⊙+Calzetti fits, we
+used a conversion factor of 10−41.37(M⊙yr−1)/(erg s−1), de-
+rived from Z = 0.02 BPASS population synthesis models in-
+cluding the effects of stellar binaries and assuming an upper-
+mass IMF cut-off of 100 M⊙. This calibration is almost iden-
+tical to the one from Hao et al. (2011) used in many other
+recent works for Hα observations of z ∼ 2 galaxies (Shiv-
+aei et al. 2015; Sanders et al. 2021; Shapley et al. 2022). For
+galaxies with 0.27 Z⊙+SMC fits, we used a conversion factor
+of 10−41.67(M⊙yr−1)/(erg s−1), derived from from Z = 0.001
+BPASS population synthesis models including the effects of
+stellar binaries and assuming an upper-mass IMF cut-off of
+100 M⊙ (Reddy et al. 2022). The latter, lower conversion
+Figure 2. SFR(Hα) vs. M∗. Green, blue, and magenta symbols are
+used, respectively, for the 2.7 ≤ z < 4.0, 4.0 ≤ z < 5.0, and 5.0 ≤
+z < 6.5 samples, and galaxies with Hβ upper limits are indicated
+as SFR(Hα) lower limits (i.e., due to the lower limit on the Balmer
+decrement). The median error bar for each sample is shown in the
+lower-right corner of the plot in its designated color. Along with
+CEERS data points, we plot the best-fit relation from Speagle et al.
+(2014) (their equation (28)), at the median redshift of each sample
+(z = 3.30,4.60 and 5.65, respectively, for the 2.7 ≤ z < 4.0, 4.0 ≤
+z < 5.0, and 5.0 ≤ z < 6.5 samples), and offset by −0.34 dex in the
+y-axis to account for different assumptions regarding the conversion
+between observables and SFR.
+factor reflects the greater efficiency of ionizing photon pro-
+duction in lower-metallicity massive stars in binary systems.3
+2.4. Sample
+For the current analysis, we require a redshift measurement
+in the range 2.7 ≤ z < 6.5. The lower bound here represents
+the limit of ground-based measurements of Hα, i.e., the be-
+ginning of uncharted territory, while the upper bound repre-
+sents the corresponding redshift limit imposed by the red cut-
+off of the G395M/F290LP setting. We also require a stellar
+mass estimate, wavelength coverage of both Hα and Hβ, a
+≥ 3σ detection of Hα, and finally a lack of indication of ac-
+tive galactic nucleus (AGN) activity. In the full sample of
+CEERS spectra, we identified 15 galaxies as candidate AGN
+on the basis of either an [NII]λ6583/Hα ratio greater than
+0.5 (10 galaxies), or else an Hα profile consisting of both a
+narrow component and broad base (5 galaxies).
+3 The stellar metallicity associated with this Hα SFR conversion factor is
+lower than what is assumed for 0.27 Z⊙+SMC broadband SED modeling,
+yet the conversion factor is not strongly metallicity-dependent in this low-
+metallicity regime.
+
+BALMER LINES AT z ∼ 3−6
+5
+Figure 3. Composite spectra for each of the three redshift bins, where, from bottom to top, we show spectra, respectively, for the 2.7 ≤ z < 4.0,
+4.0 ≤ z < 5.0, and 5.0 ≤ z < 6.5 samples. In each row, the left set of panels represents the “low-mass bin," while the right side indicates
+the “high-mass bin," where each redshift sample is divided at the median stellar mass. Each composite spectrum is zoomed in on the regions
+covering Hβ and [OIII]λλ4959,5007, as well as Hα, [NII]λλ6548,6583, and [SII]λλ6717,6731. These features are marked and labeled.
+Out of the 113 CEERS targets with redshifts measured at
+2.7 ≤ z < 6.5 (Figure 1, left), 109 show no rest-optical spec-
+troscopic evidence for AGN activity, of which 94 have stellar
+mass estimates (Figure 1, right). Of these galaxies, 77 have
+(1) Hα and Hβ wavelength coverage and (2) Hα detections,
+and they comprise our primary sample. In order to search
+for evolution within the sample, we construct three redshift
+subsamples at 2.7 ≤ z < 4 (24 galaxies), 4.0 ≤ z < 5.0 (25
+galaxies), and 5.0 ≤ z < 6.5 (28 galaxies). Of these, 62 galax-
+ies also have Hβ detections, broken down into 22, 19, and
+21 galaxies, respectively, at 2.7 ≤ z < 4, 4.0 ≤ z < 5.0, and
+5.0 ≤ z < 6.5.
+3. RESULTS
+3.1. Star Formation
+One of the key diagnostics of the evolution of the star-
+forming galaxy population across cosmic time is the so-
+called “main sequence" (e.g., Noeske et al. 2007). This cor-
+relation between SFR and M∗ is thought to reflect the grad-
+ual growth of galaxies, largely through smooth accretion and
+minor mergers. A galaxy’s position with respect to the main
+sequence (within its scatter, significantly above, significantly
+below), provides a sense of its evolutionary state.
+In order to construct the SFR vs.
+M∗ relationship for
+CEERS galaxies targeted by NIRSpec, we took some care
+in translating dust-corrected Hα luminosities. As described
+in Section 2.3, across the entire CEERS NIRSpec spectro-
+scopic sample, the adopted conversion factor is lower for
+lower-mass and higher-redshift galaxies, based on the ob-
+served trend towards lower metallicity at lower stellar mass
+and higher redshift. In fact, in our primary sample, all but
+one galaxy was modeled with a subsolar metallicity and SMC
+dust law. Accordingly, we used the low-metallicity SFR/LHα
+conversion factor for all but one galaxy as well. We note that
+the sample median SFR(Hα) estimated using this conversion
+factor shows excellent agreement (within 0.07 dex) with the
+median SFR derived from SED fitting (Section 2.3), and the
+two sets of SFR measurements are significantly correlated
+(see also Reddy et al. 2022).
+Figure 2 shows the relationship between SFR(Hα) and M∗
+among CEERS galaxies targeted by NIRSpec at 2.7 ≤ z <
+6.5, color-coded by redshift range as in Figure 1. We also
+plot the best-fit parameterized main sequence relation from
+Speagle et al. (2014), which expresses galaxy SFR as a func-
+tion of both M∗ and z, or, equivalently, the age of the uni-
+verse. Relations from Speagle et al. (2014) are plotted at the
+median redshift of each of the three subsamples (z = 3.3, 4.6,
+and 5.65). Notably, we also shift the Speagle et al. (2014)
+relations by −0.34 dex in SFR(Hα), since they are effectively
+tied to the Hao et al. (2011) SFR conversion factor for Hα.
+Both the 2.7 ≤ z < 4.0 and 4.0 ≤ z < 5.0 samples scat-
+ter symmetrically around the (shifted) main sequence fits
+from Speagle et al. (2014), suggesting that these samples are
+representative of star-forming galaxies over the stellar mass
+range 8.0 ≤ log(M∗/M⊙) ≤ 10.0. The two lower-redshift
+subsamples also show no significant offset with respect to
+each other in terms of typical SFR(Hα) at fixed M∗, consis-
+
+6
+SHAPLEY ET AL.
+tent with the lack of strong redshift dependence in the Spea-
+gle et al. (2014) over this redshift range. The 5.0 ≤ z < 6.5
+sample, however, is offset towards higher SFR(Hα) relative
+to the Speagle et al. (2014) parametrization, which, itself,
+represents an extrapolation out to such high redshifts. Re-
+gardless of the parametrized version of the main sequence,
+the highest-redshift subsample is characterized by a higher
+average SFR(Hα) at fixed stellar mass than the two lower-
+redhift subsamples within the stellar-mass range of overlap
+(8.0 ≤ log(M∗/M⊙ ≤ 9.0). More representative samples will
+be required to determine if this offset is reflective of the un-
+derlying evolving galaxy population, or rather a selection ef-
+fect.
+3.2. Dust Attenuation
+It has been shown that the strong connection between mea-
+sures of dust attenuation and M∗ does not significantly evolve
+between z ∼ 0 and z ∼ 2. Here dust attenuation has been esti-
+mated with several different tracers, including the ratio of far-
+IR to UV SFRs or luminosities, also known as “IRX" (e.g.,
+Meurer et al. 1999; Bouwens et al. 2016); the magnitude
+of far-UV (i.e., 1600Å) attenuation, or A1600 (e.g., McLure
+et al. 2018); the fraction of star formation that is obscured,
+fobscured (Whitaker et al. 2017), and the nebular attenuation
+based on the Balmer decrement (i.e., Hα/Hβ ratio; Kashino
+et al. 2013; Domínguez et al. 2013; Price et al. 2014). There
+is less consensus regarding the form of the attenuation vs.
+M∗ relation at z > 3, with some evidence that it may evolve
+towards lower attenuation at fixed M∗ (e.g., Fudamoto et al.
+2020).
+Shapley et al. (2022) presented a large sample of Balmer
+decrements at z ∼ 2.3, demonstrating that the relationship be-
+tween Balmer decrement and M∗ showed no significant evo-
+lution up to the current epoch. We extend this work for the
+first time out to z ∼ 6.5, using measured Balmer decrements
+for the CEERS NIRSpec sample. In addition to individual
+Balmer decrement measurements, we used stacked compos-
+ite spectra to estimate average quantities in two bins of stel-
+lar mass for each of the three redshift bins. These composite
+spectra, zoomed in to the regions surrounding Hβ and Hα,
+are shown in Figure 3. Each row features the results for one
+of the redshift subsamples, while the left-hand (right-hand)
+set of plots represents the lower-mass (higher-mass) half of
+each sample. 4
+The left-hand panel of Figure 4 shows the relationship be-
+tween Balmer decrement and M∗ for both z ∼ 0 star-forming
+galaxies in SDSS, and z ∼ 2.3 galaxies drawn from the MOS-
+DEF survey (Shapley et al. 2022).
+We overplot individ-
+4 The sample for stacking (N = 82) is slightly larger than for individual mea-
+surements, as there was no explicit requirement of Hβ coverage in the
+stacks.
+ual CEERS NIRSpec measurements at 2.7 ≤ z < 6.5, color-
+coded by redshift subsample. The individual z ≥ 3 measure-
+ments are noisy, but there is no obvious evolution between
+z ∼ 2.3 and z ∼ 6.5. We note that a small number of galax-
+ies in the CEERS sample scatter to either surprisingly high
+values of Hα/Hβ, or else values significantly less than the
+dust-free minimum value of 2.86. We attribute these outliers
+to remaining systematics in the NIRSpec grating-to-grating
+flux calibration (i.e., when Hα and Hβ are measured in dif-
+ferent gratings), which lacks bias on average, but also has
+scatter.
+In the right-hand panel of Figure 4, we replace individ-
+ual CEERS measurements with those taken from composite
+spectra. In these higher-S/N measurements, the two lower-
+redshift show preliminary evidence for higher Hα/Hβ ratio
+at higher stellar mass, yet the error bars are still too large to
+discern a significant trend. Furthermore, at lower redshifts,
+only a very shallow trend between Hα/Hβ and stellar mass is
+observed over the stellar mass range probed by the z > 3 sam-
+ple. The main result from these preliminary measurements of
+dust attenuation and stellar mass in CEERS is that the z > 3
+measurements scatter around those at z ∼ 0 − 2.3, with no
+obvious offset overall. We do note that the lower-mass bin
+at 5.0 ≤ z < 6.5 is offset towards higher Hα/Hβ relative to
+the SDSS distribution (there are no z ∼ 2.3 measurements at
+log(M∗/M⊙) ∼ 8.0) but the error bar for this 16-galaxy stack
+is large enough that its vertical offset relative to SDSS is not
+significant, and the lower- and higher-mass bins at this red-
+shift are statistically consistent with a flat trend.
+4. DISCUSSION
+A crucial component of our measurement of the SFR(Hα)
+vs. M∗ relation at 2.7 ≤ z < 6.5 is the adoption of an ap-
+propriate conversion factor between dust-corrected Hα lumi-
+nosity and SFR, characterized by the correct metallicity and
+treatment of the effects of stellar binaries. There are mul-
+tiple lines of evidence that the vast majority of galaxies in
+our sample have significantly subsolar metallicities. Their
+stellar masses alone suggest subsolar metallicity, given what
+is known about the evolution of the galaxy mass-metallicity
+relation at lower redshifts (e.g., Sanders et al. 2021). More
+directly, as discussed in Sanders et al. 2023 (in prep.), the
+composite spectra shown in Figure 3 indicate [NII]/Hα ≤ 0.1
+for all subsamples, another sign of low metallicity (Pettini &
+Pagel 2004). Finally, models of the rest-UV stellar contin-
+uum of z ∼ 2−3 star-forming galaxies suggests significantly
+subsolar stellar metallicities (Steidel et al. 2016; Cullen et al.
+2019; Topping et al. 2020b,a; Reddy et al. 2022).
+Star-
+forming galaxies such as those in the CEERS NIRSpec sam-
+ple, covering the same or lower stellar-mass range but at
+higher redshift, should be even less enriched. As highlighted
+by Reddy et al. (2018b) and Theios et al. (2019), the subsolar
+
+BALMER LINES AT z ∼ 3−6
+7
+Figure 4. Attenuation vs. M∗ based on the Balmer line ratio, Hα/Hβ. In each panel, the background grayscale histogram corresponds to the
+distribution of local SDSS galaxies. The running median Hα/Hβ ratio for z ∼ 2.3 star-forming galaxies in the MOSDEF survey is shown in red
+(Shapley et al. 2022). In the left panel, we show individual CEERS galaxies color-coded by redshift as in previous plots. On the right, plotted
+Hα/Hβ ratios are measured from composite spectra in two bins of stellar mass for each redshift range, as shown in Figure 3.
+conversion factor between Hα luminosity and SFR adopted
+here is a factor of ∼ 2.5 lower than the canonical conver-
+sion used for lower-redshift studies in the literature (e.g. Hao
+et al. 2011). Previously, Caputi et al. (2017) estimated the
+SFR(Hα) vs. M∗ relation at z ∼ 4−5, based on a large sam-
+ple of star-forming galaxies with photometric redshifts and
+Hα line fluxes inferred indirectly from Spitzer/IRAC 3.6µm
+photometric excesses relative to best-fit SED models. Ca-
+puti et al. (2017) used a solar-metallicity conversion factor
+for SFR(Hα), resulting in a higher overall normalization of
+the SFR(Hα) vs. M∗ relation, and also found an apparent
+bimodality in the SFRs of galaxies with strong Hα emis-
+sion.
+We recover no such bimodality in the distribution
+of SFR(Hα) values, based on direct spectroscopic measure-
+ments of Balmer lines.
+The CEERS NIRSpec sample provides tantalizing evi-
+dence that the relationship between Balmer decrement and
+stellar mass remains constant out to z ∼ 6.5. This measure of
+dust attenuation depends on both the dust mass and the way
+in which it is distributed (i.e., the effective dust-mass surface
+density), so the lack of evolution in attenuation at fixed stellar
+mass suggests a constant ratio of dust-mass surface density
+to stellar mass (Shapley et al. 2022). At the same time, other
+studies have found evidence for a lower fraction of obscured
+star-formation (“IRX") at fixed mass at z > 4 (e.g. Fudamoto
+et al. 2020), based on far-IR and UV continuum estimate of
+dust attenuation. Different redshift evolution in the IRX vs.
+M∗ and Hα/Hβ vs. M∗ relations could arise if the spatial
+distribution of dust relative to massive stars and H II regions
+evolves (Reddy et al. 2015), based on the fact that IRX probes
+stellar continuum attenuation while Hα/Hβ traces nebular at-
+tenuation in H II regions. However, the results thus far on
+the attenuation vs. mass relation at the highest redshifts –
+both our Balmer decrement analysis and the studies based on
+IRX – use small samples of galaxies, and require confirma-
+tion with an order of magnitude larger sample numbers.
+We have entered an era in which spectroscopic Balmer-
+line measurements at z > 3 are routine and can be ob-
+tained in modest exposure times on JWST. The CEERS NIR-
+Spec dataset analyzed here demonstrates the great poten-
+tial of JWST for obtaining fundamental probes of the star-
+forming galaxy population into the reionization epoch based
+on Balmer-line measurements. In addition to tracing star for-
+mation, galaxy growth, and dust attenuation, as we do here,
+the ratio of Hα to UV continuum luminosity can be used to
+infer the efficiency of ionizing photon production, ξion (Shiv-
+aei et al. 2018) – crucial for quantifying the role of star-
+forming galaxies in cosmic reionization – as well as evidence
+for bursty star-formation histories (Emami et al. 2019). We
+look forward to realizing the full potential of JWST and NIR-
+Spec with not only larger and representative galaxy samples,
+but also samples with complete NIRCam photometric cover-
+age, selected from early public JWST imaging datasets.
+ACKNOWLEDGEMENTS
+
+8
+SHAPLEY ET AL.
+This work is based on observations made with the NASA/
+ESA/CSA James Webb Space Telescope. The data were ob-
+tained from the Mikulski Archive for Space Telescopes at
+the Space Telescope Science Institute, which is operated by
+the Association of Universities for Research in Astronomy,
+Inc., under NASA contract NAS5-03127 for JWST. We also
+acknowledge support from NASA grant JWST-GO-01914.
+Support for this work was also provided through the NASA
+Hubble Fellowship grant #HST-HF2-51469.001-A awarded
+by the Space Telescope Science Institute, which is operated
+by the Association of Universities for Research in Astron-
+omy, Incorporated, under NASA contract NAS5-26555.
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+page_content=' University of Arizona,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 933 N Cherry Avenue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Tucson,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' AZ 85721,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' USA  5Cosmic Dawn Center (DAWN),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Denmark  6Niels Bohr Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' University of Copenhagen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Lyngbyvej 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' DK2100 Copenhagen Ø,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Denmark  ABSTRACT  We present an analysis of the star-formation rates (SFRs) and dust attenuation properties of star-forming  galaxies at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 drawn from the Cosmic Evolution Early Release Science (CEERS) Survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Our analy-  sis is based on JWST/NIRSpec Micro-Shutter Assembly (MSA) R ∼ 1000 spectroscopic observations covering  approximately 1−5µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Our primary rest-frame optical spectroscopic measurements are Hα/Hβ Balmer decre-  ments, which we use as an indicator of nebular dust attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In turn, we use Balmer decrements to obtain  dust-corrected Hα-based SFRs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', SFR(Hα)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We construct the relationship between SFR(Hα) and stellar  mass (M∗) in three bins of redshift (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5), which represents the first  time the star-forming main sequence has been traced at these redshifts using direct spectroscopic measurements  of Balmer emission as a proxy for SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In tracing the relationship between SFR(Hα) and M∗ back to such  early times (z > 3), it is essential to use a conversion factor between Hα and SFR that accounts for the subsolar  metallicity prevalent among distant galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We also use measured Balmer decrements to investigate the re-  lationship between dust attenuation and stellar mass out to z ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The lack of significant redshift evolution in  attenuation at fixed stellar mass, previously confirmed using Balmer decrements out to z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3, appears to hold  out to z ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Given the rapidly evolving gas, dust, and metal content of star-forming galaxies at fixed mass,  this lack of significant evolution in attenuation provides an ongoing challenge to explain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' INTRODUCTION  Hydrogen Balmer-line emission from H II regions has long  been recognized as one of the most robust probes of star  formation and dust extinction in star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The  Balmer decrement based on the Hα/Hβ flux ratio can be used  to infer the amount of nebular attenuation, and, in turn, the  dust-corrected, instantaneous star-formation rate (SFR) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=',  Kennicutt 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The flux of a Balmer line, in combination  with the UV continuum flux density, can also be used to in-  fer the efficiency of ionizing photon production (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Shiv-  aei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2018), and search for evidence of bursty past star-  formation histories (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Domínguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Emami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Atek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Vast samples of galaxies with multiple Balmer emission  line measurements exist in the local universe, from surveys  such as the Sloan Digital Sky Survey (SDSS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Abazajian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  aes@astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='ucla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='edu  ∗ NHFP Hubble Fellow  2009), and including both integrated spectra and spatially-  resolved emission-line maps (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Belfiore et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Elli-  son et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Large samples of Balmer decrements and  dust-corrected Hα SFRs (SFR(Hα)) were assembled for the  first time at z > 1 with the advent of the HST/WFC3 IR grism  (Domínguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Price et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2014) as well as multi-  object near-IR spectrographs on 8–10-meter class ground-  based telescopes (Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' These measurements  were used to trace the so-called “main sequence" of galaxy  formation during the epoch of peak SFR density in the uni-  verse (Shivaei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2015), constrain the nature of nebular  dust attenuation and ISM geometry (Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2015, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Shivaei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2020), describe the spatially-resolved growth of  galaxy disks (Nelson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2016), and investigate the relation-  ship between dust attenuation and stellar mass (Shapley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Until recently, it was impossible to perform such funda-  mental measures of the star-forming galaxy population past  z ∼ 3, because of both Earth’s atmosphere and a lack of the  required instrumentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Indeed, Hα shifts past the red edge  of the near-IR K band (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4µm) beyond a redshift of z = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='03241v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='GA]  9 Jan 2023  2  SHAPLEY ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The launch of JWST and the capabilities of its NIRSpec in-  strument (Ferruit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022) have transformed the ability  to detect both Hα and Hβ, respectively, out to z ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 and  z ∼ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Recent NIRSpec observations from the Cosmic Evo-  lution Early Release (CEERS) program (Finkelstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2022b,a) showcase this ability beautifully, for the first time  enabling Balmer decrement measurements based on Hα and  Hβ fluxes for a large sample of galaxies at z ∼ 3 − 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Here  we report on these Balmer decrements, as well as their im-  plications for the star-formation rates (SFR(Hα)) and dust  attenuation in typical star-forming galaxies extending from  “cosmic noon" back into the reionization epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  In §2, we describe our observations, data reduction, mea-  surements, and sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  In §3, we present results on the  observed relationships between SFR(Hα) and stellar mass,  and Balmer decrement and stellar mass, measured for the  first time at z ∼ 3 − 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  In §4, we consider the implica-  tions of these new measurements and consider future di-  rections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Throughout, we adopt cosmological parameters  of H0 = 70 km s−1 Mpc−1, Ωm = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='30, and ΩΛ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7, and a  Chabrier (2003) IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' OBSERVATIONS AND SAMPLE  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The CEERS NIRSpec Program  We use publicly available medium-resolution NIRSpec  Micro-Shutter Assembly (MSA) data from the CEERS pro-  gram (Program ID:1345 Finkelstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022b,a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The  CEERS NIRSpec observations we analyzed consist of 6  pointings in the AEGIS field, all of which utilized the grat-  ing/filter combination of G140M/F100LP, G235M/F170LP,  and G395M/F290LP, which provide a spectral resolution of  R ∼ 1000 over the wavelength range approximately 1−5µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  For each pointing, each grating/filter combination was ob-  served for a total of 3107 sec, broken down into three expo-  sures of 14 groups, and adopting the NRSIRS2 readout mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  A 3-point nod pattern was adopted for each observation, and  each MSA “slit" consisted of 3 microshutters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Each of the  6 pointings contained between 52 and 55 targets, for a total  sample of 321 slits and 318 distinct targets (3 galaxies were  observed on two pointings).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Data Reduction  We followed the same two-dimensional (2D) reduction  procedures to reduce data for all three NIRSpec gratings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  We began by passing individual uncalibrated detector im-  ages through the JWST calwebb_detector1 pipeline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  In this step, we masked all saturated pixels, subtracted the  bias and dark current, and masked “snowballs" and “show-  ers" associated with high-energy cosmic ray events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Images  1 https://jwst-pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='io/en/latest/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='html  were then corrected for striping by estimating and subtract-  ing the 1/ f noise in each image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We then cut out the 2D  spectrum for each MSA slit, and applied a flat-field correc-  tion, background subtraction using dithered exposures as the  background, photometric calibration, and a wavelength solu-  tion based on the up-to-date calibration reference data system  (CRDS) context (jwst_1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='pmap).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Each slitlet was rec-  tified and interpolated onto a common wavelength grid based  on its grating and filter combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Finally, individual cal-  ibrated 2D spectra exposures were combined following the  defined three-shutter dither pattern, while excluding pixels  that had been previously masked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The 2D error spectra rep-  resent a combination of the variance from Poisson noise, read  noise, flat-fielding, and variance between exposures, summed  in quadrature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' This stage of the reduction yielded 310 targets  with 2D spectra covering all three gratings, reflecting a neg-  ligible sample of 8 initial targets that did not result in a viable  2D reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  One-dimensional (1D) science and error spectra were op-  timally extracted from the rectified 2D spectra (Horne 1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The spatial profile in each grating was obtained by manually  identifying wavelength ranges in the 2D spectrum contain-  ing high-S/N emission lines when present or detected contin-  uum otherwise and summing the corresponding columns of  the 2D spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' For targets with detected lines or contin-  uum in at least one grating, a blind extraction was applied to  any remaining grating lacking such information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Out of 310  CEERS targets with the full set of 2D spectra, we extracted  1D spectra for 252.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  As described in detail in Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2023a, in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' ),  wavelength-dependent slit-loss corrections were estimated  for each target based on its intrinsic morphology and posi-  tion in the NIRSpec slit, as well as the wavelength-dependent  JWST PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Intrinsic morphologies were estimated from  JWST/NIRCam F115W imaging if available, or a Sérsic fit  to HST/F160W imaging if not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In the absence of NIRCam  F115W imaging or a robust Sérsic fit, a point source was as-  sumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The final flux calibration was achieved by scaling 1D  science spectra to match the photometric SEDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Slit-loss-  corrected NIRSpec spectra were passed through the avail-  able photometric filter transmission for each target to pro-  duce synthetic photometric flux densities and errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The ra-  tio of the image-based and synthetic flux densities was calcu-  lated for each filter in which both types of measurements had  S/N>5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' If the number of filters meeting this requirement was  ≥ 3, 1D spectra and error spectra in all three gratings were  scaled by the median of the individual ratios to achieve the fi-  nal flux calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' For the 109 targets that did not meet this  criterion, no scale factor was applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' For the remaining 143  targets, the median scale factor was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='997 with a standard  deviation of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='23 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  BALMER LINES AT z ∼ 3−6  3  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Left: Redshift distribution of all 113 CEERS galaxies at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z ≤ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5, from which the sample of star-forming galaxies we analyze  is drawn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The three redshift bins we delineate are indicated in green (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0), blue (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0), and magenta (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Right: Stellar mass distributions for the three redshift samples indicated in the left-hand panel, using the same color coding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' For each redshift  distribution, the median stellar mass is marked with a vertical dotted line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' These median stellar mass values are log(M∗/M⊙) =9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='59, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='38, and  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='38, respectively, for the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 redshift samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Measurements  Redshifts and emission-line fluxes were measured from the  1D spectra for which we were able to robustly identify emis-  sion lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Reported redshifts for 231 galaxies are based on  the best-fit centroid from a single Gaussian fit to the line with  the highest signal-to-noise ratio, usually [OIII]λ5007 (57%)  or Hα (36%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  As described in more detail in Sanders et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2023 (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' ), to estimate line fluxes, we used single  Gaussian fits for widely-separated lines, adjacent lines such  as [NII]λ6548, Hα, and [NII]λ6583 are simultaneously with  multiple Gaussians, and closely spaced lines that are blended  and unresolved at R ∼ 1000 are fit with a single Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The continuum model is taken to be the best-fit SED model  (described below), where the only free parameter is an addi-  tive offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Using the best-fit SED model as the continuum  has the advantage of self-consistently accounting for stellar  absorption such that the measured hydrogen recombination  line fluxes are robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The same emission line was measured in two adjacent  gratings for many targets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' These overlapping measurements  showed good agreement, with a median offset of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='02 dex  and an intrinsic scatter of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='08 dex, suggesting that the rel-  ative flux calibration between grating configurations is ro-  bust on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In these cases of overlapping spectra, we  adopted the inverse-variance weighted mean of the two avail-  able fluxes as our reported measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  We used existing multi-wavelength catalogs to derive best-  fit SED models from which we infer stellar masses (M∗)  and other stellar population parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Specifically, for  the 99 CEERS NIRSpec targets with coverage, we used  the publicly available catalog constructed by G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Brammer2,  which includes 7 HST bands (F435W, F606W, F814W,  F105W, F125W, F140W, and F160W), and 7 JWST/NIRCam  bands F115W, F150W, F200W, F277W, F356W, F410M, and  F444W) from the initial CEERS NIRcam observations in  June 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' For an additional 185 objects we used the spec-  tral energy distributions in the AEGIS field cataloged by the  3D-HST team (Momcheva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Skelton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2014),  which include ground-based and HST optical and near-IR  photometry, and measurements from Spitzer/IRAC at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='6–  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' There were 35 CEERS NIRSpec targets not covered  by the Brammer HST+NIRCam catalog, and lacking a robust  multi-wavelength SED in the 3D-HST catalog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Restricted  to the sample of 231 galaxies with NIRSpec spectroscopic  redshifts, we found robust SED information for 210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' When  restricted to the sample of 109 star-forming galaxies spectro-  scopically confirmed at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z ≤ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5, which forms the basis  of the current analysis, we have robust SEDs for 94 (86%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  For SED modeling, we used the FAST program (Kriek  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2009), assuming the stellar population synthesis mod-  2 https://s3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='amazonaws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='com/grizli-v2/JwstMosaics/v4/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='html  4  SHAPLEY ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  els of Conroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2009), and a Chabrier (2003) IMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Following Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2018a), we adopted two combina-  tions of metallicity and extinction curves for SED model-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' These include 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 solar metallicity (Z⊙ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='014) cou-  pled with the Calzetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2000) attenuation curve (here-  after “1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 Z⊙+Calzetti"), and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27 solar models with the  SMC extinction curve (hereafter “0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27 Z⊙+SMC").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We as-  sumed delayed-τ star-formation histories, where SFR(t) ∝  t × exp(−t/τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Here, t is the time since the onset of star for-  mation and τ is the characteristic star-formation timescale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The adoption of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 Z⊙+Calzetti or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27 Z⊙+SMC was de-  termined for each galaxy on the basis of its redshift and  mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Following Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2018) and guided by the evolving  galaxy mass-metallicity relation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2021),  at z ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 we adopted 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 Z⊙+Calzetti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' At 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 < z ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 < z ≤ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4), we adopted 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 Z⊙+Calzetti for galax-  ies above log(M∗,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4Z⊙+Calzetti/M⊙) = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='45 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='66) and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27  Z⊙+SMC for those at lower masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' At z > 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4, we adopted  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27 Z⊙+SMC models (Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We note that  all relevant photometric bands were corrected for the contri-  butions from strong nebular emission lines using the method  described in Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2021), and Balmer emission-line  fluxes were corrected for the underlying stellar absorption  implied by the best-fit stellar population model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Finally, SFR(Hα) was estimated from dust-corrected Hα  luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2020) showed that the Milky Way  dust law of Cardelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (1989) provides a good match to  the wavelength dependence of nebular attenuation in z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3  star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Accordingly, we used the measured  Hα/Hβ ratio, along with an assumption of the Cardelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  (1989) dust extinction curve, to infer E(B−V)neb, the nebular  extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Then the dust-corrected Hα luminosity was mul-  tiplied by a conversion factor depending on the metallicity  of the best-fit SED model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Following the analysis of Reddy  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2018a), for galaxies with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4 Z⊙+Calzetti fits, we  used a conversion factor of 10−41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='37(M⊙yr−1)/(erg s−1), de-  rived from Z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='02 BPASS population synthesis models in-  cluding the effects of stellar binaries and assuming an upper-  mass IMF cut-off of 100 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' This calibration is almost iden-  tical to the one from Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2011) used in many other  recent works for Hα observations of z ∼ 2 galaxies (Shiv-  aei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Shapley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' For  galaxies with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27 Z⊙+SMC fits, we used a conversion factor  of 10−41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='67(M⊙yr−1)/(erg s−1), derived from from Z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='001  BPASS population synthesis models including the effects of  stellar binaries and assuming an upper-mass IMF cut-off of  100 M⊙ (Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The latter, lower conversion  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' SFR(Hα) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' M∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Green, blue, and magenta symbols are  used, respectively, for the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤  z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 samples, and galaxies with Hβ upper limits are indicated  as SFR(Hα) lower limits (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', due to the lower limit on the Balmer  decrement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The median error bar for each sample is shown in the  lower-right corner of the plot in its designated color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Along with  CEERS data points, we plot the best-fit relation from Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  (2014) (their equation (28)), at the median redshift of each sample  (z = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='30,4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='60 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='65, respectively, for the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤  z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 samples), and offset by −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='34 dex in the  y-axis to account for different assumptions regarding the conversion  between observables and SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  factor reflects the greater efficiency of ionizing photon pro-  duction in lower-metallicity massive stars in binary systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Sample  For the current analysis, we require a redshift measurement  in the range 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The lower bound here represents  the limit of ground-based measurements of Hα, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', the be-  ginning of uncharted territory, while the upper bound repre-  sents the corresponding redshift limit imposed by the red cut-  off of the G395M/F290LP setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We also require a stellar  mass estimate, wavelength coverage of both Hα and Hβ, a  ≥ 3σ detection of Hα, and finally a lack of indication of ac-  tive galactic nucleus (AGN) activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In the full sample of  CEERS spectra, we identified 15 galaxies as candidate AGN  on the basis of either an [NII]λ6583/Hα ratio greater than  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 (10 galaxies), or else an Hα profile consisting of both a  narrow component and broad base (5 galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  3 The stellar metallicity associated with this Hα SFR conversion factor is  lower than what is assumed for 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='27 Z⊙+SMC broadband SED modeling,  yet the conversion factor is not strongly metallicity-dependent in this low-  metallicity regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  BALMER LINES AT z ∼ 3−6  5  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Composite spectra for each of the three redshift bins, where, from bottom to top, we show spectra, respectively, for the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0,  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In each row, the left set of panels represents the “low-mass bin," while the right side indicates  the “high-mass bin," where each redshift sample is divided at the median stellar mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Each composite spectrum is zoomed in on the regions  covering Hβ and [OIII]λλ4959,5007, as well as Hα, [NII]λλ6548,6583, and [SII]λλ6717,6731.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' These features are marked and labeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Out of the 113 CEERS targets with redshifts measured at  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 (Figure 1, left), 109 show no rest-optical spec-  troscopic evidence for AGN activity, of which 94 have stellar  mass estimates (Figure 1, right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Of these galaxies, 77 have  (1) Hα and Hβ wavelength coverage and (2) Hα detections,  and they comprise our primary sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In order to search  for evolution within the sample, we construct three redshift  subsamples at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4 (24 galaxies), 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 (25  galaxies), and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 (28 galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Of these, 62 galax-  ies also have Hβ detections, broken down into 22, 19, and  21 galaxies, respectively, at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0, and  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' RESULTS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Star Formation  One of the key diagnostics of the evolution of the star-  forming galaxy population across cosmic time is the so-  called “main sequence" (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Noeske et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' This cor-  relation between SFR and M∗ is thought to reflect the grad-  ual growth of galaxies, largely through smooth accretion and  minor mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' A galaxy’s position with respect to the main  sequence (within its scatter, significantly above, significantly  below), provides a sense of its evolutionary state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  In order to construct the SFR vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  M∗ relationship for  CEERS galaxies targeted by NIRSpec, we took some care  in translating dust-corrected Hα luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' As described  in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3, across the entire CEERS NIRSpec spectro-  scopic sample, the adopted conversion factor is lower for  lower-mass and higher-redshift galaxies, based on the ob-  served trend towards lower metallicity at lower stellar mass  and higher redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In fact, in our primary sample, all but  one galaxy was modeled with a subsolar metallicity and SMC  dust law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Accordingly, we used the low-metallicity SFR/LHα  conversion factor for all but one galaxy as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We note that  the sample median SFR(Hα) estimated using this conversion  factor shows excellent agreement (within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='07 dex) with the  median SFR derived from SED fitting (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3), and the  two sets of SFR measurements are significantly correlated  (see also Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Figure 2 shows the relationship between SFR(Hα) and M∗  among CEERS galaxies targeted by NIRSpec at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z <  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5, color-coded by redshift range as in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We also  plot the best-fit parameterized main sequence relation from  Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2014), which expresses galaxy SFR as a func-  tion of both M∗ and z, or, equivalently, the age of the uni-  verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Relations from Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2014) are plotted at the  median redshift of each of the three subsamples (z = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='6,  and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='65).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Notably, we also shift the Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2014)  relations by −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='34 dex in SFR(Hα), since they are effectively  tied to the Hao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2011) SFR conversion factor for Hα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Both the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 samples scat-  ter symmetrically around the (shifted) main sequence fits  from Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2014), suggesting that these samples are  representative of star-forming galaxies over the stellar mass  range 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ log(M∗/M⊙) ≤ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The two lower-redshift  subsamples also show no significant offset with respect to  each other in terms of typical SFR(Hα) at fixed M∗, consis-  6  SHAPLEY ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  tent with the lack of strong redshift dependence in the Spea-  gle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2014) over this redshift range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5  sample, however, is offset towards higher SFR(Hα) relative  to the Speagle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2014) parametrization, which, itself,  represents an extrapolation out to such high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Re-  gardless of the parametrized version of the main sequence,  the highest-redshift subsample is characterized by a higher  average SFR(Hα) at fixed stellar mass than the two lower-  redhift subsamples within the stellar-mass range of overlap  (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ log(M∗/M⊙ ≤ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' More representative samples will  be required to determine if this offset is reflective of the un-  derlying evolving galaxy population, or rather a selection ef-  fect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Dust Attenuation  It has been shown that the strong connection between mea-  sures of dust attenuation and M∗ does not significantly evolve  between z ∼ 0 and z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Here dust attenuation has been esti-  mated with several different tracers, including the ratio of far-  IR to UV SFRs or luminosities, also known as “IRX" (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=',  Meurer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Bouwens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' the magnitude  of far-UV (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', 1600Å) attenuation, or A1600 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', McLure  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' the fraction of star formation that is obscured,  fobscured (Whitaker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2017), and the nebular attenuation  based on the Balmer decrement (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Hα/Hβ ratio;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Kashino  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Domínguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Price et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' There  is less consensus regarding the form of the attenuation vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  M∗ relation at z > 3, with some evidence that it may evolve  towards lower attenuation at fixed M∗ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Fudamoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Shapley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2022) presented a large sample of Balmer  decrements at z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3, demonstrating that the relationship be-  tween Balmer decrement and M∗ showed no significant evo-  lution up to the current epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We extend this work for the  first time out to z ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5, using measured Balmer decrements  for the CEERS NIRSpec sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In addition to individual  Balmer decrement measurements, we used stacked compos-  ite spectra to estimate average quantities in two bins of stel-  lar mass for each of the three redshift bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' These composite  spectra, zoomed in to the regions surrounding Hβ and Hα,  are shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Each row features the results for one  of the redshift subsamples, while the left-hand (right-hand)  set of plots represents the lower-mass (higher-mass) half of  each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 4  The left-hand panel of Figure 4 shows the relationship be-  tween Balmer decrement and M∗ for both z ∼ 0 star-forming  galaxies in SDSS, and z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3 galaxies drawn from the MOS-  DEF survey (Shapley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  We overplot individ-  4 The sample for stacking (N = 82) is slightly larger than for individual mea-  surements, as there was no explicit requirement of Hβ coverage in the  stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  ual CEERS NIRSpec measurements at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5, color-  coded by redshift subsample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The individual z ≥ 3 measure-  ments are noisy, but there is no obvious evolution between  z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3 and z ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We note that a small number of galax-  ies in the CEERS sample scatter to either surprisingly high  values of Hα/Hβ, or else values significantly less than the  dust-free minimum value of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We attribute these outliers  to remaining systematics in the NIRSpec grating-to-grating  flux calibration (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', when Hα and Hβ are measured in dif-  ferent gratings), which lacks bias on average, but also has  scatter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  In the right-hand panel of Figure 4, we replace individ-  ual CEERS measurements with those taken from composite  spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In these higher-S/N measurements, the two lower-  redshift show preliminary evidence for higher Hα/Hβ ratio  at higher stellar mass, yet the error bars are still too large to  discern a significant trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Furthermore, at lower redshifts,  only a very shallow trend between Hα/Hβ and stellar mass is  observed over the stellar mass range probed by the z > 3 sam-  ple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The main result from these preliminary measurements of  dust attenuation and stellar mass in CEERS is that the z > 3  measurements scatter around those at z ∼ 0 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3, with no  obvious offset overall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We do note that the lower-mass bin  at 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 is offset towards higher Hα/Hβ relative to  the SDSS distribution (there are no z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3 measurements at  log(M∗/M⊙) ∼ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='0) but the error bar for this 16-galaxy stack  is large enough that its vertical offset relative to SDSS is not  significant, and the lower- and higher-mass bins at this red-  shift are statistically consistent with a flat trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' DISCUSSION  A crucial component of our measurement of the SFR(Hα)  vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' M∗ relation at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='7 ≤ z < 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 is the adoption of an ap-  propriate conversion factor between dust-corrected Hα lumi-  nosity and SFR, characterized by the correct metallicity and  treatment of the effects of stellar binaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' There are mul-  tiple lines of evidence that the vast majority of galaxies in  our sample have significantly subsolar metallicities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Their  stellar masses alone suggest subsolar metallicity, given what  is known about the evolution of the galaxy mass-metallicity  relation at lower redshifts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' More  directly, as discussed in Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2023 (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' ), the  composite spectra shown in Figure 3 indicate [NII]/Hα ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='1  for all subsamples, another sign of low metallicity (Pettini &  Pagel 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Finally, models of the rest-UV stellar contin-  uum of z ∼ 2−3 star-forming galaxies suggests significantly  subsolar stellar metallicities (Steidel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Cullen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Topping et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2020b,a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Star-  forming galaxies such as those in the CEERS NIRSpec sam-  ple, covering the same or lower stellar-mass range but at  higher redshift, should be even less enriched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' As highlighted  by Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2018b) and Theios et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2019), the subsolar  BALMER LINES AT z ∼ 3−6  7  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Attenuation vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' M∗ based on the Balmer line ratio, Hα/Hβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In each panel, the background grayscale histogram corresponds to the  distribution of local SDSS galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The running median Hα/Hβ ratio for z ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='3 star-forming galaxies in the MOSDEF survey is shown in red  (Shapley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In the left panel, we show individual CEERS galaxies color-coded by redshift as in previous plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' On the right, plotted  Hα/Hβ ratios are measured from composite spectra in two bins of stellar mass for each redshift range, as shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  conversion factor between Hα luminosity and SFR adopted  here is a factor of ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5 lower than the canonical conver-  sion used for lower-redshift studies in the literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Hao  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Previously, Caputi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2017) estimated the  SFR(Hα) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' M∗ relation at z ∼ 4−5, based on a large sam-  ple of star-forming galaxies with photometric redshifts and  Hα line fluxes inferred indirectly from Spitzer/IRAC 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='6µm  photometric excesses relative to best-fit SED models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Ca-  puti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' (2017) used a solar-metallicity conversion factor  for SFR(Hα), resulting in a higher overall normalization of  the SFR(Hα) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' M∗ relation, and also found an apparent  bimodality in the SFRs of galaxies with strong Hα emis-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  We recover no such bimodality in the distribution  of SFR(Hα) values, based on direct spectroscopic measure-  ments of Balmer lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  The CEERS NIRSpec sample provides tantalizing evi-  dence that the relationship between Balmer decrement and  stellar mass remains constant out to z ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' This measure of  dust attenuation depends on both the dust mass and the way  in which it is distributed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', the effective dust-mass surface  density), so the lack of evolution in attenuation at fixed stellar  mass suggests a constant ratio of dust-mass surface density  to stellar mass (Shapley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' At the same time, other  studies have found evidence for a lower fraction of obscured  star-formation (“IRX") at fixed mass at z > 4 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Fudamoto  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2020), based on far-IR and UV continuum estimate of  dust attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' Different redshift evolution in the IRX vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  M∗ and Hα/Hβ vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' M∗ relations could arise if the spatial  distribution of dust relative to massive stars and H II regions  evolves (Reddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2015), based on the fact that IRX probes  stellar continuum attenuation while Hα/Hβ traces nebular at-  tenuation in H II regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' However, the results thus far on  the attenuation vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' mass relation at the highest redshifts –  both our Balmer decrement analysis and the studies based on  IRX – use small samples of galaxies, and require confirma-  tion with an order of magnitude larger sample numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  We have entered an era in which spectroscopic Balmer-  line measurements at z > 3 are routine and can be ob-  tained in modest exposure times on JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The CEERS NIR-  Spec dataset analyzed here demonstrates the great poten-  tial of JWST for obtaining fundamental probes of the star-  forming galaxy population into the reionization epoch based  on Balmer-line measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' In addition to tracing star for-  mation, galaxy growth, and dust attenuation, as we do here,  the ratio of Hα to UV continuum luminosity can be used to  infer the efficiency of ionizing photon production, ξion (Shiv-  aei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2018) – crucial for quantifying the role of star-  forming galaxies in cosmic reionization – as well as evidence  for bursty star-formation histories (Emami et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We  look forward to realizing the full potential of JWST and NIR-  Spec with not only larger and representative galaxy samples,  but also samples with complete NIRCam photometric cover-  age, selected from early public JWST imaging datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  8  SHAPLEY ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  This work is based on observations made with the NASA/  ESA/CSA James Webb Space Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' The data were ob-  tained from the Mikulski Archive for Space Telescopes at  the Space Telescope Science Institute, which is operated by  the Association of Universities for Research in Astronomy,  Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', under NASA contract NAS5-03127 for JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' We also  acknowledge support from NASA grant JWST-GO-01914.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='  Support for this work was also provided through the NASA  Hubble Fellowship grant #HST-HF2-51469.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content='001-A awarded  by the Space Telescope Science Institute, which is operated  by the Association of Universities for Research in Astron-  omy, Incorporated, under NASA contract NAS5-26555.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' 2022, A&A, 661, A81  Finkelstein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' 2022a, ApJL,  940, L55  Finkelstein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' 2022b,  arXiv e-prints, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+page_content=' 2020, ApJ, 902, 123  Reddy, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ndE1T4oBgHgl3EQfhgRQ/content/2301.03241v1.pdf'}
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+Data Valuation Without Training of a Model
+Nohyun Ki∗†
+Hoyong Choi∗‡
+Hye Won Chung§
+Abstract
+Many recent works on understanding deep learning try to quantify how much individual data instances
+influence the optimization and generalization of a model, either by analyzing the behavior of the model
+during training or by measuring the performance gap of the model when the instance is removed from
+the dataset. Such approaches reveal characteristics and importance of individual instances, which may
+provide useful information in diagnosing and improving deep learning. However, most of the existing
+works on data valuation require actual training of a model, which often demands high-computational
+cost. In this paper, we provide a training-free data valuation score, called complexity-gap score, which
+is a data-centric score to quantify the influence of individual instances in generalization of two-layer
+overparameterized neural networks. The proposed score can quantify irregularity of the instances and
+measure how much each data instance contributes in the total movement of the network parameters during
+training. We theoretically analyze and empirically demonstrate the effectiveness of the complexity-gap
+score in finding ‘irregular or mislabeled’ data instances, and also provide applications of the score in
+analyzing datasets and diagnosing training dynamics.
+1
+Introduction
+Creation of large datasets has driven recent development of deep learning in diverse applications including
+computer vision (Krizhevsky et al., 2012; Dosovitskiy et al., 2021), natural language processing (Vaswani
+et al., 2017; Brown et al., 2020) and reinforcement learning (Mnih et al., 2015; Silver et al., 2016). To utilize
+the dataset in a more efficient and effective manner, many recent works have attempted to understand the role
+of individual data instances in training and generalization of neural networks. As an example, in (Ghorbani
+& Zou, 2019), a metric to quantify the contribution of each training instance in achieving a high test accuracy
+was analyzed under the assumption that not only the training data but also the test data is available. Jiang
+et al. (2021) defined a score to identify irregular examples that need to be memorized during training, in order
+for the model to accurately predict the class of the example. Swayamdipta et al. (2020), on the other hand,
+analyzed the characteristics of data instances with respect to their role in out-of-distribution generalizations.
+All these previous methods for data valuation require actual training of a model to quantify the role of
+individual instances at the model. Thus, the valuation itself often requires high-computational cost, which
+may contradict some motivations of data valuation. For example, in (Ghorbani & Zou, 2019; Jiang et al.,
+2021), to examine the effect of individual data instances in training, one needs to train a model repeatedly
+while eliminating each instance or subsets of instances, which requires training of a model at least the number
+of times proportional to the number of training instances. In (Swayamdipta et al., 2020; Toneva et al., 2019),
+on the other hand, training dynamics–the behavior of a model on each instance throughout the training–is
+analyzed to categorize data instances, which also requires the training of a model with the full dataset.
+When the motivation for data valuation lies in pruning less important examples to save computational cost
+for training, the previous valuation methods might not be suitable, since they require the training of a model
+∗Equal contribution.
+†School of Electrical Engineering, KAIST, Daejeon, 34141, Korea. email: kinohyun@kaist.ac.kr
+‡School of Electrical Engineering, KAIST, Daejeon, 34141, Korea. email: chy0707@kaist.ac.kr
+§Corresponding author. School of Electrical Engineering, KAIST, Daejeon, 34141, Korea. email: hwchung@kaist.ac.kr
+1
+arXiv:2301.00930v1  [cs.LG]  3 Jan 2023
+
+with the full dataset before one can figure out ‘important’ instances and possibly prune the rest of the
+examples.
+In this paper, our main contribution is on defining a training-free data valuation score, which can be
+directly computed from data and can effectively quantify the impact of individual instances in optimization
+and generalization of neural networks. The proposed score, called complexity-gap score, measures the gap in
+data complexity where a certain data instance is removed from the full dataset. The data complexity measure
+was originally introduced in Arora et al. (2019) to quantify the complexity of the full dataset, which was
+used in bounding the generalization error of overparameterized two-layer neural networks trained by gradient
+descent. Different from that work, where the complexity of the full dataset was main concern, our focus is on
+decomposing the effect of individual data instances in the training, and thus we newly introduce a complexity
+gap score (CG-score). We theoretically analyze and empirically demonstrate that the CG-score can quantify
+‘irregularity’ of instances within each class, and thus can be used in identifying atypical examples, either
+due to the inherent irregularity of the instance or mislabeled classification. We also demonstrate that the
+proposed score has a close relation to ‘learning difficulty’ of the instances by analyzing the training dynamics
+of data instances. Our key contributions are as below:
+• Training-free data valuation: Different from previous methods for data valuation, most of which lever-
+age the information from training itself, we provide a training-free data valuation score, CG-score,
+which is the data-centric score to quantify the effect of individual data instances in optimization and
+generalization of neural networks.
+• Geometric interpretation: We provide theoretical analysis that the CG-score can measure irregularity
+of instances within each class, i.e., how much each instance represents the instances of the same class
+and how much it is different from those of other classes.
+• Effectiveness of the score: We empirically demonstrate the effectiveness of the CG-score in data val-
+uation. We show that pruning data instances with small CG-score do not significantly degrade the
+generalization capability of a model, e.g., for CIFAR-10 we can prune 40% of the data with only 1%
+of drop in test accuracy. Our scoring method is especially useful in data pruning, since different from
+other scores, which require the training with the full dataset, our method does not require any training
+of a model.
+• Application of the score: We provide potential applications of the CG-score in analyzing datasets and
+training dynamics. We analyze the histograms of the CG-score for various datasets to demonstrate
+that the CG-score can measure irregularity of the instances. We also demonstrate that the instances
+with higher CG-score are ‘difficult’ examples, which are learned slowly by the models, by comparing
+the loss and test accuracy curves and the evolution of Neural Tangent Kernel (NTK) submatrices of
+lowest/highest-scoring groups.
+2
+Related Works
+Different from many existing works where the impact of datasets on model training is analyzed as a whole,
+some recent works have focused on understanding the impact of individual data instances. Ghorbani & Zou
+(2019) defined a method for data valuation, called Data Shapley, to evaluate the value of each data instance,
+by measuring the average gap in performances when an instance is held-out from any subsets of a given
+training data. Jiang et al. (2021) defined consistency score (C-score) of each instance by estimating the
+prediction accuracy of the instance attained by the model trained with the full dataset except the instance.
+Both Data Shapley and C-score require multiple trainings of a model to compute the scores. Another main
+stream of methods uses the training dynamics to identify ‘difficult’ instances for classification, either due to
+irregularity or mislabeling, by measuring different forms of confidence, stability or influence in the decision
+of the networks throughout the training (Toneva et al., 2019; Swayamdipta et al., 2020; Pruthi et al., 2020).
+In (Baldock et al., 2021), the computational difficulty of an instance is defined as the number of hidden
+2
+
+layers after which the networks’ prediction coincides with the prediction at the output. With application of
+robust learning, there also exist some works that quantify the difficulty of each instance by a ‘margin’ from
+the decision boundary (Zhang et al., 2021). CRAIG (Mirzasoleiman et al., 2020) finds valuable subsets of
+data as coresets that preserve the gradient of the total loss. All these previous methods are demonstrated
+to be effective in at least one or more applications of data valuation, including data pruning (Paul et al.,
+2021; Swayamdipta et al., 2020; Agarwal et al., 2022; Feldman & Zhang, 2020), importance-based weighted
+sampling (Chang et al., 2017; Koh & Liang, 2017), noise filtering (Li et al., 2020; Lee et al., 2019b; Kim
+et al., 2021), robust learning (Ren et al., 2018; Pleiss et al., 2020), or out-of-distribution generalizations
+(Swayamdipta et al., 2020). However, all these methods require the training of a model with the full dataset
+(at least for a few optimization steps). Some recent works do the data valuation at the initialization of models
+(Wu et al., 2022) or by assuming data distributions (Kwon et al., 2021), but they often require relatively
+high computational cost or additional assumptions on data distributions. Our data valuation method, on
+the other hand, is a data-centric method that can be efficiently calculated from data only without training of
+a model. We demonstrate that with our scoring method, we can effectively analyze the impact of individual
+data instance in optimization and generalization of neural networks.
+3
+Complexity-Gap Score: Data Valuation without Training
+In this section, we introduce a new data valuation score, called complexity-gap score, based on the analysis
+of overparameterized two-layer neural networks from Arora et al. (2019).
+3.1
+Preliminaries: data complexity measure in two-layer neural networks
+We first review the result from Arora et al. (2019), where a two-layer neural network trained by randomly
+initialized gradient descent is analyzed. Following the notations from Arora et al. (2019), we consider a
+two-layer ReLU activated neural network having m neurons in the hidden layer, of which the output is
+fW,a(x) =
+1
+√m
+�m
+r=1 arσ(w⊤
+r x) where x ∈ Rd is the input, w1, . . . , wm ∈ Rd are weight vectors in the
+first layer, a1, . . . , am ∈ R are weights in the second layer, and σ(x) = max(0, x) is the ReLU activation
+function. We denote W = (w1, . . . , wm) ∈ Rd×m and a = (a1, . . . , am)⊤ ∈ Rm. It is assumed that the
+network parameters are randomly initialized as wr(0) ∼ N(0, κ2Id×d) and ar ∼ unif({−1, 1}), ∀r ∈ [m],
+where κ ∈ (0, 1] is the size of random initialization. The second layer a is then fixed and only the first layer
+W is optimized through gradient descent (GD) to minimize the quadratic loss, Φ(W) = 1
+2
+�n
+i=1(yi − ui)2
+where ui = fW,a(xi) and {(xi, yi)}n
+i=1 is the dataset drawn i.i.d. from an underlying distribution D. The
+GD update rule can be written as wr(k + 1) − wr(k) = −η ∂Φ(W(k))
+∂wr
+where η > 0 is the learning rate. The
+output of the network for the input xi at the k-th iteration is denoted by ui(k) = fW(k),a(xi). For simplicity,
+it is assumed that ∥x∥2 = 1 and |y| ≤ 1.
+The data complexity measure governing the training of the two-layer ReLU activated neural network is
+defined in terms of the following Gram matrix H∞ ∈ Rn×n associated with ReLU activation:
+H∞
+ij = Ew∼N (0,Id×d)
+�
+x⊤
+i xj1{w⊤xi ≥ 0, w⊤xj ≥ 0}
+�
+= x⊤
+i xj(π − arccos(x⊤
+i xj))
+2π
+.
+(1)
+In Arora et al. (2019), a complexity measure of data was defined as y⊤(H∞)−1y where y = (y1, . . . , yn),
+and it was shown that this measure bounds the total movement of all neurons in W from their random
+initialization. Moreover, the data complexity measure bounds the generalization error by restricting the
+Rademacher complexity of the resulting function class. In the following, we write the eigen-decomposition
+of H∞ as H∞ = �n
+i=1 λiviv⊤
+i
+where λi’s are ordered such that λ1 ≥ λ2 ≥ . . . λn.
+Further, assuming
+λn ≥ λ0 > 0, we can write (H∞)−1 = �n
+i=1(λi)−1viv⊤
+i .
+Theorem 1 (Informal version of (Arora et al., 2019)). Assume that λmin(H∞) = λn ≥ λ0 > 0.
+For
+sufficiently large width m, sufficiently small learning rate η > 0 and sufficiently small random initialization
+3
+
+κ > 0, with probability at least 1 − δ over the random initialization, we have
+a) Bound in loss : ∥y − u(k)∥2 =
+�
+�
+�
+�
+n
+�
+i=1
+(1 − ηλi)2k(v⊤
+i y)2 + small constant,
+b) Bound in total movement of neurons: ∥W(k) − W(0)∥F ≤
+�
+y⊤(H∞)−1y + small constant,
+c) Bound in population loss: E(x,y)∼D[l(fW(k),a(x), y)] ≤
+�
+y⊤(H∞)−1y
+n
++ O
+�
+�
+�
+log
+n
+λ0δ
+n
+�
+� ,
+where a) and b) hold for all iteration k ≥ 0 of GD, and c) holds for k ≥ Ω (1/(ηλ0) log(n/δ)).
+The above theorem shows that if the label vector y is aligned with top eigenvectors of H∞, i.e., (v⊤
+i y)
+is large for large λi, then the loss decreases quickly and the total movement of neurons from their ran-
+dom initialization is small, which implies a small generalization error. Thus, the data complexity measure
+y⊤(H∞)−1y captures the complexity of data governing both the optimization and generalization of the
+overparameterized two-layer neural networks. However, this quantity captures the complexity of the overall
+data. To decompose the individual data instances, in the next section, we newly define a complexity-gap
+score.
+3.2
+Complexity-gap score and training dynamics
+We define the complexity-gap score (CG-score) of (xi, yi) as the difference between the data complexity
+measure when (xi, yi) is removed from a given dataset {(xi, yi)}n
+i=1:
+CG(i) = y⊤(H∞)−1y − y⊤
+−i(H∞
+−i)−1y−i
+(2)
+where y−i is the label vector except the i-th sample point and H∞
+−i is the (n − 1) × (n − 1) matrix obtained
+by removing the i-th row and column of H∞.
+We first emphasize that the proposed score can be easily calculated from given data without the need of
+training neural networks, as opposed to other data valuation scores requiring either a trained neural network
+or statistics calculated from training dynamics. Yet, the proposed score captures two important properties
+on the training and generalization of data instance, implied by Theorem 1:
+1. An instance (xi, yi) with a large CG-score is a ‘difficult’ example, in the sense that removing it from
+the dataset reduces the generalization error bound by a large amount, which implies that the dataset
+without (xi, yi) is much easier to be learned and generalized.
+2. An instance (xi, yi) with a larger CG-score contributes more on the optimization and drives the total
+movement of neurons by a larger amount, measured by ∥W(k) − W(0)∥F .
+We next discuss the computational complexity of calculating the CG-score. To calculate {CG(i)}n
+i=1, we
+need to have the inversion of matrices H∞ and H∞
+−i for all i ∈ [n], which requires O(n4) complexity when
+we use general O(n3)-complexity algorithm for the matrix inversion. By using Schur complement, however,
+we can reduce this complexity to O(n3). Without loss of generality, we can assume i = n. Denote H∞ and
+(H∞)−1 by
+H∞ =
+�H∞
+n−1
+gi
+g⊤
+i
+ci
+�
+,
+(H∞)−1 =
+�
+(H∞)−1
+n−1
+hi
+h⊤
+i
+di
+�
+,
+(3)
+where H∞
+n−1, (H∞)−1
+n−1 ∈ R(n−1)×(n−1), gi, hi ∈ Rn−1 and ci, di ∈ R. From H∞(H∞)−1 = In, we have
+g⊤
+i (H∞)−1
+n−1 + cih⊤
+i = 0, i.e., h⊤
+i = −c−1
+i g⊤
+i (H∞)−1
+n−1.
+By Schur complement, (H∞
+−i)−1, which is equal to (H∞
+n−1)−1 for i = n, can be calculated as
+(H∞
+−i)−1 = (H∞)−1
+n−1 − d−1
+i hih⊤
+i .
+(4)
+4
+
+Table 1: Spearman’s rank correlation between CG-score (CG’-score) and other data valuation scores.
+Datasets
+Correlation btwn. CG-score and
+Correlation btwn. CG’-score and
+C-score
+Forgetting
+EL2N
+C-score
+Forgetting
+EL2N
+CIFAR-10
+0.557
+0.432
+0.365
+0.115
+0.110
+0.136
+CIFAR-100
+0.529
+0.289
+0.356
+0.243
+0.090
+0.177
+Since we have
+y⊤(H∞)−1y = y⊤
+−i(H∞)−1
+n−1y−i + yih⊤
+i y−i + yiy⊤
+−ihi + y2
+i di,
+y⊤
+−i(H∞
+−i)−1y−i = y⊤
+−i(H∞)−1
+n−1y−i − d−1
+i (y⊤
+−ihi)2,
+(5)
+the CG-score, CG(i) in equation 2, can be calculated by
+CG(i) = d−1
+i (y⊤
+−ihi)2 + 2yi(y⊤
+−ihi) + y2
+i di =
+�
+(y⊤
+−ihi)/
+�
+di + yi
+�
+di
+�2
+.
+(6)
+Thus, CG(i) can be calculated by the n-th column (hi, di) of (H∞)−1, without the need of calculating
+(H∞
+−i)−1 when i = n. The case for general i ̸= n can also be readily solved by permuting the i-th row and
+column of H∞ into the last positions.
+Correlation to other scores
+We show relation between our score and other data valuation scores that
+require the training of neural networks. Toneva et al. (2019) define ‘the forgetting score’ for each training
+example as the number of times during training the decision of that sample switches from a correct one to
+incorrect one. Paul et al. (2021), on the other hand, suggest the GraNd score, which is the expected loss
+gradient norm E[∥∇W(k)l(u(k), y)∥], to bound the contribution of each training example to the decrease of
+loss on any other example over a single gradient step. The GraNd score is further approximated (under
+some assumptions) by the EL2N score, defined to be E[|y − u(k)|] where u(k) is the output of the neural
+network for the sample (x, y) at the k-th step. Since |y − u(k)|, if rescaled, is an upper bound on 0–1 loss,
+�
+k |y − u(k)| upper bounds forgetting score after rescaling. Thus, an example with a high forgetting score
+will also have a high GraND score and high EL2N score averaged over multiple time steps. We next relate
+our complexity-gap score to �
+k(y − u(k)), and thus to all the three previous scores defined using training
+dynamics.
+Arora et al. (2019) show that for the overparameterized two-layer networks trained by GD, the gap
+between the label vector and the network output at the step k can be approximated as y − u(k) ≈ (I −
+ηH∞)ky.
+By summing both sides over k, we get �∞
+k=0 y − u(k) ≈ �∞
+k=0(I − ηH∞)ky =
+1
+η(H∞)−1y.
+Without loss of generality, consider i = n. Then, the accumulated difference between yi and ui(k) over k
+can be approximated as
+∞
+�
+k=0
+(yi − ui(k)) ≈
+�
+h⊤
+i y−i + yidi
+�
+/η =
+�
+y⊤
+−ihi/
+�
+di + yi
+�
+di
+� �
+di/η.
+(7)
+Note that both the right-hand side of equation 7 and CG(i) in equation 6 depend on the term
+�
+y⊤
+−ihi/√di + yi
+√di
+�
+.
+Thus, we can expect that CG(i) will be correlated with the scores related to training dynamics, including
+the forgetting score, GraND score and EL2N score. Different from those scores, our score can be directly
+calculated from the data without training of a model.
+Inversion of H∞ is an effective step
+In the definition of CG(i) in equation 2, we use the inverse of
+H∞ to measure the alignment of the eigenvectors of H∞ with the label vector y. One could suggest another
+score that directly uses H∞ instead of (H∞)−1, which can save the computation for inversion. However,
+we argue that the score calculated by using (H∞)−1 includes more information than the score calculated
+5
+
+(a) Heat map of (H∞)−1
+n−1
+(b) CG-score (clean)
+(c) CG-score (10% label noise)
+Figure 1: (a) Heat map of (H∞)−1
+n−1 for 200 indices. We plot 200 indices only for clear visualization. (b)
+Scatter graph of CG-Score for two groups of samples from 3000-D Gaussian distributions having the same
+mean except the first dimension, where class 1 has mean +1 (red) and class 2 has mean -1 (blue). Samples
+near the boundary (x1 = 0) tend to have higher CG-score. (c) Same plot as (b) with 10% label noise.
+Samples with label noise (marked by plus symbol) tend to have higher CG-score.
+by H∞ due to the reason described below. Let us define CG′(i) := y⊤H∞y − y⊤
+−iH∞
+−iy−i. Without loss of
+generality, assume i = n. Then, CG′(i) = 2yi(g⊤
+i y−i) + y2
+i ci where gi = (H∞)1:(n−1),n and ci = H∞
+n,n as
+defined in equation 15. Since ci = 1/2 for all i ∈ [n] from the definition of H∞ in equation 1 and y2
+i = 1 for
+yi = ±1, we have CG′(i) = 2(yi(H∞y)i − 1/2) + 1/2. By using the approximation y − u(k) ≈ (I − ηH∞)ky
+from Arora et al. (2019), we have y − u(1) ≈ y − ηH∞y when k = 1, which implies u(1) ≈ ηH∞y. Thus,
+CG′(i) = 2
+ηyiui(1)+1/2. Note that an instance (xi, yi) has a large CG′(i) if yiui(1) is large, i.e., the network
+output ui(1) after 1-time step has the same sign as the targeted label yi ∈ {−1, 1} and has a large magnitude.
+Thus, CG′(i) measures how fast the training instance can be learned by the neural network. Different from
+CG′(i), our original score CG(i) is correlated with the accumulated error between yi and ui(k) averaged over
+the training as shown in equation 7. Thus, our original score CG(i), using the inverse of H∞, reflects the
+statistics averaged over the whole training steps.
+In Table 1, we compare the Spearman’a rank correlation between CG-score/CG’-score and other data
+valuation scores including C-score (Jiang et al., 2021), forgetting score (Toneva et al., 2019) and EL2N score
+(Paul et al., 2021) for CIFAR-10/100 datasets1 We can observe that CG-score has higher correlations with
+the previous scores compared to those of CG’-score. In the rest of this paper, we focus on the CG-score for
+our data valuation score.
+3.3
+Geometric interpretation of the complexity-gap score
+We next provide geometric interpretation for the CG-score. For the sake of simplicity, we consider binary
+dataset with n
+2 samples having yi = 1 and n
+2 samples having yi = −1. We further assume that E[H∞
+ij ] = p
+if yi = yj and E[H∞
+ij ] = q if yi ̸= yj for some |p| > |q|. Note that the diagonal entires H∞
+ii
+= 1/2 for
+all i ∈ [n]. Thus, E[H∞] can be decomposed as E[H∞] =
+� 1
+2 − p
+�
+In + S where S is a block matrix with
+S =
+�
+p
+q
+q
+p
+�
+⊗ In/2, and the resulting eigenvalues of E[H∞] are (p+q)n
+2
++
+� 1
+2 − p
+�
+,
+(p−q)n
+2
++
+� 1
+2 − p
+�
+and
+� 1
+2 − p
+�
+with multiplicity (n − 2). When p = Θ(q) and p = o(1/n), the matrix E[H∞] ≈ (1/2)In. From
+the representations of H∞ and (H∞)−1 in equation 15 and the implied relation h⊤
+i = −c−1
+i g⊤
+i (H∞)−1
+n−1,
+assuming H∞ ≈ (1/2)In and using ci = 1/2, we can write h⊤
+i = −4g⊤
+i . By using this approximation, our
+CG-score in equation 6 can be approximated as
+CG(i) = d−1
+i (y⊤
+−ihi)2 + 2yi(y⊤
+−ihi) + y2
+i di ≈ 8(yi(y⊤
+−igi))2 − 8yi(y⊤
+−igi) + 2
+(8)
+1The way CG-scores are calculated for multi-label datasets is explained in Appendix §A. To reduce the computation com-
+plexity, we calculated the scores by sub-sampling data and averaging them over multiple runs.
+6
+
+200
+175
+2.0
+150
+1.5
+125
+100
+1.0
+75
+50
+0.5
+25
+0.0
+0.
+0
+25
+50
+75 1001251501752005
+4
+CG-Score
+3
+2
+C
+1
+0
+-2
+-1
+0
+1
+2
+First dimension of input12
+10
+Class 1
+8
+score
+Class 1 (noise)
+6
+Class 2
+Class 2 (noise)
+C
+4
+DecBound
+2
+0
+_1
+-2
+0
+1
+2
+First dimension of inputsince di ≈ 2 and y2
+i = 1. From this approximation, we can first notice that −8yi(y⊤
+−igi) is the main term
+that determines the order of {CG(i)}n
+i=1, since yi(y⊤
+−igi) = �
+j∈{[n]:yi=yj} H∞
+ij − �
+j∈{[n]:yi̸=yj} H∞
+ij , and
+thus E[yi(y⊤
+−igi)] = (p−q)n
+2
+= o(1), assuming p = Θ(q) and p = o(1/n), which is much larger than the first
+term, proportional to (yi(y⊤
+−igi))2. Note that yi(y⊤
+−igi) measures the gap between the summation of H∞
+ij
+over the samples of the same class as (xi, yi) and that over the samples of the different class from (xi, yi).
+Since H∞
+ij = x⊤
+i xj(π−arccos(x⊤
+i xj))
+2π
+, yi(y⊤
+−igi) measures the gap between the average similarities of xi with
+other samples {xj} of the same class yj = yi and that with samples of the different class yj ̸= yi, where the
+similarity is measured by the cosine between the two samples (xi, xj) multiplied by the chance that ReLU
+is activated for both the samples. Thus, we can expect two important trends regarding the CG-score:
+1. Regular vs. irregular samples: If a sample (xi, yi) is a ‘regular’ sample representing the class yi in the
+sense that it has a larger similarity with other samples of the same class than to samples from the
+different class, then it will have a large yi(y⊤
+−igi), resulting in a lower CG-score due to the minus sign.
+On the other hand, if a sample (xi, yi) is ‘irregular’ in the sense that it does not represent the class
+and has a small similarity with the samples of the same class, then yi(y⊤
+−igi) will be small, resulting
+in a higher CG-score.
+2. Clean label vs. noisy label: A sample with label noise tend to have a large CG-score since yi(y⊤
+−igi) is
+negative for a sample with label noise, while it is positive for a sample with clean label.
+We empirically demonstrate the above two trends by a controlled experiment.
+Consider two 3000-
+dimensional Gaussian distributions with a fixed covariance matrix 0.25I3000 and different means (1, 0, . . . 0)
+and (−1, 0, . . . , 0), representing class +1 and -1, respectively. We generate 1000 samples from each class.
+We first check whether the structural assumptions on H∞ hold with this synthetic dataset. In Fig. 1a,
+we observe that (H∞)−1
+n−1 can be well approximated by 2In−1, and thus the approximation for CG(i) in
+equation 8 may hold well. We then examine the correlation between the CG-score and the sample value
+at the first dimension. In Fig. 1b, we can observe that instances near the decision boundary x1 = 0 have
+higher CG-scores compared to those located further from the boundary. This shows that irregular samples,
+e.g., samples near the boundary of the two classes, indeed have higher CG-scores. We further modify the
+generated samples by randomly flipping the labels of 10% samples and we re-calculate the CG-scores of all
+the samples. As shown in Fig. 1c, the samples with label noise tend to have higher CG-scores, agreeing with
+our intuition.
+4
+Data Valuation through Complexity Gap Score
+In this section, we show diverse applications of the CG-score in data valuation for real datasets.
+4.1
+Data pruning experiments
+To evaluate the ability of the CG-score in identifying important examples, we design data pruning experi-
+ments, similar to those in Ghorbani & Zou (2019); Paul et al. (2021). We evaluate our score on three public
+datasets, FMNIST, CIFAR-10/100 and train ResNet networks (He et al., 2016), ResNet18 for FMNIST and
+CIFAR-10 and ResNet50 for CIFAR-100 dataset, respectively. As baseline methods for data valuation, we
+use three state-of-the-art scores, C-score (Jiang et al., 2021), EL2N (Paul et al., 2021), and Forgetting score
+(Toneva et al., 2019), all of which require training of models for computation. On the contrary, our score is
+a data-centric measure and independent on the model. More details on the baselines and experiments are
+summarized in Appendix §C.
+In Figure 2, the first row shows the test accuracy of the model trained with different subset sizes,
+when low-scoring (regular) examples are removed first, and the second row shows the similar result but
+when high-scoring (irregular) examples are removed first.
+We report the mean of the result after three
+independent runs, and the shaded regions indicate the standard deviation. The red-curve (random) is the
+result when randomly ordered examples are used. We can observe that when removing low-scoring examples
+7
+
+(a) Pruning low-scoring examples first. Better score maintains the test accuracy longer.
+(b) Pruning high-scoring examples first. Better score makes the rapid performance drop.
+Figure 2: Pruning experiments with FMNIST (left), CIFAR-10 (middle) and CIFAR-100 (right).
+Only
+CG-Score does not require any training of the model to calculate the score for examples, but it achieves
+competitive performances compared to other state-of-the-art data valuation scores and significantly outper-
+forms the performance of random baseline. In (a), CG-score maintains the test accuracy up to significant
+removing portions; in (b), the test accuracy drops most rapidly for CG-score since the examples with high
+CG-score are essential in generalization of the model.
+first, networks maintain the test accuracy (with less than 1% drop) compared to the case of training with
+the full dataset up to significant removing portions, for example, 40% for CIFAR-10 and 20% for CIFAR-100
+with the CG-score. Especially, our CG-score, which does not require any training of a model, can achieve
+competitive performances as the other baseline methods and it also significantly outperforms the random
+baseline. When we remove the high-scoring examples first, the test accuracy drops most rapidly for the
+CG-score curve, implying that examples with the high CG-score are essential part of the data governing the
+generalization of the model.
+4.2
+Detecting label noise
+In Section 3.3, we analyzed the CG-score and showed that the examples with label noise tend to have higher
+CG-score. We next empirically investigate the ability of the CG-score in detecting label noise by artificially
+corrupting 20% of instances in FMNIST and CIFAR-100 with random label noise. We first examine the
+distribution of the CG-scores for each dataset after the corruption in Figure 3a. We can observe that for
+both datasets, the examples with corrupted labels (orange) tend to have higher CG-scores than those with
+clean labels (blue). For a relatively simpler dataset, FMNIST (left), the CG-score histograms can be more
+clearly separable between the clean and noisy groups, compared to a more complex dataset, CIFAR-100
+(right). With this observation, we can anticipate that the CG-score can have a better detectability of label
+noise for relatively simpler datasets.
+We next evaluate the noise detectability of the CG-score by checking a varying portion of the examples
+8
+
+FMNIST
+data
+95.4
+95.2
+Accuracy(%)
+95.0
+94.8
+CG-score
+94.6
+EL2N
+Forgetting
+94.4
+Random
+94.2
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train setCFAR-10
+95.0
+94.5
+94.0
+CG-score
+93.5
+EL2N
+Forgetting
+93.0
+C-score
+Random
+92.5
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train setCIFAR-100
+79
+78
+77
+76
+75
+CG-score
+EL2N
+74
+Forgetting
+73
+C-score
+Random
+72
+0.6
+0.7
+0.8
+0.9
+Portion of train set95
+94
+Accuracy(%)
+93
+CG-score
+92
+EL2N
+Forgetting
+91
+Random
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train set94
+92
+90
+CG-score
+EL2N
+88
+Forgetting
+C-score
+86
+Random
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train set78
+76
+74
+CG-score
+72
+EL2N
+Forgetting
+70
+：
+C-score
+68
+Random
+0.6
+0.7
+0.8
+0.9
+Portion of train set(a) Density of CG-score for clean vs. label-noise
+(b) Fraction of detected label noise
+Figure 3: (a) Density of CG-score for clean (80%) vs. label-noise (20%) examples. Examples with label
+noise tend to have higher CG-score. For FMNIST (left) dataset, the CG-score histograms betwen clean
+and label-noise groups are better separated than those for CIFAR-100 (right). (b) Fraction of label noise
+(y-axis) included in the examined portion (x-axis) for 20% label noise. CG-score (blue) achieves better noise
+detectability for FMNIST than for CIFAR-100.
+ordered by the CG-score (highest first) in Figure 3b. The curves indicate the fraction of noisy examples
+included in the examined subset. In this experiment, we compare our score with two other scores, Forgetting
+score and EL2N, as well as a random baseline and the oracle. We can observe that the CG-score achieves
+the best performance, near that of the oracle, for FMINST, and competitive performances for CIFAR-100.
+In the plot, we also compare the performance of the CG-score with that of ‘Partial CG-score,’ which is a new
+score defined by a sub-term of the CG-score. In the CG-score in equation 6, we have three terms, but only
+the second term 2yi(y⊤
+−ihi) uses the label information of the data (xi, yi). Thus, we examined the ability of
+this term only, defined as the ‘Partial CG-score’, in detecting the label noise, and found that the CG-score
+and partial CG-score have similar performances in detecting label noise, which implies that the label-noise
+detectability of the CG-score mainly comes from the term 2yi(y⊤
+−ihi).
+5
+Complexity-Gap Score and Deep Learning Phenomena
+We next demonstrate that the CG-score can capture ‘learning difficulty’ of data instances.
+5.1
+Complexity gap score captures learning difficulty
+It has been widely observed that there exists an order of instances in which a model learns to classify the
+data correctly and this order is robust within model types (Wu et al., 2021). Many previous scoring functions
+use this type of observation and define the ‘difficulty’ of a given instance based on the speed at which the
+model’s prediction converges (Toneva et al., 2019; Swayamdipta et al., 2020). Our data-centric CG-score is
+originally defined based on the gap in the generalization error bounds as in equation 2, but it also reflects
+the convergence speed of the instance, as analyzed in equation 7. We empirically demonstrate this relation
+by analyzing the training dynamics of CIFAR-10 dataset trained in ResNet18 network. We first sort the
+data instances in ascending order using the CG-score, and divide the data into 10 equal-sized subgroups. We
+then measure the mean of loss and training accuracy for the 10 subgroups as training progresses. Fig. 4a
+and Fig. 4b show the mean of loss and the training accuracy throughout the training for the 10 subgroups,
+respectively, where the blue color represents the low-scoring groups and the red color represents the high-
+scoring groups. We can observe that the mean loss and accuracy converge faster for low-scoring groups, while
+it takes longer to converge for high-scoring groups. This indicates that the CG-score is highly correlated
+with the ‘difficulty’ of an example measured by the learning speed at a model.
+9
+
+EMNIST
+0.12
+Clean
+0.10
+Noise label
+0.08
+Density
+0.06
+0.04
+0.02
+0.00
+50
+250
+100
+150
+200
+30
+CG scoreCIFAR-100
+0.07
+Clean
+0.06
+Noise label
+0.05
+0.04
+0.03
+0.02
+0.01
+0.00
+20
+40
+60
+80
+0
+100
+CG scoreEMNIST
+Fraction of noise data found(%)
+100
+80
+60
+Oracle
+Partial CG score
+40
+CG score
+EL2N
+20
+Forgetting score
+Random
+0
+20
+30
+10
+40
+50
+0
+Fraction of data checked(%)CIFAR-100
+100
+80
+60
+40
+20
+0
+10
+20
+30
+40
+50
+0
+Fraction of data checked(%)(a) Loss mean
+(b) Accuracy
+(c) Kernel velocity
+Figure 4: Training dynamics measured for each subset of CIFAR-10 examples, grouped by the CG-score.
+The line color varies over groups, where the blue lines include low-scoring examples and the red lines include
+high-scoring groups. (a) and (b) Mean loss and accuracy for subgroups of CIFAR-10 data, sorted by the
+CG-score, trained on ResNet18. The mean loss and accuracy converge faster for low-scoring groups, while
+they converge slowly for high-scoring groups. (c) Kernel velocity of CIFAR-10 examples grouped by the
+CG-score. The Kernel evolves with a higher velocity for high-scoring groups throughout the training.
+5.2
+Data sample driving movement of neurons
+We next investigate the relation between the CG-score and the evolution velocity of the data-dependent
+Neural Tangent Kernel (NTK) (Fort et al., 2020). NTK has been widely used to approximate the evolution
+of an infinite-width deep learning model via linearization around initial weights, when the network is trained
+by gradient descent with a sufficiently small learning rate (Jacot et al., 2018). The main idea is that in the
+limit of an infinite width, the network parameters do not move very far from its initialization throughout the
+training, so that the learning process can be approximated by a linear process along the tangent space to the
+manifold of the model’s function class at the initialization (Lee et al., 2019a). However, as observed in Fort
+et al. (2020), for a finite-width network, the tangent kernel is not constant but it rather rapidly changes over
+time, especially at the beginning of the training. To quantify this change, Fort et al. (2020) addressed the
+data-dependent Kernel Gram matrix, which is the Gram matrix of the logit Jacobian, and defined the Kernel
+velocity as the cosine distance between two NTK Gram matrices before and after one epoch of training. In
+Paul et al. (2021), the Kernel velocity was used to evaluate the subgroups of data instances to figure out the
+subgroup driving the learning and the change in the NTK feature space. We conduct similar experiments for
+subgroups of data, divided according to our CG-score. Fig. 4c shows the Kernel velocities for 10 different
+subgroups of CIFAR-10 data trained in ResNet18. Each group is composed of 125 consecutive instances
+from each level, where the level is defined by dividing the full dataset, sorted in ascending order by the
+CG-score, into 10 groups. The higher level (red) is composed of instances having higher CG-scores, while
+the lower level (blue) is composed of instances having lower CG-scores. We can observe that the samples
+with high CG-score (red) maintains higher Kernel velocity throughout the training, which means that NTK
+Gram matrix evolves by a larger amount for the samples of high CG-score. Thus, we can hypothesize that
+the instances with high CG-score are ‘difficult’ examples the network may struggle to optimize and try to
+fit throughout the training.
+6
+Discussion
+We proposed the CG-score, a data-centric valuation score, to quantify the effect of individual data instances in
+optimization and generalization of overparameterized two-layer neural networks trained by gradient descent.
+We theoretically and empirically demonstrated that the CG-score can identify ‘irregular’ instances within
+each class, and can be used as a score to select instances essential for generalization of a model or in filtering
+10
+
+0~10%
+10~20%
+20~30%
+30~40%
+40~50%
+50~60%
+60~70%
+70~80%
+80~90%
+90~100%
+2.5
+2.0
+Mean of Loss
+1.5
+1.0
+0.5
+0.0
+0
+25
+50
+75 100 125 150 175 200
+Epoch0~10%
+10~20%
+20~30%
+30~40%
+40~50%
+50~60%
+60~70%
+70~80%
+80~90%
+90~100%
+100
+80
+Accuracy(%)
+60
+40
+20
+0
+25
+50
+75 100 125 150 175 200
+Epochlevel 1
+level 2
+level 3
+level 4
+level 5
+level 6
+level 7
+level 8
+level 9
+level 10
+0.4
+Kernel velocity
+0.3
+0.2
+0.1
+0.0
+25
+50
+0
+75 100 125 150 175 200
+Epochinstances with label noise. We also showed the close relation between the CG-score and learning difficulty
+of instances by analyzing training dynamics. Interesting open problems related to the CG-score include 1)
+providing theoretical justification of the score for more general deep neural networks and 2) improving the
+score by modifying the definition in terms of ‘features’ of data instances.
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+13
+
+A
+Extensions to Multi-class Complexity Gap score
+In this section, we explain the details of how we calculated the CG-scores for multi-label public datasets.
+A.1
+Calculation of CG-score for multi-label datasets
+In defining the CG-score, we assumed the binary datasets y ∈ {±1} with inputs having a fixed norm ∥x∥2 = 1.
+To calculate the CG-score for multi-label (k-class) public datasets, we normalize all the inputs to have
+∥x∥2 = 1. We then calculate the CG-score for examples of each class j ∈ [k], assuming that all the examples
+from class j have label +1 and the rest of the examples from any other classes have label −1. In detail, let y =
+(y1, y2, ..., yn) ∈ {1, 2, . . . k}n be the label vector for n data instances and, without loss of generality, assume
+that x1, x2, . . . , xl belong to class 1, i.e. y1, y2, ..., yl = 1. Then, to calculate the CG-score for x1, x2, . . . xl,
+we generate the gram matrix H∞ with (x1, 1), (x2, 1), . . . , (xl, 1), (xl+1, −1), (xl+2, −1), . . . , (xn, −1) and
+calculate the CG-scores of x1, x2, . . . , xl as the two-label case.
+A.2
+Stochastic method to calculate CG-scores
+Since the calculation of the CG-score requires the inversion of n-dimensional matrix H∞ where n is the num-
+ber of total samples, it would demand expensive memory and computational cost. To lower the complexity,
+we sub-sample the examples with class −1 so that the ratio between class +1 and class -1 is reduced from
+1 : (k − 1) to 1 : 3 for MNIST and FMINST, 1 : 4 for CIFAR-10 and CIFAR-100. We repeat this process
+ten times by randomly sampling examples of label −1 and then average out the calculated CG-score of each
+example from class +1.
+A.3
+Justification of stochastic method to calculate CG-scores
+To justify the stochastic method in calculating the CG-scores, we conduct an experiment to check whether
+the CG-scores calculated by the stochastic method converges well to the true CG-scores utilizing the full
+dataset.
+We created a subset of the CIFAR-10 dataset, the Small-CIFAR-10 dataset, which consists of
+1,000 instances for each label (a total of 10,000 instances). Then, we compared the CG-score calculated by
+10,000x10,000 Gram matrix H∞ of the full dataset (true CG-score) with the CG-score calculated by the
+stochastic method, where the stochastic CG-score for the instances from a class (class 1) are calculated by
+subsampling the samples from any other classes (class -1) with the ratio between class 1 and -1 equal to 1 : 1
+(size 2,000x2,000), 1 : 2 (size 3,000x3,000), 1 : 3 (size 4,000x4,000) and 1 : 4 (size 5,000x5,000) instead of
+1 : 9. We repeat this process multiple times by randomly sampling examples of label −1 and then average
+out the calculated CG-score of each example from class +1. = In Figure 5, we plot the Spearman’s rank
+correlation and Pearson correlation between the true CG-score and the stochastic CG-score for each ratio
+(different colors) as the number of random sampling increases. We can observe that the correlations converge
+to a certain number as the number of random sampling increases, and the amount of correlation increases as
+the size of the matrix (the number of instances included in defining H∞) increases. The values of correlations
+obtained after 20 independent runs are 0.829, 0.914, 0.953, and 0.973 for Spearman rank correlations and
+0.796, 0.898, 0.943, and 0.967 for Pearson rank correlations.
+Recommended number of runs for stochastic calculation.
+The proper number of runs in stochastic
+calculation of the CG-score may need to be determined by the size and the number of classes of the datasets.
+We recommend the number of runs to include at least half of the whole dataset in calculation of the CG-score
+for each class. As an example, for the CIFAR-100 dataset, where each class includes 500 images, when the
+sampling ratio between the class of interest and the rest of classes is 1:4, we calculate the score for 500
+images from the class of interest by using 2,000 images from the rest of 99 classes. Then, about 20 images
+are selected from each of the 99 classes. To cover at least a half of the images per class (250), we need
+to repeat the runs about 10 times (ignoring overlap of samples in each run). For the FMNIST/CIFAR-10
+datasets, the similar calculation shows that only 2-3 runs will be enough.
+14
+
+Figure 5: We create Small CIFAR-10 dataset by sampling 1,000 data in each class from CIFAR-10 dataset.
+Figures show Spearman’s rank correlation(left) and Pearson correlation(right) between the CG-score of
+Small CIFAR-10 and CG-score calculated by subsampling the dataset (stochastic CG-score) as the number
+of calculations (random sampling) increases. Stochastic CG-scores are calculated with 2,000 (cyan), 3,000
+(orange), 4,000 (green), and 5,000 (red) instances, while the full data includes 10,000 instances (1,000 for each
+class). X-axis indicates the number of independent runs to calculate averaged score, and Y-axis indicates
+the correlations.
+B
+Discriminating mislabeled data from atypical (but useful) data
+by CG-scores
+Discriminating mislabeled data and atypical (but useful) data is a major challenge in data valuation, since
+both the mislabeled data and atypical data are irregular in the data distribution and tend to have high
+CG-scores. The same challenge has been observed with previous valuation scores such as forgetting score
+(Toneva et al., 2019) and EL2N score (Paul et al., 2021).
+However, we find that mislabeled data usually has a higher CG-score than atypical data, and this tendency
+gives us the possibility to separate mislabeled data from the rest of the clean data. To check the tendency, we
+perform a data window experiment. The data instances are sorted in ascending order by the CG-score, and
+we compare the test accuracy of a neural network trained with 50% of training instances selected from offset%
+to (offset+50)% scoring group, for different offset points of {0, 5, 10, . . . , 45, 50}. For example, when the offset
+is 20%, we select the data instances from 20% to 70% scoring examples. When the training instances do not
+include mislabeled data, we can expect that the window experiment will show higher accuracy as the offset
+increases up to 50%. We add 20% of random label noise to FMNIST and CIFAR-100 datasets to see how
+the trend changes when the dataset includes mislabeled instances.
+As shown in Fig. 6 (a) and (b), the test accuracy increases until the offset reaches 30% and then drops
+after the point. When the offset is 30%, the 50%-width window includes 30% to 80% scoring examples.
+Since 20% mislabeled data are mainly located within the 80% to 100% scoring group, as the offset increases
+above 30%, the 50%-width window starts to include mislabeled instances and this causes the rapid drop of
+the test accuracy. Thus, from the window experiments we can see that the mislabeled data has the highest
+CG-score and can be separable from the rest of the clean examples by the CG-score.
+Then, the next reasonable question is how to set the threshold on CG-score to detect the mislabeled
+data when the portion of mislabeled data is unknown.
+We show that the sign of the partial CG-score
+2yi(y⊤
+−ihi), which is a sub-term of the CG-score including the label information yi, can be used in this
+purpose. As explained in Sec. 3.3, the partial CG-score measures the gap between the average similarity of
+the data instance with other samples of the same class compared to that with the samples of the different
+classes. Thus, by checking the sign of the partial CG-score, we can discriminate mislabeled samples from
+clean samples. In Fig. 6 (c), we show the scatter plot of clean (blue) and mislabeled data (orange), where
+one can find that mislabeled examples tend to have positive partial CG-score. Furthermore, as shown in
+15
+
+0.95
+0.90
+0.85
+0.80
+2000x2000
+3000x3000
+0.75
+4000x4000
+5000x5000
+0.70
+2
+4
+6
+10
+12
+14
+16
+18
+20
+0
+8
+# of calculations0.95
+Pearson correlation
+0.90
+2000x2000
+3000x3000
+0.85
+4000x4000
+5000x5000
+0.80
+0.75
+2
+6
+12　14
+4
+16
+18
+20
+0
+8
+10
+# of calculationsTable 2: Number of mislabeled data and clean data in each subset selected based on partial CG-score
+Dataset
+FMNIST
+CIFAR-10
+2yi(y⊤
+−ihi)
+positive
+negative
+high 20%
+positive
+negative
+high 20%
+mislabeled
+11796
+204
+10776
+7146
+2854
+5619
+clean
+3462
+44538
+1224
+8331
+31669
+4381
+(a) Window experiment (FMNIST)
+(b) Window experiment (CIFAR-10)
+(c) Scatter graph (CIFAR-10)
+Figure 6: (a) and (b) Window experiments with 20% label noisy for FMNIST (a) and CIFAR-10 (b) datasets.
+Test accuracy (y-axis) of a model trained with 50% of training instances selected from offset% (x-axis) to
+(offset+50)% scoring group. (c) Scatter graph of Partial CG-score (x-axis) and CG-score (y-axis) for CIFAR-
+10 with 20% label noise.
+Table 2, we can check that for FMNIST with 20% label noise (12,000 mislabeled instances and 48,000 clean
+instances), 98%(=11796/12000) of mislabeled data ends up having positive partial CG-score, while only
+7%(=3462/44538) of clean data has positive partial CG-score. Thus, even when the portion of label noise
+is unknown, our partial CG-score can effectively detect the mislabeled data by the sign information. This
+tendency was less clear for CIFAR-10 dataset due to the increased dataset complexity, but still the tendency
+existed.
+C
+Implementation Details and computational cost
+C.1
+Training details
+In Section 4 and 5, we evaluate our score on three public datasets, FMNIST, CIFAR-10/100, by training
+ResNet networks (He et al., 2016) of different depths. ResNet18 is used for FMNIST and CIFAR-10 dataset
+and ResNet50 is used for CIFAR-100 dataset. Implementation of the ResNet is based on the ResNet network
+in torchvision (Paszke et al., 2019). Since FMNIST and CIFAR images are smaller than Imagenet (Deng
+et al., 2009) images, we replace the front parts of the ResNet (convolution layer with 7x7 kernel and 2x2
+stride, max pooling layer with 3x3 kernel and 2x2 stride) with a single convolution layer with 3x3 kernel and
+1x1 stride for small size image. The details on hyperparameters and optimization methods used in training
+are summarized in the Table 3.
+C.2
+Computation time
+Table 4 provides computational time (in seconds) to obtain CG-scores with different sampling ratio 1:1, 1:2,
+1:3, and 1:4 for FMNIST and CIFAR-10/100 dataset. We also report the time to compute the baseline scores,
+Forgetting (Toneva et al., 2019), EL2N (Paul et al., 2021), TracIn (Pruthi et al., 2020), and CRAIG (Pruthi
+16
+
+90
+Test accuracy
+80
+70
+60
+Partial CG-score
+50
+Random
+10
+20
+30
+0
+40
+50
+Offset of window85
+80
+Test accuracy
+75
+70
+65
+Partial CG-score
+60
+Random
+20
+30
+0
+10
+40
+50
+Offset of window100
+Clean
+Noise label
+80
+CG-Score
+60
+40
+20
+0
+-30
+-20
+-10
+0
+10
+20
+Partial CG-scoreTable 3: Details for the experiments used in the training of the dataset.
+FMNIST
+CIFAR10
+CIFAR100
+Architecture
+ResNet18
+ResNet18
+ResNet50
+Batch size
+128
+128
+128
+Epochs
+100
+200
+200
+Initial Learning Rate
+0.02
+0.05
+0.1
+Weight decay
+5e-4
+5e-4
+5e-4
+Optimizer
+SGD with momentum 0.9
+Learning Rate Scheduler
+Cosine annealing schedule (Loshchilov & Hutter, 2017)
+Data Augmentation
+Normalize by dataset’s mean, variance
+Random Zero Padded Cropping (4 pixels on all sides)
+Random left-right flipping (probability 0.5)
+Table 4: Time cost(seconds) to compute scores of the dataset.
+FMNIST
+CIFAR-10
+CIFAR-100
+CG-score 1:1
+1063
+608
+37.9
+CG-score 1:2
+2610
+1497
+40.3
+CG-score 1:3
+4834
+2773
+49.0
+CG-score 1:4
+-
+4388
+61.1
+Forgetting
+1879
+3322
+6675
+EL2N
+370
+323
+662
+TracIn
+1856
+3425
+8400
+CRAIG
+3023
+5263
+10472
+GPU
+Nvidia A100 40GB
+et al., 2020). We do not calculate the CG-score of FMNIST dataset with sampling ratio 1:4 since it requires
+a inversion for 30,000x30,000 matrix, which exceeds the limit of the device memory. Every score including
+ours and baselines needs to be calculated by averaging the results of independent multiple runs. For a fair
+comparison, we compare the time to get each score for a single run. Cost to compute CG-score depends
+on the size of the Gram matrix H∞, since we need to calculate the inverse of H∞ to get the CG-score and
+the computational complexity to conduct an inversion of n × n matrix is O(n3). Therefore, for a dataset of
+which each class includes a large number of instances (e.g., FMNIST and CIFAR-10), taking the inverse of a
+Gram matrix with large sampling ratio may cause expensive computational cost, while computing the score
+for a dataset of which each class includes relatively small number of instances (CIFAR-100) can be done in
+a short time. For example, calculating CG-score of CIFAR-10 dataset (5,000 data in a class) takes1.2 hours
+with sampling ratio 1:4, while that for CIFAR-100(500 data in a class) takes just 1 minute. EL2N score is
+time-efficient overall because it is calculate at the relatively early stage of training. Forgetting and TracIn,
+on the other hand, take relatively longer time since they require at least one full train of the model. In
+addition, we argue that our method has another computational advantage that we do not need to search
+networks and hyperparameters which would work well for the target dataset.
+C.3
+Experimental details
+Baseline scores for data valuation
+We use three state-of-the-art scores, C-score (Jiang et al., 2021),
+EL2N (Paul et al., 2021), and Forgetting score (Toneva et al., 2019) as baselines with which our CG-score
+is compared. We use pre-calculated C-score for CIFAR-10 and CIFAR-100 from Jiang et al. (2021) and
+calculate EL2N and Forgetting score by averaging the score across five independent training using the full
+17
+
+dataset. We obtain EL2N scores at 20th epochs of the training. We use the same network architectures
+to calculate EL2N and Forgetting score: ResNet18 for FMNIST and CIFAR-10 dataset and ResNet50 for
+CIFAR-100 dataset. Detailed definitions of the scores are as follows:
+• Consistency score (C-score): C-score of each instance is calculated by estimating the prediction accu-
+racy of the instance attained by the model trained with the full dataset except the instance.
+C-score(xi, yi) = En
+�
+ˆEr
+S∼{(xj,yj)}n
+j=1 [P(f(xi; S\{(xi, yi)}) = yi)]
+�
+,
+(9)
+where f(xi; S) is trained network using subset S, and ˆEr denotes empirical averaging with r i.i.d.
+samples of such subsets.
+• Error L2-Norm (EL2N): The EL2N score of a training sample (xi, yi) is defined to be E[∥f(W(t), xi)−
+yi∥2] where f(W(t), x) is the output of the neural network for the sample (x, y) at the t-th step.
+• Forgetting score: Forgetting score is defined as the number of times during training (until time step
+T) the decision of that sample switches from a correct one to an incorrect one: Forgetting(xi, yi) is
+defined as
+T
+�
+t=2
+1{arg max f(W(t − 1), xi) = yi}(1 − 1{arg max f(W(t), xi) = yi}).
+(10)
+Data pruning experiment
+We report the mean of the results after three independent runs. The shaded
+regions indicate the standard deviation. We acquire each result by training a network using a dataset pruned
+by specified portions, where the training instances are ordered by each score. We compute the number of
+iterations at which all data can be used in one epoch, and use the same number of iterations in all pruning
+experiments for a fair comparison. When we prune the dataset, we remove the instances from each class by
+the same amount, so as to preserve the original proportion between classes. As will be shown in Section H,
+the distribution of scores is different among classes, so an imbalance problem between classes may occur if
+the data pruning is performed without considering the portion of classes within the dataset.
+D
+Additional Experiments with Two More Baselines
+D.1
+Another directions of data valuation
+There are two additional branches of related works for data valuation, in addition to the methodologies
+described in the Section 2. The first branch uses the influence function. The influence function approximates
+the degree of change of parameters when specific data enters and leaves the training dataset, so it determines
+which data is valuable by calculating the effect of the data on learning. The second branch uses coreset
+selection. Coresets are weighted subsets of the data selected to resemble the model training using the full
+dataset. Coresets may need to be updated as training progresses.
+Baseline algorithms for data valuation
+We use representative scores in each branch, TracIn (Pruthi
+et al., 2020) for influence function and CRAIG (Mirzasoleiman et al., 2020) for coreset selection, as additional
+baselines. Detailed definitions of the scores are described below:
+• TracIn: TracIn CheckPoint (TracInCP) value between two data points is defined as the weighted sum
+of dot products of the loss gradients calculated at the two data points. The gradients are obtained
+from the k checkpoints {t1, . . . , tk} of the model in the middle of training and the weight ηti is the
+learning rate at each checkpoint ti:
+TracInCP(z, z′) =
+k
+�
+i=1
+ηti∇l(wti, z)⊤∇l(wti, z′),
+(11)
+18
+
+(a) Pruning low-scoring examples first. Better score maintains the test accuracy longer.
+(b) Pruning high-scoring examples first. Better score makes the rapid performance drop.
+Figure 7: Pruning experiments with three datasets FMNIST (left), CIFAR-10 (middle) and CIFAR-100
+(right). Our CG-score can achieve better performances than the Tracin score and competitive performances
+compared to the CRAIG algorithm. Different from our scoring method, TracIn requires a validation set
+to calculate the data values and CRAIG does not select a fixed subset of data to be used throughout the
+training, but keeps updating the subset the data (coresets) to be used for training every 10 epochs. CRAIG
+has been evaluated only for pruning low-valued samples due to the nature of coreset selection where coresets
+are selected with per element weights.
+where l(wti, z) is loss function at ti-th step with model parameter wti.
+• CRAIG: CoResets for Accelerating Incremental Gradient descent (CRAIG) is an algorithm that solves
+the optimization problem, which finds a subset that preserves the gradient of the total loss:
+S∗ ∈ argmaxS⊂V
+�
+i∈V
+min
+j∈S max
+w∈W ∥∇fi(w) − ∇fj(w)∥, s.t. |S| ≤ r
+(12)
+where fi(w) = l(w, (xi, yi)) is loss for the data (xi, yi) with model parameter w, V is the full dataset
+and S is the coresets with size r, and pi be the softmax output for data (xi, yi). In CRAIG, the
+gradient fi(w) is approximated by pi − yi when cross entropy loss is used with soft-max at the last
+layer.
+D.2
+Data Pruning experiments
+In this section, we conduct data pruning experiments, similar to Section 4.1. We conduct the experiments
+using the above two additional baselines, TracIn and CRAIG, separately from the experiments of the main
+text, since the two algorithms require additional assumptions/resources that have not been used for the
+baselines considered in the main text: TracIn requires a validation set to calculate the data values; CRAIG
+19
+
+FMNIST
+95.5
+95.0
+Accuracy(%)
+94.5
+CG-score
+94.0
+TracIn
+CRAIG
+93.5
+Random
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train setCFAR-10
+95.5
+95.0
+94.5
+94.0
+CG-score
+93.5
+TracIn
+93.0
+CRAIG
+Random
+92.5
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train setCIFAR-100
+79
+78
+77
+76
+75
+CG-score
+74
+TracIn
+CRAIG
+73
+Random
+72
+0.6
+0.7
+0.8
+0.9
+Portion of train set95.0
+94.5
+a
+high value
+94.0
+Accuracy(%)
+93.5
+93.0
+92.5
+Pruning
+CG-score
+92.0
+TracIn
+91.5
+Random
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train set94
+92
+90
+88
+CG-score
+Tracin
+86
+Random
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train set78
+76
+74
+72
+CG-score
+70
+Tracin
+68
+Random
+0.6
+0.7
+0.8
+0.9
+Portion of train setdoes not select a fixed subset of data to be used throughout the training, but keeps updating the subset of
+the data (coresets) to be used for training every 10 epochs.
+Experimental details
+As described in the Pruthi et al. (2020), we calculate the TracIn score by using the
+gradients of the parameters of the network’s last layer. The check points are set at every 20 epochs, starting
+from the end of the first 20th epoch. We use 5 checkpoints for FMNIST and 10 checkpoints for CIFAR-10
+and CIFAR-100. We create a validation set composed of 1,000 samples by taking a part of the test dataset,
+and calculate TracIn score with this validation set. As TracIn score is defined between two data points (z, z′)
+as in equation 11, we set the score of each training sample z by averaging TracIn scores TracInCP(z, z′) over
+all samples z′ in the validation set.
+In CRAIG, the subset selection is performed every 10 epochs. We only test CRAIG in pruning low-valued
+data but not in the reverse order (pruning high-valued data), since CRAIG extracts coresets to be used with
+per element weights for preserving the gradient of total loss but does not give what are the high-valued
+(equal weight) samples.
+TracIn score and CRAIG are calculated at the networks same as those used in the experiment in Section
+4.1: ResNet18 for FMNIST and CIFAR-10, and ResNet50 for CIFAR-100 dataset. The other experimental
+details are the same as Table 3 in Appendix §C.3
+Experimental results
+Similar to data pruning experiment in Section 4.1, in Figure 7, the first row shows
+the test accuracy of the model trained with different subset sizes, when low-scoring (regular) examples are
+removed first, and the second row shows the similar result but when high-scoring (irregular) examples are
+removed first.
+We report the mean of the results after three independent runs, and the shaded regions
+indicate the standard deviation. The red-curve (random) is the result when randomly ordered examples
+are used.
+When pruning low-scoring data first, it is preferable to maintain the accuracy up to a large
+removing portion (a small training set); when pruning high-scoring data first, the rapid drop of performance
+is preferable since it means that the score can detect high-value samples, necessary for generalization of the
+model. Our CG-score can achieve better performances than the Tracin score and competitive performances
+compared to the CRAIG algorithm. Since CRAIG updates the coresets over the training, it can choose
+different semantics of the data suitable for each phase of the training, which results in better performance.
+This result may imply the effectiveness of the scheduled batch selection, e.g., curriculum learning, in training
+neural networks. We inspect that the performance of TracIn may heavily depend on the size of the validation
+set and also the possible domain discrepancy between training and test datasets. In our test, there is no
+domain discrepancy, but if there exists a domain shift between the test dataset and the training dataset,
+TracIn may perform better than other methods with the help of validation set.
+D.3
+Detecting Label Noise
+We also compared the performance of our CG-score in detecting mislabeled data with that of TracIn. As
+suggested in Pruthi et al. (2020), we use ‘self-influence’ of each training example, i.e., the influence of
+a training point on its own loss during the training process, TracInCP(z, z), to identify mislabeled data.
+In Pruthi et al. (2020), it was shown that mislabeled examples tend to have higher TracIn values, and
+thus TracIn values can be effectively used in identifying mislabeled examples.
+In Fig.
+8, we show the
+comparison of our method with TracIn in identifying mislabeled examples in FMNIST and CIFAR-100
+datasets, respectively, each of which includes 20% label noise. TracIn achieves better performance in CIFAR-
+100, but ours outperformed TracIn in FMNIST. Since TraIn measures the ‘self-influence’ of each training
+example over the training, starting from 20th epoch, for relatively simpler dataset such as FMNIST, some
+mislabeled instances could have already been memorized at the network, which makes them not detectable
+by the TracIn values. On the other hand, our method better detects mislabeled data for easier datasets as
+discussed in Sec. 4.2. Thus, we can conclude that depending on data complexity, the outperforming method
+can be changing.
+20
+
+Figure 8: Fraction of label noise (y-axis) included in the examined portion (x-axis) for 20% label noise for
+oracle, Partial CG-score (ours), CG-score (ours), TracIn and random baseline.
+(a) Pruning low-scoring examples first.
+(b) Pruning high-scoring examples first.
+Figure 9: Pruning experiments with CIFAR-10 dataset trained on DenseNet-100. Even if the model changes
+from ResNet to DenseNet, we observe a similar trend as in Figure 2.
+E
+Robustness of CG-score over model variants
+Our CG-score is derived based on the theoretical analysis of the generalization error bounds on overparam-
+eterized two-layer ReLU activated neural network. To demonstrate that our CG-score is effective in more
+complicated networks, in the main text (Section 4.1), we used ResNets to evaluate our score for data pruning
+experiments. To further demonstrate the robustness of our score against model changes, in this section, we
+report the results of data pruning experiments on CIFAR-10 dataset using DenseNetBC-100, a more com-
+plicated convolutional network. The implementation details of the DenseNet follows that of Huang et al.
+(2017). We use the same hyperparameter and optimization method summarized in Table 3.
+In Figure 9, the left figure shows the test accuracy of the model trained with different subset sizes, when
+low-scoring (regular) examples are removed first, and the right figure shows the similar result but when
+high-scoring (irregular) examples are removed fist. We report the mean of the result after two independent
+runs, and the shaded regions indicate the standard deviation. The red-curve (random) is the result when
+randomly ordered examples are used. We can observe a similar trend as in Fig. 2, the experimental results
+using ResNets, in spite of the model change. Our CG-score achieve competitive performances as the other
+baselines. The reason that we observe a rapid performance degradation at a smaller training data portion
+in the left figure (removing low value data first) is due to the characteristics of leave-one-out method we
+used in the calculation of the CG-score. Removing a typical sample from a dataset does not change the
+21
+
+20% nosiy FMNIST
+20% noisy CIFAR-100
+100
+100/
+found(
+80
+80
+data
+Oracle
+60
+60
+Partial CG score
+noise
+CG score
+Tracln
+40
+40
+Random
+Jo
+Fraction
+20
+20
+0
+30
+20
+30
+40
+10
+20
+40
+0
+10
+50
+0
+50
+Fraction of data checked(%)
+Fraction of data checked(%)DenseNet-100 (Pruning high value)
+95.0
+94.5
+Test accuracy
+94.0
+93.5
+CG-score
+EL2N
+93.0
+Forgetting
+92.5
+C-score
+Random
+92.0
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train setDenseNet-100 (Pruning high value)
+94
+Test accuracy
+92
+90
+CG-score
+EL2N
+88
+Forgetting
+C-score
+86
+Random
+0.5
+0.6
+0.7
+0.8
+0.9
+Portion of train setgeneralization error bounds much, since similar samples already exist in the dataset. Thus, typical samples
+tend to have low CG-scores when the score is measured by the leave-one-out method. However, when we
+remove 50% of instances, samples sharing the typicality can be excluded simultaneously from the dataset,
+which might cause severe degradation of the generalization capability of the neural network. Thus, for a
+smaller training data portion, it can be better to make sure at least a small portion of typical samples is
+indeed included in the training. Similar observations have been made in Swayamdipta et al. (2020).
+F
+Details of kernel velocity
+We calculate the kernel velocity of 10 groups of instances, where each group is composed of 125 samples.
+The following is how we construct each group: Sort CIFAR-10 examples in ascending order by the CG-score,
+divide the examples into 10 groups, and select 125 consecutive samples from the beginning of each group.
+We calculate the NTK kernel velocity as described in Paul et al. (2021): Let C be the number of classes.
+Let f (c)
+t
+(xi) be the c-th logit value for input xi at the t-epoch. When W(t) is the parameters of the model, the
+c-th logit gradient at input xi is ψ(c)
+t (xi) = ∇W(t)f (c)
+t
+(xi) ∈ RN. Then, the data-dependent NTK submatrix
+of a group of m samples S := {xa1, . . . , xam} is defined as Kt(S) = Ψt(S)Ψt(S)⊤, where Ψt(S) ∈ RmC×N is
+constructed by placing {ψ(c)
+t (xai)}c∈[C],i∈[m] in rows of Ψt(S). The kernel velocity is defined as
+vt(S) = 1 −
+⟨Kt(S), Kt+1(S)⟩
+∥Kt(S)∥ ∥Kt+1(S)∥.
+(13)
+Lastly, we provide some explanations of what the kernel velocity measures if we define it for finite-
+width ReLU activated 2-layer neural network. Remind that our analysis uses the Gram matrix H∞ de-
+fined in equation 1, which is derived for an overparameterized ReLU activated 2-layer neural network.
+We can generalize the definition of the Gram matrix assuming a finite-width network, similar to Kt(S),
+as follows. The output of the network is fW,a(x) =
+1
+√m
+�m
+r=1 arσ(w⊤
+r x), and the gradient with respect
+to W = (w1, . . . , wm) ∈ Rd×m is ∇Wf(xi) = [∇w1f(xi), ∇w2f(xi), . . . , ∇wmf(xi)] =
+x⊤
+i
+√m[a11{w⊤
+1 xi ≥
+0}, a21{w⊤
+2 xi ≥ 0}, . . . , am1{w⊤
+mxi ≥ 0}]. Denoting the network parameters at the t-th step as W(t), we can
+define the Gram matrix Ht as (Ht)ij = ∇W(t)f(xi)∇W(t)f(xj)⊤ = x⊤
+i xj 1
+m
+�m
+r=1 1{w⊤
+r xi ≥ 0, w⊤
+r xj ≥ 0},
+which is proportion to the number of neurons in the hidden layer activated both for xi and xj at the epoch.
+We can define the kernel velocity similar to equation 13 by calculating Ht for a subset of data, and replacing
+Kt(S) by Ht(S). For this case, the high kernel velocity implies that Ht differs much from Ht+1, i.e., the
+portion of neurons activated for pairs of instances changes rapidly during training.
+G
+Visualization of examples sorted by CG-score
+Analysis of MNIST and FMINST by CG-score
+In Fig. 10, we show examples of MNIST (Fig. 10a)
+and FMNIST (Fig. 10b) images sorted by CG-score. The top/bottom three rows show the top-/bottom-
+ranked examples, respectively.
+We can observe that the examples with the lowest CG-score are regular
+examples representing each class and they look similar to each other, while the examples with the highest
+scores are irregular and they look different among themselves, among which we can identify (possibly)
+mislabeled instances, marked with red rectangles. Similarly, in CIFAR-10 images (Fig. 10c), we observe
+that low-scoring examples (bottom two rows) are regular ones sharing similar features representing the class
+while high-scoring examples (top two rows) are irregular ones.
+Analysis of CIFAR-100 by CG-score
+Fig. 11 shows the examples of CIFAR-100 dataset. Fig. 11a
+shows the means and standard variations of 100 classes in CIFAR-100 dataset. Among 100 classes, ‘orange’
+and ’plain’ classes have small CG-score means and variances, while ‘bottle’ and ’flatfish’ classes have larger
+CG-score means and variances. We display ten top-/bottom-ranked examples of these four classes, with the
+histograms of the scores in Fig. 11b.
+22
+
+(a) Examples of MNIST dataset
+(b) Examples of FMNIST dataset
+(c) Examples of CIFAR-10 dataset (Cat, dog, frog, and truck)
+Figure 10: Examples sorted by CG-score. In (a) and (b), top-3 rows / bottom-3 rows display top-ranked
+/ bottom-ranked examples, respectively. Among top-ranked examples, (possibly) mislabeled examples are
+marked by red rectangles. In (c), top-2 rows / bottom-2 rows display top-ranked / bottom-ranked examples,
+respectively.
+Analysis of Tiny ImageNet by CG-score
+To check the effectiveness of CG-score in analyzing more
+complicated dataset, we compute CG-score on the high-resolution tiny ImageNet dataset (64 by 64 resolution,
+100,000 samples of 200 classes) as well. The CG-score is computed with sampling ratio of 1:14 by averaging
+the results from 10 independents runs. Fig. 12 show the examples of Tiny Imagenet datset. Fig. 12a
+show the means and standard variations of classes. We examine two easiest classes, ‘Sulfur butterfly’ and
+‘Jellyfish’, having relatively smaller mean and std of CG-score, and two difficult classes, ‘Pill bottle’ and
+‘Syringe’, having higher mean and std of CG-score, and display ten top-/bottom-ranked examples of these
+four classes with CG-score histograms in Fig. 12b. For the two easy classes, low-scoring examples look very
+much similar to each other and share some typical attributes (color and shape). On the other hand, for two
+difficult classes, even low-scoring examples do not look very similar to each other but rather diverse. From
+the analysis, we can see that our CG-score is still effective in examining high-resolution complicated dataset,
+and the score reflects the instance-wise structural regularities, which can be used in analyzing or improving
+learning algorithms.
+23
+
+8
+High score
+.ow score
+3
+5T-shirt
+Trouser
+Pullover
+Dress
+Coat
+Sandal
+Shirt
+Sneaker
+Bag
+Ankleboot
+High score
+_ow scoreHigh score
+Low score(a) Distribution of CG-scores at CIFAR-100
+(b) Examples and histograms of four classes in CIFAR-100
+Figure 11: Sample analysis for CIFAR-100 dataset in terms of the CG-score. (a) shows the CG-score means
+and standard deviations of 100 classes in CIFAR-100 dataset. (b) shows ten top-ranked examples (top two
+rows) and ten bottom ranked examples (bottom two rows) for orange, plain, bottle, and flatfish classes of
+CIFAR-100 dataset. Histograms show distributions of the CG-scores for each class.
+H
+Score distribution for public datasets
+Score distributions
+In Fig. 13, we compare the CG-score distributions of three public datasets, FMNIST,
+CIFAR-10 and CIFAR-100 before and after we artificially corrupt 20% of instances with random label noise.
+The top row shows the distributions before the corruption, and the bottom row shows the distributions after
+the corruption, where the orange color displays the distribution of the CG-score for 20% instances with label
+noise and the blue displays that for 80% instances with clean label. The gap between scores of clean data
+and noisy data, which enables us to detect the noise by the CG-score, is larger for relatively simpler dataset,
+FMINST, than those for CIFAR-10/100.
+24
+
+bottle
+13
+12
+i-score
+flatfish
+11
+G
+10
+Std
+9
+plain
+8
+orange
+7.5
+10.0
+12.5
+15.0
+17.5
+20.0
+22.5
+Mean of CG-scoreLow score High score0.18
+0.18-
+0.18 
+0.18 
+orange
+0.16
+plain
+0.16
+bottle
+0.16
+flatfish
+0.16-
+0.14
+0.14
+0.14
+0.14 -
+0.12 
+0.12
+0.12
+0.12
+0.10 -
+0.10-
+0.10
+0.10
+0.08 -
+0.08
+0.08
+0.08
+0.06 -
+0.06
+0.06
+0.06
+0.04 -
+0.04 -
+0.04
+0.04
+0.02
+0.02
+0.02
+0.02
+0.00 +
+0.00
+0.00 -
+0.00 +
+10
+20
+30
+40
+50
+60
+70
+80
+90
+10
+20
+30
+40
+50
+60
+70
+80
+90
+10
+20
+30
+40
+50
+60
+70
+80
+90
+10
+20
+30
+40
+50
+60
+70
+80
+90
+CG-score
+CG-score
+CG-score
+CG-score(a) Distribution of CG-scores at Tiny Imagenet
+(b) Examples and histograms of four classes in Tiny Imagenet
+Figure 12: Sample analysis for Tiny Imagenet in terms of the CG-score. (a) shows the CG-score means and
+standard deviations of 200 classes in Tiny Imagenet dataset. (b) shows ten top-ranked examples (top two
+rows) and ten bottom ranked examples (bottom two rows) for Sulphur butterfly, Jellyfish, Pill bottle, and
+Syringe classes of Tiny Imagenet dataset. Histograms show distributions of the CG-scores for each class.
+Detecting mislabeled instances at high noise rate
+We conduct additional experiments to check the
+detectability of mislabeled instances by our CG-score, when the noise ratio increases to 50% and even to
+80% for FMNIST and CIFAR-10 dataset. In the main text, we considered a mild noise ratio of 20% and
+reported the result in Fig. 3. The results for higher noise cases are shown in Fig. 14. In the CIFAR-10
+dataset, when the noise ratio is 80%, each class includes 1,000 correctly labeled images and 4,000 mislabeled
+images, composed of 445 samples coming from each of the other nine classes. Even for such an extremely
+noisy case, our CG-score can effectively detect the mislabeled data, since our score can discover samples that
+have a relatively lower correlation to the majority of the samples of the same class as analyzed in Sec. 3.3.
+25
+
+30
+i-score
+25
+Pillbottle
+CG
+20
+Jellyfish
+Std
+15
+yringe
+10
+buttertl
+5
+12.5
+15.0
+17.5
+20.0
+22.5
+25.0
+27.5
+30.0
+Mean of CG-scoreY0.08
+0.08
+0.08
+0.08
+0.07
+Sulfur butterfly
+0.07
+Jellyfish
+0.07
+Pill bottle
+0.07
+Syringe
+0.06
+0.06
+0.06
+0.06
+0.05 
+0.05
+0.05
+0.05 
+0.04 
+0.04
+0.04
+0.04
+0.03
+0.03
+0.03
+EO'0
+0.02 
+0.02
+0.02
+0.02 
+0.01 
+0.01
+0.01
+0.01
+0.00 +
+0.00
+0.00
+20
+100
+20
+100
+20
+100
+0.00
+40
+60
+80
+120
+0
+40
+60
+80
+120
+40
+60
+%
+120
+20
+40
+60
+80
+100
+120
+CG-score
+CG-score
+CG-score
+CG-scoreFigure 13: Density of CG-scores at clean dataset and label noisy dataset.
+Figure 14: Fraction of label noise (y-axis) included in the examined portion (x-axis) for 50%(top) and
+80%(bottom) label noise for FMINST (left) and CIFAR-100 (right) datasets.
+I
+Correlations between CG-score and Partial CG-scores
+From the CG-score, which is expressed as d−1
+i (y⊤
+−ihi)2 + 2yi(y⊤
+−ihi) + y2
+i di at the equation 6, we can define
+three partial CG-scores, d−1
+i (y⊤
+−ihi)2, 2yi(y⊤
+−ihi), and y2
+i di, respectively. In this section, we analyze which
+term dominates the order of CG-scores for two public datasets, CIFAR-10/100, by analyzing the correlation
+between the CG-score and the three partial CG-scores.
+We also examine whether the correlations vary
+when we change the size of the Gram matrix H∞, whose dimension changes according to the level of sub-
+26
+
+FMNIST
+CIFAR-10
+CIFAR-100
+6
+ clean label
+0.07
+ clean label
+clean label
+0.08
+5
+0.06
+0.05
+0.06
+0.04
+0.04
+0.03
+2 
+0.02
+0.02
+1
+0.01
+%
+0.00
+40
+0.00
+2
+4
+6
+8
+10
+20
+60
+80
+100
+120
+0
+20
+40
+60
+80
+100
+CG score
+0.12
+0.040
+clean
+0.06
+clean
+clean
+0.035
+0.10
+noise label
+noise label
+noise label
+0.030
+0.05
+0.08
+0.025
+0.04
+20.06
+0.020
+0.03
+0.015
+0.04
+0.02
+0.010
+0.02
+0.005
+0.01
+0.00g
+0.000
+0.00
+50
+100
+150
+200
+250
+300
+20
+40
+60
+80
+100
+120
+20
+40
+60
+80
+100
+0
+CG score50% nosiy FMNIST
+50% noisy CIFAR-100
+100
+100
+found(
+80
+80
+data
+60
+60
+noise
+Oracle
+40
+40
+Partial CG score
+Jo
+CG score
+Fraction
+201
+EL2N
+20
+Forgetting score
+Random
+0
+100
+40
+20
+40
+60
+20
+60
+100
+0
+80
+0
+80
+Fraction of data checked(%)
+Fraction of data checked(%)80% nosiy FMNIST
+80% noisy CIFAR-100
+100
+100
+Oracle
+found(
+Partial CG score
+CG score
+80
+80.
+EL2N
+data
+Forgetting score
+60
+60
+Random
+noise
+40
+40
+Jo
+Fraction
+20t
+20
+0
+0
+100
+40
+20
+40
+60
+80
+20
+60
+80
+100
+0
+0
+Fraction of data checked(%)
+Fraction of data checked(%)Table 5: Spearman rank correlations between the CG-score and the partial CG-scores
+Dataset
+CIFAR-10
+CIFAR-100
+Subsampling Ratio
+1:1
+1:2
+1:3
+1:4
+1:1
+1:2
+1:3
+1:4
+d−1
+i (y⊤
+−ihi)2
+-0.759
+-0.461
+-0.136
+0.132
+-0.671
+-0.296
+0.035
+0.264
+2yi(y⊤
+−ihi)
+0.912
+0.948
+0.962
+0.970
+0.902
+0.939
+0.955
+0.964
+y2
+i di
+-0.015
+0.066
+0.121
+0.163
+-0.069
+0.018
+0.087
+0.136
+Figure 15: Spearman rank correlation (y-axis) between feature space CG-score calculated at each epoch (x-
+axis) and baseline scores including CG-score. The feature space CG-scores are calculated right after epoch
+1(after one epoch of training), 3, 5, 7, 9, 11, 20, 50, and 200 (end of the training).
+sampling, explained in Sec. A.2. We get H∞ with different subsampling ratios, 1:1, 1:2, 1:3, and 1:4, and
+then calculate the CG-score and partial CG-scores, defined by the three partial terms. Table 5 shows the
+Spearman rank correlations between the CG-scores and the partial CG-scores. We can see that 2yi(y⊤
+−ihi),
+which was utilized at noise detection experiments, is the partial score having the largest correlation with the
+CG-score across all subsampling ratios. On the other hand, correlations to other partial-scores are relatively
+low, and the correlations change much as the subsampling ratio changes.
+J
+Feature-space CG-score
+Our original CG-score can be calculated by data without any trained network. In this section we check
+the validity of a new CG-score, which is defined in terms of feature of data, and compare its characteristic
+with that of the original data-centric CG-score. We train ResNet18 using the full CIFAR-10 dataset to
+obtain each data’s feature at various epochs, where the feature is defined at the output of the penultimate
+layer value (512 dimensions). Then we calculate the feature-space CG scores, which are calculated by the
+feature instead of the data itself, and compare how the Spearman rank correlation between the feature-space
+CG-scores and other scores, including the original CG-score and the previous training-based scores such
+as C-score, Forgetting score, and EL2N, change over the epochs at which the feature space CG-scores are
+calculated. Figure 15 reports the result.
+In Figure 15, we can first observe that the feature space CG-score and the original CG-score has the
+highest correlation at the very beginning of the training (epoch 1), but as the training progresses, the
+correlation decreases. This trend can be explained by the fact that the feature space CG-score computes
+27
+
+0.70
+Original CG
+0.65
+correlation
+C-score
+0.60
+Forgetting
+0.55
+EL2N
+0.50
+ink
+0.45
+earman
+0.40
+0.35
+Spe
+0.30
+0.25
+1357
+9. 11
+20
+50
+200
+Epochthe value of data in the learned embedding space, while our score computes the value of the original data
+without embedding it into a latent space. As training of a model progresses, the embedded data may incur
+bias in the data valuation, depending on a particular model or training algorithm, and thus the correlation
+between the feature space CG-score and the original data-centric CG-score may decrease.
+On the other hand, correlation between feature space CG-score and other training-based scores (EL2N,
+Forgetting, and C-score) increases during the initial stage, and then decreases gradually. More specifically,
+for both EL2N and Forgetting score, which are computed at the same network as that of the feature space
+CG-score, the correlation increases as the epoch increases and then slightly drops and becomes saturated at
+a certain value. The C-score, which was calculated in a different CNN network, shows a slightly different
+tendency compared to EL2N or forgetting score, and attains its peak at an earlier epoch, epoch 5.
+This result implies that the feature-space CG score includes meaningful information for data valuation,
+correlated with other training-based scores for overall epochs. However, the feature space CG-score may incur
+some bias in data valuation as the training progresses. Understanding the effectiveness of the feature-space
+CG score in diverse applications can be an interesting future research direction.
+K
+Schur complement
+Calculating CG-score (equation 2) of n data instances requires the inversion of n × n matrix, which may
+cause expensive computational cost for a large n. Therefore, we provided computationally efficient way to
+obtain the CG-score by using Schur complement equation 4. Here we provide some details to derive the
+inverse of a sub-block matrix using Schur complement. By Schur complement, we have
+�A
+B
+C
+D
+�−1
+=
+�
+(A − BD−1C)−1
+−(A − BD−1C)−1BD−1
+−D−1C(A − BD−1C)−1
+D−1 + D−1C(A − BD−1C)−1BD−1
+�
+.
+(14)
+Remind that H∞ and (H∞)−1 are denoted by
+H∞ =
+�H∞
+n−1
+gi
+g⊤
+i
+ci
+�
+,
+(H∞)−1 =
+�
+(H∞)−1
+n−1
+hi
+h⊤
+i
+di
+�
+,
+(15)
+where H∞
+n−1, (H∞)−1
+n−1 ∈ R(n−1)×(n−1), gi, hi ∈ Rn−1 and ci, di ∈ R, i.e.,
+(H∞) =
+�
+(H∞)−1
+n−1
+hi
+h⊤
+i
+di
+�−1
+=
+�H∞
+n−1
+gi
+g⊤
+i
+ci
+�
+(16)
+By substituting A, B, C, and D in equation 14 with (H∞)−1
+n−1, hi, h⊤
+i , and di respectively, we obtain that
+H∞
+n−1 = ((H∞)−1
+n−1 − hih⊤
+i /di)−1.
+(17)
+Thus, (H∞
+n−1)−1 = (H∞)−1
+n−1 − hih⊤
+i /di.
+28
+
diff --git a/p9AzT4oBgHgl3EQfAvo4/content/tmp_files/load_file.txt b/p9AzT4oBgHgl3EQfAvo4/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dbcffa870da7398eafe40943397a4f6b188c8d3d
--- /dev/null
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@@ -0,0 +1,1224 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf,len=1223
+page_content='Data Valuation Without Training of a Model  Nohyun Ki∗†  Hoyong Choi∗‡  Hye Won Chung§  Abstract  Many recent works on understanding deep learning try to quantify how much individual data instances  influence the optimization and generalization of a model, either by analyzing the behavior of the model  during training or by measuring the performance gap of the model when the instance is removed from  the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Such approaches reveal characteristics and importance of individual instances, which may  provide useful information in diagnosing and improving deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However, most of the existing  works on data valuation require actual training of a model, which often demands high-computational  cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In this paper, we provide a training-free data valuation score, called complexity-gap score, which  is a data-centric score to quantify the influence of individual instances in generalization of two-layer  overparameterized neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The proposed score can quantify irregularity of the instances and  measure how much each data instance contributes in the total movement of the network parameters during  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We theoretically analyze and empirically demonstrate the effectiveness of the complexity-gap  score in finding ‘irregular or mislabeled’ data instances, and also provide applications of the score in  analyzing datasets and diagnosing training dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  1  Introduction  Creation of large datasets has driven recent development of deep learning in diverse applications including  computer vision (Krizhevsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Dosovitskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), natural language processing (Vaswani  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020) and reinforcement learning (Mnih et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Silver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To utilize  the dataset in a more efficient and effective manner, many recent works have attempted to understand the role  of individual data instances in training and generalization of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As an example, in (Ghorbani  & Zou, 2019), a metric to quantify the contribution of each training instance in achieving a high test accuracy  was analyzed under the assumption that not only the training data but also the test data is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Jiang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021) defined a score to identify irregular examples that need to be memorized during training, in order  for the model to accurately predict the class of the example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020), on the other hand,  analyzed the characteristics of data instances with respect to their role in out-of-distribution generalizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  All these previous methods for data valuation require actual training of a model to quantify the role of  individual instances at the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, the valuation itself often requires high-computational cost, which  may contradict some motivations of data valuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For example, in (Ghorbani & Zou, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=',  2021), to examine the effect of individual data instances in training, one needs to train a model repeatedly  while eliminating each instance or subsets of instances, which requires training of a model at least the number  of times proportional to the number of training instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In (Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019),  on the other hand, training dynamics–the behavior of a model on each instance throughout the training–is  analyzed to categorize data instances, which also requires the training of a model with the full dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  When the motivation for data valuation lies in pruning less important examples to save computational cost  for training, the previous valuation methods might not be suitable, since they require the training of a model  ∗Equal contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  †School of Electrical Engineering, KAIST, Daejeon, 34141, Korea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' email: kinohyun@kaist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='kr  ‡School of Electrical Engineering, KAIST, Daejeon, 34141, Korea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' email: chy0707@kaist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='kr  §Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' School of Electrical Engineering, KAIST, Daejeon, 34141, Korea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' email: hwchung@kaist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='kr  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00930v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='LG]  3 Jan 2023  with the full dataset before one can figure out ‘important’ instances and possibly prune the rest of the  examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In this paper, our main contribution is on defining a training-free data valuation score, which can be  directly computed from data and can effectively quantify the impact of individual instances in optimization  and generalization of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The proposed score, called complexity-gap score, measures the gap in  data complexity where a certain data instance is removed from the full dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The data complexity measure  was originally introduced in Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019) to quantify the complexity of the full dataset, which was  used in bounding the generalization error of overparameterized two-layer neural networks trained by gradient  descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Different from that work, where the complexity of the full dataset was main concern, our focus is on  decomposing the effect of individual data instances in the training, and thus we newly introduce a complexity  gap score (CG-score).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We theoretically analyze and empirically demonstrate that the CG-score can quantify  ‘irregularity’ of instances within each class, and thus can be used in identifying atypical examples, either  due to the inherent irregularity of the instance or mislabeled classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We also demonstrate that the  proposed score has a close relation to ‘learning difficulty’ of the instances by analyzing the training dynamics  of data instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our key contributions are as below:  Training-free data valuation: Different from previous methods for data valuation, most of which lever-  age the information from training itself, we provide a training-free data valuation score, CG-score,  which is the data-centric score to quantify the effect of individual data instances in optimization and  generalization of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Geometric interpretation: We provide theoretical analysis that the CG-score can measure irregularity  of instances within each class, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', how much each instance represents the instances of the same class  and how much it is different from those of other classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Effectiveness of the score: We empirically demonstrate the effectiveness of the CG-score in data val-  uation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We show that pruning data instances with small CG-score do not significantly degrade the  generalization capability of a model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', for CIFAR-10 we can prune 40% of the data with only 1%  of drop in test accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our scoring method is especially useful in data pruning, since different from  other scores, which require the training with the full dataset, our method does not require any training  of a model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Application of the score: We provide potential applications of the CG-score in analyzing datasets and  training dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We analyze the histograms of the CG-score for various datasets to demonstrate  that the CG-score can measure irregularity of the instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We also demonstrate that the instances  with higher CG-score are ‘difficult’ examples, which are learned slowly by the models, by comparing  the loss and test accuracy curves and the evolution of Neural Tangent Kernel (NTK) submatrices of  lowest/highest-scoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  2  Related Works  Different from many existing works where the impact of datasets on model training is analyzed as a whole,  some recent works have focused on understanding the impact of individual data instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Ghorbani & Zou  (2019) defined a method for data valuation, called Data Shapley, to evaluate the value of each data instance,  by measuring the average gap in performances when an instance is held-out from any subsets of a given  training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021) defined consistency score (C-score) of each instance by estimating the  prediction accuracy of the instance attained by the model trained with the full dataset except the instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Both Data Shapley and C-score require multiple trainings of a model to compute the scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Another main  stream of methods uses the training dynamics to identify ‘difficult’ instances for classification, either due to  irregularity or mislabeling, by measuring different forms of confidence, stability or influence in the decision  of the networks throughout the training (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Pruthi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In (Baldock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), the computational difficulty of an instance is defined as the number of hidden  2  layers after which the networks’ prediction coincides with the prediction at the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' With application of  robust learning, there also exist some works that quantify the difficulty of each instance by a ‘margin’ from  the decision boundary (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' CRAIG (Mirzasoleiman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020) finds valuable subsets of  data as coresets that preserve the gradient of the total loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' All these previous methods are demonstrated  to be effective in at least one or more applications of data valuation, including data pruning (Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=',  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Feldman & Zhang, 2020), importance-based weighted  sampling (Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Koh & Liang, 2017), noise filtering (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Kim  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), robust learning (Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Pleiss et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020), or out-of-distribution generalizations  (Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However, all these methods require the training of a model with the full dataset  (at least for a few optimization steps).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Some recent works do the data valuation at the initialization of models  (Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2022) or by assuming data distributions (Kwon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), but they often require relatively  high computational cost or additional assumptions on data distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our data valuation method, on  the other hand, is a data-centric method that can be efficiently calculated from data only without training of  a model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We demonstrate that with our scoring method, we can effectively analyze the impact of individual  data instance in optimization and generalization of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  3  Complexity-Gap Score: Data Valuation without Training  In this section, we introduce a new data valuation score, called complexity-gap score, based on the analysis  of overparameterized two-layer neural networks from Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Preliminaries: data complexity measure in two-layer neural networks  We first review the result from Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019), where a two-layer neural network trained by randomly  initialized gradient descent is analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Following the notations from Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019), we consider a  two-layer ReLU activated neural network having m neurons in the hidden layer, of which the output is  fW,a(x) =  1  √m  �m  r=1 arσ(w⊤  r x) where x ∈ Rd is the input, w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , wm ∈ Rd are weight vectors in the  first layer, a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , am ∈ R are weights in the second layer, and σ(x) = max(0, x) is the ReLU activation  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We denote W = (w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , wm) ∈ Rd×m and a = (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , am)⊤ ∈ Rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' It is assumed that the  network parameters are randomly initialized as wr(0) ∼ N(0, κ2Id×d) and ar ∼ unif({−1, 1}), ∀r ∈ [m],  where κ ∈ (0, 1] is the size of random initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The second layer a is then fixed and only the first layer  W is optimized through gradient descent (GD) to minimize the quadratic loss, Φ(W) = 1  2  �n  i=1(yi − ui)2  where ui = fW,a(xi) and {(xi, yi)}n  i=1 is the dataset drawn i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' from an underlying distribution D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The  GD update rule can be written as wr(k + 1) − wr(k) = −η ∂Φ(W(k))  ∂wr  where η > 0 is the learning rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The  output of the network for the input xi at the k-th iteration is denoted by ui(k) = fW(k),a(xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For simplicity,  it is assumed that ∥x∥2 = 1 and |y| ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  The data complexity measure governing the training of the two-layer ReLU activated neural network is  defined in terms of the following Gram matrix H∞ ∈ Rn×n associated with ReLU activation:  H∞  ij = Ew∼N (0,Id×d)  �  x⊤  i xj1{w⊤xi ≥ 0, w⊤xj ≥ 0}  �  = x⊤  i xj(π − arccos(x⊤  i xj))  2π  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (1)  In Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019), a complexity measure of data was defined as y⊤(H∞)−1y where y = (y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , yn),  and it was shown that this measure bounds the total movement of all neurons in W from their random  initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Moreover, the data complexity measure bounds the generalization error by restricting the  Rademacher complexity of the resulting function class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In the following, we write the eigen-decomposition  of H∞ as H∞ = �n  i=1 λiviv⊤  i  where λi’s are ordered such that λ1 ≥ λ2 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' λn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Further, assuming  λn ≥ λ0 > 0, we can write (H∞)−1 = �n  i=1(λi)−1viv⊤  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Theorem 1 (Informal version of (Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Assume that λmin(H∞) = λn ≥ λ0 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  For  sufficiently large width m,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' sufficiently small learning rate η > 0 and sufficiently small random initialization  3  κ > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' with probability at least 1 − δ over the random initialization,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' we have  a) Bound in loss : ∥y − u(k)∥2 =  �  �  �  �  n  �  i=1  (1 − ηλi)2k(v⊤  i y)2 + small constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  b) Bound in total movement of neurons: ∥W(k) − W(0)∥F ≤  �  y⊤(H∞)−1y + small constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  c) Bound in population loss: E(x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='y)∼D[l(fW(k),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='a(x),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' y)] ≤  �  y⊤(H∞)−1y  n  + O  �  �  �  log  n  λ0δ  n  �  � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  where a) and b) hold for all iteration k ≥ 0 of GD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' and c) holds for k ≥ Ω (1/(ηλ0) log(n/δ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  The above theorem shows that if the label vector y is aligned with top eigenvectors of H∞, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', (v⊤  i y)  is large for large λi, then the loss decreases quickly and the total movement of neurons from their ran-  dom initialization is small, which implies a small generalization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, the data complexity measure  y⊤(H∞)−1y captures the complexity of data governing both the optimization and generalization of the  overparameterized two-layer neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However, this quantity captures the complexity of the overall  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To decompose the individual data instances, in the next section, we newly define a complexity-gap  score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Complexity-gap score and training dynamics  We define the complexity-gap score (CG-score) of (xi, yi) as the difference between the data complexity  measure when (xi, yi) is removed from a given dataset {(xi, yi)}n  i=1:  CG(i) = y⊤(H∞)−1y − y⊤  −i(H∞  −i)−1y−i  (2)  where y−i is the label vector except the i-th sample point and H∞  −i is the (n − 1) × (n − 1) matrix obtained  by removing the i-th row and column of H∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We first emphasize that the proposed score can be easily calculated from given data without the need of  training neural networks, as opposed to other data valuation scores requiring either a trained neural network  or statistics calculated from training dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Yet, the proposed score captures two important properties  on the training and generalization of data instance, implied by Theorem 1:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' An instance (xi, yi) with a large CG-score is a ‘difficult’ example, in the sense that removing it from  the dataset reduces the generalization error bound by a large amount, which implies that the dataset  without (xi, yi) is much easier to be learned and generalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' An instance (xi, yi) with a larger CG-score contributes more on the optimization and drives the total  movement of neurons by a larger amount, measured by ∥W(k) − W(0)∥F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We next discuss the computational complexity of calculating the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To calculate {CG(i)}n  i=1, we  need to have the inversion of matrices H∞ and H∞  −i for all i ∈ [n], which requires O(n4) complexity when  we use general O(n3)-complexity algorithm for the matrix inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' By using Schur complement, however,  we can reduce this complexity to O(n3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Without loss of generality, we can assume i = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Denote H∞ and  (H∞)−1 by  H∞ =  �H∞  n−1  gi  g⊤  i  ci  �  ,  (H∞)−1 =  �  (H∞)−1  n−1  hi  h⊤  i  di  �  ,  (3)  where H∞  n−1, (H∞)−1  n−1 ∈ R(n−1)×(n−1), gi, hi ∈ Rn−1 and ci, di ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' From H∞(H∞)−1 = In, we have  g⊤  i (H∞)−1  n−1 + cih⊤  i = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', h⊤  i = −c−1  i g⊤  i (H∞)−1  n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  By Schur complement, (H∞  −i)−1, which is equal to (H∞  n−1)−1 for i = n, can be calculated as  (H∞  −i)−1 = (H∞)−1  n−1 − d−1  i hih⊤  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (4)  4  Table 1: Spearman’s rank correlation between CG-score (CG’-score) and other data valuation scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Datasets  Correlation btwn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' CG-score and  Correlation btwn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' CG’-score and  C-score  Forgetting  EL2N  C-score  Forgetting  EL2N  CIFAR-10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='557  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='432  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='365  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='115  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='110  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='136  CIFAR-100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='529  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='289  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='356  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='243  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='090  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='177  Since we have  y⊤(H∞)−1y = y⊤  −i(H∞)−1  n−1y−i + yih⊤  i y−i + yiy⊤  −ihi + y2  i di,  y⊤  −i(H∞  −i)−1y−i = y⊤  −i(H∞)−1  n−1y−i − d−1  i (y⊤  −ihi)2,  (5)  the CG-score, CG(i) in equation 2, can be calculated by  CG(i) = d−1  i (y⊤  −ihi)2 + 2yi(y⊤  −ihi) + y2  i di =  �  (y⊤  −ihi)/  �  di + yi  �  di  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (6)  Thus, CG(i) can be calculated by the n-th column (hi, di) of (H∞)−1, without the need of calculating  (H∞  −i)−1 when i = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The case for general i ̸= n can also be readily solved by permuting the i-th row and  column of H∞ into the last positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Correlation to other scores  We show relation between our score and other data valuation scores that  require the training of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019) define ‘the forgetting score’ for each training  example as the number of times during training the decision of that sample switches from a correct one to  incorrect one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021), on the other hand, suggest the GraNd score, which is the expected loss  gradient norm E[∥∇W(k)l(u(k), y)∥], to bound the contribution of each training example to the decrease of  loss on any other example over a single gradient step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The GraNd score is further approximated (under  some assumptions) by the EL2N score, defined to be E[|y − u(k)|] where u(k) is the output of the neural  network for the sample (x, y) at the k-th step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Since |y − u(k)|, if rescaled, is an upper bound on 0–1 loss,  �  k |y − u(k)| upper bounds forgetting score after rescaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, an example with a high forgetting score  will also have a high GraND score and high EL2N score averaged over multiple time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We next relate  our complexity-gap score to �  k(y − u(k)), and thus to all the three previous scores defined using training  dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019) show that for the overparameterized two-layer networks trained by GD, the gap  between the label vector and the network output at the step k can be approximated as y − u(k) ≈ (I −  ηH∞)ky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  By summing both sides over k, we get �∞  k=0 y − u(k) ≈ �∞  k=0(I − ηH∞)ky =  1  η(H∞)−1y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Without loss of generality, consider i = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then, the accumulated difference between yi and ui(k) over k  can be approximated as  ∞  �  k=0  (yi − ui(k)) ≈  �  h⊤  i y−i + yidi  �  /η =  �  y⊤  −ihi/  �  di + yi  �  di  � �  di/η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (7)  Note that both the right-hand side of equation 7 and CG(i) in equation 6 depend on the term  �  y⊤  −ihi/√di + yi  √di  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Thus, we can expect that CG(i) will be correlated with the scores related to training dynamics, including  the forgetting score, GraND score and EL2N score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Different from those scores, our score can be directly  calculated from the data without training of a model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Inversion of H∞ is an effective step  In the definition of CG(i) in equation 2, we use the inverse of  H∞ to measure the alignment of the eigenvectors of H∞ with the label vector y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' One could suggest another  score that directly uses H∞ instead of (H∞)−1, which can save the computation for inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However,  we argue that the score calculated by using (H∞)−1 includes more information than the score calculated  5  (a) Heat map of (H∞)−1  n−1  (b) CG-score (clean)  (c) CG-score (10% label noise)  Figure 1: (a) Heat map of (H∞)−1  n−1 for 200 indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We plot 200 indices only for clear visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (b)  Scatter graph of CG-Score for two groups of samples from 3000-D Gaussian distributions having the same  mean except the first dimension, where class 1 has mean +1 (red) and class 2 has mean -1 (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Samples  near the boundary (x1 = 0) tend to have higher CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (c) Same plot as (b) with 10% label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Samples with label noise (marked by plus symbol) tend to have higher CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  by H∞ due to the reason described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Let us define CG′(i) := y⊤H∞y − y⊤  −iH∞  −iy−i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Without loss of  generality, assume i = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then, CG′(i) = 2yi(g⊤  i y−i) + y2  i ci where gi = (H∞)1:(n−1),n and ci = H∞  n,n as  defined in equation 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Since ci = 1/2 for all i ∈ [n] from the definition of H∞ in equation 1 and y2  i = 1 for  yi = ±1, we have CG′(i) = 2(yi(H∞y)i − 1/2) + 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' By using the approximation y − u(k) ≈ (I − ηH∞)ky  from Arora et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2019), we have y − u(1) ≈ y − ηH∞y when k = 1, which implies u(1) ≈ ηH∞y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus,  CG′(i) = 2  ηyiui(1)+1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Note that an instance (xi, yi) has a large CG′(i) if yiui(1) is large, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', the network  output ui(1) after 1-time step has the same sign as the targeted label yi ∈ {−1, 1} and has a large magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Thus, CG′(i) measures how fast the training instance can be learned by the neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Different from  CG′(i), our original score CG(i) is correlated with the accumulated error between yi and ui(k) averaged over  the training as shown in equation 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, our original score CG(i), using the inverse of H∞, reflects the  statistics averaged over the whole training steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In Table 1, we compare the Spearman’a rank correlation between CG-score/CG’-score and other data  valuation scores including C-score (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), forgetting score (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019) and EL2N score  (Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021) for CIFAR-10/100 datasets1 We can observe that CG-score has higher correlations with  the previous scores compared to those of CG’-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In the rest of this paper, we focus on the CG-score for  our data valuation score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  Geometric interpretation of the complexity-gap score  We next provide geometric interpretation for the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For the sake of simplicity, we consider binary  dataset with n  2 samples having yi = 1 and n  2 samples having yi = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We further assume that E[H∞  ij ] = p  if yi = yj and E[H∞  ij ] = q if yi ̸= yj for some |p| > |q|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Note that the diagonal entires H∞  ii  = 1/2 for  all i ∈ [n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, E[H∞] can be decomposed as E[H∞] =  � 1  2 − p  �  In + S where S is a block matrix with  S =  �  p  q  q  p  �  ⊗ In/2, and the resulting eigenvalues of E[H∞] are (p+q)n  2  +  � 1  2 − p  �  ,  (p−q)n  2  +  � 1  2 − p  �  and  � 1  2 − p  �  with multiplicity (n − 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When p = Θ(q) and p = o(1/n), the matrix E[H∞] ≈ (1/2)In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' From  the representations of H∞ and (H∞)−1 in equation 15 and the implied relation h⊤  i = −c−1  i g⊤  i (H∞)−1  n−1,  assuming H∞ ≈ (1/2)In and using ci = 1/2, we can write h⊤  i = −4g⊤  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' By using this approximation, our  CG-score in equation 6 can be approximated as  CG(i) = d−1  i (y⊤  −ihi)2 + 2yi(y⊤  −ihi) + y2  i di ≈ 8(yi(y⊤  −igi))2 − 8yi(y⊤  −igi) + 2  (8)  1The way CG-scores are calculated for multi-label datasets is explained in Appendix §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To reduce the computation com-  plexity, we calculated the scores by sub-sampling data and averaging them over multiple runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  6  200  175  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  150  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  125  100  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  75  50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  0  25  50  75 1001251501752005  4  CG-Score  3  2  C  1  0  2  1  0  1  2  First dimension of input12  10  Class 1  8  score  Class 1 (noise)  6  Class 2  Class 2 (noise)  C  4  DecBound  2  0  _1  2  0  1  2  First dimension of inputsince di ≈ 2 and y2  i = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' From this approximation, we can first notice that −8yi(y⊤  −igi) is the main term  that determines the order of {CG(i)}n  i=1, since yi(y⊤  −igi) = �  j∈{[n]:yi=yj} H∞  ij − �  j∈{[n]:yi̸=yj} H∞  ij , and  thus E[yi(y⊤  −igi)] = (p−q)n  2  = o(1), assuming p = Θ(q) and p = o(1/n), which is much larger than the first  term, proportional to (yi(y⊤  −igi))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Note that yi(y⊤  −igi) measures the gap between the summation of H∞  ij  over the samples of the same class as (xi, yi) and that over the samples of the different class from (xi, yi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Since H∞  ij = x⊤  i xj(π−arccos(x⊤  i xj))  2π  , yi(y⊤  −igi) measures the gap between the average similarities of xi with  other samples {xj} of the same class yj = yi and that with samples of the different class yj ̸= yi, where the  similarity is measured by the cosine between the two samples (xi, xj) multiplied by the chance that ReLU  is activated for both the samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, we can expect two important trends regarding the CG-score:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Regular vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' irregular samples: If a sample (xi, yi) is a ‘regular’ sample representing the class yi in the  sense that it has a larger similarity with other samples of the same class than to samples from the  different class, then it will have a large yi(y⊤  −igi), resulting in a lower CG-score due to the minus sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  On the other hand, if a sample (xi, yi) is ‘irregular’ in the sense that it does not represent the class  and has a small similarity with the samples of the same class, then yi(y⊤  −igi) will be small, resulting  in a higher CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Clean label vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' noisy label: A sample with label noise tend to have a large CG-score since yi(y⊤  −igi) is  negative for a sample with label noise, while it is positive for a sample with clean label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We empirically demonstrate the above two trends by a controlled experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Consider two 3000-  dimensional Gaussian distributions with a fixed covariance matrix 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='25I3000 and different means (1, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 0)  and (−1, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , 0), representing class +1 and -1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We generate 1000 samples from each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We first check whether the structural assumptions on H∞ hold with this synthetic dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 1a,  we observe that (H∞)−1  n−1 can be well approximated by 2In−1, and thus the approximation for CG(i) in  equation 8 may hold well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We then examine the correlation between the CG-score and the sample value  at the first dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 1b, we can observe that instances near the decision boundary x1 = 0 have  higher CG-scores compared to those located further from the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' This shows that irregular samples,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', samples near the boundary of the two classes, indeed have higher CG-scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We further modify the  generated samples by randomly flipping the labels of 10% samples and we re-calculate the CG-scores of all  the samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 1c, the samples with label noise tend to have higher CG-scores, agreeing with  our intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  4  Data Valuation through Complexity Gap Score  In this section, we show diverse applications of the CG-score in data valuation for real datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Data pruning experiments  To evaluate the ability of the CG-score in identifying important examples, we design data pruning experi-  ments, similar to those in Ghorbani & Zou (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We evaluate our score on three public  datasets, FMNIST, CIFAR-10/100 and train ResNet networks (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2016), ResNet18 for FMNIST and  CIFAR-10 and ResNet50 for CIFAR-100 dataset, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As baseline methods for data valuation, we  use three state-of-the-art scores, C-score (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), EL2N (Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), and Forgetting score  (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019), all of which require training of models for computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' On the contrary, our score is  a data-centric measure and independent on the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' More details on the baselines and experiments are  summarized in Appendix §C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In Figure 2, the first row shows the test accuracy of the model trained with different subset sizes,  when low-scoring (regular) examples are removed first, and the second row shows the similar result but  when high-scoring (irregular) examples are removed first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We report the mean of the result after three  independent runs, and the shaded regions indicate the standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The red-curve (random) is the  result when randomly ordered examples are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe that when removing low-scoring examples  7  (a) Pruning low-scoring examples first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Better score maintains the test accuracy longer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (b) Pruning high-scoring examples first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Better score makes the rapid performance drop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Figure 2: Pruning experiments with FMNIST (left), CIFAR-10 (middle) and CIFAR-100 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Only  CG-Score does not require any training of the model to calculate the score for examples, but it achieves  competitive performances compared to other state-of-the-art data valuation scores and significantly outper-  forms the performance of random baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In (a), CG-score maintains the test accuracy up to significant  removing portions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' in (b), the test accuracy drops most rapidly for CG-score since the examples with high  CG-score are essential in generalization of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  first, networks maintain the test accuracy (with less than 1% drop) compared to the case of training with  the full dataset up to significant removing portions, for example, 40% for CIFAR-10 and 20% for CIFAR-100  with the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Especially, our CG-score, which does not require any training of a model, can achieve  competitive performances as the other baseline methods and it also significantly outperforms the random  baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When we remove the high-scoring examples first, the test accuracy drops most rapidly for the  CG-score curve, implying that examples with the high CG-score are essential part of the data governing the  generalization of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Detecting label noise  In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3, we analyzed the CG-score and showed that the examples with label noise tend to have higher  CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We next empirically investigate the ability of the CG-score in detecting label noise by artificially  corrupting 20% of instances in FMNIST and CIFAR-100 with random label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We first examine the  distribution of the CG-scores for each dataset after the corruption in Figure 3a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe that for  both datasets, the examples with corrupted labels (orange) tend to have higher CG-scores than those with  clean labels (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For a relatively simpler dataset, FMNIST (left), the CG-score histograms can be more  clearly separable between the clean and noisy groups, compared to a more complex dataset, CIFAR-100  (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' With this observation, we can anticipate that the CG-score can have a better detectability of label  noise for relatively simpler datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We next evaluate the noise detectability of the CG-score by checking a varying portion of the examples  8  FMNIST  data  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='4  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Accuracy(%)  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  CG-score  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  EL2N  Forgetting  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='4  Random  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setCFAR-10  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  CG-score  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  EL2N  Forgetting  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  C-score  Random  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setCIFAR-100  79  78  77  76  75  CG-score  EL2N  74  Forgetting  73  C-score  Random  72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train set95  94  Accuracy(%)  93  CG-score  92  EL2N  Forgetting  91  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='9  Portion of train set94  92  90  CG-score  EL2N  88  Forgetting  C-score  86  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train set78  76  74  CG-score  72  EL2N  Forgetting  70  ：  C-score  68  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train set(a) Density of CG-score for clean vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' label-noise  (b) Fraction of detected label noise  Figure 3: (a) Density of CG-score for clean (80%) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' label-noise (20%) examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Examples with label  noise tend to have higher CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For FMNIST (left) dataset, the CG-score histograms betwen clean  and label-noise groups are better separated than those for CIFAR-100 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (b) Fraction of label noise  (y-axis) included in the examined portion (x-axis) for 20% label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' CG-score (blue) achieves better noise  detectability for FMNIST than for CIFAR-100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  ordered by the CG-score (highest first) in Figure 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The curves indicate the fraction of noisy examples  included in the examined subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In this experiment, we compare our score with two other scores, Forgetting  score and EL2N, as well as a random baseline and the oracle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe that the CG-score achieves  the best performance, near that of the oracle, for FMINST, and competitive performances for CIFAR-100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In the plot, we also compare the performance of the CG-score with that of ‘Partial CG-score,’ which is a new  score defined by a sub-term of the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In the CG-score in equation 6, we have three terms, but only  the second term 2yi(y⊤  −ihi) uses the label information of the data (xi, yi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, we examined the ability of  this term only, defined as the ‘Partial CG-score’, in detecting the label noise, and found that the CG-score  and partial CG-score have similar performances in detecting label noise, which implies that the label-noise  detectability of the CG-score mainly comes from the term 2yi(y⊤  −ihi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  5  Complexity-Gap Score and Deep Learning Phenomena  We next demonstrate that the CG-score can capture ‘learning difficulty’ of data instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Complexity gap score captures learning difficulty  It has been widely observed that there exists an order of instances in which a model learns to classify the  data correctly and this order is robust within model types (Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Many previous scoring functions  use this type of observation and define the ‘difficulty’ of a given instance based on the speed at which the  model’s prediction converges (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our data-centric CG-score is  originally defined based on the gap in the generalization error bounds as in equation 2, but it also reflects  the convergence speed of the instance, as analyzed in equation 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We empirically demonstrate this relation  by analyzing the training dynamics of CIFAR-10 dataset trained in ResNet18 network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We first sort the  data instances in ascending order using the CG-score, and divide the data into 10 equal-sized subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We  then measure the mean of loss and training accuracy for the 10 subgroups as training progresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 4a  and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 4b show the mean of loss and the training accuracy throughout the training for the 10 subgroups,  respectively, where the blue color represents the low-scoring groups and the red color represents the high-  scoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe that the mean loss and accuracy converge faster for low-scoring groups, while  it takes longer to converge for high-scoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' This indicates that the CG-score is highly correlated  with the ‘difficulty’ of an example measured by the learning speed at a model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  9  EMNIST  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='12  Clean  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='10  Noise label  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='08  Density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  50  250  100  150  200  30  CG scoreCIFAR-100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='07  Clean  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='06  Noise label  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  20  40  60  80  0  100  CG scoreEMNIST  Fraction of noise data found(%)  100  80  60  Oracle  Partial CG score  40  CG score  EL2N  20  Forgetting score  Random  0  20  30  10  40  50  0  Fraction of data checked(%)CIFAR-100  100  80  60  40  20  0  10  20  30  40  50  0  Fraction of data checked(%)(a) Loss mean  (b) Accuracy  (c) Kernel velocity  Figure 4: Training dynamics measured for each subset of CIFAR-10 examples, grouped by the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  The line color varies over groups, where the blue lines include low-scoring examples and the red lines include  high-scoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (a) and (b) Mean loss and accuracy for subgroups of CIFAR-10 data, sorted by the  CG-score, trained on ResNet18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The mean loss and accuracy converge faster for low-scoring groups, while  they converge slowly for high-scoring groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (c) Kernel velocity of CIFAR-10 examples grouped by the  CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The Kernel evolves with a higher velocity for high-scoring groups throughout the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Data sample driving movement of neurons  We next investigate the relation between the CG-score and the evolution velocity of the data-dependent  Neural Tangent Kernel (NTK) (Fort et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' NTK has been widely used to approximate the evolution  of an infinite-width deep learning model via linearization around initial weights, when the network is trained  by gradient descent with a sufficiently small learning rate (Jacot et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The main idea is that in the  limit of an infinite width, the network parameters do not move very far from its initialization throughout the  training, so that the learning process can be approximated by a linear process along the tangent space to the  manifold of the model’s function class at the initialization (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However, as observed in Fort  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020), for a finite-width network, the tangent kernel is not constant but it rather rapidly changes over  time, especially at the beginning of the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To quantify this change, Fort et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020) addressed the  data-dependent Kernel Gram matrix, which is the Gram matrix of the logit Jacobian, and defined the Kernel  velocity as the cosine distance between two NTK Gram matrices before and after one epoch of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In  Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021), the Kernel velocity was used to evaluate the subgroups of data instances to figure out the  subgroup driving the learning and the change in the NTK feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We conduct similar experiments for  subgroups of data, divided according to our CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 4c shows the Kernel velocities for 10 different  subgroups of CIFAR-10 data trained in ResNet18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Each group is composed of 125 consecutive instances  from each level, where the level is defined by dividing the full dataset, sorted in ascending order by the  CG-score, into 10 groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The higher level (red) is composed of instances having higher CG-scores, while  the lower level (blue) is composed of instances having lower CG-scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe that the samples  with high CG-score (red) maintains higher Kernel velocity throughout the training, which means that NTK  Gram matrix evolves by a larger amount for the samples of high CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, we can hypothesize that  the instances with high CG-score are ‘difficult’ examples the network may struggle to optimize and try to  fit throughout the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  6  Discussion  We proposed the CG-score, a data-centric valuation score, to quantify the effect of individual data instances in  optimization and generalization of overparameterized two-layer neural networks trained by gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We theoretically and empirically demonstrated that the CG-score can identify ‘irregular’ instances within  each class, and can be used as a score to select instances essential for generalization of a model or in filtering  10  0~10%  10~20%  20~30%  30~40%  40~50%  50~60%  60~70%  70~80%  80~90%  90~100%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  Mean of Loss  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  0  25  50  75 100 125 150 175 200  Epoch0~10%  10~20%  20~30%  30~40%  40~50%  50~60%  60~70%  70~80%  80~90%  90~100%  100  80  Accuracy(%)  60  40  20  0  25  50  75 100 125 150 175 200  Epochlevel 1  level 2  level 3  level 4  level 5  level 6  level 7  level 8  level 9  level 10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='4  Kernel velocity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  25  50  0  75 100 125 150 175 200  Epochinstances with label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We also showed the close relation between the CG-score and learning difficulty  of instances by analyzing training dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Interesting open problems related to the CG-score include 1)  providing theoretical justification of the score for more general deep neural networks and 2) improving the  score by modifying the definition in terms of ‘features’ of data instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content=' Human-level control through deep reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Nature, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen,  Zeming Lin, Natalia Gimelshein, Luca Antiga, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Pytorch: An imperative style, high-performance deep  learning library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Advances in neural information processing systems, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Mansheej Paul, Surya Ganguli, and Gintare Karolina Dziugaite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Deep learning on a data diet: Finding  important examples early in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Geoff Pleiss, Tianyi Zhang, Ethan Elenberg, and Kilian Q Weinberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Identifying mislabeled data using  the area under the margin ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Garima Pruthi, Frederick Liu, Satyen Kale, and Mukund Sundararajan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Estimating training data influence  by tracing gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Mengye Ren, Wenyuan Zeng, Bin Yang, and Raquel Urtasun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Learning to reweight examples for robust deep  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Proceedings of the 35th International Conference on Machine Learning, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  12  David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian  Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Mastering the game of go  with deep neural networks and tree search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Nature, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Swabha Swayamdipta, Roy Schwartz, Nicholas Lourie, Yizhong Wang, Hannaneh Hajishirzi, Noah A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Smith,  and Yejin Choi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Dataset cartography: Mapping and diagnosing datasets with training dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In  Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Mariya Toneva, Alessandro Sordoni, Remi Tachet des Combes, Adam Trischler, Yoshua Bengio, and Geof-  frey J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Gordon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' An empirical study of example forgetting during deep neural network learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In 7th  International Conference on Learning Representations, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, �L ukasz Kaiser,  and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Xiaoxia Wu, Ethan Dyer, and Behnam Neyshabur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When do curricula work?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In 9th International Conference  on Learning Representations, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Zhaoxuan Wu, Yao Shu, and Bryan Kian Hsiang Low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' DAVINZ: Data valuation using deep neural networks  at initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Proceedings of the 39th International Conference on Machine Learning, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Jingfeng Zhang, Jianing Zhu, Gang Niu, Bo Han, Masashi Sugiyama, and Mohan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Kankanhalli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Geometry-  aware instance-reweighted adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In 9th International Conference on Learning Representa-  tions, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  13  A  Extensions to Multi-class Complexity Gap score  In this section, we explain the details of how we calculated the CG-scores for multi-label public datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Calculation of CG-score for multi-label datasets  In defining the CG-score, we assumed the binary datasets y ∈ {±1} with inputs having a fixed norm ∥x∥2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  To calculate the CG-score for multi-label (k-class) public datasets, we normalize all the inputs to have  ∥x∥2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We then calculate the CG-score for examples of each class j ∈ [k], assuming that all the examples  from class j have label +1 and the rest of the examples from any other classes have label −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In detail, let y =  (y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', yn) ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' k}n be the label vector for n data instances and, without loss of generality, assume  that x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , xl belong to class 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', yl = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then, to calculate the CG-score for x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' xl,  we generate the gram matrix H∞ with (x1, 1), (x2, 1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , (xl, 1), (xl+1, −1), (xl+2, −1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , (xn, −1) and  calculate the CG-scores of x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , xl as the two-label case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Stochastic method to calculate CG-scores  Since the calculation of the CG-score requires the inversion of n-dimensional matrix H∞ where n is the num-  ber of total samples, it would demand expensive memory and computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To lower the complexity,  we sub-sample the examples with class −1 so that the ratio between class +1 and class -1 is reduced from  1 : (k − 1) to 1 : 3 for MNIST and FMINST, 1 : 4 for CIFAR-10 and CIFAR-100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We repeat this process  ten times by randomly sampling examples of label −1 and then average out the calculated CG-score of each  example from class +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  Justification of stochastic method to calculate CG-scores  To justify the stochastic method in calculating the CG-scores, we conduct an experiment to check whether  the CG-scores calculated by the stochastic method converges well to the true CG-scores utilizing the full  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We created a subset of the CIFAR-10 dataset, the Small-CIFAR-10 dataset, which consists of  1,000 instances for each label (a total of 10,000 instances).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then, we compared the CG-score calculated by  10,000x10,000 Gram matrix H∞ of the full dataset (true CG-score) with the CG-score calculated by the  stochastic method, where the stochastic CG-score for the instances from a class (class 1) are calculated by  subsampling the samples from any other classes (class -1) with the ratio between class 1 and -1 equal to 1 : 1  (size 2,000x2,000), 1 : 2 (size 3,000x3,000), 1 : 3 (size 4,000x4,000) and 1 : 4 (size 5,000x5,000) instead of  1 : 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We repeat this process multiple times by randomly sampling examples of label −1 and then average  out the calculated CG-score of each example from class +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' = In Figure 5, we plot the Spearman’s rank  correlation and Pearson correlation between the true CG-score and the stochastic CG-score for each ratio  (different colors) as the number of random sampling increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe that the correlations converge  to a certain number as the number of random sampling increases, and the amount of correlation increases as  the size of the matrix (the number of instances included in defining H∞) increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The values of correlations  obtained after 20 independent runs are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='829, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='914, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='953, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='973 for Spearman rank correlations and  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='796, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='898, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='943, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='967 for Pearson rank correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Recommended number of runs for stochastic calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  The proper number of runs in stochastic  calculation of the CG-score may need to be determined by the size and the number of classes of the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We recommend the number of runs to include at least half of the whole dataset in calculation of the CG-score  for each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As an example, for the CIFAR-100 dataset, where each class includes 500 images, when the  sampling ratio between the class of interest and the rest of classes is 1:4, we calculate the score for 500  images from the class of interest by using 2,000 images from the rest of 99 classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then, about 20 images  are selected from each of the 99 classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To cover at least a half of the images per class (250), we need  to repeat the runs about 10 times (ignoring overlap of samples in each run).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For the FMNIST/CIFAR-10  datasets, the similar calculation shows that only 2-3 runs will be enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  14  Figure 5: We create Small CIFAR-10 dataset by sampling 1,000 data in each class from CIFAR-10 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Figures show Spearman’s rank correlation(left) and Pearson correlation(right) between the CG-score of  Small CIFAR-10 and CG-score calculated by subsampling the dataset (stochastic CG-score) as the number  of calculations (random sampling) increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Stochastic CG-scores are calculated with 2,000 (cyan), 3,000  (orange), 4,000 (green), and 5,000 (red) instances, while the full data includes 10,000 instances (1,000 for each  class).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' X-axis indicates the number of independent runs to calculate averaged score, and Y-axis indicates  the correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  B  Discriminating mislabeled data from atypical (but useful) data  by CG-scores  Discriminating mislabeled data and atypical (but useful) data is a major challenge in data valuation, since  both the mislabeled data and atypical data are irregular in the data distribution and tend to have high  CG-scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The same challenge has been observed with previous valuation scores such as forgetting score  (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019) and EL2N score (Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  However, we find that mislabeled data usually has a higher CG-score than atypical data, and this tendency  gives us the possibility to separate mislabeled data from the rest of the clean data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To check the tendency, we  perform a data window experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The data instances are sorted in ascending order by the CG-score, and  we compare the test accuracy of a neural network trained with 50% of training instances selected from offset%  to (offset+50)% scoring group, for different offset points of {0, 5, 10, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , 45, 50}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For example, when the offset  is 20%, we select the data instances from 20% to 70% scoring examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When the training instances do not  include mislabeled data, we can expect that the window experiment will show higher accuracy as the offset  increases up to 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We add 20% of random label noise to FMNIST and CIFAR-100 datasets to see how  the trend changes when the dataset includes mislabeled instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 6 (a) and (b), the test accuracy increases until the offset reaches 30% and then drops  after the point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When the offset is 30%, the 50%-width window includes 30% to 80% scoring examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Since 20% mislabeled data are mainly located within the 80% to 100% scoring group, as the offset increases  above 30%, the 50%-width window starts to include mislabeled instances and this causes the rapid drop of  the test accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, from the window experiments we can see that the mislabeled data has the highest  CG-score and can be separable from the rest of the clean examples by the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Then, the next reasonable question is how to set the threshold on CG-score to detect the mislabeled  data when the portion of mislabeled data is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We show that the sign of the partial CG-score  2yi(y⊤  −ihi), which is a sub-term of the CG-score including the label information yi, can be used in this  purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3, the partial CG-score measures the gap between the average similarity of  the data instance with other samples of the same class compared to that with the samples of the different  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, by checking the sign of the partial CG-score, we can discriminate mislabeled samples from  clean samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 6 (c), we show the scatter plot of clean (blue) and mislabeled data (orange), where  one can find that mislabeled examples tend to have positive partial CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Furthermore, as shown in  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='95  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='80  2000x2000  3000x3000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='75  4000x4000  5000x5000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='70  2  4  6  10  12  14  16  18  20  0  8  # of calculations0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='95  Pearson correlation  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='90  2000x2000  3000x3000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='85  4000x4000  5000x5000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='12 14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='# of calculationsTable 2: Number of mislabeled data and clean data in each subset selected based on partial CG-score  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='Dataset  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='FMNIST  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='CIFAR-10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2yi(y⊤  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='−ihi)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='positive  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='negative  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='high 20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='positive  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='negative  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='high 20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='mislabeled  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='11796  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='204  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='10776  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7146  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2854  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5619  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='clean  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3462  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='44538  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1224  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8331  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='31669  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='4381  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='(a) Window experiment (FMNIST)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='(b) Window experiment (CIFAR-10)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='(c) Scatter graph (CIFAR-10)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='Figure 6: (a) and (b) Window experiments with 20% label noisy for FMNIST (a) and CIFAR-10 (b) datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Test accuracy (y-axis) of a model trained with 50% of training instances selected from offset% (x-axis) to  (offset+50)% scoring group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (c) Scatter graph of Partial CG-score (x-axis) and CG-score (y-axis) for CIFAR-  10 with 20% label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Table 2, we can check that for FMNIST with 20% label noise (12,000 mislabeled instances and 48,000 clean  instances), 98%(=11796/12000) of mislabeled data ends up having positive partial CG-score, while only  7%(=3462/44538) of clean data has positive partial CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, even when the portion of label noise  is unknown, our partial CG-score can effectively detect the mislabeled data by the sign information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' This  tendency was less clear for CIFAR-10 dataset due to the increased dataset complexity, but still the tendency  existed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  C  Implementation Details and computational cost  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Training details  In Section 4 and 5, we evaluate our score on three public datasets, FMNIST, CIFAR-10/100, by training  ResNet networks (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2016) of different depths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' ResNet18 is used for FMNIST and CIFAR-10 dataset  and ResNet50 is used for CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Implementation of the ResNet is based on the ResNet network  in torchvision (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Since FMNIST and CIFAR images are smaller than Imagenet (Deng  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2009) images, we replace the front parts of the ResNet (convolution layer with 7x7 kernel and 2x2  stride, max pooling layer with 3x3 kernel and 2x2 stride) with a single convolution layer with 3x3 kernel and  1x1 stride for small size image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The details on hyperparameters and optimization methods used in training  are summarized in the Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Computation time  Table 4 provides computational time (in seconds) to obtain CG-scores with different sampling ratio 1:1, 1:2,  1:3, and 1:4 for FMNIST and CIFAR-10/100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We also report the time to compute the baseline scores,  Forgetting (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019), EL2N (Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), TracIn (Pruthi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020), and CRAIG (Pruthi  16  90  Test accuracy  80  70  60  Partial CG-score  50  Random  10  20  30  0  40  50  Offset of window85  80  Test accuracy  75  70  65  Partial CG-score  60  Random  20  30  0  10  40  50  Offset of window100  Clean  Noise label  80  CG-Score  60  40  20  0  30  20  10  0  10  20  Partial CG-scoreTable 3: Details for the experiments used in the training of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  FMNIST  CIFAR10  CIFAR100  Architecture  ResNet18  ResNet18  ResNet50  Batch size  128  128  128  Epochs  100  200  200  Initial Learning Rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Weight decay  5e-4  5e-4  5e-4  Optimizer  SGD with momentum 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Learning Rate Scheduler  Cosine annealing schedule (Loshchilov & Hutter, 2017)  Data Augmentation  Normalize by dataset’s mean, variance  Random Zero Padded Cropping (4 pixels on all sides)  Random left-right flipping (probability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5)  Table 4: Time cost(seconds) to compute scores of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  FMNIST  CIFAR-10  CIFAR-100  CG-score 1:1  1063  608  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  CG-score 1:2  2610  1497  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  CG-score 1:3  4834  2773  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  CG-score 1:4 4388  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Forgetting  1879  3322  6675  EL2N  370  323  662  TracIn  1856  3425  8400  CRAIG  3023  5263  10472  GPU  Nvidia A100 40GB  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We do not calculate the CG-score of FMNIST dataset with sampling ratio 1:4 since it requires  a inversion for 30,000x30,000 matrix, which exceeds the limit of the device memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Every score including  ours and baselines needs to be calculated by averaging the results of independent multiple runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For a fair  comparison, we compare the time to get each score for a single run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Cost to compute CG-score depends  on the size of the Gram matrix H∞, since we need to calculate the inverse of H∞ to get the CG-score and  the computational complexity to conduct an inversion of n × n matrix is O(n3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Therefore, for a dataset of  which each class includes a large number of instances (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', FMNIST and CIFAR-10), taking the inverse of a  Gram matrix with large sampling ratio may cause expensive computational cost, while computing the score  for a dataset of which each class includes relatively small number of instances (CIFAR-100) can be done in  a short time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For example, calculating CG-score of CIFAR-10 dataset (5,000 data in a class) takes1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2 hours  with sampling ratio 1:4, while that for CIFAR-100(500 data in a class) takes just 1 minute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' EL2N score is  time-efficient overall because it is calculate at the relatively early stage of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Forgetting and TracIn,  on the other hand, take relatively longer time since they require at least one full train of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In  addition, we argue that our method has another computational advantage that we do not need to search  networks and hyperparameters which would work well for the target dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  Experimental details  Baseline scores for data valuation  We use three state-of-the-art scores, C-score (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021),  EL2N (Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2021), and Forgetting score (Toneva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2019) as baselines with which our CG-score  is compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We use pre-calculated C-score for CIFAR-10 and CIFAR-100 from Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021) and  calculate EL2N and Forgetting score by averaging the score across five independent training using the full  17  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We obtain EL2N scores at 20th epochs of the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We use the same network architectures  to calculate EL2N and Forgetting score: ResNet18 for FMNIST and CIFAR-10 dataset and ResNet50 for  CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Detailed definitions of the scores are as follows:  Consistency score (C-score): C-score of each instance is calculated by estimating the prediction accu-  racy of the instance attained by the model trained with the full dataset except the instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  C-score(xi, yi) = En  �  ˆEr  S∼{(xj,yj)}n  j=1 [P(f(xi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' S\\{(xi, yi)}) = yi)]  �  ,  (9)  where f(xi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' S) is trained network using subset S, and ˆEr denotes empirical averaging with r i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  samples of such subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Error L2-Norm (EL2N): The EL2N score of a training sample (xi, yi) is defined to be E[∥f(W(t), xi)−  yi∥2] where f(W(t), x) is the output of the neural network for the sample (x, y) at the t-th step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Forgetting score: Forgetting score is defined as the number of times during training (until time step  T) the decision of that sample switches from a correct one to an incorrect one: Forgetting(xi, yi) is  defined as  T  �  t=2  1{arg max f(W(t − 1), xi) = yi}(1 − 1{arg max f(W(t), xi) = yi}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (10)  Data pruning experiment  We report the mean of the results after three independent runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The shaded  regions indicate the standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We acquire each result by training a network using a dataset pruned  by specified portions, where the training instances are ordered by each score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We compute the number of  iterations at which all data can be used in one epoch, and use the same number of iterations in all pruning  experiments for a fair comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When we prune the dataset, we remove the instances from each class by  the same amount, so as to preserve the original proportion between classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As will be shown in Section H,  the distribution of scores is different among classes, so an imbalance problem between classes may occur if  the data pruning is performed without considering the portion of classes within the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  D  Additional Experiments with Two More Baselines  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1  Another directions of data valuation  There are two additional branches of related works for data valuation, in addition to the methodologies  described in the Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The first branch uses the influence function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The influence function approximates  the degree of change of parameters when specific data enters and leaves the training dataset, so it determines  which data is valuable by calculating the effect of the data on learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The second branch uses coreset  selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Coresets are weighted subsets of the data selected to resemble the model training using the full  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Coresets may need to be updated as training progresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Baseline algorithms for data valuation  We use representative scores in each branch, TracIn (Pruthi  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020) for influence function and CRAIG (Mirzasoleiman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', 2020) for coreset selection, as additional  baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Detailed definitions of the scores are described below:  TracIn: TracIn CheckPoint (TracInCP) value between two data points is defined as the weighted sum  of dot products of the loss gradients calculated at the two data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The gradients are obtained  from the k checkpoints {t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , tk} of the model in the middle of training and the weight ηti is the  learning rate at each checkpoint ti:  TracInCP(z, z′) =  k  �  i=1  ηti∇l(wti, z)⊤∇l(wti, z′),  (11)  18  (a) Pruning low-scoring examples first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Better score maintains the test accuracy longer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (b) Pruning high-scoring examples first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Better score makes the rapid performance drop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Figure 7: Pruning experiments with three datasets FMNIST (left), CIFAR-10 (middle) and CIFAR-100  (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our CG-score can achieve better performances than the Tracin score and competitive performances  compared to the CRAIG algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Different from our scoring method, TracIn requires a validation set  to calculate the data values and CRAIG does not select a fixed subset of data to be used throughout the  training, but keeps updating the subset the data (coresets) to be used for training every 10 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' CRAIG  has been evaluated only for pruning low-valued samples due to the nature of coreset selection where coresets  are selected with per element weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  where l(wti, z) is loss function at ti-th step with model parameter wti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  CRAIG: CoResets for Accelerating Incremental Gradient descent (CRAIG) is an algorithm that solves  the optimization problem, which finds a subset that preserves the gradient of the total loss:  S∗ ∈ argmaxS⊂V  �  i∈V  min  j∈S max  w∈W ∥∇fi(w) − ∇fj(w)∥, s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' |S| ≤ r  (12)  where fi(w) = l(w, (xi, yi)) is loss for the data (xi, yi) with model parameter w, V is the full dataset  and S is the coresets with size r, and pi be the softmax output for data (xi, yi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In CRAIG, the  gradient fi(w) is approximated by pi − yi when cross entropy loss is used with soft-max at the last  layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2  Data Pruning experiments  In this section, we conduct data pruning experiments, similar to Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We conduct the experiments  using the above two additional baselines, TracIn and CRAIG, separately from the experiments of the main  text, since the two algorithms require additional assumptions/resources that have not been used for the  baselines considered in the main text: TracIn requires a validation set to calculate the data values;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' CRAIG  19  FMNIST  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  Accuracy(%)  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  CG-score  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  TracIn  CRAIG  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setCFAR-10  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  CG-score  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  TracIn  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  CRAIG  Random  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setCIFAR-100  79  78  77  76  75  CG-score  74  TracIn  CRAIG  73  Random  72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train set95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  a  high value  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  Accuracy(%)  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  Pruning  CG-score  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  TracIn  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train set94  92  90  88  CG-score  Tracin  86  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train set78  76  74  72  CG-score  70  Tracin  68  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setdoes not select a fixed subset of data to be used throughout the training, but keeps updating the subset of  the data (coresets) to be used for training every 10 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Experimental details  As described in the Pruthi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020), we calculate the TracIn score by using the  gradients of the parameters of the network’s last layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The check points are set at every 20 epochs, starting  from the end of the first 20th epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We use 5 checkpoints for FMNIST and 10 checkpoints for CIFAR-10  and CIFAR-100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We create a validation set composed of 1,000 samples by taking a part of the test dataset,  and calculate TracIn score with this validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As TracIn score is defined between two data points (z, z′)  as in equation 11, we set the score of each training sample z by averaging TracIn scores TracInCP(z, z′) over  all samples z′ in the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In CRAIG, the subset selection is performed every 10 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We only test CRAIG in pruning low-valued  data but not in the reverse order (pruning high-valued data), since CRAIG extracts coresets to be used with  per element weights for preserving the gradient of total loss but does not give what are the high-valued  (equal weight) samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  TracIn score and CRAIG are calculated at the networks same as those used in the experiment in Section  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1: ResNet18 for FMNIST and CIFAR-10, and ResNet50 for CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The other experimental  details are the same as Table 3 in Appendix §C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  Experimental results  Similar to data pruning experiment in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1, in Figure 7, the first row shows  the test accuracy of the model trained with different subset sizes, when low-scoring (regular) examples are  removed first, and the second row shows the similar result but when high-scoring (irregular) examples are  removed first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We report the mean of the results after three independent runs, and the shaded regions  indicate the standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The red-curve (random) is the result when randomly ordered examples  are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  When pruning low-scoring data first, it is preferable to maintain the accuracy up to a large  removing portion (a small training set);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' when pruning high-scoring data first, the rapid drop of performance  is preferable since it means that the score can detect high-value samples, necessary for generalization of the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our CG-score can achieve better performances than the Tracin score and competitive performances  compared to the CRAIG algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Since CRAIG updates the coresets over the training, it can choose  different semantics of the data suitable for each phase of the training, which results in better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  This result may imply the effectiveness of the scheduled batch selection, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', curriculum learning, in training  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We inspect that the performance of TracIn may heavily depend on the size of the validation  set and also the possible domain discrepancy between training and test datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In our test, there is no  domain discrepancy, but if there exists a domain shift between the test dataset and the training dataset,  TracIn may perform better than other methods with the help of validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3  Detecting Label Noise  We also compared the performance of our CG-score in detecting mislabeled data with that of TracIn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As  suggested in Pruthi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020), we use ‘self-influence’ of each training example, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', the influence of  a training point on its own loss during the training process, TracInCP(z, z), to identify mislabeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In Pruthi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020), it was shown that mislabeled examples tend to have higher TracIn values, and  thus TracIn values can be effectively used in identifying mislabeled examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  8, we show the  comparison of our method with TracIn in identifying mislabeled examples in FMNIST and CIFAR-100  datasets, respectively, each of which includes 20% label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' TracIn achieves better performance in CIFAR-  100, but ours outperformed TracIn in FMNIST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Since TraIn measures the ‘self-influence’ of each training  example over the training, starting from 20th epoch, for relatively simpler dataset such as FMNIST, some  mislabeled instances could have already been memorized at the network, which makes them not detectable  by the TracIn values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' On the other hand, our method better detects mislabeled data for easier datasets as  discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, we can conclude that depending on data complexity, the outperforming method  can be changing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  20  Figure 8: Fraction of label noise (y-axis) included in the examined portion (x-axis) for 20% label noise for  oracle, Partial CG-score (ours), CG-score (ours), TracIn and random baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (a) Pruning low-scoring examples first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (b) Pruning high-scoring examples first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Figure 9: Pruning experiments with CIFAR-10 dataset trained on DenseNet-100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Even if the model changes  from ResNet to DenseNet, we observe a similar trend as in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  E  Robustness of CG-score over model variants  Our CG-score is derived based on the theoretical analysis of the generalization error bounds on overparam-  eterized two-layer ReLU activated neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To demonstrate that our CG-score is effective in more  complicated networks, in the main text (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='1), we used ResNets to evaluate our score for data pruning  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' To further demonstrate the robustness of our score against model changes, in this section, we  report the results of data pruning experiments on CIFAR-10 dataset using DenseNetBC-100, a more com-  plicated convolutional network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The implementation details of the DenseNet follows that of Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We use the same hyperparameter and optimization method summarized in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In Figure 9, the left figure shows the test accuracy of the model trained with different subset sizes, when  low-scoring (regular) examples are removed first, and the right figure shows the similar result but when  high-scoring (irregular) examples are removed fist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We report the mean of the result after two independent  runs, and the shaded regions indicate the standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The red-curve (random) is the result when  randomly ordered examples are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can observe a similar trend as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 2, the experimental results  using ResNets, in spite of the model change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Our CG-score achieve competitive performances as the other  baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The reason that we observe a rapid performance degradation at a smaller training data portion  in the left figure (removing low value data first) is due to the characteristics of leave-one-out method we  used in the calculation of the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Removing a typical sample from a dataset does not change the  21  20% nosiy FMNIST  20% noisy CIFAR-100  100  100/  found(  80  80  data  Oracle  60  60  Partial CG score  noise  CG score  Tracln  40  40  Random  Jo  Fraction  20  20  0  30  20  30  40  10  20  40  0  10  50  0  50  Fraction of data checked(%)  Fraction of data checked(%)DenseNet-100 (Pruning high value)  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  Test accuracy  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  CG-score  EL2N  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  Forgetting  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  C-score  Random  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setDenseNet-100 (Pruning high value)  94  Test accuracy  92  90  CG-score  EL2N  88  Forgetting  C-score  86  Random  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='9  Portion of train setgeneralization error bounds much, since similar samples already exist in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, typical samples  tend to have low CG-scores when the score is measured by the leave-one-out method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However, when we  remove 50% of instances, samples sharing the typicality can be excluded simultaneously from the dataset,  which might cause severe degradation of the generalization capability of the neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Thus, for a  smaller training data portion, it can be better to make sure at least a small portion of typical samples is  indeed included in the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Similar observations have been made in Swayamdipta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  F  Details of kernel velocity  We calculate the kernel velocity of 10 groups of instances, where each group is composed of 125 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  The following is how we construct each group: Sort CIFAR-10 examples in ascending order by the CG-score,  divide the examples into 10 groups, and select 125 consecutive samples from the beginning of each group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We calculate the NTK kernel velocity as described in Paul et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (2021): Let C be the number of classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Let f (c)  t  (xi) be the c-th logit value for input xi at the t-epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' When W(t) is the parameters of the model, the  c-th logit gradient at input xi is ψ(c)  t (xi) = ∇W(t)f (c)  t  (xi) ∈ RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then, the data-dependent NTK submatrix  of a group of m samples S := {xa1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , xam} is defined as Kt(S) = Ψt(S)Ψt(S)⊤, where Ψt(S) ∈ RmC×N is  constructed by placing {ψ(c)  t (xai)}c∈[C],i∈[m] in rows of Ψt(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The kernel velocity is defined as  vt(S) = 1 −  ⟨Kt(S), Kt+1(S)⟩  ∥Kt(S)∥ ∥Kt+1(S)∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (13)  Lastly, we provide some explanations of what the kernel velocity measures if we define it for finite-  width ReLU activated 2-layer neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Remind that our analysis uses the Gram matrix H∞ de-  fined in equation 1, which is derived for an overparameterized ReLU activated 2-layer neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We can generalize the definition of the Gram matrix assuming a finite-width network, similar to Kt(S),  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The output of the network is fW,a(x) =  1  √m  �m  r=1 arσ(w⊤  r x), and the gradient with respect  to W = (w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , wm) ∈ Rd×m is ∇Wf(xi) = [∇w1f(xi), ∇w2f(xi), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , ∇wmf(xi)] =  x⊤  i  √m[a11{w⊤  1 xi ≥  0}, a21{w⊤  2 xi ≥ 0}, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' , am1{w⊤  mxi ≥ 0}].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Denoting the network parameters at the t-th step as W(t), we can  define the Gram matrix Ht as (Ht)ij = ∇W(t)f(xi)∇W(t)f(xj)⊤ = x⊤  i xj 1  m  �m  r=1 1{w⊤  r xi ≥ 0, w⊤  r xj ≥ 0},  which is proportion to the number of neurons in the hidden layer activated both for xi and xj at the epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We can define the kernel velocity similar to equation 13 by calculating Ht for a subset of data, and replacing  Kt(S) by Ht(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For this case, the high kernel velocity implies that Ht differs much from Ht+1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=', the  portion of neurons activated for pairs of instances changes rapidly during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  G  Visualization of examples sorted by CG-score  Analysis of MNIST and FMINST by CG-score  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 10, we show examples of MNIST (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 10a)  and FMNIST (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 10b) images sorted by CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The top/bottom three rows show the top-/bottom-  ranked examples, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We can observe that the examples with the lowest CG-score are regular  examples representing each class and they look similar to each other, while the examples with the highest  scores are irregular and they look different among themselves, among which we can identify (possibly)  mislabeled instances, marked with red rectangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Similarly, in CIFAR-10 images (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 10c), we observe  that low-scoring examples (bottom two rows) are regular ones sharing similar features representing the class  while high-scoring examples (top two rows) are irregular ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Analysis of CIFAR-100 by CG-score  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 11 shows the examples of CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 11a  shows the means and standard variations of 100 classes in CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Among 100 classes, ‘orange’  and ’plain’ classes have small CG-score means and variances, while ‘bottle’ and ’flatfish’ classes have larger  CG-score means and variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We display ten top-/bottom-ranked examples of these four classes, with the  histograms of the scores in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 11b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  22  (a) Examples of MNIST dataset  (b) Examples of FMNIST dataset  (c) Examples of CIFAR-10 dataset (Cat, dog, frog, and truck)  Figure 10: Examples sorted by CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In (a) and (b), top-3 rows / bottom-3 rows display top-ranked  / bottom-ranked examples, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Among top-ranked examples, (possibly) mislabeled examples are  marked by red rectangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In (c), top-2 rows / bottom-2 rows display top-ranked / bottom-ranked examples,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Analysis of Tiny ImageNet by CG-score  To check the effectiveness of CG-score in analyzing more  complicated dataset, we compute CG-score on the high-resolution tiny ImageNet dataset (64 by 64 resolution,  100,000 samples of 200 classes) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The CG-score is computed with sampling ratio of 1:14 by averaging  the results from 10 independents runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 12 show the examples of Tiny Imagenet datset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 12a  show the means and standard variations of classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We examine two easiest classes, ‘Sulfur butterfly’ and  ‘Jellyfish’, having relatively smaller mean and std of CG-score, and two difficult classes, ‘Pill bottle’ and  ‘Syringe’, having higher mean and std of CG-score, and display ten top-/bottom-ranked examples of these  four classes with CG-score histograms in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 12b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' For the two easy classes, low-scoring examples look very  much similar to each other and share some typical attributes (color and shape).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' On the other hand, for two  difficult classes, even low-scoring examples do not look very similar to each other but rather diverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' From  the analysis, we can see that our CG-score is still effective in examining high-resolution complicated dataset,  and the score reflects the instance-wise structural regularities, which can be used in analyzing or improving  learning algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  23  8  High score  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='ow score  3  5T-shirt  Trouser  Pullover  Dress  Coat  Sandal  Shirt  Sneaker  Bag  Ankleboot  High score  _ow scoreHigh score  Low score(a) Distribution of CG-scores at CIFAR-100  (b) Examples and histograms of four classes in CIFAR-100  Figure 11: Sample analysis for CIFAR-100 dataset in terms of the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (a) shows the CG-score means  and standard deviations of 100 classes in CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (b) shows ten top-ranked examples (top two  rows) and ten bottom ranked examples (bottom two rows) for orange, plain, bottle, and flatfish classes of  CIFAR-100 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Histograms show distributions of the CG-scores for each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  H  Score distribution for public datasets  Score distributions  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 13, we compare the CG-score distributions of three public datasets, FMNIST,  CIFAR-10 and CIFAR-100 before and after we artificially corrupt 20% of instances with random label noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  The top row shows the distributions before the corruption, and the bottom row shows the distributions after  the corruption, where the orange color displays the distribution of the CG-score for 20% instances with label  noise and the blue displays that for 80% instances with clean label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The gap between scores of clean data  and noisy data, which enables us to detect the noise by the CG-score, is larger for relatively simpler dataset,  FMINST, than those for CIFAR-10/100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  24  bottle  13  12  i-score  flatfish  11  G  10  Std  9  plain  8  orange  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  Mean of CG-scoreLow score High score0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='18-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='18  orange  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='00 +  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00 +  10  20  30  40  50  60  70  80  90  10  20  30  40  50  60  70  80  90  10  20  30  40  50  60  70  80  90  10  20  30  40  50  60  70  80  90  CG-score  CG-score  CG-score  CG-score(a) Distribution of CG-scores at Tiny Imagenet  (b) Examples and histograms of four classes in Tiny Imagenet  Figure 12: Sample analysis for Tiny Imagenet in terms of the CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (a) shows the CG-score means and  standard deviations of 200 classes in Tiny Imagenet dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' (b) shows ten top-ranked examples (top two  rows) and ten bottom ranked examples (bottom two rows) for Sulphur butterfly, Jellyfish, Pill bottle, and  Syringe classes of Tiny Imagenet dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Histograms show distributions of the CG-scores for each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Detecting mislabeled instances at high noise rate  We conduct additional experiments to check the  detectability of mislabeled instances by our CG-score, when the noise ratio increases to 50% and even to  80% for FMNIST and CIFAR-10 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In the main text, we considered a mild noise ratio of 20% and  reported the result in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The results for higher noise cases are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In the CIFAR-10  dataset, when the noise ratio is 80%, each class includes 1,000 correctly labeled images and 4,000 mislabeled  images, composed of 445 samples coming from each of the other nine classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Even for such an extremely  noisy case, our CG-score can effectively detect the mislabeled data, since our score can discover samples that  have a relatively lower correlation to the majority of the samples of the same class as analyzed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  25  30  i-score  25  Pillbottle  CG  20  Jellyfish  Std  15  yringe  10  buttertl  5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='0  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='5  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='0  Mean of CG-scoreY0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='07  Sulfur butterfly  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='07  Jellyfish  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='07  Pill bottle  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='07  Syringe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content="03  EO'0  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='00 +  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  20  100  20  100  20  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  40  60  80  120  0  40  60  80  120  40  60  %  120  20  40  60  80  100  120  CG-score  CG-score  CG-score  CG-scoreFigure 13: Density of CG-scores at clean dataset and label noisy dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  Figure 14: Fraction of label noise (y-axis) included in the examined portion (x-axis) for 50%(top) and  80%(bottom) label noise for FMINST (left) and CIFAR-100 (right) datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  I  Correlations between CG-score and Partial CG-scores  From the CG-score, which is expressed as d−1  i (y⊤  −ihi)2 + 2yi(y⊤  −ihi) + y2  i di at the equation 6, we can define  three partial CG-scores, d−1  i (y⊤  −ihi)2, 2yi(y⊤  −ihi), and y2  i di, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In this section, we analyze which  term dominates the order of CG-scores for two public datasets, CIFAR-10/100, by analyzing the correlation  between the CG-score and the three partial CG-scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  We also examine whether the correlations vary  when we change the size of the Gram matrix H∞, whose dimension changes according to the level of sub-  26  FMNIST  CIFAR-10  CIFAR-100  6  clean label  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='07  clean label  clean label  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='08  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='03  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='02  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='01  %  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='00  2  4  6  8  10  20  60  80  100  120  0  20  40  60  80  100  CG score  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='00  50  100  150  200  250  300  20  40  60  80  100  120  20  40  60  80  100  0  CG score50% nosiy FMNIST  50% noisy CIFAR-100  100  100  found(  80  80  data  60  60  noise  Oracle  40  40  Partial CG score  Jo  CG score  Fraction  201  EL2N  20  Forgetting score  Random  0  100  40  20  40  60  20  60  100  0  80  0  80  Fraction of data checked(%)  Fraction of data checked(%)80% nosiy FMNIST  80% noisy CIFAR-100  100  100  Oracle  found(  Partial CG score  CG score  80  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  EL2N  data  Forgetting score  60  60  Random  noise  40  40  Jo  Fraction  20t  20  0  0  100  40  20  40  60  80  20  60  80  100  0  0  Fraction of data checked(%)  Fraction of data checked(%)Table 5: Spearman rank correlations between the CG-score and the partial CG-scores  Dataset  CIFAR-10  CIFAR-100  Subsampling Ratio  1:1  1:2  1:3  1:4  1:1  1:2  1:3  1:4  d−1  i (y⊤  −ihi)2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+page_content='136  Figure 15: Spearman rank correlation (y-axis) between feature space CG-score calculated at each epoch (x-  axis) and baseline scores including CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The feature space CG-scores are calculated right after epoch  1(after one epoch of training), 3, 5, 7, 9, 11, 20, 50, and 200 (end of the training).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  sampling, explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We get H∞ with different subsampling ratios, 1:1, 1:2, 1:3, and 1:4, and  then calculate the CG-score and partial CG-scores, defined by the three partial terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Table 5 shows the  Spearman rank correlations between the CG-scores and the partial CG-scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We can see that 2yi(y⊤  −ihi),  which was utilized at noise detection experiments, is the partial score having the largest correlation with the  CG-score across all subsampling ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' On the other hand, correlations to other partial-scores are relatively  low, and the correlations change much as the subsampling ratio changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  J  Feature-space CG-score  Our original CG-score can be calculated by data without any trained network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' In this section we check  the validity of a new CG-score, which is defined in terms of feature of data, and compare its characteristic  with that of the original data-centric CG-score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' We train ResNet18 using the full CIFAR-10 dataset to  obtain each data’s feature at various epochs, where the feature is defined at the output of the penultimate  layer value (512 dimensions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Then we calculate the feature-space CG scores, which are calculated by the  feature instead of the data itself, and compare how the Spearman rank correlation between the feature-space  CG-scores and other scores, including the original CG-score and the previous training-based scores such  as C-score, Forgetting score, and EL2N, change over the epochs at which the feature space CG-scores are  calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Figure 15 reports the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  In Figure 15, we can first observe that the feature space CG-score and the original CG-score has the  highest correlation at the very beginning of the training (epoch 1), but as the training progresses, the  correlation decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' This trend can be explained by the fact that the feature space CG-score computes  27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='70  Original CG  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='65  correlation  C-score  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='60  Forgetting  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='55  EL2N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='50  ink  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='45  earman  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='35  Spe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='25  1357  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' 11  20  50  200  Epochthe value of data in the learned embedding space, while our score computes the value of the original data  without embedding it into a latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' As training of a model progresses, the embedded data may incur  bias in the data valuation, depending on a particular model or training algorithm, and thus the correlation  between the feature space CG-score and the original data-centric CG-score may decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  On the other hand, correlation between feature space CG-score and other training-based scores (EL2N,  Forgetting, and C-score) increases during the initial stage, and then decreases gradually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' More specifically,  for both EL2N and Forgetting score, which are computed at the same network as that of the feature space  CG-score, the correlation increases as the epoch increases and then slightly drops and becomes saturated at  a certain value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' The C-score, which was calculated in a different CNN network, shows a slightly different  tendency compared to EL2N or forgetting score, and attains its peak at an earlier epoch, epoch 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  This result implies that the feature-space CG score includes meaningful information for data valuation,  correlated with other training-based scores for overall epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' However, the feature space CG-score may incur  some bias in data valuation as the training progresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Understanding the effectiveness of the feature-space  CG score in diverse applications can be an interesting future research direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  K  Schur complement  Calculating CG-score (equation 2) of n data instances requires the inversion of n × n matrix, which may  cause expensive computational cost for a large n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Therefore, we provided computationally efficient way to  obtain the CG-score by using Schur complement equation 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' Here we provide some details to derive the  inverse of a sub-block matrix using Schur complement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=' By Schur complement, we have  �A  B  C  D  �−1  =  �  (A − BD−1C)−1  −(A − BD−1C)−1BD−1  −D−1C(A − BD−1C)−1  D−1 + D−1C(A − BD−1C)−1BD−1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (14)  Remind that H∞ and (H∞)−1 are denoted by  H∞ =  �H∞  n−1  gi  g⊤  i  ci  �  ,  (H∞)−1 =  �  (H∞)−1  n−1  hi  h⊤  i  di  �  ,  (15)  where H∞  n−1, (H∞)−1  n−1 ∈ R(n−1)×(n−1), gi, hi ∈ Rn−1 and ci, di ∈ R, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content=',  (H∞) =  �  (H∞)−1  n−1  hi  h⊤  i  di  �−1  =  �H∞  n−1  gi  g⊤  i  ci  �  (16)  By substituting A, B, C, and D in equation 14 with (H∞)−1  n−1, hi, h⊤  i , and di respectively, we obtain that  H∞  n−1 = ((H∞)−1  n−1 − hih⊤  i /di)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  (17)  Thus, (H∞  n−1)−1 = (H∞)−1  n−1 − hih⊤  i /di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
+page_content='  28' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/p9AzT4oBgHgl3EQfAvo4/content/2301.00930v1.pdf'}
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+Faculty of Mathematics and Computer Science
+Heidelberg University
+Master thesis
+in Computer Science
+submitted by
+Stefan Machmeier
+born in Heidelberg
+2022
+arXiv:2301.00710v1  [cs.CR]  2 Jan 2023
+
+Honeypot Implementation in a Cloud Environment
+This Master thesis has been carried out by Stefan Machmeier
+at the
+Engineering Mathematics and Computing Lab
+under the supervision of
+Prof. Dr. Vincent Heuveline
+
+Erklärung
+Ich versichere hiermit, dass ich die vorliegende Arbeit selbständig verfasst und keine
+anderen als die angegebenen Hilfsmittel benutzt habe. Sowohl inhaltlich als auch
+wörtlich entnommene Inhalte wurden als solche kenntlich gemacht.
+Die Arbeit ist in gleicher oder vergleichbarer Form noch bei keiner anderen Prü-
+fungsbehörde eingereicht worden.
+Heidelberg, den 21.01.2022
+Stefan Machmeier
+
+Acknowledgements
+The research included in this thesis could not have been performed if not for many
+individuals’ assistance, patience, and support.
+First and foremost, I am deeply grateful to my supervisor, Prof. Dr. Vincent Heuve-
+line for his valuable and constructive input. Without his guidance and mentorship,
+I would not have been able to finish this thesis. Moreover, I grew as a researcher,
+and I am immensely grateful for the opportunity to continue my research as a future
+Ph.D. candidate under his supervision.
+I want to extend my gratitude towards Stefan Steiger and Olaf Pichler from the
+Computing Centre at Heidelberg University. Thank you for offering insightful com-
+ments and brilliant suggestions when the task got challenging. They always had
+time and provided me with ample support no matter what happened.
+I am indebted to Joachim Peeck for generously agreeing to examine my results and
+providing valuable inputs. His timely advice and scientific knowledge helped me
+understand essential parts of the topic assisted me to a great extent in accomplishing
+this task.
+Lastly, I could not have completed this thesis without the support of my girlfriend,
+Carmen. Thank you for being so patient in providing emotional support and stim-
+ulating discussions during my research.
+
+Contents
+Acronyms
+V
+List of Figures
+VIII
+List of Tables
+IX
+Listings
+X
+1
+Introduction
+1
+2
+Background
+3
+2.1
+Virtualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3
+2.2
+Cloud Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+4
+2.2.1
+Definition of Cloud Computing
+. . . . . . . . . . . . . . . . .
+4
+2.2.2
+Service models
+. . . . . . . . . . . . . . . . . . . . . . . . . .
+5
+2.2.3
+Deployment models . . . . . . . . . . . . . . . . . . . . . . . .
+6
+2.3
+Honeypots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+7
+2.3.1
+Definition of Honeypots
+. . . . . . . . . . . . . . . . . . . . .
+7
+2.3.2
+Level of Interaction . . . . . . . . . . . . . . . . . . . . . . . .
+10
+2.3.3
+Security concepts . . . . . . . . . . . . . . . . . . . . . . . . .
+10
+2.3.4
+Value of Honeypots . . . . . . . . . . . . . . . . . . . . . . . .
+11
+2.3.5
+Honeynets . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+13
+2.3.6
+Legal Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14
+3
+Analyze Honeypot Attacks in the Cloud
+15
+3.1
+Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+15
+3.2
+Methodology
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+17
+3.2.1
+heiCLOUD
+. . . . . . . . . . . . . . . . . . . . . . . . . . . .
+17
+3.2.2
+T-Pot
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+19
+3.3
+Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+25
+3.4
+Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+32
+4
+Catching Attackers in Restricted Network Zones
+36
+4.1
+University Network . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+36
+4.2
+Honeypot-like Connection Detection Tool . . . . . . . . . . . . . . . .
+38
+4.3
+Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+42
+III
+
+4.4
+Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+47
+5
+Mitigate Fingerprint Activities of Honeypots
+50
+5.1
+OpenSSH
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+50
+5.2
+Preliminary Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+52
+5.3
+Experiment 1: Reproduce Vetterl et al.’s findings
+. . . . . . . . . . .
+55
+5.4
+Attempt to Disguise Cowrie . . . . . . . . . . . . . . . . . . . . . . .
+58
+5.5
+Experiment 2: Avoid fingerprinting of Cowrie
+. . . . . . . . . . . . .
+60
+5.6
+Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+61
+6
+Conclusion
+68
+Bibliography
+70
+IV
+
+Acronyms
+ACL Access Control List
+ADB Android Debug Bridge
+ADC Application Delivery Controller
+API Application Programming Interface
+AS Autonomous System
+ASA Adaptive Security Appliance
+ASN Autonomous System Number
+AWS Amazon Web Services
+BelWÜ Baden-Württembergs extended LAN
+BPP Binary Packet Protocol
+CERT Computer Emergency Response Team
+CGI Common Gateway Interface
+CHARGEN Character Generator Protocol
+CPU central processing unit
+CVE Common Vulnerabilities and Exposures
+DaaS Data-as-a-Service
+DDoS Distributed Denial of Service
+DICOM Digital Imaging and Communications in Medicine
+DMZ demilitarized zone
+DNS Domain Name System
+DTK Deception Toolkit
+EU European Union
+FHIR Fast Healthcare Interoperability Resources
+V
+
+FTP File Transport Protocol
+GB gigabyte
+GCP Google Cloud Platform
+GPU graphics processing unit
+HaaS Hardware-as-a-Service
+HTTP Hypertext Transfer Protocol
+IaaS Infrastructure-as-a-Service
+ICMP Internet Control Message Protocol
+ICS Industrial Control System
+IDENT Identification Protocol
+IDS intrusion detection system
+IMAP Internet Message Access Protocol
+IOCTA Internet Organised Crime Threat Assessment
+IP Internet Protocol
+IPD intrusion prevention system
+IPP Internet Printing Protocol
+MAC Message Authentication Code
+MITM man-in-the-middle
+NAT network address translation
+NIST National Institute of Standards and Technology
+NLA Network Level Authentication
+NSM network security monitoring
+NTP Network Time Protocol
+OS operating system
+PaaS Platform-as-a-Service
+POP Post Office Protocol
+RAM random-access memory
+RDBMS relational database management system
+RDP Remote Desktop Protocol
+VI
+
+SaaS Software-as-a-Service
+SCADA Supervisory Control and Data Acquisition
+SIP Session Initiation Protocol
+SMB Server Message Block
+SMTP Simple Mail Transfer Protocol
+SNMP Simple Network Management Protocol
+SOHO small office/home office
+SSDP Simple Service Discovery Protocol
+SSH Secure Shell
+TCP Transmission Control Protocol
+TLS Transport Layer Security
+UDP User Datagram Protocol
+USB Universal Serial Bus
+vCPU virtual central processing unit
+VLAN Virtual Local Area Network
+VM virtual machine
+VMM virtual machine monitors
+VNC Virtual Network Computing
+VoIP Voice over Internet Protocol
+VPN virtual private network
+XML Extensible Markup Language
+VII
+
+List of Figures
+2.1
+Abstract visualization of service models . . . . . . . . . . . . . . . . .
+5
+2.2
+Example of honeypots in a simplified network
+. . . . . . . . . . . . .
+9
+2.3
+Example of honeynets in a simplified network
+. . . . . . . . . . . . .
+13
+3.1
+Concept to collect honeypot attacks . . . . . . . . . . . . . . . . . . .
+18
+3.2
+T-Pot architecture
+. . . . . . . . . . . . . . . . . . . . . . . . . . . .
+20
+3.3
+Distribution of honeypot attacks . . . . . . . . . . . . . . . . . . . . .
+25
+3.4
+Attack distribution of T-Pot . . . . . . . . . . . . . . . . . . . . . . .
+26
+3.5
+Attack histogram of T-Pot . . . . . . . . . . . . . . . . . . . . . . . .
+27
+3.6
+Suricata results of T-Pot . . . . . . . . . . . . . . . . . . . . . . . . .
+28
+3.7
+RDPY results of T-Pot . . . . . . . . . . . . . . . . . . . . . . . . . .
+29
+3.8
+Honeytrap results of T-Pot . . . . . . . . . . . . . . . . . . . . . . . .
+30
+3.9
+Cowrie results of T-Pot . . . . . . . . . . . . . . . . . . . . . . . . . .
+30
+3.10 Cowrie top 10 credentials on T-Pot . . . . . . . . . . . . . . . . . . .
+31
+4.1
+Draft of the University network . . . . . . . . . . . . . . . . . . . . .
+37
+4.2
+Concept to detect connection attempts . . . . . . . . . . . . . . . . .
+40
+4.3
+Visualization of the MADCAT packet flow . . . . . . . . . . . . . . .
+41
+4.4
+Protocol distribution of MADCAT
+. . . . . . . . . . . . . . . . . . .
+42
+4.5
+Attack distribution of MADCAT
+. . . . . . . . . . . . . . . . . . . .
+43
+4.6
+Suricata results of T-Pot . . . . . . . . . . . . . . . . . . . . . . . . .
+44
+4.7
+Attack port histogram of T-Pot . . . . . . . . . . . . . . . . . . . . .
+45
+4.8
+Attack distribution of T-Pot . . . . . . . . . . . . . . . . . . . . . . .
+47
+4.9
+Attack port histogram of T-Pot . . . . . . . . . . . . . . . . . . . . .
+48
+5.1
+OpenSSH architecture
+. . . . . . . . . . . . . . . . . . . . . . . . . .
+51
+5.2
+Process to obtain the cosine similarity coefficient . . . . . . . . . . . .
+53
+5.3
+Architecture of OpenSSH and Cowrie . . . . . . . . . . . . . . . . . .
+54
+5.4
+Architecture of OpenSSH and Cowrie . . . . . . . . . . . . . . . . . .
+59
+5.5
+OpenSSH sample session flow diagram
+. . . . . . . . . . . . . . . . .
+62
+VIII
+
+List of Tables
+2.1
+Distinction between security concepts . . . . . . . . . . . . . . . . . .
+11
+3.1
+Overview of attacks on cloud providers . . . . . . . . . . . . . . . . .
+16
+3.2
+Overview of honeypots of T-Pot . . . . . . . . . . . . . . . . . . . . .
+24
+3.3
+Overview of attacks on heiCLOUD, AWS, GCP, and Azure . . . . . .
+33
+4.1
+Overview of firewall stages . . . . . . . . . . . . . . . . . . . . . . . .
+38
+5.1
+Overview of the cosine similarity of OpenSSH, Cowrie, and Twisted .
+55
+IX
+
+Listings
+3.1
+Cowrie attack to gather various information about the system
+. . . .
+34
+3.2
+Cowrie attack to exploit the host machine as a crypto miner . . . . .
+35
+4.1
+MADCAT connection attempt to exploit SIP connection . . . . . . .
+45
+4.2
+MADCAT connection attempt to exploit SMB connection
+. . . . . .
+46
+5.1
+Example OpenSSH connection with probed SSH packet . . . . . . . .
+53
+5.2
+OpenSSH connection attempt with probed message . . . . . . . . . .
+56
+5.3
+Cowrie connection attempt with probed message . . . . . . . . . . . .
+57
+5.4
+TwistedConch packet length validation . . . . . . . . . . . . . . . . .
+58
+5.5
+Cowrie version string validation . . . . . . . . . . . . . . . . . . . . .
+63
+5.6
+Tweaked OpenSSH authentication . . . . . . . . . . . . . . . . . . . .
+64
+5.7
+Tweaked OpenSSH channel
+. . . . . . . . . . . . . . . . . . . . . . .
+65
+5.8
+Tweaked OpenSSH server loop . . . . . . . . . . . . . . . . . . . . . .
+66
+5.9
+Cowrie log information . . . . . . . . . . . . . . . . . . . . . . . . . .
+67
+X
+
+Chapter 1
+Introduction
+Recently, Europol1 raised awareness of new cyber threats related to the ongoing
+pandemic. As stated in their yearly Internet Organised Crime Threat Assessment
+(IOCTA) report, scanning of corporate infrastructures has been skyrocketing within
+the last 12 months by ransomware groups, respectively increasing malware usage.
+Attackers use scans to find potential vulnerabilities in remote desktop sharing soft-
+ware, or virtual private networks (VPNs) in order to deploy malware and blackmail
+companies [27]. The rapid increase dates back to the pandemic and the shift to home
+office, forcing companies to adapt their infrastructures quickly. Such changes come
+with the downside of adding new threats to an organization. The latest incident
+at the SRH University Heidelberg points out the obstacles institutions face when
+ransomware groups have access and exploit various parts of the infrastructure with
+malware. An unknown group infected systems with malware and distributed internal
+data in the darknet. Such incidents emphasize the rise of malicious activities.
+Especially in cloud computing, controlling access to services is becoming a stricter
+challenge due to access to large data sets and computing resources. Besides tradi-
+tional security measures such as firewalls or intrusion detection systems, one known
+methodology to strengthen infrastructures is learning from those who attack them.
+Honeypots are a proper instrument to gather information about attackers. It is
+“a security resource whose value lies in being probed, attacked, or compromised”
+[65]. Collecting attacks can reveal shell-code exploitation or bot activity. In retro-
+spect, this would help to harden infrastructures before proper damage occurs. For
+a cloud provider, it is crucial to know whether and how attacks on its service can
+be prevented. Considering the Global Security Report by Trustwave, the number
+of attacks doubled in 2019 and increased by 20% in 2020 [1], respectively putting
+cloud providers to the third most targeted environments for cyberattacks, behind
+corporate and internal networks.
+The Heidelberg University offers its own cloud service, called heiCLOUD. It enables
+users to maintain and control computational resources easily. Thus, it is interesting
+1An agency that fights against terrorism, cybercrime, and other threats [28]
+1
+
+to elaborate on the value of honeypots for this cloud solution. This thesis tries to
+answer the general research question of whether honeypots can contribute to a more
+secure infrastructure in a cloud environment. This includes deploying a honeypot
+solution in heiCLOUD and presenting the results. Prior to that, an insight into
+a recent study investigating honeypots for the cloud providers AWS, GCP, and
+Microsoft Azure is given. These findings help to validate the results in heiCLOUD.
+In addition, the university network will be investigated to find potential leaks in
+the stateless firewall. Therefore, a concept is created using the BSI’s honeypot-like
+detection tool MADACT and deployed on desktop computers inside the university
+building. Furthermore, to consider an attacker’s point of view, this thesis introduces
+a recent work to detect honeypots on the transport level.
+Lastly, a solution to
+mitigate these efforts will be presented.
+This thesis includes six chapters.
+After the introduction, chapter 2 outlines the
+background knowledge that is needed to comprehend the upcoming experiments.
+It gives the reader a profound understanding of cloud computing, honeypots, and
+virtualization.
+Chapter 3, Analyze Honeypot Attacks in the Cloud, presents the
+status quo of malicious activities in heiCLOUD. In the beginning, it shows the
+results that Kelly et al. [40] claim for AWS, GCP, and Microsoft Azure. Next, it
+gives an insight into the T-Pot solution used to collect the data and shows the results
+after collecting them for three weeks. Furthermore, chapter 4, Catching Attackers
+in Restricted Network Zones, investigates the university network in which the new
+concept is deployed for three weeks. It shows that the concept was able to adapt the
+firewall, thus, improving the network security at the university. Chapter 5, Mitigate
+Fingerprint Activities of Honeypots, presents two experiments. First, it describes the
+preliminary work to detect honeypots and finishes with an experiment to prove this
+assumption. Next, it drafts the counterpart of mitigating this activity, also closing
+up with an experiment. Lastly, chapter 6 completes this thesis with a conclusion
+that summarizes the results and describes future work in this regard.
+2
+
+Chapter 2
+Background
+A honeypot is a security resource
+whose value lies in being probed,
+attacked, or compromised.
+Lance Spitzner
+Using honeypots in a cloud environment merges two varying principles. This chapter
+introduces the fundamental knowledge needed to comprehend the upcoming exper-
+iments. If the reader has a profound understanding of cloud computing, honeypots,
+and virtualization, he can skip this chapter.
+2.1 Virtualization
+Virtualization, often referred to as virtual machines (VMs), is defined by Kreuter
+[43] as “an abstraction layer or environment between hardware component and the
+end-user”. A VM runs on top of the operating system’s (OS’s) core components.
+Through an abstraction layer, the virtual machine is connected with the real ma-
+chine by hypervisors or virtual machine monitors (VMM). Hypervisors can use real
+machine hardware components but also support virtual machine’s operating systems
+and configurations. Both are similar to emulators, which are defined by Lichstein
+[45] as a “process whereby one computer is set up to permit the execution of programs
+written for another computer”. This allows managing multiple VMs with real ma-
+chine resources. There are three different types of virtualization, (i) software virtual
+machines, (ii) hardware virtual machines, and (iii) virtual OS/containers. Software
+virtual machines manage interactions between the host and guest operating sys-
+tems [21]. Hardware virtual machines offer direct and fast access to the underlying
+resources [21]. It uses hypervisors, modified code, or Application Programming In-
+terfaces (APIs). Lastly, virtual OS/container partitions the host operating system
+into containers or zones [21].
+3
+
+2.2 Cloud Computing
+Cloud Computing has become a buzzword these days. It has been used by various
+large companies such as Google and Amazon. However, the term “cloud computing”
+dates back to late 1996, when a small group of technology executives of Compaq
+Computer framed new business ideas around the Internet [56]. Starting from 2007,
+cloud computing evolved into a serious competitor and outnumbered the keywords’
+“virtualization”, and “grid computing” as reported by Google trends [73]. Shortly,
+various cloud providers become publicly available, each with its strengths and weak-
+nesses. For example IBM’s Cloud1, Amazon Web Services2, and Google Cloud3. So,
+why are clouds so attractive in practice?
+• It offers major advantages in terms of cost and reliability. When demand is
+needed, consumers do not have to invest in hardware when launching new
+services. Pay-as-you-go allows flexibility.
+• Consumers can easily scale with demand. When more computational resources
+are required due to more requests, scaling up instances in conjunction with a
+suited price model is straightforward.
+• Geographically distributed capabilities supply the need for worldwide scattered
+services.
+2.2.1 Definition of Cloud Computing
+According to the definition by Brian Hayes, cloud computing is “a shift in the geog-
+raphy of computation” [33]. Thus, the computational workload is moved away from
+local instances towards services and data centers that provide the user’s needs [3].
+The National Institute of Standards and Technology (NIST) defines cloud computing
+as “a model for enabling ubiquitous, convenient, on-demand network access to a
+shared pool of configurable computing resources (e.g., networks, servers, storage,
+applications, and services) that can be rapidly provisioned and released with minimal
+management effort or service provider interaction” [47]. NIST not only reflects the
+geographical shift of resources such as data centers but also mentions on-demand
+usage that contributes to flexible resource management. Moreover, NIST composes
+the term into five essential characteristics, three service models (see subsection 2.2.2),
+and four deployment models (see subsection 2.2.3) [47].
+On-demand-self-service refers to the unilateral provision computing capabilities.
+Consumers can acquire server time and network storage on demand without hu-
+man interaction.
+1https://www.ibm.com/cloud
+2https://aws.amazon.com/
+3https://cloud.google.com/
+4
+
+Application
+IaaS
+SaaS
+HaaS
+DaaS
+Cloud Resources
+Figure 2.1: Abstract visualization of service models. The container “cloud resources”
+represents the depth of functionalities. Therefore, Infrastructure-as-a-
+Service (IaaS) offers the most functionalities, whereas the others have a
+user-friendly abstraction.
+Broad network access characterizes the access of capabilities of the network through
+standard protocols such as Hypertext Transfer Protocol (HTTP). Heterogeneous
+thin and thick client platforms should be supported.
+Resource pooling allows the provider’s computing resources to be pooled across sev-
+eral consumers. Different physical and virtual resources are assigned on-demand
+with a multi-tenant model. Other aspects such as location are independent and
+cannot be controlled on a low-level by consumers. Moreover, high-level access to
+specify continent, state, or datacenter can be available.
+Rapid elasticity offers consumers to extend and release capabilities quickly. Further
+automation to quickly increase resources when demand surges can be supported at
+any time, regardless of limit or quantity.
+Measured service handles resources in an automated and optimized manner. It uses
+additional metering capabilities to trace storage, processing, bandwidth, and active
+user accounts. This helps to monitor and control resource usage. Thus, contributing
+to transparency between provider and consumer.
+2.2.2 Service models
+Service models are categorized by NIST into three basic models based on usage
+and abstraction level. Figure 2.1 shows the connection between each model whereas
+cloud resource are defined in subsection 2.2.3.
+Infrastructure-as-a-Service (IaaS)
+builds with a vast range of functionalities the foundation of service models. Each
+model on top represents a user-friendly abstraction with derated capabilities.
+Software-as-a-Service (SaaS) is a high-level abstraction to consumers. Controlling
+the underlying infrastructure is not supported. Providers often use a multi-tenancy
+5
+
+system architecture to organize each consumer’s application in a different environ-
+ment. It helps to employ scaling with respect to speed, security availability, disaster
+recovery, and maintenance [47]. The main objective of SaaS is to host a consumer’s
+software or application that can be accessed over the Internet using either a thin or
+rich client [23]. Users can apply custom configuration settings [47].
+Platform-as-a-Service (PaaS) pivots on the full “Software Lifecycle” of an application
+whereas SaaS distinct on hosting complete applications. PaaS offers ongoing devel-
+opment and includes programming environment, tools, configuration management,
+and other services. In addition, the underlying infrastructure is not managed by the
+consumer [47].
+Infrastructure-as-a-Service (IaaS) offers a low-level abstraction to consumers with
+the ability to run arbitrary software regardless of the operating system or appli-
+cation.
+In contrast to SaaS, IT infrastructure capabilities (such as storage and
+networks) can be used. It strongly depends on virtualization due to the integration
+or decomposition of physical resources [47].
+Data-as-a-Service (DaaS) serves as a virtualized data storage service on demand.
+Motivations behind such services could be upfront costs of on-premise enterprise
+database systems [23]. Mostly they require “dedicated server, software license, post-
+delivery services, and in-house IT maintenance” [23] whereas DaaS costs solely what
+consumers need. When dealing with a tremendous amount of data, file systems and
+relational database management systems (RDBMSs) often lack performance. DaaS
+outruns such weak links by employing a table-style abstraction that can be scaled
+[23].
+Hardware-as-a-Service (HaaS) offers IT hardware or datacenters to buy as a pay-as-
+you-go subscription service. The term dates back to 2006 when hardware virtual-
+ization became more powerful. It is flexible, scalable, and manageable [73].
+2.2.3 Deployment models
+Deployment models are categorized by NIST into four basic models. Each differs in
+data privacy, location, and manageability [47].
+With private clouds, users have the highest control regarding data privacy and
+utilization. Such clouds are mostly deployed within a single organization, managed
+by in-house teams or third-party suppliers. In addition, it can be on- or off-premise.
+Within private clouds, consumers have full control of their data.
+Especially for
+European data privacy laws, it is not negligible when data is stored abroad, and
+thus, under the law of foreign countries.
+However, its popularity has not been
+diminished due to the immense cost of switching to public clouds [23, 47].
+6
+
+Community clouds can be seen as a conglomerate of multiple organizations that
+merge their infrastructure with respect to a commonly defined policy, terms, and
+conditions beforehand [47].
+Public clouds represent the most used deployment models. Contrary to private ones,
+public clouds are fully owned by service providers such as businesses, academics, or
+government organizations. Consumers do not know where their data is distributed.
+In addition, contracts underlie custom policies [47].
+A hybrid cloud mixes two or more cloud infrastructures, such as private and public
+clouds. However, each entity keeps its core element. Hybrid clouds define “standard-
+ized or proprietary technology to enable data and application portability”[47].
+2.3 Honeypots
+The term “honeypot” has been established for more than two decades. 1997 was the
+first time that a free honeypot solution became public. Deception Toolkit (DTK),
+developed by Fred Cohen, released the first honeypot solution. However, the earliest
+drafts of honeypots are from 1990/91 and built the foundation for Fred Cohen’s
+DTK. Clifford Stoll’s book “The Cuckoo’s Egg”[66], and Bill Cheswick’s whitepaper
+“An Evening With Berferd”[7] describe concepts that are considered nowadays as
+honeypots [65]. A honeypot itself is a security instrument that collects information
+on buzzing attacks. It disguises itself as a system or application with weak links,
+so it gets exploited and gathers knowledge about the adversary. In 2002, a Solaris
+honeypot helped to detect an unknown dtspcd exploit. Interestingly, a year before
+in 2001, the Coordination Center of CERT4 shared their concerns regarding the
+dtspcd. Communities were aware that the service could be exploited to get access
+and remotely compromise any Unix system.
+However, such an exploit was not
+known during this time, and experts did not expect any in the near future. Luckily,
+early instances based on honeypot technologies could detect new exploits and avoid
+further incidents. Such events emphasize the importance of honeypots.
+2.3.1 Definition of Honeypots
+Many definitions for honeypots circulate through the web that causing confusion and
+misunderstandings. In general, the objective of a honeypot is to gather information
+about attacks or attack patterns [51]. Thus, contributing as an additional source of
+security measure. See subsection 2.3.3 for a detailed view regarding honeypots in
+the security concept. As Spitzner [65] has listed, the most misleading definitions:
+a honeypot is a tool for deception, it is a weapon to lure adversaries or a part of
+4Computer Emergency Response Team is an expert group that handles computer security
+incidents[31]
+7
+
+an intrusion detection system. In order to get a basic understanding, this section
+wants to exhibit some key definitions. Spitzner [65] defines honeypots as a “security
+resource whose value lies in being probed, attacked, or compromised”. Independent
+of its source (e.g., server, application, or router), he expects the instance to be
+probed, attacked, and eventually exploited.
+If a honeypot does not match this
+behavior, it will not provide any value. It is essential to mention that honeypots
+do not have any production value; thus, any communication that is acquired is
+suspicious by nature [65]. In addition, Spitzner [65] points out that honeypots are
+not bound to solve a single problem; hence, they function as a generic perimeter
+and fit into different situations.
+Such functions are attack detection, capturing
+automated attacks, or alert/warning generators. Figure 2.2 shows an example of
+how honeypots could be used in an IT infrastructure.
+In general, he differentiates two types of honeypots (i) production honeypots (ii) re-
+search honeypots. This categorization has its origin from Mark Rosch, a developer
+of Snort, during his work at GTE Internetworking [72].
+Production honeypots are the most common type of honeypots that people would
+think of. The objective is to protect production environments and mitigate the risk
+of attacks. Usually, production honeypots are easy to deploy within an organization.
+Mostly, low-interaction honeypots are chosen due to a significant risk reduction, so
+adversaries cannot exploit honeypots to attack other systems [65]. The downside
+of a low-interaction honeypot is a lack of information, which means only standard
+information like the origin of attacks or what exploits have been used can be collected
+[50]. On the contrary, insides about the communication of attackers or deployment of
+such attacks are unlikely to obtain, whereas research honeypots fulfill this objective
+[65].
+Research honeypots are used to learn more in detail about attacks. The objective
+is to collect information about clandestine organizations, new tools for attacks, or
+the origin of attacks [65, 50]. Research honeypots are unlikely suitable for produc-
+tion environments due to a higher risk increase. Facing an increase in deployment
+complexity and maintenance does not attract production usage either [65].
+It is worth mentioning that there is no exact line between research or production
+honeypots. A possible use case is a honeypot that functions as a production or a
+research honeypot. Due to the dynamic range in which they are applicable, it is
+difficult to distinguish them.
+In addition, Provos [55] adds a differentiation for the virtual honeypot framework
+and splits it into the following types:
+• Physical honeypots are “real machines on the network with its own Internet
+Protocol (IP) address” [55]
+• Virtual honeypots are “simulated by another machine that responds to network
+traffic sent to the virtual honeypot” [55]
+8
+
+Gateway
+Router
+Internet
+DMZ
+Internal
+Mail
+Web
+Honeypot
+A 
+Desktop
+Desktop
+Honeypot
+B
+Figure 2.2: Example of honeypots in a simplified network (derived from [65]). Each
+of the demilitarized zones (DMZs) and internal networks are separated
+by a router and a Layer-3 switch. In each network a honeypot is available
+(honeypot A, B). The red path symbolizes the path of an attacker coming
+from the gateway router.
+9
+
+2.3.2 Level of Interaction
+When building and deploying a honeypot, the depth of information has to be defined
+beforehand. Should it gather unauthorized activities, such as an nmap scan? Do
+you want to learn about buzzing tools and tactics? Each depth brings a different
+level of interaction because some information depends on more actions of adversaries.
+Therefore, honeypots differ in their level of interaction.
+Low-interaction honeypots provide the lowest level of interaction between an at-
+tacker and a system. Only a small set of services like Secure Shell (SSH), Telnet, or
+File Transport Protocol (FTP) are supported, contributing to the deployment time.
+In terms of risk, a low-interaction honeypot does not give access to the underlying
+OS which makes it safe to use in a production environment [65]. For example, us-
+ing an SSH honeypot with emulated services allows attackers to log in and execute
+commands by brute force or guesswork. The adversary will never gain more access
+because it is not a real OS. However, safety comes with the downside of less informa-
+tion. The collection is limited for the statistical purpose such as (i) time and data
+of attack (ii) source IP address and source port of the attack (iii) destination IP
+address and destination port of the attack [65, 50]. The transactional information
+can not be collected [65].
+A medium-interaction honeypot offers more sophisticated services with a higher
+level of interaction. It is capable of responding to specific activities. For example, a
+Microsoft IIS Web server honeypot could respond in a way that a worm is expecting.
+The worm would get emulated answers and could be able to interact with it in more
+detail.
+In this way, more severe information about the attack can be gathered,
+including privilege assessment, toolkit capture, and command execution Spitzner
+[65]. In comparison, medium-interaction honeypots allocate more time to install
+and configure [65, 50]. Also, more security checks have to be performed due to a
+higher interaction level than low-interaction honeypots [65].
+High-interaction honeypots represent a real OS to provide a full set of interactions to
+attackers [65]. They are so powerful because other production servers do not differ
+much from high-interaction honeypots. They represent real systems in a controlled
+environment [65, 50]. The amount of information is tremendous. It helps to learn
+about (i) new tools (ii) finding new bugs in the OS (iii) the black hat community [65].
+However, the risk of such a honeypot is extremely high. It needs severe deployment
+and maintenance processes; thus, it is time-consuming.
+2.3.3 Security concepts
+Security concepts are classified by Schneier [63] in prevention, detection, and reac-
+tion. Prevention includes any process that (i) discourages intruders and (ii) hardens
+systems to avoid any breaches. Detection scrutinizes the identification of attacks
+10
+
+Table 2.1: Distinction between security concepts based on areas of operations (de-
+rived from [51]).
+Objective
+Prevention
+Detection
+Reaction
+Honeypot
++
+++
++++
+Firewall
++++
+++
++
+Intrusion Detection Sys.
++
++++
++
+Intrusion Prevention Sys.
+++
++++
+++
+Anti-Virus
+++
+++
+++
+Log-Monitoring
++
+++
++
+Cybersecurity Standard
++++
++
++
+that threatens the systems’ (i) confidentiality (ii) integrity and (iii) availability. Re-
+action treats the active part of the security concept. When attacks are detected,
+it conducts reactive measures to remove the threat. Each part is designed to be
+sophisticated so that all of them contribute to a secure environment [51].
+Honeypots contribute to the security concept like firewalls, or intrusion detection
+systems (IDSs). However, honeypots add only a small value towards prevention
+because security breaches cannot be identified. Moreover, attackers would avoid
+wasting time on honeypots and go straight for production systems instead.
+Detection is one of the strengths of honeypots. Attacks often vanish in the sheer
+quantity of production activities. If any connection is established to a honeypot,
+it is suspicious by nature.
+In conjunction with an alerting tool, attacks can be
+detected.
+Honeypots strongly supply reaction tools due to their clear data. It is difficult to find
+attacks for further data analysis in production environments. Often data submerge
+with other activities, which complicates the process of reaction [51]. Nawrocki et al.
+[51] distinguish honeypots from other objectives such as firewall or log-monitoring.
+2.3.4 Value of Honeypots
+To assess the value of honeypots, this section looks at their advantages and disad-
+vantages [50, 39, 65].
+Advantages
+• Data Value: Collected data is often immaculate and does not contain noise
+from other activities. Thus, reducing the total data size and speeding up the
+analysis.
+11
+
+• Resources: Firewalls and IDS are often overwhelmed by the gigabits of traffic,
+thus, dropping network packets for analysis. This results in far less effective
+detection of malicious network activities. However, honeypots are indepen-
+dent of resources because they only capture their activities. Due to resource
+limitations, expensive hardware is not needed.
+• Simplicity: A honeypot does not require complex algorithms or databases. If
+a honeypot is too complex, it will lead to misconfigurations, breakdowns, and
+failures. The challenging research honeypots might come with an inevitable
+increase in complexity in maintenance.
+• Return on Investment: Capturing attacks immediately informs users that sus-
+picious activities occur on the infrastructure. This helps to demonstrate their
+value and contributes to new investments in other security measurements.
+In addition, Nawrocki et al. [51] listed four more advantages of honeypots:
+• Independent of Workload: Honeypots only process traffic directed to them.
+• Zero-Day-Exploit Detection: It helps to detect unknown strategies and zero-
+day-exploits.
+• Flexibility: Well-adjusted honeypots for various specific tasks are available.
+• Reduced False Positives and Negatives: Any traffic or connection to a honey-
+pot is suspicious. Client-honeypots verify such attacks based on system state
+changes. This results in either false positive or false negatives.
+Disadvantages
+• Narrow Field of View: Only direct attacks on honeypots can be investigated,
+whereas attacks on the production system are not detected.
+• Fingerprinting: A honeypot often has a certain fingerprint that attackers can
+identify. Especially commercial ones can be detected by their responses or
+behaviors.
+• Risk to the Environment: Using honeypots in an environment always increases
+risk. However, it depends on the level of interaction.
+12
+
+Gateway
+Router
+Internet
+Honeynet
+Internal
+Honeypot
+Honeypot Honeypot
+Mail
+Web
+FTP
+Figure 2.3: Example of honeynets in a simplified network (derived from [65]). This
+network presents the honeynet consisting of several other honeypots on
+the left. On the right, the network presents a common subnet consisting
+of mail, web, and FTP server.
+2.3.5 Honeynets
+Instead of having single honeypots that can be attacked, a honeynet offers a complete
+network of standard production systems such as you would find in an organization
+[64]. Those systems are high-interaction honeypots, thus, allowing them to fully
+interact with the OS and applications. The key idea is that an adversary can probe,
+attack, and exploit these systems so that the maintainer can derive interaction
+within this network [65, 64]. It should be mentioned that a honeynet has to be
+protected by firewalls. For example, Figure 2.3 represents such a honeynet within
+an organization.
+Compared to a traditional honeypot, the most significant value of honeynets is the
+usage of proper production systems. Black hats often do not know that they attack
+13
+
+a honeynet, thus, adding value to prevention. However, the downsides are the high
+complexity and maintenance needed to keep a honeynet running [65].
+2.3.6 Legal Issues
+Considering questions related to legal issues of honeypots can easily exceed this
+thesis. In this regard, this section restricts the study to the country the author
+resides in. Thus, only the European Union (EU) regulations, EU directives, and
+international agreements are considered. Honeypots collect (i) content data that
+is used for communication, and (ii) transactional data that is used to establish
+the connection.
+Sokol et al. [64] studied the legal conditions for data collection
+and data retention. They have concluded that administrators of honeypots have a
+legal ground of legitimate interest to store and process personal data, such as IP
+addresses. Moreover, for production honeypots, the legitimate interest is to secure
+services. Regarding the length of data retention, the principle of data minimization
+has to be considered, which means there is no clear answer. Any published data of
+research honeypots needs to be anonymized.
+14
+
+Chapter 3
+Analyze Honeypot Attacks in the
+Cloud
+Attacks from the Internet often originate from bots. A bot, short for “robot”, is an
+automated process that interacts with different network services. Despite good in-
+tentions, bots can be used for malicious purposes. Mostly, bots try to self-propagate
+malware across the Internet and try to capture hosts that merge into a botnet [29].
+Recently, Universities in Germany received more cyberattacks than ever, respec-
+tively increasing their costs for damage repairs. Honeypots are a good solution to
+catch attackers and learn from their exploits. However, it is not clear whether hon-
+eypots are an appropriate countermeasure to prevent such damage in the age of
+bots. Following the rise of cyberattacks, this chapter introduces a method to collect
+and analyze cyberattacks in a cloud environment. It further proposes an answer if
+honeypots are helpful to detect bot activities.
+3.1 Introduction
+As previously mentioned in section 2.2, using cloud resources is becoming the go-to
+option for new services and applications. Kelly et al. [40] thoroughly investigated
+honeypots on Azure, Amazon Web Services (AWS), and Google Cloud Platform
+(GCP). Consequently, this chapter presents their results briefly to compare them
+with the ones heiCLOUD achieves.
+The results are collected by T-Pot version
+20.06.0 for three weeks. In addition, Kelly et al. [40] considered different server
+geographical locations. They have collected data from East US, West Europe, and
+Southeast Asia. Table 3.1 shows the results presented by Kelly et al. [40]. Dionaea
+(a honeypot to capture malicious payload), Cowrie (SSH and Telnet honeypot), and
+Conpot (industrial honeypot for ICS and SCADA) are the most attacked honey-
+pots in comparison to the others. Regarding AWS, Dionaea accounts for 91% of
+the total attacks, Glutton and Cowrie are minor with 5%, and 2%. Interestingly,
+Cowrie reported several attacks related to the COVID-19 pandemic to enable social
+15
+
+engineering methods. In contrast to AWS, Cowrie logged the majority of attacks
+with 51% on GCP. Besides several automated attacks trying to log in with default
+credentials, adversaries tried to gather information about the GPU architecture,
+scheduled tasks, and privilege escalation. Microsoft Azure reflects nearly the same
+results as the other two cloud providers beforehand.
+Table 3.1: Overview of attacks on cloud providers. For a better overview, only the
+three most attacked honeypots are listed. The remaining honeypots are
+listed in the column named "others".
+Provider
+Honeypot
+In Total
+Dionaea
+Cowrie
+Glutton
+others
+Amazon Web Services
+228,075
+4,503
+11,878
+3,688
+248,144
+Google Cloud Platform
+162,570
+297,818
+84,375
+36,403
+581,116
+Microsoft Azure
+308,102
+9,012
+17,256
+6,365
+340,735
+The overall results show an average ratio of 55,000 attacks per day, summing up
+to roughly 1.17 million in total.
+Similar results for different regions could have
+been reproduced. Their results clearly show the Europe, US, and Asia disparity.
+An important question that Kelly et al. [40] answered is if attackers target services
+on cloud providers based on the cloud providers’ market share. The study could
+not confirm this assumption because Google Cloud received most of the attacks
+with the smallest market share. In total, most of the attacks are originated from
+Vietnam, Russia, the United States, and China. Due to technologies such as VPN
+or Tor, the geolocation only indicates the last node so that location data might be
+distorted. Across all providers, roughly 80% of the source IP addresses had a bad
+reputation (identified by Suricata) and could have been filtered by the organization.
+The operating devices used for attacking the services are mostly Windows 7 or 8 and
+different Linux kernels and distributions. Windows devices target vulnerabilities in
+remote desktop sharing software. Such vulnerabilities are (i) CVE-2006-2369[14]
+(RealVNC) in the US region, (ii) CVE-2001-0540[11] (Remote Desktop Protocol
+(RDP)) in EU and Asia regions, (iii) CVE-2012-0152[15] (RDP) in the Asia region,
+and (iv) CVE-2005-4050[13] (Voice over Internet Protocol (VoIP)) in EU region.
+In addition, attackers were also capable of disguising any fingerprinting activity of
+P0f.
+This chapter compares the findings Kelly et al. [40] claimed in the paper “A Com-
+parative Analysis of Honeypots on Different Cloud Platforms” with ours using the
+Heidelberg University’s cloud solution. First, a short introduction of heiCLOUD
+is given, followed by a closer lookup of the T-Pot used to acquire data. Lastly, it
+presents the results and does a thorough comparison closing up with a discussion
+based on a technical report of Cambridge University.
+16
+
+3.2 Methodology
+The foremost goal is to track as many attacks as possible. Figure 3.1 sketches the
+concept to achieve this goal to gather various attacks from the Internet. Honeypots
+should be deployed on a single instance, and their data or log files are stored in a
+database. The attacks are analyzed with the help of data visualization tools. For
+security reasons, honeypots should run in a virtualized environment to avoid harming
+the host system. The host machine runs on a Debian distribution. The instance
+runs on heiCLOUD, a cloud service provided by Heidelberg University. It is capable
+of 16 GB of RAM, 8 vCPUs, and volatile memory of 30 GB. In addition, it mounts
+a 125 GB permanent volume to store the data securely. In the very early stage
+of this chapter, different approaches to achieve this goal have been compared. For
+example, native implementation approaches, additional frameworks, and ready-to-
+use solutions have been evaluated. However, the T-Pot, developed by Telekom, offers
+a profoundly ready-to-use solution with significant advantages. It combines several
+honeypots with various analytic tools to trace the newest attacks. Furthermore, it
+helps to compare the findings with the ones Kelly et al. [40] claim.
+Running the instance and exposing it to the Internet needs some adjustments be-
+forehand. Therefore, a virtual network with subnet 192.168.145.0/24 has been
+created wherein the IP address 192.168.145.4 is assigned to the instance. The
+instance is accessible from the outside with a floating IP address 129.206.5.74.
+Access rules are similar to a stateless firewall, and thus, do not block any attacks.
+Ports 1−64000 are exposed and can be attacked by anyone. Ports higher than 64000
+are only accessible through the university network 129.206.0.0/16 or eduroam
+147.142.0.0/16 and should provide a basic authentication with username and
+password.
+3.2.1 heiCLOUD
+University Computing Center Heidelberg offers a “IaaS specially tailored for higher
+education and research institutions”[69] called heiCLOUD. It supplies multiple de-
+partments at Heidelberg University with storage, virtual machines, or network com-
+ponents. In addition, heiCLOUD is a DFN1 member and offers others to use their
+services. As stated on their information website[68], it (i) is capable of freely manage-
+able IT resources, (ii) beholds a stable and fast connection, (iii) ensures high avail-
+ability and scalability, (iv) has freely selectable VM operating systems, and (v) has
+a transparent payment model [68]. Users can easily create their network areas and
+manage their space individually based on the open-source application OpenStack.
+Unlike well-known cloud providers, heiCLOUD servers are located within Germany,
+1German National Research and Education Network is the communications network for Science
+and research in Germany
+17
+
+heiCLOUD
+Network
+Internet
+Gateway
+Switch
+stores logs
+runs
+database
+(persistence 90 days) 
+m1.xlarge
+Debian 10, Buster
+Honeypot
+Honeypot
+Honeypot
+Figure 3.1: Concept to collect honeypot attacks. The instance size is referred to the
+available resources of OpenStack. The network is an encapsulated subnet
+with a switch for incoming and outgoing connections. The database is
+independent of the instance and could run on a separate host.
+18
+
+thus, abide by the European data privacy law. HeiCLOUD has never considered
+implementing honeypots for additional cybersecurity measurements.
+3.2.2 T-Pot
+To be able to compare the results with Kelly et al. [40], the same approach to
+capture recent cyberattacks is used. The T-Pot solution, a mixture of Telekom and
+Honeypot, stands out with its sheer quantity of various honeypots. It requires at
+least 8 GB of RAM and a minimum of 128 GB of hard drive storage. Based on a
+Debian 10 Buster distribution, it relies on Docker to run their services [25]. T-Pot
+has to be deployed in a reachable network where intruders are expected. Either
+Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) traffic
+are forwarded without filtering to the network interface, or it runs behind a firewall
+with forwarding rules. Specified ports for attackers are 1-64000; higher ports are
+reserved for trusted IPs; thus, a reverse proxy asks for basic authentication. All
+daemons and tools run on the same network interface, but some are encapsulated
+in their own Docker network.
+The lightweight virtualization technology Docker
+uses containers to run on the host system [9].
+Unlike virtual machines, Docker
+reduces overhead with the downside of a greater attack surface. To mitigate attacks,
+Docker wraps containers in an isolated environment. This is achieved by restricting
+the kernel namespace and control groups (cgroups) [9]. Figure 3.2 visualizes the
+technical concept of T-Pot. Each service has dedicated ports or port ranges that
+are exposed. Attackers can communicate either with TCP or UDP. All honeypots
+and tools create log files used to get any knowledge about attackers. In order to
+view and trace current attacks, T-Pot uses the ELK stack. ELK is the acronym
+of Elasticsearch, Logstash, and Kibana [26].
+The search engine Elasticsearch is
+based on the Lucene library. It is multitenant-capable and offers full-text search
+via HTTP. Logstash is used to feed Elasticsearch.
+In general, it offers an open
+server-side data processing pipeline that helps to send data from multiple sources
+to an Elasticsearch node. Kibana is the primary data visualization tool. It enables
+users to create plots and dashboards, crawl Elasticsearch, and trace the system’s
+health.
+All logs of the honeypots and tools are forwarded to the search engine
+Elasticsearch by Logstash. The ELK stack is not directly exposed to the Internet;
+thus, authentication is unnecessary. Users can monitor all log files with Kibana
+by pre-defined dashboards or custom search queries. In addition, T-Pot features
+different services types, namely (i) standard, (ii) sensor, (iii) industrial, (iv) collector,
+(v) next generation, and (vi) medical.
+Each service type has a different set of
+honeypots and tools tailored to its core idea. T-Pot feeds their data to an external
+Telekom service; however, this data submission can be turned off. The latest version,
+20.06.0, has been used in this chapter. Newer versions might be available by the
+end of this study and could differ from this.
+19
+
+https://IP:64295
+basic authentication 
+https://IP:64297
+basic authentication
+IP:1-64000
+no authentication 
+FATT
+p0f
+Suricata
+NSM
+host
+Heimdall /
+NGINX 
+ADBHoney
+network
+Cisco ASA
+Honeypot 
+network
+Citrix
+Honeypot 
+network
+Conpot
+network
+Cowire
+network
+Dicompot
+network
+ElasticPot
+network
+Glutton
+network
+Honeytrap
+network
+IPPHoney
+network
+Mailoney
+network
+Medpot
+network
+RDPY
+network
+Honeypots
+Host Network Interface
+ElasticSearch
+Logstash
+Kibana
+Head
+ELK
+localhost
+localhost
+CyberChef
+network
+Tools
+Spiderfoot
+network
+EWS
+Poster 
+network
+Cockpit
+Debian 10, Buster
+Hardware Requirements:
+RAM  8 GB <
+SSD 128 GB < 
+Figure 3.2: T-Pot architecture derived from [52].
+Honeypots are encapsulated in their network.
+NSM runs on the host
+network, and thus, receives every packet. ELK and tools run on localhost and are accessible through NGINX.
+The Cockpit application is a web-based graphical interface for servers.
+20
+
+Honeypots
+T-Pot consists of 20 honeypots. Albeit the sheer quantity of it, a short explanation
+is given. In addition, Table 3.2 gives a quick overview of all available honeypots in
+conjunction with (i) the port they are running on, (ii) their interaction level, and
+(iii) a short description.
+ADBHoney [8] is a low-interaction Android Debug Bridge (ADB) honeypot over
+TCP/IP. The importance of it lies in the ADB protocol that is used for debugging
+and pushing content to an Android device. However, unlike a Universal Serial Bus
+(USB) connection, it does not support any kind of ample mechanisms of authenti-
+cation and protection. By exposing the ADB service over any port, an adversary
+could connect and exploit it. ADBHoney is designed to catch malware that has been
+pushed onto devices.
+Cisco Adaptive Security Appliance (ASA) [57] is a low-interaction honeypot
+that detects CVE-2018-0101[16]. It is a vulnerability that could allow an unau-
+thenticated, remote attacker to cause a reload of the affected system and remotely
+execute code. This can be achieved by flooding a webvpn-configured interface with
+crafted Extensible Markup Language (XML) packets. Consequently, the attacker
+obtains full control by executing arbitrary code.
+Citrix Application Delivery Controller (ADC) honeypot [34] detects and
+logs CVE-2019-19781[18] scans and exploitation attempts. This vulnerability al-
+lows adversaries to perform directory traversal attacks. Files are accessible by path
+strings to denote the file or directory. In addition, some file systems include spe-
+cial characters to traverse the hierarchy easily. Attackers take advantage of it by
+combining special characters to get access to restricted areas. [30]
+Conpot [58] is a low-interaction industrial honeypot for Industrial Control System
+(ICS), and Supervisory Control and Data Acquisition (SCADA). It provides a variety
+of different standard industrial control protocols. An adversary should be tricked
+by the complex infrastructure and lured into attacks. In addition, a custom human-
+machine interface can be connected to increase the attack surface. By randomly
+delaying the response time, Conpot tries to emulate a real machine handling a
+certain amount of load.
+Cowrie [53] is a medium- to high-interaction SSH and Telnet honeypot. It offers to
+log brute-force attacks and shell interactions with attackers. In medium-interaction
+mode, Cowrie emulates a Unix shell in Python, whereas in high-interaction mode,
+it proxies all commands to another system.
+DDoSPot [22] is a low-interaction honeypot to log and detect UDP-based Dis-
+tributed Denial of Service (DDoS) attacks. It is a platform used to support various
+plugins for different honeypot services and servers. Currently, it supports Domain
+21
+
+Name System (DNS), Network Time Protocol (NTP), Simple Service Discovery Pro-
+tocol (SSDP), Character Generator Protocol (CHARGEN), and random/mock UDP
+server.
+Dicompot [41] is a low-interaction honeypot for the Digital Imaging and Commu-
+nications in Medicine (DICOM) protocol. As with other honeypots before, it mocks
+a DICOM server in Go to collect logs and detect attacks.
+Dionaea [24] is a medium-interaction honeypot that tries to capture malware copies
+by exposing services. It supports various protocols such as FTP, Server Message
+Block (SMB), and HTTP. Several modules can be integrated to work with Dionaea
+for further malware results, such as VirusTotal.
+Elasticpot [4] is a low-interaction honeypot for Elasticsearch, a search engine based
+on the Lucene library.
+Glutton [59] is a generic low-interaction honeypot that works as a man-in-the-
+middle (MITM) for SSH and TCP. However, lacking documentation does not provide
+a deeper insight into this honeypot.
+Heralding [71] is a credential catching honeypot for protocols like FTP, Telnet,
+SSH, HTTP, or Internet Message Access Protocol (IMAP).
+HoneyPy [32] is a low to medium-interaction honeypot that supports several pro-
+tocols such as UDP or TCP. New protocols can be added by writing a custom
+plugin for them. HoneyPy gives the freedom of quickly deploying and extending
+honeypots.
+HoneySAP [32] is a low-interaction honeypot tailored for SAP services.
+Honeytrap [75] is a low-interaction honeypot network security tool. As stated by
+Werner [75], Honeytrap is vulnerable to buffer overflow attacks.
+IPPHoney [5] is a low-interaction Internet Printing Protocol (IPP) honeypot.
+Mailoney [46] is a low-interaction Simple Mail Transfer Protocol (SMTP) honeypot
+written in Python.
+MEDpot [62] is a low-interaction honeypot focused on Fast Healthcare Interoper-
+ability Resources (FHIR). It is a standard description data format to transfer and
+exchange medical health records.
+RDPY [54] is a low-interaction honeypot of the Microsoft RDP written in Python.
+It features client and server-side, and it is based on the event-driven network en-
+gine Twisted. It supports authentication over Transport Layer Security (TLS) and
+Network Level Authentication (NLA).
+SNARE and TANNER [60, 61] is a honeypot project. SNARE is an abbrevia-
+tion for Super Next-generation Advanced Reactive honEypot. It is a successor of
+22
+
+Glastopf, a web application sensor. In addition, it supports the feature of convert-
+ing existing web pages into attack surfaces. TANNER [61] can be seen as SNARES’
+brain. Whenever a request has been sent to SNARE, TANNER decides how the
+response should be.
+Tools
+T-Pot integrates tools to screen network traffic and block DoS attacks.
+FATT [37] is used to extract metadata and fingerprints such as JA3 [2] and HASSH
+[38] from captured packets. JA3 is a method for “creating SSL/TLS client finger-
+prints” whereas HASSH is a network fingerprinting standard that is used to identify
+specific client and server SSH implementations. In addition, it features live network
+traffic. As noted by the author, FATT is based on a python wrapper for tshark,
+namely pyshark, and thus has performance downturns.
+T-Pot applies FATT on
+every request made on the host network.
+Spiderfoot [48] is an open-source intelligence automation tool that helps to screen
+targets to get information about what is exposed over the Internet. It can target
+different entities such as IP address, domain, hostname, or network subnet.
+In
+addition, it features more than 200 modules that can be integrated as an extension.
+T-Pot uses it to scan defensively and thus not include any other module.
+Suricata [67] is “a high performance IDS, intrusion prevention system (IPD) and
+network security monitoring (NSM) engine”. T-Pot lets Suricata analyze and assess
+any request made on the host network.
+P0f [77] is a fingerprinting tool that uses passive traffic fingerprinting mechanisms
+to check TCP/IP communications. T-Pot lets P0f passively check any request made
+on the host network.
+Endlessh [74] is an SSH server that sends an endless, random SSH banner. The
+key idea is to lock up SSH clients that try to connect to the SSH server. It low-
+ers the transaction speed by intentionally inserting delays. Due to the established
+connection before the cryptographic exchange, this module does not require any
+cryptographic libraries.
+HellPot [35] is an “endless honeypot”. If someone connects to this honeypot, it
+results in a memory overflow. Its key idea is to send an endless data stream to the
+attacker until its memory or storage runs out.
+23
+
+Table 3.2: Overview of all available honeypots of T-Pot with interaction level, port, and a short description. Ports are marked
+with either TCP or UDP; if a port misses any definition, both TCP and UDP are allowed.
+Honeypots
+Port
+Interaction-level
+Description
+ADBHoney [8]
+5555/TCP
+low
+ADB protocol honeypot
+Cisco ASA [57]
+5000/UDP, 8443/TCP
+low
+honeypot for CVE-2018-0101[16] de-
+tection
+Citrix honeypot [34]
+443/TCP
+low
+detects
+and
+logs
+CVE-2019-
+19781[18]
+scans
+and
+exploitation
+attempts
+Conpot [58]
+80, 102, 161, 502, 623, 1025, 2404,
+10001, 44818, 47808, 50100
+low
+industrial honeypot for ICS and
+SCADA
+Cowrie [53]
+2222, 23
+high
+SSH and Telnet honeypot
+DDoSPot [22]
+1112/TCP
+low
+log and detect UDP-based DDoS at-
+tacks
+Dicompot [41]
+1112/TCP
+medium
+honeypot for the DICOM protocol
+Dionaea [24]
+21, 42, 69/UDP, 8081, 135, 443, 445,
+1433, 1723, 1883, 1900/UDP,
+3306, 5060/UDP, 5061/UDP
+low
+capture malware copies
+Elasticpot [4]
+9200
+low
+honeypot for Elasticsearch
+Glutton [59]
+NFQ
+medium
+MitM proxy for SSH and TCP
+Heralding [71]
+21, 22, 23, 25, 80, 110, 143, 443,
+993, 995, 1080, 5432, 5900
+low
+credential catching honeypot
+HoneyPy [32]
+7, 8, 2048, 2323, 2324, 4096, 9200
+low
+extendable honeypot
+HoneySAP [32]
+3299/TCP
+low
+honeypot for SAP services
+Honeytrap [75]
+NFQ
+medium
+captures attacks via unknown proto-
+cols
+IPPHoney [5]
+631
+low
+IPP honeypot
+Mailoney [46]
+25
+low
+SMTP honeypot
+MEDpot [62]
+2575
+low
+FHIR honeypot
+RDPY [54]
+3389
+low
+Microsoft RDP honeypot
+SNARE/TANNER [60]
+80
+low
+web application honeypot
+24
+
+3.3 Results
+The T-Pot has been deployed for three weeks (from 26th of September to 16th of Oc-
+tober) and collected in total 607,747 attacks. Overall, RDPY (46.08%), Honeytrap
+(33.23%), and Cowrie (12.42%) received most of the attacks with a total amount of
+540,398 attacks. Figure 3.3 shows the distribution of honeypot attacks. The total
+numbers are based on Table 3.3.
+Adbhoney
+Ciscoasa
+CitrixHoneypot
+ConPot
+Cowrie
+Dicompot
+Dionaea
+ElasticPot
+Heralding
+Honeysap
+Honeytrap
+Medpot
+Rdpy
+Tanner
+Honeypots
+0
+50000
+100000
+150000
+200000
+250000
+300000
+350000
+Number of Attacks
+Figure 3.3: Distribution of honeypot attacks. Timestamp; 26th of September to 16th
+of October. A description of each honeypot can be found in section 3.2.2.
+What is striking is the large disparity between the previously mentioned attacks
+on AWS, GCP, and Azure. Especially with the honeypot Dionaea, it is unclear
+why only 2,368 attacks have been performed. 96% of IP addresses connected to
+Dionaea are known attackers, and 70% were acquired on port 81, unofficially known
+for Tor routing. Neither any malware nor suspicious payload could be identified.
+An assumption is that the packets run through a static filter. Heidelberg has a
+centralized stateless firewall, indicating that specific ports or protocols are excluded.
+A nmap TCP SYN scan (nmap -sS -A 129.206.5.74) has been performed to prove
+this assumption that ports are excluded. The result clearly shows that port 139
+for SMB is filtered, although the access security explicitly allows it. The stateless
+firewall runs in front of heiCLOUD and filters many ports, including 113. Based
+on this, it can be assumed that most of the attacks on Dionaea are carried out via
+25
+
+SMB, which would explain the total number of attacks. The administrator of the
+university firewall had been consulted to exclude the T-Pot instance to validate if the
+actual number is even higher without any packet filter in front of it. Respectively, no
+stateless packet filter has been applied to the T-Pot for three weeks (2nd of December
+until 23rd of December). It could identify a drastic increase in Dionaea attacks with
+a total number of 213,053. Overall, 93% of all attacks are on the SMB protocol
+followed by many database protocols such as MongoDB and MSSQL. This confirms
+the assumption that a higher total number of attacks would be the result without
+the packet filter in front of the instance.
+Comparing the number with Kelly et al. [40] it shows that Dionaea attacks surpass
+every other cloud provider. However, Dionaea attacks will not be included in later
+results because usually, a server is not allowed to be excluded from the university
+firewall. Only for this research purpose to assess the effect of the packet filter has
+an exclusion been granted.
+25000
+50000
+75000
+100000
+125000
+150000
+175000
+Figure 3.4: Attack distribution of T-Pot. The USA, Russia, China, and Germany
+are the most attacking countries. Timestamp; 26th of September to 16th
+of October.
+Logstash uses GeoLite2 to resolve the source IP address with information such as
+location, Autonomous System Number (ASN), continent code, country name, and
+Autonomous System (AS) organization. Figure 3.4 indicates the geographical lo-
+cation of connections acquired to any honeypot. Most attacks are originated from
+the United States, Germany, Russia, and China. Large security scans of DFN or
+Baden-Württembergs extended LAN (BelWÜ) pushes Germany to second place;
+therefore, Germany can be considered negligible. On the contrary, the geographical
+location of an IP address merely indicates the true origin. Due to technologies like
+VPN or Tor, the last known node of an IP address could be spoofed, and thus as
+stated by Kelly et al. [40], would remain insufficient to use. Hence, no one should
+rely on geographical information.
+Attacks are not equally distributed among all honeypots, and thus, different proto-
+cols and applications receive more attention than others. Figure 3.5 shows the time-
+26
+
+2021-09-26
+2021-09-30
+2021-10-04
+2021-10-08
+2021-10-12
+Timestamp
+0
+10000
+20000
+30000
+40000
+Number of Attacks
+Adbhoney
+Cowrie
+Heralding
+Honeytrap
+Rdpy
+Figure 3.5: Attack histogram of T-Pot. Only the five most attacked honeypots are
+considered. Timestamp; 26th of September to 16th of October. A de-
+scription of each honeypot can be found in section 3.2.2.
+line of attacks that are executed on our instance separated by honeypots. RDPY,
+Honeytrap, and Cowrie are the most attacked honeypots. The high peak of Honey-
+trap in the middle indicates a full nmap scan from Germany that has been done to
+get an insight of the packet filtering at the Heidelberg University. It identifies a bias
+towards remote desktop protocol attacks, shell-code exploitations, and commands
+to retrieve information about the CPU, scheduled tasks (cat /proc/cpuinfo, or
+crontab), or privilege escalation.
+Suricata registered several alerts and CVEs. The vast majority of alerts are RDP-
+related policies, Virtual Network Computing (VNC) authentication failures, and
+nmap scans. Most used vulnerabilities are (i) CVE-2001-0540[11] which is a memory
+leak in terminal servers in Windows NT and Windows 2000 causing a denial of
+service (memory exhaustion) by malformed RDP requests, (ii) CVE-2006-2369[14]
+which is a RealVNC vulnerability allowing hackers to bypass authentication, and
+(iii) CVE-2012-0152[15] which enables attackers for RDP in Microsoft Windows
+Server 2008 R2 and R2 SP1 and Windows 7 Gold and SP1 to cause a denial of
+service by sending a series of crafted packets. As derived from Figure 3.6, the T-Pot
+has not received many attacks in the first week. Starting from the 28th of September,
+the number of alerts is skyrocketing. This would indicate that bots crawl IP address
+ranges to find new machines and probe them. Interestingly, zero-day exploits like
+the Apache vulnerability [20] that came with version 2.49.0 got registered in CVE on
+27
+
+2021-09-26
+2021-09-30
+2021-10-04
+2021-10-08
+2021-10-12
+Timestamp
+0
+20000
+40000
+60000
+80000
+100000
+120000
+140000
+Number of Attacks
+Misc activity
+Misc Attack
+Generic Protocol Command Decode
+Attempted Information Leak
+Attempted Administrator Privilege Gain
+Figure 3.6: Suricata results of T-Pot. Displays the five most listed alert categories.
+Timestamp; 26th of September to 16th of October.
+the 6th of October and immediately recognized by Suricata on the 15th of October.
+Attackers could perform a remote code execution using path traversal attacks when
+the Common Gateway Interface (CGI) scripts of Apache are enabled. The logs could
+trace back similar attacks like /cgi-bin/.\%2e/\%2e\%2e/bin/sh until the 7th of
+October, leaving an even smaller time frame to adapt to new exposures. This shows
+how fast bots adapt to new vulnerabilities to compromise more systems.
+The results from RDPY in Figure 3.7 backups the assumption that attacks originate
+from bots. It shows that only a small margin represents unique source IP addresses.
+The rest of the attacks result in either a bad reputation, bot, crawler, or known at-
+tacker. Figure 3.6 shows the distribution of alert categories that Suricata identified.
+Respectively, misc activities sum up to roughly 1.5 million entries, RDP related
+alerts account for two-thirds of it. Several RDP attacks from 2021 back to 2001
+had been executed on the T-Pot. Respectively, CVE-2012-0152 and CVE-2001-0540
+coincide with the ones Kelly et al. [40] claim.
+For NFQ related attacks, Honeytrap could identify three major services that are
+not provided by default. Honeytrap functions as a honeypot to provide a service
+on ports that are not specified by default. NFQ intercepts incoming TCP connec-
+tions during the TCP handshake, and Honeytrap provides a service for it. Most of
+these interceptions are made on (i) port 5038, which is used by a machine learning
+database called MLDB, (ii) port 5905, which an Intel Online Connect Access uses on
+Windows machines, and (iii) port 7070 which is used by Apple’s QuickTime stream-
+ing server (RTSP). Nearly all ports attacks focused on RDP connection attempts
+(Cookie: mstshash=Administr). However, 94% of all connected IP addresses on
+Honeytrap are resolved as known attackers.
+28
+
+2021-09-29
+2021-10-03
+2021-10-07
+2021-10-11
+2021-10-15
+Timestamp
+0
+5000
+10000
+15000
+20000
+25000
+30000
+35000
+Number of Attacks
+Attacks
+Unique Src IPs
+Figure 3.7: RDPY attacks are separated into attacks and unique source IP addresses.
+Timestamp; 26th of September to 16th of October. A description of the
+honeypot can be found in section 3.2.2.
+29
+
+2021-09-29
+2021-10-03
+2021-10-07
+2021-10-11
+2021-10-15
+Timestamp
+0
+500
+1000
+1500
+2000
+2500
+3000
+3500
+Number of Attacks
+5038
+5901
+6379
+7070
+8000
+Figure 3.8: Honeytrap results of T-Pot. Timestamp; 26th of September to 16th of
+October. A description of the honeypot can be found in section 3.2.2.
+2021-09-26
+2021-09-30
+2021-10-04
+2021-10-08
+2021-10-12
+Timestamp
+0
+200
+400
+600
+800
+Number of Attacks
+22
+23
+80
+443
+Figure 3.9: Cowrie results of T-Pot. Timestamp; 26th of September to 16th of Octo-
+ber. A description of the honeypot can be found in section 3.2.2.
+30
+
+The third most compromised honeypot is Cowrie, with a strong bias towards SSH
+and FTP. Figure 3.9 shows all attacks executed on Cowrie separated by their port.
+Respectively, SSH port 22 is the most considered port, resulting in high use for
+privilege escalation. Besides using default credentials to log in (username: root,
+password: root, see Figure 3.10 for top 10 credentials), adversaries used various
+commands to retrieve any information about the host system (nproc;uname -a,
+cat /proc/cpuinfo). A unique information gathering attack could be identified
+that has been widely used on the T-Pot.
+Listing 3.1 shows all shell commands
+that are executed. Attackers try to gain knowledge about running processes on the
+system (/bin/busybox). Interestingly, crypto mining attacks are getting more at-
+tractive to criminals. For example, XMRig has been the most downloaded malware
+for cryptocurrency mining. Some adversaries even executed complex tailored shell
+commands to exploit the host machine as a crypto miner (Listing 3.2). It is not
+surprising that such attacks gain attraction concerning the current time. Attack-
+ers could exploit machines for crypto mining in order to earn more money. This
+looks more appealing than acquiring mining machines and hijacking electricity from
+surrounding apartments.
+root
+user
+admin
+!root
+blank
+pi
+0
+ubuntu
+test
+guest
+Username
+0
+1000
+2000
+3000
+4000
+5000
+6000
+7000
+Number of Usage
+(a) Cowrie username credentials
+1
+123456
+1234
+!ishtar
+x
+blank
+0
+123
+admin
+root
+Password
+0
+200
+400
+600
+800
+Number of Usage
+(b) Cowrie password credentials
+Figure 3.10: Cowrie top 10 credentials used on T-Pot. Timestamp; 26th of Septem-
+ber to 16th of October. A description of the honeypot can be found in
+section 3.2.2.
+P0f identified different Windows versions and Linux distributions in conjunction
+with various SSH clients to compromise the T-Pot. Like Kelly et al. [40] presented,
+Windows 7 or 8 and Windows NT Kernel are the most used OS with 81%. Unfor-
+tunately, disguising OS fingerprinting activities account for 84% of all fingerprints.
+Lastly, the results are cleaned up and all IPs from DFN and BelWÜ are excluded.
+Both scan frequently and check if any vulnerability exists. This distorts the findings,
+and thus, they have been filtered based on their subnet addresses. However, the re-
+sults show no notable changes. The total number of attacks was hardly influenced
+by it. This indicates that these scans do not greatly interfere with the findings.
+31
+
+On average, heiCLOUD has received 55.83% more than Azure, GCP, and AWS.
+Attacks on Cowrie, RDPY, and Honeytrap are the most compromised honeypots.
+In contrast to Kelly et al. [40], Dionaea and Glutton used to be the most considered
+honeypots for adversaries. It can be assumed that attacks by bots had increased
+significantly since last year when Kelly et al. [40] did their research. Respectively,
+one unresolved question is if other cloud providers filter their network traffic. It
+would explain the major difference between Heidelberg University and the big tech
+companies. The cause for such an increase remains doubtful. One explanation could
+root back to the Corona pandemic and the skyrocketing increase in home office ac-
+tivities. Related to that is a higher usage in screen sharing software. Considering the
+BSI2, report for cybersecurity 2021 [6], they revealed an increase of attack surfaces
+during the pandemic. Respectively, the IT infrastructure could not keep up with
+this fast change and widen the company’s attack surface. Their conclusion overlays
+our assumption that attackers took advantage and increased their activities. This
+phenomenon shows that nearly all attacks originate from bots that scan through
+IP address ranges. In total, 73% of all IP addresses are unresolved. The known
+attacker reputation represents the largest part of resolved IP addresses with 23%.
+Fortunately, such reputations could technically be filtered by an organization’s fire-
+wall and would lower the chance of an exploit. Interestingly, after three weeks, the
+number of attacks originating from China decreased to almost zero percent. This
+might indicate that the honeypot has been exposed, and further attacks represent a
+risk of revealing their compromises. However, this assumption cannot be confirmed
+due to the lax geographical reliability of IP addresses.
+Our results emphasize the importance of honeypots. It gives a proper security mea-
+sure of an IT infrastructure and helps to identify potential leaks or vulnerabilities.
+Moreover, it shows that T-Pot helps detect recent bot activities and gives an outlook
+on the newest trends of attacks.
+3.4 Discussion
+One downside of T-Pot is the static hostname representation of Cowrie.
+It al-
+ways returns #1 SMP Debian 3.2.68-1+deb7u1 (uname -a) as hostname informa-
+tion, leaving a tiny footprint when bots crawl through the web. A random choice of
+hostname information could harden Cowrie from being exposed. Next, if attackers
+scan open ports on T-Pot, it might be suspicious when many ports with services are
+open. From a technical perspective, bots could check this state if it is uncommon
+and thus, exclude T-Pot from being probed. However, T-Pot includes reasonable
+preventions like a random hostname and scheduled tasks. Another major drawback
+2The Federal Office for Information Security is responsible for managing communication security
+for the German government. Each year they publish a report for recent cybersecurity threats.
+32
+
+Table 3.3: Overview of attacks on heiCLOUD, AWS, GCP, and Azure.
+Only the top 10 most attacked honeypots are
+considered. “-” entails that a honeypot is not part of the top 10. The red and green arrows indicate whether
+heiCLOUD received more or fewer attacks than the other cloud providers on average .
+Honeypots
+BASIS
+comparison
+heiCLOUD
+AWS
+GC
+Azure
+Number
+Pct.
+Number
+Pct.
+Number
+Pct.
+Number
+Pct.
+ADBHoney
+9,302
+1.65%
+↑
+413
+0.17%
+2,497
+0.43%
+442
+0.13%
+Cisco ASA
+674
+0.11%
+↑
+260
+0.10%
+750
+0.13%
+134
+0.04%
+Citrix honeypot
+1,121
+0.18%
+-
+-
+-
+-
+-
+-
+Conpot
+615
+0.10%
+-
+-
+-
+-
+-
+-
+Cowrie
+75,511
+11.97%
+↓
+4,503
+1.81%
+297,818
+51.25%
+9,012
+2.64%
+DDoSPot
+0
+0%
+-
+-
+-
+-
+-
+-
+Dicompot
+22
+0%
+-
+-
+-
+-
+-
+-
+Dionaea
+2,368
+0.40%
+↓
+228,075
+91.91%
+162,570
+27.98%
+308,102
+90.42%
+Elasticpot
+385
+0.06%
+-
+-
+-
+-
+-
+-
+Glutton
+0
+0%
+↓
+11,878
+4.79%
+84,375
+15.52%
+17,256
+5.06%
+Heralding
+35,680
+4.34%
+↑
+1,885
+0.76%
+12,255
+2.11%
+3,370
+0.99%
+HoneyPy
+0
+0%
+↓
+172
+0.07%
+2,149
+0.37%
+497
+0.15%
+HoneySAP
+15
+0%
+-
+-
+-
+-
+-
+-
+Honeytrap
+201,949
+32.01%
+-
+-
+-
+-
+-
+-
+IPPHoney
+0
+0%
+-
+-
+-
+-
+-
+-
+Mailoney
+0
+0%
+↓
+720
+0.29%
+9,419
+1.62%
+146
+0.04%
+MEDpot
+2
+0%
+-
+-
+-
+-
+-
+-
+RDPY
+280,040
+49.15%
+↑
+100
+0.04%
+7,916
+1.36%
+1,463
+0.43%
+SNARE/TANNER
+63
+0.02%
+↓
+138
+0.06%
+1,367
+0.24%
+313
+0.09%
+In total
+607,747
+100%
+248,144
+100%
+581,116
+100%
+340,735
+100%
+33
+
+is the latest endeavor to detect honeypots on the transport level. As recently inves-
+tigated by Vetterl [72], detecting honeypots is becoming easier due to a fatal flaw
+in the underlying protocol implementation. Vetterl [72] states that attackers always
+try to prevent their methods, exploits, and tools from being divulged. Therefore,
+detecting honeypots before attacking them strongly motivates black hats. Chapter 5
+will present a way to avoid such fingerprint activities with the honeypot Cowrie.
+Listing 3.1: Cowrie attack to gather various information about the system.
+1
+enable
+2
+system
+3
+shell
+4
+sh
+5
+cat /proc/mounts; /bin/busybox
+$PROCESS_NAME
+6
+cd /dev/shm; cat .s || cp /bin/echo .s; /bin/busybox
+�→ $PROCESS_NAME
+7
+tftp; wget; /bin/busybox
+$PROCESS_NAME
+8
+dd bs=52 count =1 if=.s || cat .s || while read i; do echo
+�→
+$i; done < .s
+9
+while read i
+10
+/bin/busybox
+$PROCESS_NAME
+11
+rm .s; exit
+34
+
+Listing 3.2: Cowrie attack to exploit the host machine as a crypto miner.
+1
+mkdir -p /home/osmc /.ssh/
+2
+echo ssh -rsa
+$RSA_KEY >> /home/osmc /.ssh//
+�→ authorized_keys
+3
+echo '<cmd7uname >'; uname -a
+4
+echo '</cmd7uname ><cmd7uptime >'; uptime
+5
+echo '</cmd7uptime ><cmd7w >'; w
+6
+echo '</cmd7w ><cmd7who >'; who
+7
+echo '</cmd7who ><cmd7last >'; last
+8
+echo '</cmd7last ><cmd7lastlog >'; lastlog
+9
+echo '</cmd7lastlog ><cmd7authkey >'; cat /home/osmc /.ssh//
+�→ authorized_keys
+10
+echo '</cmd7authkey ><cmd7lshome >'; ls -la /home
+11
+echo '</cmd7lshome ><cmd7passwd >'; cat /etc/passwd
+12
+echo '</cmd7passwd ><cmd7shadow >'; sudo -n cat /etc/shadow
+13
+echo '</cmd7shadow ><cmd7psfaux >'; ps -faux
+14
+echo '</cmd7psfaux ><cmd7netstat >'; netstat -npta
+15
+echo '</cmd7netstat ><cmd7arpan >'; /usr/sbin/arp -an
+16
+echo '</cmd7arpan ><cmd7ifconfig >'
+17
+/usr/sbin/ifconfig
+18
+echo '</cmd7ifconfig ><cmd7localconf >'; cat /home/ethos/
+�→ local.conf
+19
+echo '</cmd7localconf ><cmd7remoteconf >'
+20
+cat /home/ethos/remote.conf
+21
+echo '</cmd7remoteconf ><cmd7rclocal >'
+22
+cat /etc/rc.local
+23
+echo '</cmd7rclocal ><cmd7claymorestub >'; cat /home/ethos/
+�→ claymore.stub.conf
+24
+cat /hive -config/rig.conf; cat /hive -config/wallet.conf
+25
+cat /hive -config/vnc -password.txt
+26
+echo '</cmd7claymorestub ><cmd7claymorezstub >'
+27
+cat /home/ethos/claymore -zcash.stub.conf
+28
+echo '</cmd7claymorezstub ><cmd7sgminerconf >'
+29
+cat /var/run/ethos/sgminer.conf
+30
+echo '</cmd7sgminerconf ><cmd7iptables >'
+31
+sudo -n iptables -S
+&& sudo -n iptables -t nat -S
+32
+echo '</cmd7iptables ><cmdcrontab >'; crontab -l; echo '</
+�→ cmdcrontab >'
+33
+exit
+35
+
+Chapter 4
+Catching Attackers in Restricted
+Network Zones
+The T-Pot identified a flood of threats when it was available on the Internet. How-
+ever, capacious networks have separated compartments, and services are usually not
+directly available without any protection. Zoning is a well-known method to seg-
+ment a network. Heidelberg University applies zoning, and thus, it is an interesting
+question if an attacker probes services outside or within the network. This chapter
+presents a concept that uses a honeypot-like detection tool to detect any dubious
+packets in the network. It shows that attacks occurred in a restricted network zone
+of the Heidelberg University’s internal network and contributed to an adaption of
+the stateless firewall. Thus, improving the security of the network.
+4.1 University Network
+Honeypots that are accessible via the Internet receive a broad range of attacks. As
+Spitzner [65] noted, a honeypot is not strictly bound to run in a demilitarized zone
+(DMZ) or a network with direct Internet access. The correct location has to be
+chosen based on the goals of the honeypot. For example, one goal could be to catch
+attackers behind a perimeter firewall to reveal leaks or vulnerabilities. As described
+in the chapter before, the honeypot was broadly available on the Internet, and at-
+tackers could probe it easily. It collected on average 29,840 attacks per day, resulting
+in a total amount of 607,747 attacks. Zoning a network into logical groups mitigates
+the risk of an open network. Thus, the T-Pot would receive significantly fewer at-
+tacks in a controlled network zone. A network infrastructure is segmented into the
+same communication security policies and security requirements. For example, the
+Canadian government created its baseline for infrastructures, called Baseline Secu-
+rity Architecture Requirements for Network Security Zones in the Government of
+Canada (ITSG-22) [10]. The four most common zones are: (i) Public Zone (PZ),
+which is entirely open, (ii) Public Access Zone (PAZ), which interacts as an interface
+36
+
+between the PZ and internal services, (iii) Operation Zone (OZ), which processes
+sensitive information, and (iv) Restricted Zone (RZ), which includes business-criti-
+cal services [10]. A network zone restricts access and controls data communication
+flows [10].
+University
+Firewall 
+Internet
+Institutes Firewall
+self-administrated 
+URZ Firewall
+Stage 1 
+University Network
+URZ Firewall
+TagungsLAN
+eduroam
+Institute
+Institute
+HDnet
+Figure 4.1: Draft of the University network. The main doorkeeper is the univer-
+sity firewall. The HDnet is the internal network allowing institutes to
+communicate with each other.
+The network at the Heidelberg University includes a central stateless firewall (Ac-
+cess Control List (ACL)) that enfolds all institutes. It entails a default blacklist
+that blocks certain services (such as SMTP or Simple Network Management Pro-
+tocol (SNMP)) and a stateless filter provided by BelWÜ. Each institute can either
+use a pre-defined stateless firewall provided by the University Computing Center
+Heidelberg or use a self-administrated firewall inside the network. Figure 4.1 out-
+lines the association between these components. The internal “HDnet” enables the
+communication between institutes without leaving the internal network. Institute
+firewalls can be set up by each institute and are self-administrated. They do have
+37
+
+the possibility to use SOHO routers1 to disconnect certain network zones from the
+network. It is recommended to configure the global ACL as a fallback solution in
+case of any downtime. The University Computing Center Heidelberg offers stateless
+firewalls for router interfaces or Virtual Local Area Networks (VLANs). This state-
+less firewall whitelists certain services and splits up into four stages. Each stage can
+be individually activated per router interface. Its key value is to maintain baseline
+security to avoid misconfigurations and port scans. Table 4.1 outlines these stages
+including the IP address range. Before applying one of these zones, the respective
+network has to oblige to client IP addresses below 129.206.218.240/24. In
+addition, 129.206.218.1 is allocated for the gateway. A network must adhere to
+these obligations if it applies to any pre-defined stages.
+Table 4.1: Overview of firewall stages at the Heidelberg University. As an example,
+it applies the rules to subnet 129.206.218.0/24. Rules are applied
+to any subnet.
+Name
+Description
+range
+Stage 0
+Filters broadcast communication
+129.206.218.0-15/24
+No filtering
+129.206.239.16-255/24
+Stage 1
+Allows common network protocol
+129.206.239.0-255/24
+Allows services
+129.206.239.240-255/24
+Stage 3
+Internet access only via internal
+proxies
+129.206.239.0-255/24
+Stage 4
+Only internal network communica-
+tion
+129.206.239.0-255/24
+An interesting question is if attackers have access to restricted zones at the Heidel-
+berg University. It arises during the research of T-Pot if an adversary would try to
+probe any hosts in the internal university network. In order to detect such events,
+a honeypot-like packet detection application is presented that helps identify any
+threats in a network. In addition, it offers to deploy multiple instances and collect
+their data at a centralized instance.
+4.2 Honeypot-like Connection Detection Tool
+Recording and investigating connection attempts assimilates new honeypots. Re-
+spectively, a new honeypot-like detection tool called MADCAT will be presented.
+MADCAT has been developed by the BSI and helps to log any connection attempt
+being made on the host machine. The acronym MADCAT stands for Mass Attack
+1A small office/home office router is a broadband router used in small offices and home offices
+environments.
+38
+
+Detection Connection Acceptance Tools. It works as a honeypot-like detection ap-
+plication with a low-interaction level. Its key idea is to log every connection attempt
+and further process it to retrieve credentials or shell exploitation. Figure 4.3 gives
+an insight into how MADCAT works. It runs on an Ubuntu distribution, either
+18.04 or 20.04, and has been tested on Ubuntu 18.04. It processes packets from
+any interface that has been configured. As an example, it could process Ethernet
+and wireless packets. MADCAT itself consists of six independent modules for TCP,
+UDP, Internet Control Message Protocol (ICMP), and raw packets that communi-
+cate with each other through a pipeline. A module analyzes packets and logs the
+results in a queue. In addition, UDP and TCP offer a proxy to tunnel packets to
+another service. Every 5 seconds TCP postprocessor reads the newly arrived TCP
+packets and processes them accordingly. It resolves packets to log data, including
+source IP address, protocol, and event type. The enrichment processor is the final
+process step. Its purpose is to log all queue-written packets in a specified format
+for further analysis. The key idea of MADCAT is to get an insight into whether
+attackers have access to a particular network. In contrast to T-Pot, the concept does
+not know what specific attacks are operated on the honeypot. Instead, it ensures
+that no one else than authorized users has access. Especially in high confidential
+areas, no attacker should be capable of sending even a single packet to a host in
+the network. The vast range of honeypots does not provide tracking packets on a
+detailed level.
+In addition, a T-Pot instance will be deployed to have comparison data to the
+new concept. It focuses on the 129.206.218.0/24 and 147.142.0.0/16 sub-
+net. The 129.206.218.0/24 subnet is used within University Computing Cen-
+ter Heidelberg building. Every client in the building has a compelling connection
+in this subnet. Otherwise, an Internet connection would not be feasible. The sub-
+net 147.142.0.0/16 connects clients to “eduroam”2. Like the four stages of the
+institute firewall, the “eduroam” network, also called “Tagungslan”, builds various
+permits into the subnet. One essential difference is that services like SMTP and
+HTTP are not allowed, so attackers cannot deploy traps for users. Moreover, each
+client is encapsulated in its subnet, which disables communication to other clients.
+The instances are located in the building with IP addresses 129.206.219.62 and
+129.206.219.88. Figure 4.2 outlines the concept using MADCAT and a separate
+instance to visualize our data. The first instance with IP address 129.206.5.157
+provides Kibana and Elasticsearch to visualize and crawl logs. The honeypot with
+IP address 129.206.5.88 consists of MADCAT in conjunction with P0f, Suricata,
+and FATT. Like T-Pot, it uses Logstash to forward data to Elasticsearch. One ben-
+efit is the centralized approach to store data. This allows to deploy more instances
+to randomly collect data from other zones.
+2The eduroam is an international Wi-Fi internet access point for researchers.
+39
+
+Network
+Internet
+Gateway
+Switch
+store
+logs
+database
+(persistence 90 days) 
+m1.xlarge
+Debian 10, Buster
+ELK
+runs
+runs
+runs
+runs
+runs
+m1.xlarge
+Ubuntu 18.04
+send
+log 
+Logstash
+P0f
+Suricata
+FATT
+MADCAT
+Figure 4.2: Concept to detect connection attempts. It has been drafted to work in
+various scenarios. Kibana and Elasticsearch are deployed in heiCLOUD.
+40
+
+forward
+packets
+Ethernet
+forward
+packets 
+write
+TCP
+write
+ICMP
+forward
+packets
+write
+UDP
+Proxy
+forward
+packets 
+Wireless
+write
+RAW
+store
+Enrichment Processor
+write
+TCP Postprocessor
+logs
+MADCAT
+Ubuntu 18.04 or 20.04 
+FIFO
+read
+reads
+Figure 4.3: Visualization of the MADCAT packet flow starting at the network inter-
+face. The Ethernet and wireless interface forwards packets to the desired
+module.
+41
+
+4.3 Results
+MADCAT (28th of October till 18th of November) and T-Pot (16th of November till
+7th of December) have been deployed for three weeks. All instances had a connection
+to both subnets. First, the results obtained in the subnet 129.206.218.0/24 will
+be presented, closing up with the ones claimed in the eduroam network.
+In total, MADCAT received 35,372 packets. Overall, the modules TCP (66.62%)
+and raw (33.26%) received the majority of all connection attempts. The minority
+with less than one percent are suspicious packets with individual TCP flags like
+reset or syn set. On the contrary, it could not identify any harmful activity based on
+these packets. Overall, ConPot (56.98%), Honeytrap (31.35%), and Dionaea (7.09%)
+received most of the attacks with a total number of 437.
+Interestingly, it could
+identify SNMP connections that are used by print servers to discover printers.
+2021-10-30
+2021-11-03
+2021-11-07
+2021-11-11
+2021-11-15
+Timestamp
+0
+200
+400
+600
+800
+1000
+1200
+Number of Attacks
+ICMP
+IPv6
+UDP
+Figure 4.4: Protocol distribution of MADCAT. ICMP, IPv6, and UDP are the most
+used protocols. Timestamp; 28th of October to 18th of November.
+Figure 4.4 shows the protocol distribution indicating a high amount of ICMP and
+IPv6 packets. Only 11.59% of all IP address reputations could be resolved, splitting
+up into known attacker (11.26%), mass scanner (0.14%), bad reputation (0.12%),
+and tor exit node (0.08%). Focusing on TCP packets, 88.3% are known attackers
+with source port 113 as the primary target. The port 113 is officially known as
+the Identification Protocol (IDENT)[36] used for identification/authorization on a
+remote server such as Post Office Protocol (POP), IMAP, and SMTP. A potential
+42
+
+leak that allows adversaries to send IDENT requests to the network could be spotted
+by comparing the results with the stateless firewall settings. Decoding the payload
+of these TCP packets shows that attackers instead used this port to get an SMB
+connection than deploying IDENT protocol attacks. It identified attempts to acquire
+an SSH session using SMB and Session Initiation Protocol (SIP) connection attempts
+and various HTTP requests. For example, two payloads that have been sent to the
+instance show probing actions. Listing 4.1 outlines a SIP probe that checks if any
+VoIP service is active by answering the request packet. Next, Listing 4.2 shows an
+SMB probe trying to achieve the same. The IP address reputation could help answer
+if a real user or an attacker sends these packets. Both IP addresses in this example
+were resolved as a known attacker; thus, it identified them as a probe packet before
+executing their attack. A vital security interest in port 113 is negligible; however,
+the concept helps to detect such leaks, especially when stateless firewalls are the
+main doorkeeper for packets.
+2000
+4000
+6000
+8000
+10000
+Figure 4.5: Attack distribution of MADCAT. The USA, Russia, and China are the
+most attacking countries. Timestamp; 28th of October to 18th of Novem-
+ber.
+Figure 4.5 shows the attack distribution indicating the origin of an IP address.
+Most of the connections originate from the United States, Germany, and China.
+As shown beforehand in chapter 3, geographical information only outlines the last
+known location of a node. Like the results in heiCLOUD, it can be assumed that
+this information is not reliable as an indicator of where attacks occur. Nevertheless,
+it is interesting to see where the last node originated from.
+Suricata identified odd behaviors in the network (Figure 4.6). In total, it detected
+292,953 alerts and CVEs. Besides minor alerts like nmap scans, Suricata registered
+alerts in SNMP requests, TCP stack, and Wind River VxWorks. CVE-2020-11899
+[19] accounts nearly 73.35% with a total number of 214,879. This CVE is one of 19
+others forming the Ripple20 vulnerability in the low-level TCP/IP library developed
+by Treck, Inc. One of the Track TCP/IP stack tasks is to reassemble fragmented
+packets. Whenever a fragmented packet arrives, the stack tries to validate the to-
+43
+
+2021-11-19
+2021-11-23
+2021-11-27
+2021-12-01
+Timestamp
+0
+5000
+10000
+15000
+20000
+25000
+Number of Attacks
+Potentially Bad Traffic
+Misc activity
+Generic Protocol Command Decode
+Attempted Information Leak
+Attempted Administrator Privilege Gain
+Figure 4.6: Suricata results of T-Pot. Timestamp; from 16th of November to 7th of
+December.
+tal length in the IP header. If the total length is not correct, it trims the data.
+However, this leads to inconsistency, and thus, resulting in a buffer overflow when
+someone sends fragmented packets through a tunnel. A detailed description of the
+vulnerability can be found in [42]. An adversary could send malformed IPv6 pack-
+ets that cause an Out-of-bounds Read, resulting in potential remote code execution.
+Only TCP/IP stack versions until 6.0.1.66 are affected by this vulnerability. Never-
+theless, the tremendous alerts show the importance of adapting the IPv6 permits.
+The second most recorded vulnerability with the highest score is CVE-2002-0013
+[12] that allows remote attackers to cause a denial of service or gain privileges in
+the SNMPv1 protocol. The root cause for the CVE alert is the usage of the default
+public community for broadcast requests instead of configuring a private commu-
+nity with mandatory authentication. To compromise SNMP, attackers have to have
+access to the network. However, the university firewall blocks SNMP port 161 and
+162 for TCP and UDP, thus, restricting any access from outside. If adversaries
+plan to deploy an attack on the SNMP protocol, they need to have a connection
+to the internal network. Acquiring such a connection is rather hard to accomplish
+without any credentials. On the contrary, all connection attempts registered by the
+concept have been made within the network, and they do reflect a normal SNMP
+communication. Lastly, Wind River VxWorks 6.9.4 and vx7 in CVE-2019-12263
+[17] cause a buffer overflow due to the underlying TCP component that results in a
+race condition. Each connection attempt with CVE-2019-12263 is originated from
+Russia. Hence, the assumption is that the source IP address maliciously intended to
+send an urgent flag. For the other CVEs, the IP reputation could not be resolved.
+Results from the T-Pot instance are exiguous, and in short, no real attacks such
+as shell exploitation have been performed. All connection attempts originated from
+Germany within the same network and are made on ports 161 and 4567. Conpot
+44
+
+Listing 4.1: MADCAT connection attempt to exploit SIP connection. Received on
+the 16th of November. IP reputation: known attacker. Location Ger-
+many.
+1
+OPTIONS sip:nm SIP /2.0 Via: SIP /2.0/ TCP nm;
+2
+branch=foo From: <sip:nm@nm >;
+3
+tag=root To: <sip:nm2@nm2 > Call -ID: 50000 CSeq: 42
+�→ OPTIONS Max -Forwards: 70 Content -Length: 0 Contact:
+�→ <sip:nm@nm > Accept: application/sdp
+2021-11-17
+2021-11-21
+2021-11-25
+2021-11-29
+2021-12-03
+Timestamp
+0
+20
+40
+60
+80
+Number of Attacks
+161
+1025
+2049
+4567
+6000
+Figure 4.7: Attack port histogram of T-Pot. Timestamp; from 16th of November to
+7th of December.
+45
+
+registered minor SNMPv2 Get, SNMPv1 Get, and GetNext requests. A possible
+attack vector could be an SNMP reflection/amplification attack. As previously dis-
+cussed, the assumption is that devices within the network have a misconfigured
+printer and send broadcast requests frequently to find the machines. This SNMP
+requests affiliate with day-to-day traffic in an internal network, and thus, are not
+suspicious. The second most attacked honeypot is Honeytrap which received nu-
+merous packets on different ports, whereas 39% evince an empty payload. All of
+these received packets have a resolved IP address in the subnet 129.206.0.0/16.
+It remains unclear if these connections are malicious or are acquired by accident.
+Investigating the payload of outliers does not confirm the assumption of a vicious in-
+tention. Thus, declaring these results as negligible. Overall, most of the connection
+attempt received by the instance are from these IP addresses: 129.206.217.118,
+129.206.218.23, and 129.206.218.194.
+Listing 4.2: MADCAT connection attempt to exploit SMB connection. Received
+on the 16th of November.
+IP reputation: known attacker.
+Location
+Germany.
+1
+PC NETWORK PROGRAM 1.0 MICROSOFT
+NETWORKS 1.03 MICROSOFT
+�→ NETWORKS 3.0 LANMAN1 .0 LM12X002 Samba NT LANMAN 1.0
+�→ NT LM 0.12.
+Lastly, the results from the eduroam network are considered. Neither T-Pot nor
+MADCAT could identify any significant behavior for three weeks. Unlike the subnet
+129.206.218.0/24, the honeypot did not register any suspicious packets, TCP
+flags, or other CVEs.
+In retrospect, the eduroam configuration has been shown
+to work as designed. Thus, the client seemed to be encapsulated from others and
+received no other packets.
+Besides the subtle output it has received, the results have given an insight into the
+value of honeypots in a restricted network zone. For Heidelberg University, using
+honeypots to evaluate their stateless firewall has never been considered. The initial
+concept has shown that it delivered minor findings in the subnet 129.206.218.0/24
+with stage 1 firewall. As a result, the port 113 used for the IDENT protocol will
+be removed in the future to reduce the attack surface, thus, contributing to the
+firewall definition. Overall, the two instances received numerous packets containing
+interesting payloads. Compared to the T-Pot, which has been used in heiCLOUD,
+results are as expected delicate, and data analysis turns out to be more detailed.
+The statement from Spitzner [65] that honeypots only receive little input and nearly
+every input is suspicious matches the results only halfway. As shown beforehand,
+the results are dramatically little; however, only a few requests seemed suspicious.
+Nonetheless, the initial question of whether attackers have access to the restricted
+network zone at the Heidelberg University has been answered.
+46
+
+4.4 Discussion
+This chapter has shown that honeypots help find potential leaks in restricted network
+zones. Though, it remains questionable if the concept can deliver accurate results.
+The instance has been running for three weeks in the two different subnets. The
+honeypot has to be detected as a vulnerable target to deliver meaningful data.
+However, it could not detect any large scans on the instance; thus, it is very likely
+that either an attacker could not find the instance or no one had any access. In the
+eduroam network, large scans are negligible due to the firewall permits. It can be
+assumed that the results are accurate and do not show any discrepancy. Considering
+the subnet with stage one institute firewall, it identified attacks on port 113, resulting
+in an adaption of the stage one permits. On the contrary, it could not register any
+other odd packets on other ports. A detailed investigation could resolve whether
+the honeypot is available to attackers. A misconfiguration of the university firewall
+has been detected which proves this assumption.
+In December, from the 21st to the 23rd, a misconfiguration of the university firewall
+resulted in a flood of attacks. In total, the T-Pot instance received 46,328 attacks
+in three days. It turns out that five ports were open during that time, allowing
+attackers to probe the instance (Figure 4.9).
+The most attacked honeypots are
+RDPY (58.58%), Honeytrap (24.53%), and Cowrie (11.69%).
+2000
+4000
+6000
+8000
+10000
+12000
+14000
+16000
+Figure 4.8: Attack distribution of T-Pot. USA, Russia, China, and Germany are the
+most attacking countries. Timestamp; from 21st of December to 23rd of
+December.
+Like the geographical information of other honeypots, most of the connections orig-
+inate from the United States, Russia, and China (Figure 4.8). These similarities
+indicate a bias of the origin even though the location information is not reliable.
+On RDPY and Honeytrap, many connection attempts on various ports have been
+made. Based on the Suricata results, adversaries tried to gain administrator priv-
+ileges. For Cowrie, attackers tried to log in and execute commands by brute force
+47
+
+2021-12-22 04-00
+2021-12-22 16-00
+2021-12-23 04-00
+2021-12-23 16-00
+Timestamp
+0
+200
+400
+600
+800
+1000
+Number of Attacks
+22
+3389
+5555
+5900
+6379
+Figure 4.9: Attack port histogram of T-Pot. Timestamp; from 21st of December to
+23rd of December.
+48
+
+or guesswork. Moreover, the latest crypto-mining malware has been used, which
+resembles the findings of other honeypots. These results overlap strongly with those
+obtained by the T-Pot instance in heiCLOUD.
+The firewall administrator stated that the misconfiguration was fixed on the 23rd of
+December, resulting in a decrease in attacks on the T-Pot instance. These results
+have successfully answered our discussion of whether an attacker could detect the
+host machines at the university building. It clearly shows that attackers scan these
+IP address ranges and send malicious packets whenever they can.
+49
+
+Chapter 5
+Mitigate Fingerprint Activities of
+Honeypots
+There is a generic weakness in the
+current generation of low- and
+medium-interaction honeypots
+because of their reliance on
+off-the-shelf libraries to implement
+large parts of the transport layer.
+Alexander Vetterl
+Detecting honeypots before launching attacks helps to avoid the disclosure of infor-
+mation. Chapter 3 has shown that bot activities are on the rise, and more attacks
+than ever have been launched. However, the vast majority of attacks have been
+identified to be repetitive. This chapter conducts two experiments on whether it is
+possible to fingerprint honeypots. First, it reproduces the findings from Vetterl [72]
+to prove the initial question if any fingerprint activity is feasible. Consequently, it
+presents a concept to disguise Cowrie and verify this assumption with an experi-
+ment.
+5.1 OpenSSH
+OpenSSH is one of the most used applications that enables SSH. Before proceeding
+with generic weaknesses of honeypots, a short intermezzo about OpenSSH is given.
+OpenSSH consists of three major layers, namely ssh-connection, ssh-userauth,
+and ssh-transport (Figure 5.1) [70]. The last layer is the most important because
+it provides the basic functionalities for crypto operations, such as key exchange and
+encryption.
+50
+
+ssh-connection
+(Session multiplexer, X11 forwarding, TCP forwarding,
+interactive login, invoking sftp subsystem, remove command
+execution)
+ssh-userauth
+(Challenge response authentication (PAM), public key based,
+password authentication, rhost style host auth, smart card
+support, etc.)
+ssh-transport
+(Diffie Hellmann Key (KEX) agreement, ssh-rsa public key
+signatures, Server Host authentication, MAC & Encryption
+algorithm and key negotiation, rekeying )
+TCP/IP
+ssh layers
+Figure 5.1: OpenSSH architecture (derived from [70]).
+The ssh-transport layer
+builds the foundation for the other layers on top.
+In addition, each
+layer lists examples of functionalities that it supports.
+The first layer is responsible for authenticating the user to the SSH daemon, namely
+sshd. Based on two-way authentication, the client authenticates the SSH daemon
+with the help of the ssh-transport [70]. Finally, a secure connection is established,
+and the key exchange is done. The next step is to authenticate the user of the client.
+It offers authentication methods such as username/password, public key, or smart-
+card authentication [70]. If the ssh-userauth layer is successful, it will establish a
+secure channel through the ssh-connection layer [70]. Each session is handled in
+a so-called channel.
+The ssh-connection layer handles multiple sessions simultaneously over a single
+ssh-userauth layer with the TCP/IP layer below [70]. It is responsible for executing
+arbitrary commands, forwarding X11 connections, establishing VPN tunnels, and
+more.
+In addition, OpenSSH has built-in features such as keeping alive messages and redi-
+recting stdin to /dev/null for specialized X11 windows [70].
+Figure 5.5 outlines a sample session between a client and a server. The key exchange
+initialization is the first message between them to negotiate all ciphers and keys for
+communication.
+For this chapter, no other than the key exchange initialization
+message will be considered.
+51
+
+5.2 Preliminary Work
+Attackers have a strong motivation to reveal honeypots before launching an attack.
+Without any protection, attackers would disclose their methods, and thus, newly
+developed attacks would become useless. As shown in chapter 3, attackers do try
+to get information about the host system. Vetterl [72] discussed various methods of
+fingerprinting; however, executing commands in a shell and examining the response
+leaves precarious information to the honeypot itself. His technical report evaluated
+methods to detect honeypots at the transport level. As stated, the value of a hon-
+eypot would be merely zero if detection on transport level would work. He presents
+fingerprinting methods for SSH, Telnet, and HTTP/Web.
+Due to the complex-
+ity of each method, this section focuses on SSH fingerprinting using the honeypot
+Cowrie.
+The idea to detect SSH honeypots is to look for deviations in the response. There-
+fore, Vetterl [72] sends a set of probes P = {P1, P2, . . . , Pn} to a given set of imple-
+mentations of a network protocol I = {I1, I2, . . . , In} and stores the set of responses
+R = {R1, R2, . . . , Rn}. He calculated the cosine similarity coefficient C for the given
+set of responses. The goal is to find the best Pi where the sum of C is the lowest.
+Figure 5.2 presents these steps.
+The cosine similarity outputs the similarity between vectors of numerical attributes.
+It is widely used in text semantics to measure the similarity of sets of information
+such as two sentences. Vetterl [72] outlines that it can be used in “traffic analysis to
+find abnormalities and to measure domain similarity”. Mathematically, it computes
+the angle between two vectors. For each set of information A, we create a vector
+DA. Referring to the use case with SSH, we use the response from the server as
+information A. If θ is the angle between DA and DB, then:
+cos θ =
+DA · DB
+∥DA∥∥DB∥
+(5.1)
+where “·” is the dot product obtained by:
+DA · DB =
+n
+�
+i=1
+(DAi × DBi)
+(5.2)
+and ∥DA∥ (resp.
+∥DB∥) is the Euclidean norm, obtained by
+��n
+i=1 D2
+Ai (resp.
+��n
+i=1 D2
+Bi). The values of vectors are non-negative. The similarity between items
+is the value cos θ, cos θ = 1 indicates equality.
+52
+
+send
+Probes (P)
+output
+Implementation (I)
+calculate
+Responses (Rp)
+Cosine similarity
+coefficient (C)
+Figure 5.2: Process to obtain the cosine similarity coefficient (derived from [72]).
+Listing 5.1: OpenSSH connection attempt with probed SSH packet.
+All non-
+essential debug information have been removed to lay emphasis on the
+modified key exchange initialization.
+1
+Local version string SSH -2.2- OpenSSH
+2
+SSH2_MSG_KEXINIT sent
+3
+SSH2_MSG_KEXINIT
+received
+4
+kex: algorithm: ecdh -sha2 -nistp521
+5
+kex: host key algorithm: ssh -dss
+6
+kex: server ->client cipher: blowfish -cbc@openssh.com MAC:
+�→
+<implicit > compression: zlib@openssh.com
+7
+kex: client ->server cipher: blowfish -cbc@openssh.com MAC:
+�→
+<implicit > compression: zlib@openssh.com
+In order to find the best Pi for SSH, Vetterl [72] first created different SSH version
+strings based on the format: SSH-protoversion-swversion SP comment crlf. He
+used different lower and upper case variations, 12 different protoversions ranging
+from 0.0 to 3.2, swversion set to OpenSSH or empty string, comment set to FreeBSD
+or empty string, and crlf to either \r\n or empty string. In total, summing up
+to 192 client version strings. Second, he created different SSH2_MSG_KEXINIT pack-
+ets with 16 key-exchange algorithms, two host key algorithms, 15 encryption algo-
+rithms, 5 Message Authentication Code (MAC) algorithms, and three compression
+algorithms. In total, he sent 58,752 key exchange initialization messages. Combin-
+ing them with the 192 client versions, he ended up sending 157,925,376 packets.
+The version string SSH-2.2-OpenSSH \r\n and the SSH2_MSG_KEXINIT packet in-
+cluding ecdh-sha2-nistp521 as the key-exchange algorithm, ssh-dss as host key al-
+gorithm, blowfish-cbc as encryption algorithm, hmac-sha1 as mac algorithm, and
+zlib@openssh.com as compression algorithm, with the wrong padding, resulting in
+the lowest cosine similarity coefficient C. Listing 5.1 shows the SSH debug informa-
+tion with the modified version string and key exchange message.
+53
+
+Table 5.1 has been derived from Vetterl [72] to present his results of the cosine
+similarity of OpenSSH, Twisted, and Cowrie.
+Twisted has been added to have
+an example with an older SSH honeypot. As seen, it differs fundamentally from
+OpenSSH. At most, it scores 0.52 whereas various OpenSSH versions start at 0.98.
+The number of hosts significantly decreases with a cosine similarity score of 0.90 and
+higher. Cowrie responses are not too far away from OpenSSH, with an average of
+0.80. However, scanning through the web with a minimum score of 0.90 and higher
+would exclude all honeypots. Thus, distinguishing Cowrie from OpenSSH with SSH
+packets is a feasible method. Moreover, Vetterl [72] performed an Internet-wide
+scan, and detected 758 Kippo and 2,021 Cowrie honeypots. These results show that
+the values of honeypots would decrease to zero when fingerprinting activities are
+used.
+TwistedConch
+Cowrie
+OpenSSH
+sshd
+bash
+RFCs
+Figure 5.3: Architecture of OpenSSH and Cowrie.
+OpenSSH and TwistedConch
+have subtle protocol differences (derived from [72]).
+Vetterl [72] states that current low- and medium-interaction honeypots have a
+generic weakness due to the underlying off-the-shelf libraries. Cowrie is based on
+TwistedConch1, a Python 2/3 library that implements the SSH protocol. Any bash
+command and its response are tweaked by Cowrie, and thus, resulting in a discrep-
+ancy to OpenSSH. For example, Cowrie version 1.1.0 missed tftp2 that later came
+with version 1.2.0. Therefore, it is a continuous struggle to add new commands to
+avoid early disclosures of Cowrie.
+Figure 5.3 shows the difference between OpenSSH and Cowrie. Both have to fulfill
+the RFC4250 [44] which defines the protocol. OpenSSH and TwistedConch imple-
+ment the RFC requirement. As an example, Vetterl [72] found that Cowrie used
+to have random bytes for the key exchange initialization packet3. With respect to
+RFC4253 [76] that defines the Binary Packet Protocol (BPP) of SSH, the random
+padding is used to solidify the total length of the packet to be a multiple of the cipher
+block size. The RFC in section 6 defines that the padding consists of 4 random bytes.
+1TwistedConch 27.0.1 on GitHub
+2Trivial File Transfer Protocol (TFTP) is a lockstep File Transfer Protocol
+3Each packet consists of the packet and padding length, the MAC, a payload, and random
+padding.
+54
+
+Based on the statement of the OpenSSH authors, random bytes have been changed
+to NULL characters due to no security implications. Thus, an adversary could have
+detected a Cowrie honeypot with a single key exchange initialization packet. Nowa-
+days, Cowrie adapted itself to have NULL characters as padding to mitigate such an
+exploit. However, these subtle differences give adversaries precautionary information
+and influence the cosine similarity coefficient.
+Table 5.1: Overview of the cosine similarity of OpenSSH, Cowrie, and Twisted.
+Twisted has been added to have a comparison to an older honeypot.
+A
+B
+C
+D
+E
+F
+G
+H
+I
+J
+OpenSSH 6.6
+A
+-
+0.98
+0.98
+0.94
+0.94
+0.42
+0.78
+0.79
+0.79
+0.79
+OpenSSH 6.7
+B
+-
+0.98
+0.98
+0.98
+0.41
+0.80
+0.81
+0.81
+0.80
+OpenSSH 6.8
+C
+-
+0.96
+0.96
+0.42
+0.78
+0.79
+0.79
+0.79
+OpenSSH 7.2
+D
+-
+0.98
+0.42
+0.80
+0.80
+0.80
+0.80
+OpenSSH 7.5
+E
+-
+0.42
+0.78
+0.79
+0.79
+0.79
+Twisted 15.2.1
+F
+-
+0.50
+0.51
+0.51
+0.52
+Cowrie 96ca2ba
+G
+-
+0.98
+0.98
+0.98
+Cowrie dc45961
+H
+-
+0.99
+0.99
+Cowrie dbe88ed
+I
+-
+0.99
+Cowrie fd801d1
+J
+-
+5.3 Experiment 1: Reproduce Vetterl et al.’s
+findings
+First, the reproduction of the outdated OpenSSH library that Vetterl [72] used will
+be investigated. In his work, he used the version 7.5P1, which deviates from the
+latest version 8.8P1. Older versions rely on OpenSSL 1.0.2, including outdated algo-
+rithms and functions. For the SSH2_MSG_KEXINIT packet, the encryption algorithm
+blowfish-cbc is outdated and has been removed with version 7.6P1. Building the ver-
+sion 7.5P1 requires the libraries libssl (1.0.2), libssl-dev (1.0), libssh-dev (0.7.3 − 2),
+and libssh-4 (0.9.6 − 1). All of these libraries are outdated and have been removed
+from any Debian installation. Using the latest versions of these libraries results
+in missing encryption algorithms and host key algorithms. Thus, replacing the li-
+braries is a necessary task.
+It is required to download the libraries, remove the
+current versions, and install the outdated ones. The version 7.5P1 allows modifying
+the key exchange initialization message proposal in a single file. On the contrary,
+55
+
+this has been removed starting from version 7.6P1. After compiling the application,
+its behavior has been tested with a Debian 11 Buster and a Debian Jessie 9 Docker
+image. Both are new machines with no other installed packages than the SSH dae-
+mon. Debian 11 uses the latest OpenSSH version, whereas Jessie is at 6.7P1. These
+environments help to uniquely identify variations in the protocol version.
+Listing 5.2: OpenSSH connection attempt for version 7.5P1 and 8.8P1 with probed
+key exchange initialization message. All non-essential debug informa-
+tion have been removed to lay emphasis on the modified key exchange
+initialization.
+1
+OpenSSH_7 .5p1 , OpenSSL 1.0.2u
+20 Dec 2019
+2
+Local version string SSH -2.2- OpenSSH
+3
+SSH2_MSG_KEXINIT sent
+4
+SSH2_MSG_KEXINIT
+received
+5
+kex: algorithm: ecdh -sha2 -nistp256
+6
+kex: host key algorithm: ssh -dss
+7
+Unable to negotiate with ::1 port 22: no matching cipher
+�→ found. Their offer: aes128 -ctr ,aes192 -ctr ,aes256 -ctr
+�→ ,aes128 -gcm@openssh.com ,aes256 -gcm@openssh.com ,
+�→ chacha20 -poly1305@openssh.com
+Listing 5.2 shows the connection attempt with the adjusted version string and
+SSH2_MSG_KEXINIT packet. Both Debian machines return the same response. Using
+the outdated version 7.5P1, it results in an incompatibility. The return message
+outlines that blowfish-cbc is not supported anymore. OpenSSH kept the encryption
+algorithm usable for compatibility reasons for clients until 7.6P1. Later patches
+removed the blowfish-cbc from the application; thus, a reproduction of Vetterl [72]
+remains not feasible with the latest version. Testing it with version 7.3P1 that has
+been compiled on the machine results in a successful connection attempt. Vetterl [72]
+does not outline any expected response of OpenSSH; thus, it can be assumed that
+a connection attempt would have been successful due to the existing ciphers during
+that time. Adapting the version 8.8P1 with chacha20-poly1305 instead of blowfish-
+cbc for the encryption algorithm results in a successful connection attempt. There-
+fore, the key exchange initialization has been adapted to use chacha20-poly1305 as
+encryption algorithm instead. Next, the DSA host key algorithms are marked as
+too weak and are not included automatically during the key exchange initialization.
+Using ssh-dss requires the extra flag -oHostKeyAlgorithms=+ssh-dss. In order to
+avoid weak algorithms, the ssh-ed25519 host key algorithm is used, and the response
+has been promising to probe instances. So far, the key exchange initialization packet
+with ecdh-sha2-nistp521 as key exchange algorithm, ssh-ed25519 as host key algo-
+rithm, chacha20-poly1305 as encryption algorithm, hmac-sha1 as mac algorithm,
+and zlib@openssh.com as compression algorithm have been successfully tested on
+the two Debian instances.
+56
+
+Listing 5.3: Cowrie connection attempt with probed key exchange initialization mes-
+sage.
+All non-essential debug information have been removed to lay
+emphasis on the modified key exchange initialization.
+1
+OpenSSH_8 .8p1 , OpenSSL 1.1.1l
+24 Aug 2021
+2
+Local version string SSH -2.2- OpenSSH
+3
+SSH2_MSG_KEXINIT sent
+4
+Bad packet length
+1349676916.
+5
+ssh_dispatch_run_fatal : Connection to 129.206.5.74 port
+�→ 22: message
+authentication code incorrect
+The most interesting question remains about Cowrie’s response deviation. Vetterl
+[72] claims that it results in a bad version * exception. Cowrie has fixed this issue
+in the meantime, and thus, it does not leak vulnerable information anymore. For the
+experiment, the default Cowrie implementation version v.2.3.04 of the T-Pot instance
+is used. Listing 5.3 outlines the connection attempt. Unambiguously, Cowrie results
+in a bad packet length * exception, and thus, deviates fundamentally from an
+OpenSSH response. The underlying off-the-shelf library TwistedConch checks if a
+packet is within 1,048,576 bytes (1 MB) (Listing 5.4). Any packet that exceeds that
+threshold causes this exception, which results in a loss of connection for the client.
+This static check is performed when Cowrie tries to get the request packet. It remains
+dubious why TwistedConch has added it whenever a packet has to be returned. In
+the RFC4253, the minimum packet size is 5 bytes whereas maximum packet size is
+set to 32,768 bytes (256 KB). Debugging Cowrie shows that the exception occurs
+during the version string validation (Listing 5.5, line 16).
+The server validates
+if the version string matches the allowed versions 1.99 and 2.0.
+Any higher or
+lower version will result in a Protocol major versions differ.\n exception by
+calling the function _unsupportedVersionReceived. This response would match
+the behavior of OpenSSH.
+Therefore, the version strings 1.0, 1.99, 2.0, and 2.2 have been tested on Cowrie and
+OpenSSH. As a result, Cowrie’s bad packet length * exception occurs when the
+version does not match the expected one. This result diverges from OpenSSH, as
+only versions under 1.99 lead to the same exception as Cowrie. For any higher ver-
+sion, the connection can be established successfully. It can be assumed that Cowrie
+has an error in validating the version string.
+Debugging Cowrie shows that the
+method to return the Protocol major versions differ.\n exception is called,
+but the client does not receive this message. Hence, the assumption is that the
+underlying library TwistedConch is responsible for the incorrect message.
+Calculating the cosine similarity coefficient of both responses shows that the coeffi-
+cient with 0.46 is lower than the results from Vetterl [72]. In his study, the coeffi-
+4Cowrie v2.3.0 on GitHub
+57
+
+cient between Cowrie and OpenSSH was on average 0.80. Different implementation
+approaches to reproduce his results have been considered. The standard implemen-
+tation to retrieve the coefficient returned the best result with 0.46. Moreover, a soft
+cosine similarity with English word vectors from Mikolov et al. [49] has been used;
+however, it did not improve the result. In summary, the same response could not
+be reproduced. Nevertheless, it shows that both responses have similarities.
+In conclusion, these are the protocol deviations that Vetterl [72] has presented in
+his technical report. Thus, this section could successfully recreate his findings by
+detecting Cowrie on the transport level. Adversaries who modify their SSH client to
+send the specific version string and key exchange initialization message could detect
+Cowrie honeypots and stop further activities.
+Listing 5.4: TwistedConch packet length validation. Line 3 validates if the packet
+length is not greater than 1 MB. If this check is not successful, the client
+receives a bad packet length exception.
+1
+def getPacket(self):
+2
+...
+3
+if packetLen > 1048576: # 1024 ** 2
+4
+self.sendDisconnect(DISCONNECT_PROTOCOL_ERROR ,
+5
+'bad packet length %s' %
+�→ packetLen)
+6
+return
+7
+...
+5.4 Attempt to Disguise Cowrie
+Cowrie has to be tweaked to hide its generic weakness. Fixing the significant flaws
+in Cowrie to avoid early detection remains an ephemeral patch. The continued use
+of libraries that reimplement the behavior of OpenSSH leads attackers to try to
+find subtle protocol differences and exclude any host machine that deviates. Such
+approaches could be achieved by arbitrary Internet-wide scanning and calculating
+the cosine similarity coefficient. Thus, the value of honeypots would decrease to
+almost zero. Therefore, a new solution is required to disguise SSH honeypots. Vet-
+terl [72] presented a solution to use OpenSSH as an intermediary instance between
+the attacker and Cowrie. Unfortunately, this solution is outdated, and newer ver-
+sions contain significant changes in structure and functions. The concept is based
+on Vetterl [72] solution, but due to newer versions available, the solution has to
+be updated to the latest version. By default, OpenSSH itself cannot act as an in-
+termediary; therefore, it is necessary to customize the latest version to enable this
+feature.
+Figure 5.4 visualizes the flow of SSH packets between an attacker and
+58
+
+Cowrie. Cowrie is hidden in the background, and it is only accessible via the loop-
+back address 127.0.0.1 on port 65522. The updated daemon is exposed to the
+Internet, and it is accessible via 129.206.5.157 on port 22. Each connection
+to OpenSSH is forwarded to the honeypot through a network address translation
+(NAT) rule5. Accordingly, an attacker should not be able to detect Cowrie through
+response deviations.
+sshd
+Internet
+Cowrie
+Gateway
+127.0.0.1:65522
+129.206.5.157:65522
+Figure 5.4: Architecture of OpenSSH and Cowrie (derived from [72]). A NAT rule
+forwards the communication from port 22. Only the SSH daemon is
+accessible from extern.
+For instance, the latest OpenSSH version 8.8P16 is used. The implementation is
+based on Vetterl [72] version 6.3P17. As mentioned beforehand, due to major differ-
+ences between both versions, a smooth transition is unattainable without modifica-
+tions. Fortunately, the basic idea to morph OpenSSH into an intermediary instance
+stays the same.
+In total, the connection and user authentication layer has to be modified. These are
+the following steps required to change the SSH daemon:
+• User authentication layer: permit any connection to communicate to Cowrie
+without an authentication running in front of it.
+• Connection layer: create a separate channel to communicate with the attacker
+that forwards the packets to Cowrie.
+• Connection layer: handle the communication with Cowrie in a new channel
+separated from others.
+The first step is to tweak the authentication to permit any session to forward an
+incoming connection to Cowrie (Listing 5.6). Initially, it checks each session to see if
+the chosen authentication method returns true. In order to skip the authentication
+process, the server must return true for any client that tries to connect to the
+honeypot. Therefore, the authentication method has to be overridden in the main
+method and the allowed user method that checks if the user is permitted to log
+5iptables -t nat -A PREROUTING -p tcp –dport 22 -j REDIRECT –to-port 65222
+6OpenSSH 8.8P1 on GitHub
+7sshd-honeypot on GitHub
+59
+
+in. The authentication process validates if a connection to Cowrie is successful and
+returns true. In case of failure, the authentication would fail, resulting in a loss of
+connection for the client. Next, the libssh library expects a different integer for a
+successful authentication; therefore, the result is converted to the expected format.
+The allowed user method is changed to return true for any user trying to connect to
+the honeypot. Cowrie continues the authentication process and communicates with
+the attacker.
+Second, the communication has to be forwarded to the honeypot (Listing 5.7). In
+OpenSSH, communications are handled in channels as seen beforehand in section 5.1.
+Technically, the daemon opens a SOCKS connection for each session to communicate
+with the client. SOCKS is a network protocol to exchange packets between servers
+and clients. The SSH daemon needs a separate channel to store the attacker’s session
+and forward packets to communicate with Cowrie. The channel is implemented in
+version 6.3P1 and can be used in 8.8P1 with minor adaptions. The method validates
+if the Cowrie channel is open and writes the new packets into the buffer. In the main
+method, when the daemon is started, the channel is created, and a connection to the
+running Cowrie instance is opened to forward a new session. If Cowrie is unavailable,
+the startup will fail; thus, it has to run prior to the SSH daemon.
+Lastly, the server loop responsible for connecting the client to the correct port
+must be modified. It puts direct TCP/IP connections in the respective channel.
+The connection layer handles multiple sessions simultaneously over a single user
+authentication layer. Without this adaption, Cowrie would not receive any packet.
+The function in Listing 5.8 handles these connections. For instance, it checks if TCP
+forwarding is allowed and if the port of Cowrie is defined. Then, it connects the
+current session to the respective port. The SSH daemon has to be adapted to start
+and set up the channel in the main method at startup. In addition, the configuration
+has to be extended to configure the daemon to set the Cowrie IP address and the
+port.
+After compiling the version, a brief test proved a valid connection to the SSH dae-
+mon.
+5.5 Experiment 2: Avoid fingerprinting of Cowrie
+The last experiment to conclude this chapter is to test if the concept helps to disguise
+Cowrie and avoid fingerprint activities based on a custom local string version and
+key exchange initialization message.
+For instance, Vetterl [72] original 6.3P1 sshd-honeypot and the newly implemented
+version 8.8P1 will be used for this experiment. The forwarding communications are
+handled by an unmodified Cowrie version 2.3.0 running in a Docker environment.
+The version 6.3P1 has been tested in heiCLOUD on a Debian 9 Jessie distribution,
+60
+
+whereas the version 8.8P1 with our latest adaption has been tested on a Debian 10
+Buster. In addition, both versions are validated locally in an encapsulated environ-
+ment. The clients to test the two concepts are a standard OpenSSH 8.8.P1 and the
+modified version with custom local version string and key exchange initialization
+message to fingerprint honeypots.
+The standard client’s requests do not result in a bad packet length exception for
+both servers. This behavior reflects an original SSH daemon communication and
+represents a successful test. The requests from the modified client are successful on
+the latest version, whereas the older server 6.3P1 had problems with new encryption
+and host key algorithms. A successful connection to the original server from Vetterl
+[72] could be recreated by using the 7.3P1 version. This version has been used to
+verify Cowrie beforehand. The concept can forward any related packet to Cowrie
+and hide the generic weakness of TwistedConch. Therefore, whether Cowrie can
+be disguised to prevent any fingerprint activities with the help of OpenSSH has
+been answered successfully.
+This section can confirm this assumption based on
+the reproduction and implementation of the concept. On the other side, Cowrie
+receives the connection and log information (Listing 5.9). However, one downside is
+the connection loss due to timeout restrictions. This issue is a minor bug and could
+be fixed in the future.
+In conclusion, this experiment has shown that the initial idea of hiding Cowrie in the
+background and directing the communication through OpenSSH prevents fingerprint
+activities of an adversary. In addition, it has shown that protocol implementations
+change rapidly to adapt to new security standards, leading to outdated honeypots.
+5.6 Discussion
+Depending on the interaction level, honeypots will always deviate from production
+instances. As seen in the two experiments beforehand, detecting a generic weakness
+is doable in a respective time, as well as mitigating it. Thus, finding and fixing
+the weaknesses of honeypots becomes a continuous cycle. However, this chapter
+also outlined the importance of the libraries that were used. TwistedConch is the
+bottleneck of Cowrie, and it is updated8 frequently.
+Libraries that reimplement
+protocols have to be always up-to-date.
+In conclusion, such libraries should be
+chosen carefully to avoid bugs that leave harmful information to attackers.
+8Based on the lastest GitHub commit of the Python library
+61
+
+Client
+Server
+(KEX) SSH_MSG_KEXINIT
+SSH_MSG_NEWKEYS
+SSH_MSG_SERVICE_REQUEST
+SSH_MSG_SERVICE_ACCEPT
+SSH_MSG_USERAUTH_REQUEST
+SSH_MSG_USERAUTH_SUCCESS
+SSH_MSG_CHANNEL_OPEN
+SSH_MSG_CHANNEL_OPEN_CONFIRMATION
+SSH_MSG_CHANNEL_WINDOW_ADJUST
+SSH_MSG_CHANNEL_DATA
+SSH_MSG_CHANNEL_EXTENDED_DATA
+SSH_MSG_CHANNEL_REQUEST
+SSH_MSG_CHANNEL_REQUEST
+SSH_MSG_GLOBAL_REQUEST
+SSH_MSG_CHANNEL_OPEN
+SSH_MSG_CHANNEL_OPEN_CONFIRMATION
+...
+SSH_MSG_CHANNEL_CLOSE
+SSH_MSG_CHANNEL_CLOSE
+ssh-transport
+ssh-connection
+ssh-userauth
+Figure 5.5: OpenSSH sample session flow diagram (derived from [70]). In addition,
+the right side indicates the layers that are responsible for handling the
+messages.
+62
+
+Listing 5.5: Cowrie version string validation. It tweaks the same results as OpenSSH
+in line 16.
+1
+def _unsupportedVersionReceived (self , remoteVersion:
+�→ bytes) -> None:
+2
+"""
+3
+Change message to be like OpenSSH
+4
+"""
+5
+self.transport.write(b"Protocol major versions differ
+�→ .\n")
+6
+self.transport.loseConnection ()
+7
+8
+def dataReceived(self , data: bytes) -> None
+9
+...
+10
+if not self.gotVersion:
+11
+...
+12
+self.otherVersionString = self.buf.split(b"\n")
+�→ [0]. strip ()
+13
+...
+14
+# Checks if the version string has a correct
+�→ format
+15
+m = re.match(br"SSH -(\d+.\d+) -(.*)", self.
+�→ otherVersionString)
+16
+if m is None:
+17
+...
+18
+self.transport.write(b"Invalid SSH
+�→ identification
+string .\n")
+19
+self.transport.loseConnection ()
+20
+return
+21
+else:
+22
+...
+23
+# Checks if version string is either 1.99 or
+�→ 2.0
+24
+if remote_version not in self.
+�→ supportedVersions:
+25
+self. _unsupportedVersionReceived (self.
+�→ otherVersionString)
+26
+return
+27
+...
+28
+...
+29
+...
+63
+
+Listing 5.6: Tweaked OpenSSH authentication to connect to Cowrie. Only the essen-
+tial code parts to change the authentication method have been added.
+1
+int
+2
+auth_password(struct ssh *ssh , const char *password)
+3
+{
+4
+Authctxt *authctxt = ssh ->authctxt;
+5
+/* Send the request to Cowrie */
+6
+int rc;
+7
+rc = authenticate_password (authctxt ->user , password);
+8
+authctxt ->valid = 1;
+9
+/* libssh returns
+different
+values compared to
+�→ OpenSSH , for SSH_AUTH_SUCCESS =0 returns 1 */
+10
+if (rc == 0)
+11
+{
+12
+finish_connection_setup ();
+13
+return 1;
+14
+}
+15
+else
+16
+{
+17
+return 0;
+18
+}
+19
+...
+20
+}
+21
+int authenticate_password(const char *username , const
+�→ char *password)
+22
+{
+23
+int rc = -1;
+24
+/* No logins if we could not connect to Cowrie */
+25
+if (ssh_client_conns1 [0]. error != 1)
+26
+{
+27
+rc = ssh_userauth_password (ssh_client_conns1 [0].
+�→ initial_session , username , password);
+28
+}
+29
+return rc;
+30
+}
+31
+int
+32
+allowed_user(struct ssh *ssh , struct passwd * pw)
+33
+{
+34
+return 1;
+35
+}
+64
+
+Listing 5.7: Tweaked OpenSSH channel to connect to Cowrie. Only the essential
+code parts to change the authentication method have been added.
+1
+static int
+2
+channel_handle_wfd(struct ssh *ssh , Channel *c,
+3
+fd_set *readset , fd_set *writeset)
+4
+{
+5
+...
+6
+// Implement
+channel logic to forward data to Cowrie
+7
+int nbytes;
+8
+char buffer [65507] = {0};
+9
+ssh_client_conns1 [0]. rfd = c->rfd;
+10
+ssh_client_conns1 [0]. wfd = c->wfd;
+11
+ssh_client_conns1 [0]. efd = c->efd;
+12
+// Check the connection to Cowrie , if not , close the
+�→ sshd -client connection
+13
+if (ssh_channel_is_open(channel_rw1.channel_data) &&
+14
+!ssh_channel_is_eof(channel_rw1.channel_data))
+15
+{
+16
+// Read data from the channel (Cowrie)
+17
+nbytes = ssh_channel_read_nonblocking (channel_rw1
+�→ .channel_data , buffer , sizeof(buffer), 0);
+18
+if (nbytes > 0 && ssh_client_conns1 [0].
+�→ got_command != 1 && ssh_client_conns1 [0].
+�→ subsystem_req != 1)
+19
+{
+20
+write(ssh_client_conns1 [0].wfd , buffer ,
+�→ nbytes);
+21
+}
+22
+else if (nbytes > 0 && ssh_client_conns1 [0].
+�→ got_command == 1)
+23
+{
+24
+sshbuf_putf (&c->input , buffer , nbytes);
+25
+}
+26
+} else
+27
+{
+28
+if (ssh_client_conns1 [0]. counter_disconnect == 0)
+29
+{
+30
+ssh_client_conns1 [0]. to_disconnect = 1;
+31
+}
+32
+}
+33
+...
+34
+}
+65
+
+Listing 5.8: Tweaked OpenSSH server loop to connect to Cowrie. Only the essential
+code parts to change the authentication method have been added.
+1
+static Channel *
+2
+server_request_direct_tcpip (struct ssh *ssh , int *reason ,
+�→
+const char ** errmsg)
+3
+{
+4
+...
+5
+...
+6
+/* Implement direct -TCP/IP forwarding */
+7
+if (sshd_honey_options.tcpForwardingPort != 0)
+8
+{
+9
+/* Redirect to the host specified in
+�→ sshd_config */
+10
+c = channel_connect_to_port (
+11
+ssh ,
+12
+sshd_honey_options.tcpForwardingHost ,
+13
+sshd_honey_options.tcpForwardingPort ,
+14
+"direct -tcpip",
+15
+"direct -tcpip",
+16
+reason ,
+17
+errmsg
+18
+);
+19
+}
+20
+else
+21
+{
+22
+/* Redirect to any host */
+23
+c = channel_connect_to_port (ssh , target ,
+�→ target_port , "direct -tcpip", "direct -
+�→ tcpip", reason , errmsg);
+24
+}
+25
+...
+26
+/* Make sure cowrie is aware of all requests (
+�→ successful or not) */
+27
+ssh_channel_open_forward (channel_rw1.channel_data_1 ,
+28
+target , target_port ,
+29
+originator , originator_port)
+�→ ;
+30
+31
+sprintf(ssh_client_conns1 [0]. target_ip , "%s", target)
+�→ ;
+32
+sprintf(ssh_client_conns1 [0]. target_port , "%d",
+�→ target_port);
+33
+...
+34
+}
+66
+
+Listing 5.9: Cowrie log information. The new connection from this experiment has
+been acquired. Cowrie fetched information about the local string version
+and kex message.
+1
+New connection: 127.0.0.1:65522 [session: 2ca9a619ceb8]
+2
+Remote SSH version: SSH -2.0- libssh_0 .9.6
+3
+SSH client hassh fingerprint: ....
+4
+kex alg=b'curve25519 -sha256 ' key alg= b'ssh -ed25519 '
+5
+outgoing: b'aes256 -ctr ' b'hmac -sha2 -512' b'none '
+6
+incoming: b'aes256 -ctr ' b'hmac -sha2 -512' b'none '
+67
+
+Chapter 6
+Conclusion
+This thesis has shown that organizations can spot malicious activities using honeypot
+solutions. The result in this thesis successfully answered the original question of
+whether honeypots contribute to a more secure infrastructure. It can confirm this
+assumption based on its results in the cloud and in the university network. The first
+approach was to collect data with the help of the T-Pot solution and compare them
+to a previous study of similar cloud providers. It has shown that these activities
+increased significantly. The universitys’ cloud solution heiCLOUD has received more
+attacks than ever, putting it in the first place compared to other cloud providers.
+It has seen various attacks in RDP, VoIP, and SSH. The number of attacks related
+to cryptocurrencies is particularly striking, reflecting the current situation of highly
+traded GPUs. In addition, the latest attacks like the Apache vulnerability in version
+2.49.0 could be traced back to very early stages, showing how fast attackers adapt to
+new vulnerabilities. It is assumed that most of the executed attacks on the instance
+came from bots.
+Next, this thesis has focused on the university’s internal network and implemented
+a new concept to detect every single packet sent to a host machine. The MADCAT
+solution, in conjunction with IDS tools, helped identify the open port 113 that has
+been used to deploy attacks. It has shown that known attackers with an IP address
+originating from Russia have probed the instance, and as an assumption, further
+attacks would have been carried out. In retrospect, this helped remove the port from
+the firewall’s permits, thus improving the security at the Heidelberg University. Any
+other suspicious behavior in the eduroam network could not be registered, proving
+that the firewall works as intented.
+Moreover, honeypots like Cowrie have a fundamental flaw because they rely on
+off-the-shelf libraries.
+These libraries often reimplement protocol behaviors like
+OpenSSH and add a subtle difference to the response. On the contrary, this devia-
+tion of responses can be used to detect honeypots on the transport level. Adversaries
+could spot honeypots before deploying any attack based on a cosine similarity coeffi-
+cient, thus avoiding exposures to newly developed attacks. The findings Vetterl [72]
+claims in his work have been recreated by adapting OpenSSH 8.8P1 and testing it
+68
+
+on different Debian instances. Due to outdated algorithms, the key exchange initial-
+ization message has been updated to work with the latest version. It shows that the
+latest Cowrie version 2.3.0 results in a bad packet length because the local version
+string does not match the expected ones of the underlying library TwistedConch.
+This result deviates fundamentally from OpenSSH. Lastly, an attempt to protect
+Cowrie from early exposure has been made by hiding it in the background and tun-
+neling requests through a customized OpenSSH daemon. This has successfully fixed
+the generic weakness of Cowrie so that connecting to Cowrie works without run-
+ning into a bad packet length error. The last chapter shows that honeypots are not
+flawless, and developers should be careful when deciding on additional libraries.
+In conclusion, this thesis has presented concepts to catch attackers for different sce-
+narios and shows that malicious activities have increased tremendously. In addition,
+it has taken a deep dive into an edge-breaking study to detect honeypots on trans-
+port level and has disguised Cowrie to block such activities. An interesting future
+study could involve the development of a generic method to fingerprint honeypots.
+Future research could also examine other libraries that reimplement protocols to
+find generic weaknesses and deviations. Ultimately, using honeypots as a security
+parameter has been proven promising for further implementation.
+69
+
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+[74] Christopher Wellons. Endlessh: an ssh tarpit. https://github.com/skeeto/
+endlessh, 2021. Accessed: 2021-09-26.
+[75] Tillmann Werner. Honeytrap. https://github.com/armedpot/honeytrap/,
+2021. Accessed: 2021-09-26.
+[76] Tatu Ylonen and Chris Lonvick. The Secure Shell (SSH) Transport Layer Pro-
+tocol. RFC 4253, RFC Editor, January 2006. URL https://www.rfc-editor.
+org/rfc/rfc4253.txt.
+[77] Michal Zalewski. p0f v3: passive fingerprinter. https://github.com/p0f/p0f,
+2021. Accessed: 2021-09-26.
+75
+
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+page_content='Faculty of Mathematics and Computer Science  Heidelberg University  Master thesis  in Computer Science  submitted by  Stefan Machmeier  born in Heidelberg  2022  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='CR]  2 Jan 2023  Honeypot Implementation in a Cloud Environment  This Master thesis has been carried out by Stefan Machmeier  at the  Engineering Mathematics and Computing Lab  under the supervision of  Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vincent Heuveline  Erklärung  Ich versichere hiermit, dass ich die vorliegende Arbeit selbständig verfasst und keine  anderen als die angegebenen Hilfsmittel benutzt habe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Sowohl inhaltlich als auch  wörtlich entnommene Inhalte wurden als solche kenntlich gemacht.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Die Arbeit ist in gleicher oder vergleichbarer Form noch bei keiner anderen Prü-  fungsbehörde eingereicht worden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Heidelberg, den 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2022  Stefan Machmeier  Acknowledgements  The research included in this thesis could not have been performed if not for many  individuals’ assistance, patience, and support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vincent Heuve-  line for his valuable and constructive input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Without his guidance and mentorship,  I would not have been able to finish this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, I grew as a researcher,  and I am immensely grateful for the opportunity to continue my research as a future  Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' candidate under his supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  I want to extend my gratitude towards Stefan Steiger and Olaf Pichler from the  Computing Centre at Heidelberg University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thank you for offering insightful com-  ments and brilliant suggestions when the task got challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' They always had  time and provided me with ample support no matter what happened.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  I am indebted to Joachim Peeck for generously agreeing to examine my results and  providing valuable inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' His timely advice and scientific knowledge helped me  understand essential parts of the topic assisted me to a great extent in accomplishing  this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Lastly, I could not have completed this thesis without the support of my girlfriend,  Carmen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thank you for being so patient in providing emotional support and stim-  ulating discussions during my research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Contents  Acronyms  V  List of Figures  VIII  List of Tables  IX  Listings  X  1  Introduction  1  2  Background  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='5  Honeynets .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='List of Figures  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1  Abstract visualization of service models .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='4  Attack distribution of T-Pot .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='5  Attack histogram of T-Pot .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='9  Cowrie results of T-Pot .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='10 Cowrie top 10 credentials on T-Pot .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='1  Draft of the University network .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  51  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2  Process to obtain the cosine similarity coefficient .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='3  Architecture of OpenSSH and Cowrie .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='4  Architecture of OpenSSH and Cowrie .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='5  OpenSSH sample session flow diagram  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  62  VIII  List of Tables  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1  Distinction between security concepts .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='1  Overview of attacks on cloud providers .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='2  Overview of honeypots of T-Pot .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='3  Overview of attacks on heiCLOUD, AWS, GCP, and Azure .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='1  Overview of firewall stages .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  55  IX  Listings  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1  Cowrie attack to gather various information about the system  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='2  Cowrie attack to exploit the host machine as a crypto miner .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='1  Example OpenSSH connection with probed SSH packet .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='2  OpenSSH connection attempt with probed message .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='3  Cowrie connection attempt with probed message .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  58  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5  Cowrie version string validation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  63  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6  Tweaked OpenSSH authentication .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='7  Tweaked OpenSSH channel  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  65  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8  Tweaked OpenSSH server loop .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  66  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9  Cowrie log information .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  67  X  Chapter 1  Introduction  Recently, Europol1 raised awareness of new cyber threats related to the ongoing  pandemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As stated in their yearly Internet Organised Crime Threat Assessment  (IOCTA) report, scanning of corporate infrastructures has been skyrocketing within  the last 12 months by ransomware groups, respectively increasing malware usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Attackers use scans to find potential vulnerabilities in remote desktop sharing soft-  ware, or virtual private networks (VPNs) in order to deploy malware and blackmail  companies [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The rapid increase dates back to the pandemic and the shift to home  office, forcing companies to adapt their infrastructures quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Such changes come  with the downside of adding new threats to an organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The latest incident  at the SRH University Heidelberg points out the obstacles institutions face when  ransomware groups have access and exploit various parts of the infrastructure with  malware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' An unknown group infected systems with malware and distributed internal  data in the darknet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Such incidents emphasize the rise of malicious activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Especially in cloud computing, controlling access to services is becoming a stricter  challenge due to access to large data sets and computing resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Besides tradi-  tional security measures such as firewalls or intrusion detection systems, one known  methodology to strengthen infrastructures is learning from those who attack them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeypots are a proper instrument to gather information about attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is  “a security resource whose value lies in being probed, attacked, or compromised”  [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Collecting attacks can reveal shell-code exploitation or bot activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In retro-  spect, this would help to harden infrastructures before proper damage occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For  a cloud provider, it is crucial to know whether and how attacks on its service can  be prevented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Considering the Global Security Report by Trustwave, the number  of attacks doubled in 2019 and increased by 20% in 2020 [1], respectively putting  cloud providers to the third most targeted environments for cyberattacks, behind  corporate and internal networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The Heidelberg University offers its own cloud service, called heiCLOUD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It enables  users to maintain and control computational resources easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, it is interesting  1An agency that fights against terrorism, cybercrime, and other threats [28]  1  to elaborate on the value of honeypots for this cloud solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This thesis tries to  answer the general research question of whether honeypots can contribute to a more  secure infrastructure in a cloud environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This includes deploying a honeypot  solution in heiCLOUD and presenting the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Prior to that, an insight into  a recent study investigating honeypots for the cloud providers AWS, GCP, and  Microsoft Azure is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These findings help to validate the results in heiCLOUD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, the university network will be investigated to find potential leaks in  the stateless firewall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, a concept is created using the BSI’s honeypot-like  detection tool MADACT and deployed on desktop computers inside the university  building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Furthermore, to consider an attacker’s point of view, this thesis introduces  a recent work to detect honeypots on the transport level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Lastly, a solution to  mitigate these efforts will be presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  This thesis includes six chapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  After the introduction, chapter 2 outlines the  background knowledge that is needed to comprehend the upcoming experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It gives the reader a profound understanding of cloud computing, honeypots, and  virtualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Chapter 3, Analyze Honeypot Attacks in the Cloud, presents the  status quo of malicious activities in heiCLOUD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In the beginning, it shows the  results that Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] claim for AWS, GCP, and Microsoft Azure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Next, it  gives an insight into the T-Pot solution used to collect the data and shows the results  after collecting them for three weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Furthermore, chapter 4, Catching Attackers  in Restricted Network Zones, investigates the university network in which the new  concept is deployed for three weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It shows that the concept was able to adapt the  firewall, thus, improving the network security at the university.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Chapter 5, Mitigate  Fingerprint Activities of Honeypots, presents two experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' First, it describes the  preliminary work to detect honeypots and finishes with an experiment to prove this  assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Next, it drafts the counterpart of mitigating this activity, also closing  up with an experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Lastly, chapter 6 completes this thesis with a conclusion  that summarizes the results and describes future work in this regard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2  Chapter 2  Background  A honeypot is a security resource  whose value lies in being probed,  attacked, or compromised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Lance Spitzner  Using honeypots in a cloud environment merges two varying principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This chapter  introduces the fundamental knowledge needed to comprehend the upcoming exper-  iments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If the reader has a profound understanding of cloud computing, honeypots,  and virtualization, he can skip this chapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 Virtualization  Virtualization, often referred to as virtual machines (VMs), is defined by Kreuter  [43] as “an abstraction layer or environment between hardware component and the  end-user”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A VM runs on top of the operating system’s (OS’s) core components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Through an abstraction layer, the virtual machine is connected with the real ma-  chine by hypervisors or virtual machine monitors (VMM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hypervisors can use real  machine hardware components but also support virtual machine’s operating systems  and configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Both are similar to emulators, which are defined by Lichstein  [45] as a “process whereby one computer is set up to permit the execution of programs  written for another computer”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This allows managing multiple VMs with real ma-  chine resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' There are three different types of virtualization, (i) software virtual  machines, (ii) hardware virtual machines, and (iii) virtual OS/containers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Software  virtual machines manage interactions between the host and guest operating sys-  tems [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hardware virtual machines offer direct and fast access to the underlying  resources [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It uses hypervisors, modified code, or Application Programming In-  terfaces (APIs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Lastly, virtual OS/container partitions the host operating system  into containers or zones [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 Cloud Computing  Cloud Computing has become a buzzword these days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It has been used by various  large companies such as Google and Amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the term “cloud computing”  dates back to late 1996, when a small group of technology executives of Compaq  Computer framed new business ideas around the Internet [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Starting from 2007,  cloud computing evolved into a serious competitor and outnumbered the keywords’  “virtualization”, and “grid computing” as reported by Google trends [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Shortly,  various cloud providers become publicly available, each with its strengths and weak-  nesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example IBM’s Cloud1, Amazon Web Services2, and Google Cloud3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' So,  why are clouds so attractive in practice?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It offers major advantages in terms of cost and reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' When demand is  needed, consumers do not have to invest in hardware when launching new  services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Pay-as-you-go allows flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Consumers can easily scale with demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' When more computational resources  are required due to more requests, scaling up instances in conjunction with a  suited price model is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Geographically distributed capabilities supply the need for worldwide scattered  services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 Definition of Cloud Computing  According to the definition by Brian Hayes, cloud computing is “a shift in the geog-  raphy of computation” [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, the computational workload is moved away from  local instances towards services and data centers that provide the user’s needs [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The National Institute of Standards and Technology (NIST) defines cloud computing  as “a model for enabling ubiquitous, convenient, on-demand network access to a  shared pool of configurable computing resources (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', networks, servers, storage,  applications, and services) that can be rapidly provisioned and released with minimal  management effort or service provider interaction” [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' NIST not only reflects the  geographical shift of resources such as data centers but also mentions on-demand  usage that contributes to flexible resource management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, NIST composes  the term into five essential characteristics, three service models (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2),  and four deployment models (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3) [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  On-demand-self-service refers to the unilateral provision computing capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Consumers can acquire server time and network storage on demand without hu-  man interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ibm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/cloud  2https://aws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/  3https://cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/  4  Application  IaaS  SaaS  HaaS  DaaS  Cloud Resources  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Abstract visualization of service models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The container “cloud resources”  represents the depth of functionalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, Infrastructure-as-a-  Service (IaaS) offers the most functionalities, whereas the others have a  user-friendly abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Broad network access characterizes the access of capabilities of the network through  standard protocols such as Hypertext Transfer Protocol (HTTP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Heterogeneous  thin and thick client platforms should be supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Resource pooling allows the provider’s computing resources to be pooled across sev-  eral consumers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Different physical and virtual resources are assigned on-demand  with a multi-tenant model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Other aspects such as location are independent and  cannot be controlled on a low-level by consumers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, high-level access to  specify continent, state, or datacenter can be available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Rapid elasticity offers consumers to extend and release capabilities quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Further  automation to quickly increase resources when demand surges can be supported at  any time, regardless of limit or quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Measured service handles resources in an automated and optimized manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It uses  additional metering capabilities to trace storage, processing, bandwidth, and active  user accounts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This helps to monitor and control resource usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, contributing  to transparency between provider and consumer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 Service models  Service models are categorized by NIST into three basic models based on usage  and abstraction level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 shows the connection between each model whereas  cloud resource are defined in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Infrastructure-as-a-Service (IaaS)  builds with a vast range of functionalities the foundation of service models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each  model on top represents a user-friendly abstraction with derated capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Software-as-a-Service (SaaS) is a high-level abstraction to consumers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Controlling  the underlying infrastructure is not supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Providers often use a multi-tenancy  5  system architecture to organize each consumer’s application in a different environ-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It helps to employ scaling with respect to speed, security availability, disaster  recovery, and maintenance [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The main objective of SaaS is to host a consumer’s  software or application that can be accessed over the Internet using either a thin or  rich client [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Users can apply custom configuration settings [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Platform-as-a-Service (PaaS) pivots on the full “Software Lifecycle” of an application  whereas SaaS distinct on hosting complete applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' PaaS offers ongoing devel-  opment and includes programming environment, tools, configuration management,  and other services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, the underlying infrastructure is not managed by the  consumer [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Infrastructure-as-a-Service (IaaS) offers a low-level abstraction to consumers with  the ability to run arbitrary software regardless of the operating system or appli-  cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In contrast to SaaS, IT infrastructure capabilities (such as storage and  networks) can be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It strongly depends on virtualization due to the integration  or decomposition of physical resources [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Data-as-a-Service (DaaS) serves as a virtualized data storage service on demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Motivations behind such services could be upfront costs of on-premise enterprise  database systems [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Mostly they require “dedicated server, software license, post-  delivery services, and in-house IT maintenance” [23] whereas DaaS costs solely what  consumers need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' When dealing with a tremendous amount of data, file systems and  relational database management systems (RDBMSs) often lack performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' DaaS  outruns such weak links by employing a table-style abstraction that can be scaled  [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Hardware-as-a-Service (HaaS) offers IT hardware or datacenters to buy as a pay-as-  you-go subscription service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The term dates back to 2006 when hardware virtual-  ization became more powerful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is flexible, scalable, and manageable [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 Deployment models  Deployment models are categorized by NIST into four basic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each differs in  data privacy, location, and manageability [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  With private clouds, users have the highest control regarding data privacy and  utilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Such clouds are mostly deployed within a single organization, managed  by in-house teams or third-party suppliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, it can be on- or off-premise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Within private clouds, consumers have full control of their data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Especially for  European data privacy laws, it is not negligible when data is stored abroad, and  thus, under the law of foreign countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  However, its popularity has not been  diminished due to the immense cost of switching to public clouds [23, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  6  Community clouds can be seen as a conglomerate of multiple organizations that  merge their infrastructure with respect to a commonly defined policy, terms, and  conditions beforehand [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Public clouds represent the most used deployment models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Contrary to private ones,  public clouds are fully owned by service providers such as businesses, academics, or  government organizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Consumers do not know where their data is distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, contracts underlie custom policies [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  A hybrid cloud mixes two or more cloud infrastructures, such as private and public  clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, each entity keeps its core element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hybrid clouds define “standard-  ized or proprietary technology to enable data and application portability”[47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 Honeypots  The term “honeypot” has been established for more than two decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 1997 was the  first time that a free honeypot solution became public.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Deception Toolkit (DTK),  developed by Fred Cohen, released the first honeypot solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the earliest  drafts of honeypots are from 1990/91 and built the foundation for Fred Cohen’s  DTK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Clifford Stoll’s book “The Cuckoo’s Egg”[66], and Bill Cheswick’s whitepaper  “An Evening With Berferd”[7] describe concepts that are considered nowadays as  honeypots [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A honeypot itself is a security instrument that collects information  on buzzing attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It disguises itself as a system or application with weak links,  so it gets exploited and gathers knowledge about the adversary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In 2002, a Solaris  honeypot helped to detect an unknown dtspcd exploit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Interestingly, a year before  in 2001, the Coordination Center of CERT4 shared their concerns regarding the  dtspcd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Communities were aware that the service could be exploited to get access  and remotely compromise any Unix system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  However, such an exploit was not  known during this time, and experts did not expect any in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Luckily,  early instances based on honeypot technologies could detect new exploits and avoid  further incidents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Such events emphasize the importance of honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 Definition of Honeypots  Many definitions for honeypots circulate through the web that causing confusion and  misunderstandings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In general, the objective of a honeypot is to gather information  about attacks or attack patterns [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, contributing as an additional source of  security measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' See subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 for a detailed view regarding honeypots in  the security concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As Spitzner [65] has listed, the most misleading definitions:  a honeypot is a tool for deception, it is a weapon to lure adversaries or a part of  4Computer Emergency Response Team is an expert group that handles computer security  incidents[31]  7  an intrusion detection system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In order to get a basic understanding, this section  wants to exhibit some key definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Spitzner [65] defines honeypots as a “security  resource whose value lies in being probed, attacked, or compromised”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Independent  of its source (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', server, application, or router), he expects the instance to be  probed, attacked, and eventually exploited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  If a honeypot does not match this  behavior, it will not provide any value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is essential to mention that honeypots  do not have any production value;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, any communication that is acquired is  suspicious by nature [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, Spitzner [65] points out that honeypots are  not bound to solve a single problem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' hence, they function as a generic perimeter  and fit into different situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Such functions are attack detection, capturing  automated attacks, or alert/warning generators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 shows an example of  how honeypots could be used in an IT infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In general, he differentiates two types of honeypots (i) production honeypots (ii) re-  search honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This categorization has its origin from Mark Rosch, a developer  of Snort, during his work at GTE Internetworking [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Production honeypots are the most common type of honeypots that people would  think of.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The objective is to protect production environments and mitigate the risk  of attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Usually, production honeypots are easy to deploy within an organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Mostly, low-interaction honeypots are chosen due to a significant risk reduction, so  adversaries cannot exploit honeypots to attack other systems [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The downside  of a low-interaction honeypot is a lack of information, which means only standard  information like the origin of attacks or what exploits have been used can be collected  [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary, insides about the communication of attackers or deployment of  such attacks are unlikely to obtain, whereas research honeypots fulfill this objective  [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Research honeypots are used to learn more in detail about attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The objective  is to collect information about clandestine organizations, new tools for attacks, or  the origin of attacks [65, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Research honeypots are unlikely suitable for produc-  tion environments due to a higher risk increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Facing an increase in deployment  complexity and maintenance does not attract production usage either [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It is worth mentioning that there is no exact line between research or production  honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A possible use case is a honeypot that functions as a production or a  research honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Due to the dynamic range in which they are applicable, it is  difficult to distinguish them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, Provos [55] adds a differentiation for the virtual honeypot framework  and splits it into the following types:  Physical honeypots are “real machines on the network with its own Internet  Protocol (IP) address” [55]  Virtual honeypots are “simulated by another machine that responds to network  traffic sent to the virtual honeypot” [55]  8  Gateway  Router  Internet  DMZ  Internal  Mail  Web  Honeypot  A  Desktop  Desktop  Honeypot  B  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: Example of honeypots in a simplified network (derived from [65]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each  of the demilitarized zones (DMZs) and internal networks are separated  by a router and a Layer-3 switch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In each network a honeypot is available  (honeypot A, B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The red path symbolizes the path of an attacker coming  from the gateway router.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 Level of Interaction  When building and deploying a honeypot, the depth of information has to be defined  beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Should it gather unauthorized activities, such as an nmap scan?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Do  you want to learn about buzzing tools and tactics?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each depth brings a different  level of interaction because some information depends on more actions of adversaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Therefore, honeypots differ in their level of interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Low-interaction honeypots provide the lowest level of interaction between an at-  tacker and a system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only a small set of services like Secure Shell (SSH), Telnet, or  File Transport Protocol (FTP) are supported, contributing to the deployment time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In terms of risk, a low-interaction honeypot does not give access to the underlying  OS which makes it safe to use in a production environment [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, us-  ing an SSH honeypot with emulated services allows attackers to log in and execute  commands by brute force or guesswork.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The adversary will never gain more access  because it is not a real OS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, safety comes with the downside of less informa-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The collection is limited for the statistical purpose such as (i) time and data  of attack (ii) source IP address and source port of the attack (iii) destination IP  address and destination port of the attack [65, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The transactional information  can not be collected [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  A medium-interaction honeypot offers more sophisticated services with a higher  level of interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is capable of responding to specific activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, a  Microsoft IIS Web server honeypot could respond in a way that a worm is expecting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The worm would get emulated answers and could be able to interact with it in more  detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In this way, more severe information about the attack can be gathered,  including privilege assessment, toolkit capture, and command execution Spitzner  [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In comparison, medium-interaction honeypots allocate more time to install  and configure [65, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Also, more security checks have to be performed due to a  higher interaction level than low-interaction honeypots [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  High-interaction honeypots represent a real OS to provide a full set of interactions to  attackers [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' They are so powerful because other production servers do not differ  much from high-interaction honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' They represent real systems in a controlled  environment [65, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The amount of information is tremendous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It helps to learn  about (i) new tools (ii) finding new bugs in the OS (iii) the black hat community [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  However, the risk of such a honeypot is extremely high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It needs severe deployment  and maintenance processes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, it is time-consuming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 Security concepts  Security concepts are classified by Schneier [63] in prevention, detection, and reac-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Prevention includes any process that (i) discourages intruders and (ii) hardens  systems to avoid any breaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Detection scrutinizes the identification of attacks  10  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Distinction between security concepts based on areas of operations (de-  rived from [51]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Objective  Prevention  Detection  Reaction  Honeypot  +  ++  +++  Firewall  +++  ++  +  Intrusion Detection Sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  +  +++  +  Intrusion Prevention Sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  ++  +++  ++  Anti-Virus  ++  ++  ++  Log-Monitoring  +  ++  +  Cybersecurity Standard  +++  +  +  that threatens the systems’ (i) confidentiality (ii) integrity and (iii) availability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Re-  action treats the active part of the security concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' When attacks are detected,  it conducts reactive measures to remove the threat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each part is designed to be  sophisticated so that all of them contribute to a secure environment [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeypots contribute to the security concept like firewalls, or intrusion detection  systems (IDSs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, honeypots add only a small value towards prevention  because security breaches cannot be identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, attackers would avoid  wasting time on honeypots and go straight for production systems instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Detection is one of the strengths of honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Attacks often vanish in the sheer  quantity of production activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If any connection is established to a honeypot,  it is suspicious by nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In conjunction with an alerting tool, attacks can be  detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeypots strongly supply reaction tools due to their clear data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is difficult to find  attacks for further data analysis in production environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Often data submerge  with other activities, which complicates the process of reaction [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Nawrocki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [51] distinguish honeypots from other objectives such as firewall or log-monitoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 Value of Honeypots  To assess the value of honeypots, this section looks at their advantages and disad-  vantages [50, 39, 65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Advantages  Data Value: Collected data is often immaculate and does not contain noise  from other activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, reducing the total data size and speeding up the  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  11  Resources: Firewalls and IDS are often overwhelmed by the gigabits of traffic,  thus, dropping network packets for analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This results in far less effective  detection of malicious network activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, honeypots are indepen-  dent of resources because they only capture their activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Due to resource  limitations, expensive hardware is not needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Simplicity: A honeypot does not require complex algorithms or databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If  a honeypot is too complex, it will lead to misconfigurations, breakdowns, and  failures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The challenging research honeypots might come with an inevitable  increase in complexity in maintenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Return on Investment: Capturing attacks immediately informs users that sus-  picious activities occur on the infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This helps to demonstrate their  value and contributes to new investments in other security measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, Nawrocki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [51] listed four more advantages of honeypots:  Independent of Workload: Honeypots only process traffic directed to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Zero-Day-Exploit Detection: It helps to detect unknown strategies and zero-  day-exploits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Flexibility: Well-adjusted honeypots for various specific tasks are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Reduced False Positives and Negatives: Any traffic or connection to a honey-  pot is suspicious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Client-honeypots verify such attacks based on system state  changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This results in either false positive or false negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Disadvantages  Narrow Field of View: Only direct attacks on honeypots can be investigated,  whereas attacks on the production system are not detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Fingerprinting: A honeypot often has a certain fingerprint that attackers can  identify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Especially commercial ones can be detected by their responses or  behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Risk to the Environment: Using honeypots in an environment always increases  risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, it depends on the level of interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  12  Gateway  Router  Internet  Honeynet  Internal  Honeypot  Honeypot Honeypot  Mail  Web  FTP  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3: Example of honeynets in a simplified network (derived from [65]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This  network presents the honeynet consisting of several other honeypots on  the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the right, the network presents a common subnet consisting  of mail, web, and FTP server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5 Honeynets  Instead of having single honeypots that can be attacked, a honeynet offers a complete  network of standard production systems such as you would find in an organization  [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Those systems are high-interaction honeypots, thus, allowing them to fully  interact with the OS and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The key idea is that an adversary can probe,  attack, and exploit these systems so that the maintainer can derive interaction  within this network [65, 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It should be mentioned that a honeynet has to be  protected by firewalls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 represents such a honeynet within  an organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Compared to a traditional honeypot, the most significant value of honeynets is the  usage of proper production systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Black hats often do not know that they attack  13  a honeynet, thus, adding value to prevention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the downsides are the high  complexity and maintenance needed to keep a honeynet running [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6 Legal Issues  Considering questions related to legal issues of honeypots can easily exceed this  thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In this regard, this section restricts the study to the country the author  resides in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, only the European Union (EU) regulations, EU directives, and  international agreements are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Honeypots collect (i) content data that  is used for communication, and (ii) transactional data that is used to establish  the connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Sokol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [64] studied the legal conditions for data collection  and data retention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' They have concluded that administrators of honeypots have a  legal ground of legitimate interest to store and process personal data, such as IP  addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, for production honeypots, the legitimate interest is to secure  services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Regarding the length of data retention, the principle of data minimization  has to be considered, which means there is no clear answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Any published data of  research honeypots needs to be anonymized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  14  Chapter 3  Analyze Honeypot Attacks in the  Cloud  Attacks from the Internet often originate from bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A bot, short for “robot”, is an  automated process that interacts with different network services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Despite good in-  tentions, bots can be used for malicious purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Mostly, bots try to self-propagate  malware across the Internet and try to capture hosts that merge into a botnet [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Recently, Universities in Germany received more cyberattacks than ever, respec-  tively increasing their costs for damage repairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Honeypots are a good solution to  catch attackers and learn from their exploits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, it is not clear whether hon-  eypots are an appropriate countermeasure to prevent such damage in the age of  bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Following the rise of cyberattacks, this chapter introduces a method to collect  and analyze cyberattacks in a cloud environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It further proposes an answer if  honeypots are helpful to detect bot activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 Introduction  As previously mentioned in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2, using cloud resources is becoming the go-to  option for new services and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] thoroughly investigated  honeypots on Azure, Amazon Web Services (AWS), and Google Cloud Platform  (GCP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Consequently, this chapter presents their results briefly to compare them  with the ones heiCLOUD achieves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The results are collected by T-Pot version  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 for three weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] considered different server  geographical locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' They have collected data from East US, West Europe, and  Southeast Asia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 shows the results presented by Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Dionaea  (a honeypot to capture malicious payload), Cowrie (SSH and Telnet honeypot), and  Conpot (industrial honeypot for ICS and SCADA) are the most attacked honey-  pots in comparison to the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Regarding AWS, Dionaea accounts for 91% of  the total attacks, Glutton and Cowrie are minor with 5%, and 2%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Interestingly,  Cowrie reported several attacks related to the COVID-19 pandemic to enable social  15  engineering methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In contrast to AWS, Cowrie logged the majority of attacks  with 51% on GCP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Besides several automated attacks trying to log in with default  credentials, adversaries tried to gather information about the GPU architecture,  scheduled tasks, and privilege escalation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Microsoft Azure reflects nearly the same  results as the other two cloud providers beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Overview of attacks on cloud providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For a better overview, only the  three most attacked honeypots are listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The remaining honeypots are  listed in the column named "others".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Provider  Honeypot  In Total  Dionaea  Cowrie  Glutton  others  Amazon Web Services  228,075  4,503  11,878  3,688  248,144  Google Cloud Platform  162,570  297,818  84,375  36,403  581,116  Microsoft Azure  308,102  9,012  17,256  6,365  340,735  The overall results show an average ratio of 55,000 attacks per day, summing up  to roughly 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='17 million in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Similar results for different regions could have  been reproduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Their results clearly show the Europe, US, and Asia disparity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  An important question that Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] answered is if attackers target services  on cloud providers based on the cloud providers’ market share.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The study could  not confirm this assumption because Google Cloud received most of the attacks  with the smallest market share.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In total, most of the attacks are originated from  Vietnam, Russia, the United States, and China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Due to technologies such as VPN  or Tor, the geolocation only indicates the last node so that location data might be  distorted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Across all providers, roughly 80% of the source IP addresses had a bad  reputation (identified by Suricata) and could have been filtered by the organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The operating devices used for attacking the services are mostly Windows 7 or 8 and  different Linux kernels and distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Windows devices target vulnerabilities in  remote desktop sharing software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Such vulnerabilities are (i) CVE-2006-2369[14]  (RealVNC) in the US region, (ii) CVE-2001-0540[11] (Remote Desktop Protocol  (RDP)) in EU and Asia regions, (iii) CVE-2012-0152[15] (RDP) in the Asia region,  and (iv) CVE-2005-4050[13] (Voice over Internet Protocol (VoIP)) in EU region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, attackers were also capable of disguising any fingerprinting activity of  P0f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  This chapter compares the findings Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] claimed in the paper “A Com-  parative Analysis of Honeypots on Different Cloud Platforms” with ours using the  Heidelberg University’s cloud solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' First, a short introduction of heiCLOUD  is given, followed by a closer lookup of the T-Pot used to acquire data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Lastly, it  presents the results and does a thorough comparison closing up with a discussion  based on a technical report of Cambridge University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  16  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 Methodology  The foremost goal is to track as many attacks as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 sketches the  concept to achieve this goal to gather various attacks from the Internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Honeypots  should be deployed on a single instance, and their data or log files are stored in a  database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The attacks are analyzed with the help of data visualization tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For  security reasons, honeypots should run in a virtualized environment to avoid harming  the host system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The host machine runs on a Debian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The instance  runs on heiCLOUD, a cloud service provided by Heidelberg University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is capable  of 16 GB of RAM, 8 vCPUs, and volatile memory of 30 GB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, it mounts  a 125 GB permanent volume to store the data securely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In the very early stage  of this chapter, different approaches to achieve this goal have been compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For  example, native implementation approaches, additional frameworks, and ready-to-  use solutions have been evaluated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the T-Pot, developed by Telekom, offers  a profoundly ready-to-use solution with significant advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It combines several  honeypots with various analytic tools to trace the newest attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Furthermore, it  helps to compare the findings with the ones Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Running the instance and exposing it to the Internet needs some adjustments be-  forehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, a virtual network with subnet 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24 has been  created wherein the IP address 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 is assigned to the instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The  instance is accessible from the outside with a floating IP address 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Access rules are similar to a stateless firewall, and thus, do not block any attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Ports 1−64000 are exposed and can be attacked by anyone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Ports higher than 64000  are only accessible through the university network 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/16 or eduroam  147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/16 and should provide a basic authentication with username and  password.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 heiCLOUD  University Computing Center Heidelberg offers a “IaaS specially tailored for higher  education and research institutions”[69] called heiCLOUD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It supplies multiple de-  partments at Heidelberg University with storage, virtual machines, or network com-  ponents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, heiCLOUD is a DFN1 member and offers others to use their  services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As stated on their information website[68], it (i) is capable of freely manage-  able IT resources, (ii) beholds a stable and fast connection, (iii) ensures high avail-  ability and scalability, (iv) has freely selectable VM operating systems, and (v) has  a transparent payment model [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Users can easily create their network areas and  manage their space individually based on the open-source application OpenStack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Unlike well-known cloud providers, heiCLOUD servers are located within Germany,  1German National Research and Education Network is the communications network for Science  and research in Germany  17  heiCLOUD  Network  Internet  Gateway  Switch  stores logs  runs  database  (persistence 90 days)  m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='xlarge  Debian 10, Buster  Honeypot  Honeypot  Honeypot  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Concept to collect honeypot attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The instance size is referred to the  available resources of OpenStack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The network is an encapsulated subnet  with a switch for incoming and outgoing connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The database is  independent of the instance and could run on a separate host.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  18  thus, abide by the European data privacy law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' HeiCLOUD has never considered  implementing honeypots for additional cybersecurity measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 T-Pot  To be able to compare the results with Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40], the same approach to  capture recent cyberattacks is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The T-Pot solution, a mixture of Telekom and  Honeypot, stands out with its sheer quantity of various honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It requires at  least 8 GB of RAM and a minimum of 128 GB of hard drive storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Based on a  Debian 10 Buster distribution, it relies on Docker to run their services [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' T-Pot  has to be deployed in a reachable network where intruders are expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Either  Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) traffic  are forwarded without filtering to the network interface, or it runs behind a firewall  with forwarding rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Specified ports for attackers are 1-64000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' higher ports are  reserved for trusted IPs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, a reverse proxy asks for basic authentication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All  daemons and tools run on the same network interface, but some are encapsulated  in their own Docker network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The lightweight virtualization technology Docker  uses containers to run on the host system [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Unlike virtual machines, Docker  reduces overhead with the downside of a greater attack surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' To mitigate attacks,  Docker wraps containers in an isolated environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This is achieved by restricting  the kernel namespace and control groups (cgroups) [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 visualizes the  technical concept of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each service has dedicated ports or port ranges that  are exposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Attackers can communicate either with TCP or UDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All honeypots  and tools create log files used to get any knowledge about attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In order to  view and trace current attacks, T-Pot uses the ELK stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ELK is the acronym  of Elasticsearch, Logstash, and Kibana [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The search engine Elasticsearch is  based on the Lucene library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is multitenant-capable and offers full-text search  via HTTP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Logstash is used to feed Elasticsearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In general, it offers an open  server-side data processing pipeline that helps to send data from multiple sources  to an Elasticsearch node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Kibana is the primary data visualization tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It enables  users to create plots and dashboards, crawl Elasticsearch, and trace the system’s  health.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  All logs of the honeypots and tools are forwarded to the search engine  Elasticsearch by Logstash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The ELK stack is not directly exposed to the Internet;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  thus, authentication is unnecessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Users can monitor all log files with Kibana  by pre-defined dashboards or custom search queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, T-Pot features  different services types, namely (i) standard, (ii) sensor, (iii) industrial, (iv) collector,  (v) next generation, and (vi) medical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Each service type has a different set of  honeypots and tools tailored to its core idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' T-Pot feeds their data to an external  Telekom service;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' however, this data submission can be turned off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The latest version,  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0, has been used in this chapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Newer versions might be available by the  end of this study and could differ from this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='https://IP:64295  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='basic authentication  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='https://IP:64297  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='basic authentication  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='IP:1-64000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='no authentication  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='FATT  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='p0f  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Suricata  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='NSM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='host  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Heimdall /  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='NGINX  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ADBHoney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Cisco ASA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Honeypot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Citrix  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Honeypot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Conpot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Cowire  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Dicompot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ElasticPot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Glutton  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Honeytrap  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='IPPHoney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Mailoney  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Medpot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='RDPY  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Honeypots  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Host Network Interface  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ElasticSearch  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Logstash  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Kibana  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Head  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ELK  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='localhost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='localhost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='CyberChef  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Tools  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Spiderfoot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='EWS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Poster  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='network  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Cockpit  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='Debian 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Buster  Hardware Requirements:  RAM  8 GB <  SSD 128 GB <  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: T-Pot architecture derived from [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeypots are encapsulated in their network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  NSM runs on the host  network, and thus, receives every packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ELK and tools run on localhost and are accessible through NGINX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The Cockpit application is a web-based graphical interface for servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  20  Honeypots  T-Pot consists of 20 honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Albeit the sheer quantity of it, a short explanation  is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 gives a quick overview of all available honeypots in  conjunction with (i) the port they are running on, (ii) their interaction level, and  (iii) a short description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  ADBHoney [8] is a low-interaction Android Debug Bridge (ADB) honeypot over  TCP/IP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The importance of it lies in the ADB protocol that is used for debugging  and pushing content to an Android device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, unlike a Universal Serial Bus  (USB) connection, it does not support any kind of ample mechanisms of authenti-  cation and protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' By exposing the ADB service over any port, an adversary  could connect and exploit it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ADBHoney is designed to catch malware that has been  pushed onto devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Cisco Adaptive Security Appliance (ASA) [57] is a low-interaction honeypot  that detects CVE-2018-0101[16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is a vulnerability that could allow an unau-  thenticated, remote attacker to cause a reload of the affected system and remotely  execute code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This can be achieved by flooding a webvpn-configured interface with  crafted Extensible Markup Language (XML) packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Consequently, the attacker  obtains full control by executing arbitrary code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Citrix Application Delivery Controller (ADC) honeypot [34] detects and  logs CVE-2019-19781[18] scans and exploitation attempts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This vulnerability al-  lows adversaries to perform directory traversal attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Files are accessible by path  strings to denote the file or directory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, some file systems include spe-  cial characters to traverse the hierarchy easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Attackers take advantage of it by  combining special characters to get access to restricted areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [30]  Conpot [58] is a low-interaction industrial honeypot for Industrial Control System  (ICS), and Supervisory Control and Data Acquisition (SCADA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It provides a variety  of different standard industrial control protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' An adversary should be tricked  by the complex infrastructure and lured into attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, a custom human-  machine interface can be connected to increase the attack surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' By randomly  delaying the response time, Conpot tries to emulate a real machine handling a  certain amount of load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Cowrie [53] is a medium- to high-interaction SSH and Telnet honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It offers to  log brute-force attacks and shell interactions with attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In medium-interaction  mode, Cowrie emulates a Unix shell in Python, whereas in high-interaction mode,  it proxies all commands to another system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  DDoSPot [22] is a low-interaction honeypot to log and detect UDP-based Dis-  tributed Denial of Service (DDoS) attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is a platform used to support various  plugins for different honeypot services and servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Currently, it supports Domain  21  Name System (DNS), Network Time Protocol (NTP), Simple Service Discovery Pro-  tocol (SSDP), Character Generator Protocol (CHARGEN), and random/mock UDP  server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Dicompot [41] is a low-interaction honeypot for the Digital Imaging and Commu-  nications in Medicine (DICOM) protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As with other honeypots before, it mocks  a DICOM server in Go to collect logs and detect attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Dionaea [24] is a medium-interaction honeypot that tries to capture malware copies  by exposing services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It supports various protocols such as FTP, Server Message  Block (SMB), and HTTP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Several modules can be integrated to work with Dionaea  for further malware results, such as VirusTotal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Elasticpot [4] is a low-interaction honeypot for Elasticsearch, a search engine based  on the Lucene library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Glutton [59] is a generic low-interaction honeypot that works as a man-in-the-  middle (MITM) for SSH and TCP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, lacking documentation does not provide  a deeper insight into this honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Heralding [71] is a credential catching honeypot for protocols like FTP, Telnet,  SSH, HTTP, or Internet Message Access Protocol (IMAP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  HoneyPy [32] is a low to medium-interaction honeypot that supports several pro-  tocols such as UDP or TCP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' New protocols can be added by writing a custom  plugin for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' HoneyPy gives the freedom of quickly deploying and extending  honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  HoneySAP [32] is a low-interaction honeypot tailored for SAP services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeytrap [75] is a low-interaction honeypot network security tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As stated by  Werner [75], Honeytrap is vulnerable to buffer overflow attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  IPPHoney [5] is a low-interaction Internet Printing Protocol (IPP) honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Mailoney [46] is a low-interaction Simple Mail Transfer Protocol (SMTP) honeypot  written in Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  MEDpot [62] is a low-interaction honeypot focused on Fast Healthcare Interoper-  ability Resources (FHIR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is a standard description data format to transfer and  exchange medical health records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  RDPY [54] is a low-interaction honeypot of the Microsoft RDP written in Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It features client and server-side, and it is based on the event-driven network en-  gine Twisted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It supports authentication over Transport Layer Security (TLS) and  Network Level Authentication (NLA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  SNARE and TANNER [60, 61] is a honeypot project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' SNARE is an abbrevia-  tion for Super Next-generation Advanced Reactive honEypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is a successor of  22  Glastopf, a web application sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, it supports the feature of convert-  ing existing web pages into attack surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' TANNER [61] can be seen as SNARES’  brain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Whenever a request has been sent to SNARE, TANNER decides how the  response should be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Tools  T-Pot integrates tools to screen network traffic and block DoS attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  FATT [37] is used to extract metadata and fingerprints such as JA3 [2] and HASSH  [38] from captured packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' JA3 is a method for “creating SSL/TLS client finger-  prints” whereas HASSH is a network fingerprinting standard that is used to identify  specific client and server SSH implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, it features live network  traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As noted by the author, FATT is based on a python wrapper for tshark,  namely pyshark, and thus has performance downturns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  T-Pot applies FATT on  every request made on the host network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Spiderfoot [48] is an open-source intelligence automation tool that helps to screen  targets to get information about what is exposed over the Internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It can target  different entities such as IP address, domain, hostname, or network subnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In  addition, it features more than 200 modules that can be integrated as an extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  T-Pot uses it to scan defensively and thus not include any other module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Suricata [67] is “a high performance IDS, intrusion prevention system (IPD) and  network security monitoring (NSM) engine”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' T-Pot lets Suricata analyze and assess  any request made on the host network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  P0f [77] is a fingerprinting tool that uses passive traffic fingerprinting mechanisms  to check TCP/IP communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' T-Pot lets P0f passively check any request made  on the host network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Endlessh [74] is an SSH server that sends an endless, random SSH banner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The  key idea is to lock up SSH clients that try to connect to the SSH server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It low-  ers the transaction speed by intentionally inserting delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Due to the established  connection before the cryptographic exchange, this module does not require any  cryptographic libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  HellPot [35] is an “endless honeypot”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If someone connects to this honeypot, it  results in a memory overflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Its key idea is to send an endless data stream to the  attacker until its memory or storage runs out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  23  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: Overview of all available honeypots of T-Pot with interaction level, port, and a short description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Ports are marked  with either TCP or UDP;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' if a port misses any definition, both TCP and UDP are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeypots  Port  Interaction-level  Description  ADBHoney [8]  5555/TCP  low  ADB protocol honeypot  Cisco ASA [57]  5000/UDP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 8443/TCP  low  honeypot for CVE-2018-0101[16] de-  tection  Citrix honeypot [34]  443/TCP  low  detects  and  logs  CVE-2019-  19781[18]  scans  and  exploitation  attempts  Conpot [58]  80,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 102,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' 502,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 623,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 1025,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 2404,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  10001,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 44818,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 47808,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 50100  low  industrial honeypot for ICS and  SCADA  Cowrie [53]  2222,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 23  high  SSH and Telnet honeypot  DDoSPot [22]  1112/TCP  low  log and detect UDP-based DDoS at-  tacks  Dicompot [41]  1112/TCP  medium  honeypot for the DICOM protocol  Dionaea [24]  21,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 42,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 69/UDP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 8081,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 135,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 443,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 445,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1433,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 1723,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 1883,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 1900/UDP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3306,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 5060/UDP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 5061/UDP  low  capture malware copies  Elasticpot [4]  9200  low  honeypot for Elasticsearch  Glutton [59]  NFQ  medium  MitM proxy for SSH and TCP  Heralding [71]  21,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 25,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 80,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 110,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 143,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 443,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  993,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 995,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 1080,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 5432,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 5900  low  credential catching honeypot  HoneyPy [32]  7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 2048,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 2323,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 2324,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 4096,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 9200  low  extendable honeypot  HoneySAP [32]  3299/TCP  low  honeypot for SAP services  Honeytrap [75]  NFQ  medium  captures attacks via unknown proto-  cols  IPPHoney [5]  631  low  IPP honeypot  Mailoney [46]  25  low  SMTP honeypot  MEDpot [62]  2575  low  FHIR honeypot  RDPY [54]  3389  low  Microsoft RDP honeypot  SNARE/TANNER [60]  80  low  web application honeypot  24  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 Results  The T-Pot has been deployed for three weeks (from 26th of September to 16th of Oc-  tober) and collected in total 607,747 attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Overall, RDPY (46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='08%), Honeytrap  (33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='23%), and Cowrie (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='42%) received most of the attacks with a total amount of  540,398 attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 shows the distribution of honeypot attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The total  numbers are based on Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Adbhoney  Ciscoasa  CitrixHoneypot  ConPot  Cowrie  Dicompot  Dionaea  ElasticPot  Heralding  Honeysap  Honeytrap  Medpot  Rdpy  Tanner  Honeypots  0  50000  100000  150000  200000  250000  300000  350000  Number of Attacks  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3: Distribution of honeypot attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th  of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A description of each honeypot can be found in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  What is striking is the large disparity between the previously mentioned attacks  on AWS, GCP, and Azure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Especially with the honeypot Dionaea, it is unclear  why only 2,368 attacks have been performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 96% of IP addresses connected to  Dionaea are known attackers, and 70% were acquired on port 81, unofficially known  for Tor routing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Neither any malware nor suspicious payload could be identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  An assumption is that the packets run through a static filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Heidelberg has a  centralized stateless firewall, indicating that specific ports or protocols are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  A nmap TCP SYN scan (nmap -sS -A 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='74) has been performed to prove  this assumption that ports are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The result clearly shows that port 139  for SMB is filtered, although the access security explicitly allows it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The stateless  firewall runs in front of heiCLOUD and filters many ports, including 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Based  on this, it can be assumed that most of the attacks on Dionaea are carried out via  25  SMB, which would explain the total number of attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The administrator of the  university firewall had been consulted to exclude the T-Pot instance to validate if the  actual number is even higher without any packet filter in front of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Respectively, no  stateless packet filter has been applied to the T-Pot for three weeks (2nd of December  until 23rd of December).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It could identify a drastic increase in Dionaea attacks with  a total number of 213,053.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Overall, 93% of all attacks are on the SMB protocol  followed by many database protocols such as MongoDB and MSSQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This confirms  the assumption that a higher total number of attacks would be the result without  the packet filter in front of the instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Comparing the number with Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] it shows that Dionaea attacks surpass  every other cloud provider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, Dionaea attacks will not be included in later  results because usually, a server is not allowed to be excluded from the university  firewall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only for this research purpose to assess the effect of the packet filter has  an exclusion been granted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  25000  50000  75000  100000  125000  150000  175000  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4: Attack distribution of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The USA, Russia, China, and Germany  are the most attacking countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th  of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Logstash uses GeoLite2 to resolve the source IP address with information such as  location, Autonomous System Number (ASN), continent code, country name, and  Autonomous System (AS) organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 indicates the geographical lo-  cation of connections acquired to any honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Most attacks are originated from  the United States, Germany, Russia, and China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Large security scans of DFN or  Baden-Württembergs extended LAN (BelWÜ) pushes Germany to second place;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  therefore, Germany can be considered negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary, the geographical  location of an IP address merely indicates the true origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Due to technologies like  VPN or Tor, the last known node of an IP address could be spoofed, and thus as  stated by Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40], would remain insufficient to use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hence, no one should  rely on geographical information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Attacks are not equally distributed among all honeypots, and thus, different proto-  cols and applications receive more attention than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5 shows the time-  26  2021-09-26  2021-09-30  2021-10-04  2021-10-08  2021-10-12  Timestamp  0  10000  20000  30000  40000  Number of Attacks  Adbhoney  Cowrie  Heralding  Honeytrap  Rdpy  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5: Attack histogram of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only the five most attacked honeypots are  considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A de-  scription of each honeypot can be found in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  line of attacks that are executed on our instance separated by honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' RDPY,  Honeytrap, and Cowrie are the most attacked honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The high peak of Honey-  trap in the middle indicates a full nmap scan from Germany that has been done to  get an insight of the packet filtering at the Heidelberg University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It identifies a bias  towards remote desktop protocol attacks, shell-code exploitations, and commands  to retrieve information about the CPU, scheduled tasks (cat /proc/cpuinfo, or  crontab), or privilege escalation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Suricata registered several alerts and CVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The vast majority of alerts are RDP-  related policies, Virtual Network Computing (VNC) authentication failures, and  nmap scans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Most used vulnerabilities are (i) CVE-2001-0540[11] which is a memory  leak in terminal servers in Windows NT and Windows 2000 causing a denial of  service (memory exhaustion) by malformed RDP requests,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' (ii) CVE-2006-2369[14]  which is a RealVNC vulnerability allowing hackers to bypass authentication,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' and  (iii) CVE-2012-0152[15] which enables attackers for RDP in Microsoft Windows  Server 2008 R2 and R2 SP1 and Windows 7 Gold and SP1 to cause a denial of  service by sending a series of crafted packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As derived from Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6, the T-Pot  has not received many attacks in the first week.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Starting from the 28th of September,  the number of alerts is skyrocketing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This would indicate that bots crawl IP address  ranges to find new machines and probe them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Interestingly, zero-day exploits like  the Apache vulnerability [20] that came with version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 got registered in CVE on  27  2021-09-26  2021-09-30  2021-10-04  2021-10-08  2021-10-12  Timestamp  0  20000  40000  60000  80000  100000  120000  140000  Number of Attacks  Misc activity  Misc Attack  Generic Protocol Command Decode  Attempted Information Leak  Attempted Administrator Privilege Gain  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6: Suricata results of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Displays the five most listed alert categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  the 6th of October and immediately recognized by Suricata on the 15th of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Attackers could perform a remote code execution using path traversal attacks when  the Common Gateway Interface (CGI) scripts of Apache are enabled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The logs could  trace back similar attacks like /cgi-bin/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='\\%2e/\\%2e\\%2e/bin/sh until the 7th of  October, leaving an even smaller time frame to adapt to new exposures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This shows  how fast bots adapt to new vulnerabilities to compromise more systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The results from RDPY in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7 backups the assumption that attacks originate  from bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It shows that only a small margin represents unique source IP addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The rest of the attacks result in either a bad reputation, bot, crawler, or known at-  tacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6 shows the distribution of alert categories that Suricata identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Respectively, misc activities sum up to roughly 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5 million entries, RDP related  alerts account for two-thirds of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Several RDP attacks from 2021 back to 2001  had been executed on the T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Respectively, CVE-2012-0152 and CVE-2001-0540  coincide with the ones Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  For NFQ related attacks, Honeytrap could identify three major services that are  not provided by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Honeytrap functions as a honeypot to provide a service  on ports that are not specified by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' NFQ intercepts incoming TCP connec-  tions during the TCP handshake, and Honeytrap provides a service for it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Most of  these interceptions are made on (i) port 5038, which is used by a machine learning  database called MLDB, (ii) port 5905, which an Intel Online Connect Access uses on  Windows machines, and (iii) port 7070 which is used by Apple’s QuickTime stream-  ing server (RTSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Nearly all ports attacks focused on RDP connection attempts  (Cookie: mstshash=Administr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, 94% of all connected IP addresses on  Honeytrap are resolved as known attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  28  2021-09-29  2021-10-03  2021-10-07  2021-10-11  2021-10-15  Timestamp  0  5000  10000  15000  20000  25000  30000  35000  Number of Attacks  Attacks  Unique Src IPs  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7: RDPY attacks are separated into attacks and unique source IP addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A description of the  honeypot can be found in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  29  2021-09-29  2021-10-03  2021-10-07  2021-10-11  2021-10-15  Timestamp  0  500  1000  1500  2000  2500  3000  3500  Number of Attacks  5038  5901  6379  7070  8000  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8: Honeytrap results of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th of  October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A description of the honeypot can be found in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2021-09-26  2021-09-30  2021-10-04  2021-10-08  2021-10-12  Timestamp  0  200  400  600  800  Number of Attacks  22  23  80  443  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9: Cowrie results of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of September to 16th of Octo-  ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A description of the honeypot can be found in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  30  The third most compromised honeypot is Cowrie, with a strong bias towards SSH  and FTP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9 shows all attacks executed on Cowrie separated by their port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Respectively, SSH port 22 is the most considered port, resulting in high use for  privilege escalation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Besides using default credentials to log in (username: root,  password: root, see Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='10 for top 10 credentials), adversaries used various  commands to retrieve any information about the host system (nproc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='uname -a,  cat /proc/cpuinfo).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A unique information gathering attack could be identified  that has been widely used on the T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 shows all shell commands  that are executed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Attackers try to gain knowledge about running processes on the  system (/bin/busybox).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Interestingly, crypto mining attacks are getting more at-  tractive to criminals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, XMRig has been the most downloaded malware  for cryptocurrency mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Some adversaries even executed complex tailored shell  commands to exploit the host machine as a crypto miner (Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is not  surprising that such attacks gain attraction concerning the current time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Attack-  ers could exploit machines for crypto mining in order to earn more money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This  looks more appealing than acquiring mining machines and hijacking electricity from  surrounding apartments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  root  user  admin  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='root  blank  pi  0  ubuntu  test  guest  Username  0  1000  2000  3000  4000  5000  6000  7000  Number of Usage  (a) Cowrie username credentials  1  123456  1234  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ishtar  x  blank  0  123  admin  root  Password  0  200  400  600  800  Number of Usage  (b) Cowrie password credentials  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='10: Cowrie top 10 credentials used on T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 26th of Septem-  ber to 16th of October.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A description of the honeypot can be found in  section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  P0f identified different Windows versions and Linux distributions in conjunction  with various SSH clients to compromise the T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Like Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] presented,  Windows 7 or 8 and Windows NT Kernel are the most used OS with 81%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Unfor-  tunately, disguising OS fingerprinting activities account for 84% of all fingerprints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Lastly, the results are cleaned up and all IPs from DFN and BelWÜ are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Both scan frequently and check if any vulnerability exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This distorts the findings,  and thus, they have been filtered based on their subnet addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the re-  sults show no notable changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The total number of attacks was hardly influenced  by it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This indicates that these scans do not greatly interfere with the findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  31  On average, heiCLOUD has received 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='83% more than Azure, GCP, and AWS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Attacks on Cowrie, RDPY, and Honeytrap are the most compromised honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In contrast to Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40], Dionaea and Glutton used to be the most considered  honeypots for adversaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It can be assumed that attacks by bots had increased  significantly since last year when Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [40] did their research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Respectively,  one unresolved question is if other cloud providers filter their network traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It  would explain the major difference between Heidelberg University and the big tech  companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The cause for such an increase remains doubtful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' One explanation could  root back to the Corona pandemic and the skyrocketing increase in home office ac-  tivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Related to that is a higher usage in screen sharing software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Considering the  BSI2, report for cybersecurity 2021 [6], they revealed an increase of attack surfaces  during the pandemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Respectively, the IT infrastructure could not keep up with  this fast change and widen the company’s attack surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Their conclusion overlays  our assumption that attackers took advantage and increased their activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This  phenomenon shows that nearly all attacks originate from bots that scan through  IP address ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In total, 73% of all IP addresses are unresolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The known  attacker reputation represents the largest part of resolved IP addresses with 23%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Fortunately, such reputations could technically be filtered by an organization’s fire-  wall and would lower the chance of an exploit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Interestingly, after three weeks, the  number of attacks originating from China decreased to almost zero percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This  might indicate that the honeypot has been exposed, and further attacks represent a  risk of revealing their compromises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, this assumption cannot be confirmed  due to the lax geographical reliability of IP addresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Our results emphasize the importance of honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It gives a proper security mea-  sure of an IT infrastructure and helps to identify potential leaks or vulnerabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Moreover, it shows that T-Pot helps detect recent bot activities and gives an outlook  on the newest trends of attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 Discussion  One downside of T-Pot is the static hostname representation of Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It al-  ways returns #1 SMP Debian 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='68-1+deb7u1 (uname -a) as hostname informa-  tion, leaving a tiny footprint when bots crawl through the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A random choice of  hostname information could harden Cowrie from being exposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Next, if attackers  scan open ports on T-Pot, it might be suspicious when many ports with services are  open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' From a technical perspective, bots could check this state if it is uncommon  and thus, exclude T-Pot from being probed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, T-Pot includes reasonable  preventions like a random hostname and scheduled tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Another major drawback  2The Federal Office for Information Security is responsible for managing communication security  for the German government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each year they publish a report for recent cybersecurity threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  32  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3: Overview of attacks on heiCLOUD, AWS, GCP, and Azure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Only the top 10 most attacked honeypots are  considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' “-” entails that a honeypot is not part of the top 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The red and green arrows indicate whether  heiCLOUD received more or fewer attacks than the other cloud providers on average .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeypots  BASIS  comparison  heiCLOUD  AWS  GC  Azure  Number  Pct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Number  Pct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Number  Pct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Number  Pct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  ADBHoney  9,302  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='65%  ↑  413  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='17%  2,497  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='43%  442  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='13%  Cisco ASA  674  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='11%  ↑  260  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='10%  750  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='13%  134  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04%  Citrix honeypot  1,121  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='18% Conpot  615  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='10% Cowrie  75,511  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='97%  ↓  4,503  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='81%  297,818  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='25%  9,012  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='64%  DDoSPot  0  0% Dicompot  22  0% Dionaea  2,368  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='40%  ↓  228,075  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='91%  162,570  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98%  308,102  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='42%  Elasticpot  385  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='06% Glutton  0  0%  ↓  11,878  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79%  84,375  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='52%  17,256  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='06%  Heralding  35,680  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='34%  ↑  1,885  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='76%  12,255  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='11%  3,370  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99%  HoneyPy  0  0%  ↓  172  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='07%  2,149  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='37%  497  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='15%  HoneySAP  15  0% Honeytrap  201,949  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='01% IPPHoney  0  0% Mailoney  0  0%  ↓  720  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='29%  9,419  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='62%  146  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04%  MEDpot  2  0% RDPY  280,040  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='15%  ↑  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04%  7,916  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='36%  1,463  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='43%  SNARE/TANNER  63  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='02%  ↓  138  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='06%  1,367  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='24%  313  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='09%  In total  607,747  100%  248,144  100%  581,116  100%  340,735  100%  33  is the latest endeavor to detect honeypots on the transport level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As recently inves-  tigated by Vetterl [72], detecting honeypots is becoming easier due to a fatal flaw  in the underlying protocol implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vetterl [72] states that attackers always  try to prevent their methods, exploits, and tools from being divulged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore,  detecting honeypots before attacking them strongly motivates black hats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Chapter 5  will present a way to avoid such fingerprint activities with the honeypot Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Cowrie attack to gather various information about the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  enable  2  system  3  shell  4  sh  5  cat /proc/mounts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' /bin/busybox  $PROCESS_NAME  6  cd /dev/shm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' cat .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='s || cp /bin/echo .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' /bin/busybox  �→ $PROCESS_NAME  7  tftp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' wget;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' /bin/busybox  $PROCESS_NAME  8  dd bs=52 count =1 if=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='s || cat .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='s || while read i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' do echo  �→  $i;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' done < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='s  9  while read i  10  /bin/busybox  $PROCESS_NAME  11  rm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' exit  34  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: Cowrie attack to exploit the host machine as a crypto miner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  mkdir -p /home/osmc /.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ssh/  2  echo ssh -rsa  $RSA_KEY >> /home/osmc /.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="ssh//  �→ authorized_keys  3  echo '<cmd7uname >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" uname -a  4  echo '</cmd7uname ><cmd7uptime >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" uptime  5  echo '</cmd7uptime ><cmd7w >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" w  6  echo '</cmd7w ><cmd7who >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" who  7  echo '</cmd7who ><cmd7last >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" last  8  echo '</cmd7last ><cmd7lastlog >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" lastlog  9  echo '</cmd7lastlog ><cmd7authkey >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' cat /home/osmc /.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="ssh//  �→ authorized_keys  10  echo '</cmd7authkey ><cmd7lshome >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" ls -la /home  11  echo '</cmd7lshome ><cmd7passwd >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" cat /etc/passwd  12  echo '</cmd7passwd ><cmd7shadow >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" sudo -n cat /etc/shadow  13  echo '</cmd7shadow ><cmd7psfaux >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" ps -faux  14  echo '</cmd7psfaux ><cmd7netstat >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" netstat -npta  15  echo '</cmd7netstat ><cmd7arpan >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" /usr/sbin/arp -an  16  echo '</cmd7arpan ><cmd7ifconfig >'  17  /usr/sbin/ifconfig  18  echo '</cmd7ifconfig ><cmd7localconf >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' cat /home/ethos/  �→ local.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="conf  19  echo '</cmd7localconf ><cmd7remoteconf >'  20  cat /home/ethos/remote." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="conf  21  echo '</cmd7remoteconf ><cmd7rclocal >'  22  cat /etc/rc." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="local  23  echo '</cmd7rclocal ><cmd7claymorestub >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' cat /home/ethos/  �→ claymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='stub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='conf  24  cat /hive -config/rig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='conf;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' cat /hive -config/wallet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='conf  25  cat /hive -config/vnc -password.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="txt  26  echo '</cmd7claymorestub ><cmd7claymorezstub >'  27  cat /home/ethos/claymore -zcash." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='stub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="conf  28  echo '</cmd7claymorezstub ><cmd7sgminerconf >'  29  cat /var/run/ethos/sgminer." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="conf  30  echo '</cmd7sgminerconf ><cmd7iptables >'  31  sudo -n iptables -S  && sudo -n iptables -t nat -S  32  echo '</cmd7iptables ><cmdcrontab >';" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' crontab -l;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=" echo '</  �→ cmdcrontab >'  33  exit  35  Chapter 4  Catching Attackers in Restricted  Network Zones  The T-Pot identified a flood of threats when it was available on the Internet." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' How-  ever, capacious networks have separated compartments, and services are usually not  directly available without any protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Zoning is a well-known method to seg-  ment a network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Heidelberg University applies zoning, and thus, it is an interesting  question if an attacker probes services outside or within the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This chapter  presents a concept that uses a honeypot-like detection tool to detect any dubious  packets in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It shows that attacks occurred in a restricted network zone  of the Heidelberg University’s internal network and contributed to an adaption of  the stateless firewall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, improving the security of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 University Network  Honeypots that are accessible via the Internet receive a broad range of attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As  Spitzner [65] noted, a honeypot is not strictly bound to run in a demilitarized zone  (DMZ) or a network with direct Internet access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The correct location has to be  chosen based on the goals of the honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, one goal could be to catch  attackers behind a perimeter firewall to reveal leaks or vulnerabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As described  in the chapter before, the honeypot was broadly available on the Internet, and at-  tackers could probe it easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It collected on average 29,840 attacks per day, resulting  in a total amount of 607,747 attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Zoning a network into logical groups mitigates  the risk of an open network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, the T-Pot would receive significantly fewer at-  tacks in a controlled network zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A network infrastructure is segmented into the  same communication security policies and security requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, the  Canadian government created its baseline for infrastructures, called Baseline Secu-  rity Architecture Requirements for Network Security Zones in the Government of  Canada (ITSG-22) [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The four most common zones are: (i) Public Zone (PZ),  which is entirely open, (ii) Public Access Zone (PAZ), which interacts as an interface  36  between the PZ and internal services, (iii) Operation Zone (OZ), which processes  sensitive information, and (iv) Restricted Zone (RZ), which includes business-criti-  cal services [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A network zone restricts access and controls data communication  flows [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  University  Firewall  Internet  Institutes Firewall  self-administrated  URZ Firewall  Stage 1  University Network  URZ Firewall  TagungsLAN  eduroam  Institute  Institute  HDnet  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Draft of the University network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The main doorkeeper is the univer-  sity firewall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The HDnet is the internal network allowing institutes to  communicate with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The network at the Heidelberg University includes a central stateless firewall (Ac-  cess Control List (ACL)) that enfolds all institutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It entails a default blacklist  that blocks certain services (such as SMTP or Simple Network Management Pro-  tocol (SNMP)) and a stateless filter provided by BelWÜ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each institute can either  use a pre-defined stateless firewall provided by the University Computing Center  Heidelberg or use a self-administrated firewall inside the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 out-  lines the association between these components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The internal “HDnet” enables the  communication between institutes without leaving the internal network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Institute  firewalls can be set up by each institute and are self-administrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' They do have  37  the possibility to use SOHO routers1 to disconnect certain network zones from the  network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is recommended to configure the global ACL as a fallback solution in  case of any downtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The University Computing Center Heidelberg offers stateless  firewalls for router interfaces or Virtual Local Area Networks (VLANs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This state-  less firewall whitelists certain services and splits up into four stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each stage can  be individually activated per router interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Its key value is to maintain baseline  security to avoid misconfigurations and port scans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 outlines these stages  including the IP address range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Before applying one of these zones, the respective  network has to oblige to client IP addresses below 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='240/24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In  addition, 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 is allocated for the gateway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A network must adhere to  these obligations if it applies to any pre-defined stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Overview of firewall stages at the Heidelberg University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As an example,  it applies the rules to subnet 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Rules are applied  to any subnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Name  Description  range  Stage 0  Filters broadcast communication  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0-15/24  No filtering  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='16-255/24  Stage 1  Allows common network protocol  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0-255/24  Allows services  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='240-255/24  Stage 3  Internet access only via internal  proxies  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0-255/24  Stage 4  Only internal network communica-  tion  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0-255/24  An interesting question is if attackers have access to restricted zones at the Heidel-  berg University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It arises during the research of T-Pot if an adversary would try to  probe any hosts in the internal university network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In order to detect such events,  a honeypot-like packet detection application is presented that helps identify any  threats in a network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, it offers to deploy multiple instances and collect  their data at a centralized instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 Honeypot-like Connection Detection Tool  Recording and investigating connection attempts assimilates new honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Re-  spectively, a new honeypot-like detection tool called MADCAT will be presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  MADCAT has been developed by the BSI and helps to log any connection attempt  being made on the host machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The acronym MADCAT stands for Mass Attack  1A small office/home office router is a broadband router used in small offices and home offices  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  38  Detection Connection Acceptance Tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It works as a honeypot-like detection ap-  plication with a low-interaction level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Its key idea is to log every connection attempt  and further process it to retrieve credentials or shell exploitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 gives  an insight into how MADCAT works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It runs on an Ubuntu distribution, either  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04 or 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04, and has been tested on Ubuntu 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It processes packets from  any interface that has been configured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As an example, it could process Ethernet  and wireless packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' MADCAT itself consists of six independent modules for TCP,  UDP, Internet Control Message Protocol (ICMP), and raw packets that communi-  cate with each other through a pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A module analyzes packets and logs the  results in a queue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, UDP and TCP offer a proxy to tunnel packets to  another service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Every 5 seconds TCP postprocessor reads the newly arrived TCP  packets and processes them accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It resolves packets to log data, including  source IP address, protocol, and event type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The enrichment processor is the final  process step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Its purpose is to log all queue-written packets in a specified format  for further analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The key idea of MADCAT is to get an insight into whether  attackers have access to a particular network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In contrast to T-Pot, the concept does  not know what specific attacks are operated on the honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Instead, it ensures  that no one else than authorized users has access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Especially in high confidential  areas, no attacker should be capable of sending even a single packet to a host in  the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The vast range of honeypots does not provide tracking packets on a  detailed level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, a T-Pot instance will be deployed to have comparison data to the  new concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It focuses on the 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24 and 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/16 sub-  net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24 subnet is used within University Computing Cen-  ter Heidelberg building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Every client in the building has a compelling connection  in this subnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Otherwise, an Internet connection would not be feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The sub-  net 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/16 connects clients to “eduroam”2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Like the four stages of the  institute firewall, the “eduroam” network, also called “Tagungslan”, builds various  permits into the subnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' One essential difference is that services like SMTP and  HTTP are not allowed, so attackers cannot deploy traps for users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, each  client is encapsulated in its subnet, which disables communication to other clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The instances are located in the building with IP addresses 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='62 and  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 outlines the concept using MADCAT and a separate  instance to visualize our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The first instance with IP address 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='157  provides Kibana and Elasticsearch to visualize and crawl logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The honeypot with  IP address 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='88 consists of MADCAT in conjunction with P0f, Suricata,  and FATT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Like T-Pot, it uses Logstash to forward data to Elasticsearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' One ben-  efit is the centralized approach to store data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This allows to deploy more instances  to randomly collect data from other zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2The eduroam is an international Wi-Fi internet access point for researchers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  39  Network  Internet  Gateway  Switch  store  logs  database  (persistence 90 days)  m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='xlarge  Debian 10, Buster  ELK  runs  runs  runs  runs  runs  m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='xlarge  Ubuntu 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04  send  log  Logstash  P0f  Suricata  FATT  MADCAT  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: Concept to detect connection attempts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It has been drafted to work in  various scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Kibana and Elasticsearch are deployed in heiCLOUD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  40  forward  packets  Ethernet  forward  packets  write  TCP  write  ICMP  forward  packets  write  UDP  Proxy  forward  packets  Wireless  write  RAW  store  Enrichment Processor  write  TCP Postprocessor  logs  MADCAT  Ubuntu 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04 or 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04  FIFO  read  reads  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3: Visualization of the MADCAT packet flow starting at the network inter-  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The Ethernet and wireless interface forwards packets to the desired  module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  41  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 Results  MADCAT (28th of October till 18th of November) and T-Pot (16th of November till  7th of December) have been deployed for three weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All instances had a connection  to both subnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' First, the results obtained in the subnet 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24 will  be presented, closing up with the ones claimed in the eduroam network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In total, MADCAT received 35,372 packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Overall, the modules TCP (66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='62%)  and raw (33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='26%) received the majority of all connection attempts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The minority  with less than one percent are suspicious packets with individual TCP flags like  reset or syn set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary, it could not identify any harmful activity based on  these packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Overall, ConPot (56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98%), Honeytrap (31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='35%), and Dionaea (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='09%)  received most of the attacks with a total number of 437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Interestingly, it could  identify SNMP connections that are used by print servers to discover printers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2021-10-30  2021-11-03  2021-11-07  2021-11-11  2021-11-15  Timestamp  0  200  400  600  800  1000  1200  Number of Attacks  ICMP  IPv6  UDP  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4: Protocol distribution of MADCAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ICMP, IPv6, and UDP are the most  used protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 28th of October to 18th of November.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 shows the protocol distribution indicating a high amount of ICMP and  IPv6 packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='59% of all IP address reputations could be resolved, splitting  up into known attacker (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='26%), mass scanner (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='14%), bad reputation (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='12%),  and tor exit node (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='08%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Focusing on TCP packets, 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3% are known attackers  with source port 113 as the primary target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The port 113 is officially known as  the Identification Protocol (IDENT)[36] used for identification/authorization on a  remote server such as Post Office Protocol (POP), IMAP, and SMTP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A potential  42  leak that allows adversaries to send IDENT requests to the network could be spotted  by comparing the results with the stateless firewall settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Decoding the payload  of these TCP packets shows that attackers instead used this port to get an SMB  connection than deploying IDENT protocol attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It identified attempts to acquire  an SSH session using SMB and Session Initiation Protocol (SIP) connection attempts  and various HTTP requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, two payloads that have been sent to the  instance show probing actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 outlines a SIP probe that checks if any  VoIP service is active by answering the request packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Next, Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 shows an  SMB probe trying to achieve the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The IP address reputation could help answer  if a real user or an attacker sends these packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Both IP addresses in this example  were resolved as a known attacker;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, it identified them as a probe packet before  executing their attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A vital security interest in port 113 is negligible;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' however,  the concept helps to detect such leaks, especially when stateless firewalls are the  main doorkeeper for packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2000  4000  6000  8000  10000  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5: Attack distribution of MADCAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The USA, Russia, and China are the  most attacking countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 28th of October to 18th of Novem-  ber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5 shows the attack distribution indicating the origin of an IP address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Most of the connections originate from the United States, Germany, and China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  As shown beforehand in chapter 3, geographical information only outlines the last  known location of a node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Like the results in heiCLOUD, it can be assumed that  this information is not reliable as an indicator of where attacks occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Nevertheless,  it is interesting to see where the last node originated from.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Suricata identified odd behaviors in the network (Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In total, it detected  292,953 alerts and CVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Besides minor alerts like nmap scans, Suricata registered  alerts in SNMP requests, TCP stack, and Wind River VxWorks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2020-11899  [19] accounts nearly 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='35% with a total number of 214,879.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This CVE is one of 19  others forming the Ripple20 vulnerability in the low-level TCP/IP library developed  by Treck, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' One of the Track TCP/IP stack tasks is to reassemble fragmented  packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Whenever a fragmented packet arrives, the stack tries to validate the to-  43  2021-11-19  2021-11-23  2021-11-27  2021-12-01  Timestamp  0  5000  10000  15000  20000  25000  Number of Attacks  Potentially Bad Traffic  Misc activity  Generic Protocol Command Decode  Attempted Information Leak  Attempted Administrator Privilege Gain  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6: Suricata results of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' from 16th of November to 7th of  December.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  tal length in the IP header.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If the total length is not correct, it trims the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  However, this leads to inconsistency, and thus, resulting in a buffer overflow when  someone sends fragmented packets through a tunnel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A detailed description of the  vulnerability can be found in [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' An adversary could send malformed IPv6 pack-  ets that cause an Out-of-bounds Read, resulting in potential remote code execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Only TCP/IP stack versions until 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='66 are affected by this vulnerability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Never-  theless, the tremendous alerts show the importance of adapting the IPv6 permits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The second most recorded vulnerability with the highest score is CVE-2002-0013  [12] that allows remote attackers to cause a denial of service or gain privileges in  the SNMPv1 protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The root cause for the CVE alert is the usage of the default  public community for broadcast requests instead of configuring a private commu-  nity with mandatory authentication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' To compromise SNMP, attackers have to have  access to the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the university firewall blocks SNMP port 161 and  162 for TCP and UDP, thus, restricting any access from outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If adversaries  plan to deploy an attack on the SNMP protocol, they need to have a connection  to the internal network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Acquiring such a connection is rather hard to accomplish  without any credentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary, all connection attempts registered by the  concept have been made within the network, and they do reflect a normal SNMP  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Lastly, Wind River VxWorks 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 and vx7 in CVE-2019-12263  [17] cause a buffer overflow due to the underlying TCP component that results in a  race condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each connection attempt with CVE-2019-12263 is originated from  Russia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hence, the assumption is that the source IP address maliciously intended to  send an urgent flag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For the other CVEs, the IP reputation could not be resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Results from the T-Pot instance are exiguous, and in short, no real attacks such  as shell exploitation have been performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All connection attempts originated from  Germany within the same network and are made on ports 161 and 4567.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Conpot  44  Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: MADCAT connection attempt to exploit SIP connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Received on  the 16th of November.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' IP reputation: known attacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Location Ger-  many.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  OPTIONS sip:nm SIP /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 Via: SIP /2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/ TCP nm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2  branch=foo From: <sip:nm@nm >;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3  tag=root To: <sip:nm2@nm2 > Call -ID: 50000 CSeq: 42  �→ OPTIONS Max -Forwards: 70 Content -Length: 0 Contact:  �→ <sip:nm@nm > Accept: application/sdp  2021-11-17  2021-11-21  2021-11-25  2021-11-29  2021-12-03  Timestamp  0  20  40  60  80  Number of Attacks  161  1025  2049  4567  6000  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7: Attack port histogram of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' from 16th of November to  7th of December.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  45  registered minor SNMPv2 Get, SNMPv1 Get, and GetNext requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A possible  attack vector could be an SNMP reflection/amplification attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As previously dis-  cussed, the assumption is that devices within the network have a misconfigured  printer and send broadcast requests frequently to find the machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This SNMP  requests affiliate with day-to-day traffic in an internal network, and thus, are not  suspicious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The second most attacked honeypot is Honeytrap which received nu-  merous packets on different ports, whereas 39% evince an empty payload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All of  these received packets have a resolved IP address in the subnet 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It remains unclear if these connections are malicious or are acquired by accident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Investigating the payload of outliers does not confirm the assumption of a vicious in-  tention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, declaring these results as negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Overall, most of the connection  attempt received by the instance are from these IP addresses: 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='118,  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='23, and 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: MADCAT connection attempt to exploit SMB connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Received  on the 16th of November.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  IP reputation: known attacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Location  Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  PC NETWORK PROGRAM 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 MICROSOFT  NETWORKS 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='03 MICROSOFT  �→ NETWORKS 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 LANMAN1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 LM12X002 Samba NT LANMAN 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0  �→ NT LM 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Lastly, the results from the eduroam network are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Neither T-Pot nor  MADCAT could identify any significant behavior for three weeks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Unlike the subnet  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24, the honeypot did not register any suspicious packets, TCP  flags, or other CVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In retrospect, the eduroam configuration has been shown  to work as designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, the client seemed to be encapsulated from others and  received no other packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Besides the subtle output it has received, the results have given an insight into the  value of honeypots in a restricted network zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For Heidelberg University, using  honeypots to evaluate their stateless firewall has never been considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The initial  concept has shown that it delivered minor findings in the subnet 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0/24  with stage 1 firewall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As a result, the port 113 used for the IDENT protocol will  be removed in the future to reduce the attack surface, thus, contributing to the  firewall definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Overall, the two instances received numerous packets containing  interesting payloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Compared to the T-Pot, which has been used in heiCLOUD,  results are as expected delicate, and data analysis turns out to be more detailed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The statement from Spitzner [65] that honeypots only receive little input and nearly  every input is suspicious matches the results only halfway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As shown beforehand,  the results are dramatically little;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' however, only a few requests seemed suspicious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Nonetheless, the initial question of whether attackers have access to the restricted  network zone at the Heidelberg University has been answered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  46  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 Discussion  This chapter has shown that honeypots help find potential leaks in restricted network  zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Though, it remains questionable if the concept can deliver accurate results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The instance has been running for three weeks in the two different subnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The  honeypot has to be detected as a vulnerable target to deliver meaningful data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  However, it could not detect any large scans on the instance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, it is very likely  that either an attacker could not find the instance or no one had any access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In the  eduroam network, large scans are negligible due to the firewall permits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It can be  assumed that the results are accurate and do not show any discrepancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Considering  the subnet with stage one institute firewall, it identified attacks on port 113, resulting  in an adaption of the stage one permits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary, it could not register any  other odd packets on other ports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A detailed investigation could resolve whether  the honeypot is available to attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A misconfiguration of the university firewall  has been detected which proves this assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In December, from the 21st to the 23rd, a misconfiguration of the university firewall  resulted in a flood of attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In total, the T-Pot instance received 46,328 attacks  in three days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It turns out that five ports were open during that time, allowing  attackers to probe the instance (Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The most attacked honeypots are  RDPY (58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='58%), Honeytrap (24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='53%), and Cowrie (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='69%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  2000  4000  6000  8000  10000  12000  14000  16000  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8: Attack distribution of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' USA, Russia, China, and Germany are the  most attacking countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' from 21st of December to 23rd of  December.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Like the geographical information of other honeypots, most of the connections orig-  inate from the United States, Russia, and China (Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These similarities  indicate a bias of the origin even though the location information is not reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  On RDPY and Honeytrap, many connection attempts on various ports have been  made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Based on the Suricata results, adversaries tried to gain administrator priv-  ileges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For Cowrie, attackers tried to log in and execute commands by brute force  47  2021-12-22 04-00  2021-12-22 16-00  2021-12-23 04-00  2021-12-23 16-00  Timestamp  0  200  400  600  800  1000  Number of Attacks  22  3389  5555  5900  6379  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9: Attack port histogram of T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' from 21st of December to  23rd of December.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  48  or guesswork.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, the latest crypto-mining malware has been used, which  resembles the findings of other honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These results overlap strongly with those  obtained by the T-Pot instance in heiCLOUD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The firewall administrator stated that the misconfiguration was fixed on the 23rd of  December, resulting in a decrease in attacks on the T-Pot instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These results  have successfully answered our discussion of whether an attacker could detect the  host machines at the university building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It clearly shows that attackers scan these  IP address ranges and send malicious packets whenever they can.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  49  Chapter 5  Mitigate Fingerprint Activities of  Honeypots  There is a generic weakness in the  current generation of low- and  medium-interaction honeypots  because of their reliance on  off-the-shelf libraries to implement  large parts of the transport layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Alexander Vetterl  Detecting honeypots before launching attacks helps to avoid the disclosure of infor-  mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Chapter 3 has shown that bot activities are on the rise, and more attacks  than ever have been launched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, the vast majority of attacks have been  identified to be repetitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This chapter conducts two experiments on whether it is  possible to fingerprint honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' First, it reproduces the findings from Vetterl [72]  to prove the initial question if any fingerprint activity is feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Consequently, it  presents a concept to disguise Cowrie and verify this assumption with an experi-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 OpenSSH  OpenSSH is one of the most used applications that enables SSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Before proceeding  with generic weaknesses of honeypots, a short intermezzo about OpenSSH is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  OpenSSH consists of three major layers, namely ssh-connection, ssh-userauth,  and ssh-transport (Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1) [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The last layer is the most important because  it provides the basic functionalities for crypto operations, such as key exchange and  encryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  50  ssh-connection  (Session multiplexer, X11 forwarding, TCP forwarding,  interactive login, invoking sftp subsystem, remove command  execution)  ssh-userauth  (Challenge response authentication (PAM), public key based,  password authentication, rhost style host auth, smart card  support, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=')  ssh-transport  (Diffie Hellmann Key (KEX) agreement, ssh-rsa public key  signatures, Server Host authentication, MAC & Encryption  algorithm and key negotiation, rekeying )  TCP/IP  ssh layers  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: OpenSSH architecture (derived from [70]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The ssh-transport layer  builds the foundation for the other layers on top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, each  layer lists examples of functionalities that it supports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The first layer is responsible for authenticating the user to the SSH daemon, namely  sshd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Based on two-way authentication, the client authenticates the SSH daemon  with the help of the ssh-transport [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Finally, a secure connection is established,  and the key exchange is done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The next step is to authenticate the user of the client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It offers authentication methods such as username/password, public key, or smart-  card authentication [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If the ssh-userauth layer is successful, it will establish a  secure channel through the ssh-connection layer [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each session is handled in  a so-called channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The ssh-connection layer handles multiple sessions simultaneously over a single  ssh-userauth layer with the TCP/IP layer below [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is responsible for executing  arbitrary commands, forwarding X11 connections, establishing VPN tunnels, and  more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In addition, OpenSSH has built-in features such as keeping alive messages and redi-  recting stdin to /dev/null for specialized X11 windows [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5 outlines a sample session between a client and a server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The key exchange  initialization is the first message between them to negotiate all ciphers and keys for  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  For this chapter, no other than the key exchange initialization  message will be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  51  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 Preliminary Work  Attackers have a strong motivation to reveal honeypots before launching an attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Without any protection, attackers would disclose their methods, and thus, newly  developed attacks would become useless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As shown in chapter 3, attackers do try  to get information about the host system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vetterl [72] discussed various methods of  fingerprinting;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' however, executing commands in a shell and examining the response  leaves precarious information to the honeypot itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' His technical report evaluated  methods to detect honeypots at the transport level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As stated, the value of a hon-  eypot would be merely zero if detection on transport level would work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' He presents  fingerprinting methods for SSH, Telnet, and HTTP/Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Due to the complex-  ity of each method, this section focuses on SSH fingerprinting using the honeypot  Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The idea to detect SSH honeypots is to look for deviations in the response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' There-  fore, Vetterl [72] sends a set of probes P = {P1, P2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' , Pn} to a given set of imple-  mentations of a network protocol I = {I1, I2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' , In} and stores the set of responses  R = {R1, R2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' , Rn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' He calculated the cosine similarity coefficient C for the given  set of responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The goal is to find the best Pi where the sum of C is the lowest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 presents these steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The cosine similarity outputs the similarity between vectors of numerical attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It is widely used in text semantics to measure the similarity of sets of information  such as two sentences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vetterl [72] outlines that it can be used in “traffic analysis to  find abnormalities and to measure domain similarity”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Mathematically, it computes  the angle between two vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For each set of information A, we create a vector  DA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Referring to the use case with SSH, we use the response from the server as  information A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If θ is the angle between DA and DB, then:  cos θ =  DA · DB  ∥DA∥∥DB∥  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1)  where “·” is the dot product obtained by:  DA · DB =  n  �  i=1  (DAi × DBi)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2)  and ∥DA∥ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  ∥DB∥) is the Euclidean norm, obtained by  ��n  i=1 D2  Ai (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  ��n  i=1 D2  Bi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The values of vectors are non-negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The similarity between items  is the value cos θ, cos θ = 1 indicates equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  52  send  Probes (P)  output  Implementation (I)  calculate  Responses (Rp)  Cosine similarity  coefficient (C)  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: Process to obtain the cosine similarity coefficient (derived from [72]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: OpenSSH connection attempt with probed SSH packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  All non-  essential debug information have been removed to lay emphasis on the  modified key exchange initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  Local version string SSH -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2- OpenSSH  2  SSH2_MSG_KEXINIT sent  3  SSH2_MSG_KEXINIT  received  4  kex: algorithm: ecdh -sha2 -nistp521  5  kex: host key algorithm: ssh -dss  6  kex: server ->client cipher: blowfish -cbc@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com MAC:  �→  <implicit > compression: zlib@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com  7  kex: client ->server cipher: blowfish -cbc@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com MAC:  �→  <implicit > compression: zlib@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com  In order to find the best Pi for SSH, Vetterl [72] first created different SSH version  strings based on the format: SSH-protoversion-swversion SP comment crlf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' He  used different lower and upper case variations, 12 different protoversions ranging  from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2, swversion set to OpenSSH or empty string, comment set to FreeBSD  or empty string, and crlf to either \\r\\n or empty string.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In total, summing up  to 192 client version strings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Second, he created different SSH2_MSG_KEXINIT pack-  ets with 16 key-exchange algorithms, two host key algorithms, 15 encryption algo-  rithms, 5 Message Authentication Code (MAC) algorithms, and three compression  algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In total, he sent 58,752 key exchange initialization messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Combin-  ing them with the 192 client versions, he ended up sending 157,925,376 packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The version string SSH-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2-OpenSSH \\r\\n and the SSH2_MSG_KEXINIT packet in-  cluding ecdh-sha2-nistp521 as the key-exchange algorithm, ssh-dss as host key al-  gorithm, blowfish-cbc as encryption algorithm, hmac-sha1 as mac algorithm, and  zlib@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com as compression algorithm, with the wrong padding, resulting in  the lowest cosine similarity coefficient C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 shows the SSH debug informa-  tion with the modified version string and key exchange message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  53  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 has been derived from Vetterl [72] to present his results of the cosine  similarity of OpenSSH, Twisted, and Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Twisted has been added to have  an example with an older SSH honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As seen, it differs fundamentally from  OpenSSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' At most, it scores 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='52 whereas various OpenSSH versions start at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The number of hosts significantly decreases with a cosine similarity score of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='90 and  higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cowrie responses are not too far away from OpenSSH, with an average of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, scanning through the web with a minimum score of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='90 and higher  would exclude all honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, distinguishing Cowrie from OpenSSH with SSH  packets is a feasible method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, Vetterl [72] performed an Internet-wide  scan, and detected 758 Kippo and 2,021 Cowrie honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These results show that  the values of honeypots would decrease to zero when fingerprinting activities are  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  TwistedConch  Cowrie  OpenSSH  sshd  bash  RFCs  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3: Architecture of OpenSSH and Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  OpenSSH and TwistedConch  have subtle protocol differences (derived from [72]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Vetterl [72] states that current low- and medium-interaction honeypots have a  generic weakness due to the underlying off-the-shelf libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cowrie is based on  TwistedConch1, a Python 2/3 library that implements the SSH protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Any bash  command and its response are tweaked by Cowrie, and thus, resulting in a discrep-  ancy to OpenSSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For example, Cowrie version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 missed tftp2 that later came  with version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, it is a continuous struggle to add new commands to  avoid early disclosures of Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 shows the difference between OpenSSH and Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Both have to fulfill  the RFC4250 [44] which defines the protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' OpenSSH and TwistedConch imple-  ment the RFC requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As an example, Vetterl [72] found that Cowrie used  to have random bytes for the key exchange initialization packet3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' With respect to  RFC4253 [76] that defines the Binary Packet Protocol (BPP) of SSH, the random  padding is used to solidify the total length of the packet to be a multiple of the cipher  block size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The RFC in section 6 defines that the padding consists of 4 random bytes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1TwistedConch 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 on GitHub  2Trivial File Transfer Protocol (TFTP) is a lockstep File Transfer Protocol  3Each packet consists of the packet and padding length, the MAC, a payload, and random  padding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  54  Based on the statement of the OpenSSH authors, random bytes have been changed  to NULL characters due to no security implications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, an adversary could have  detected a Cowrie honeypot with a single key exchange initialization packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Nowa-  days, Cowrie adapted itself to have NULL characters as padding to mitigate such an  exploit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, these subtle differences give adversaries precautionary information  and influence the cosine similarity coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1: Overview of the cosine similarity of OpenSSH, Cowrie, and Twisted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Twisted has been added to have a comparison to an older honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  A  B  C  D  E  F  G  H  I  J  OpenSSH 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6  A 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  OpenSSH 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7  B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='81  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='81  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80  OpenSSH 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8  C 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  OpenSSH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2  D 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80  OpenSSH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5  E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='79  Twisted 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1  F 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='52  Cowrie 96ca2ba  G 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='98  Cowrie dc45961  H 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99  Cowrie dbe88ed  I 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99  Cowrie fd801d1  J 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 Experiment 1: Reproduce Vetterl et al.’s  findings  First, the reproduction of the outdated OpenSSH library that Vetterl [72] used will  be investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In his work, he used the version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5P1, which deviates from the  latest version 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Older versions rely on OpenSSL 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2, including outdated algo-  rithms and functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For the SSH2_MSG_KEXINIT packet, the encryption algorithm  blowfish-cbc is outdated and has been removed with version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Building the ver-  sion 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5P1 requires the libraries libssl (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2), libssl-dev (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0), libssh-dev (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 − 2),  and libssh-4 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6 − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All of these libraries are outdated and have been removed  from any Debian installation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Using the latest versions of these libraries results  in missing encryption algorithms and host key algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, replacing the li-  braries is a necessary task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It is required to download the libraries, remove the  current versions, and install the outdated ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5P1 allows modifying  the key exchange initialization message proposal in a single file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary,  55  this has been removed starting from version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' After compiling the application,  its behavior has been tested with a Debian 11 Buster and a Debian Jessie 9 Docker  image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Both are new machines with no other installed packages than the SSH dae-  mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Debian 11 uses the latest OpenSSH version, whereas Jessie is at 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These  environments help to uniquely identify variations in the protocol version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2: OpenSSH connection attempt for version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5P1 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 with probed  key exchange initialization message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' All non-essential debug informa-  tion have been removed to lay emphasis on the modified key exchange  initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  OpenSSH_7 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5p1 , OpenSSL 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2u  20 Dec 2019  2  Local version string SSH -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2- OpenSSH  3  SSH2_MSG_KEXINIT sent  4  SSH2_MSG_KEXINIT  received  5  kex: algorithm: ecdh -sha2 -nistp256  6  kex: host key algorithm: ssh -dss  7  Unable to negotiate with ::1 port 22: no matching cipher  �→ found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Their offer: aes128 -ctr ,aes192 -ctr ,aes256 -ctr  �→ ,aes128 -gcm@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com ,aes256 -gcm@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com ,  �→ chacha20 -poly1305@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 shows the connection attempt with the adjusted version string and  SSH2_MSG_KEXINIT packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Both Debian machines return the same response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Using  the outdated version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5P1, it results in an incompatibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The return message  outlines that blowfish-cbc is not supported anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' OpenSSH kept the encryption  algorithm usable for compatibility reasons for clients until 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Later patches  removed the blowfish-cbc from the application;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, a reproduction of Vetterl [72]  remains not feasible with the latest version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Testing it with version 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P1 that has  been compiled on the machine results in a successful connection attempt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vetterl [72]  does not outline any expected response of OpenSSH;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, it can be assumed that  a connection attempt would have been successful due to the existing ciphers during  that time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Adapting the version 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 with chacha20-poly1305 instead of blowfish-  cbc for the encryption algorithm results in a successful connection attempt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' There-  fore, the key exchange initialization has been adapted to use chacha20-poly1305 as  encryption algorithm instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Next, the DSA host key algorithms are marked as  too weak and are not included automatically during the key exchange initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Using ssh-dss requires the extra flag -oHostKeyAlgorithms=+ssh-dss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In order to  avoid weak algorithms, the ssh-ed25519 host key algorithm is used, and the response  has been promising to probe instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' So far, the key exchange initialization packet  with ecdh-sha2-nistp521 as key exchange algorithm, ssh-ed25519 as host key algo-  rithm, chacha20-poly1305 as encryption algorithm, hmac-sha1 as mac algorithm,  and zlib@openssh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com as compression algorithm have been successfully tested on  the two Debian instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  56  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3: Cowrie connection attempt with probed key exchange initialization mes-  sage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  All non-essential debug information have been removed to lay  emphasis on the modified key exchange initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  OpenSSH_8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8p1 , OpenSSL 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1l  24 Aug 2021  2  Local version string SSH -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2- OpenSSH  3  SSH2_MSG_KEXINIT sent  4  Bad packet length  1349676916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5  ssh_dispatch_run_fatal : Connection to 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='74 port  �→ 22: message  authentication code incorrect  The most interesting question remains about Cowrie’s response deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vetterl  [72] claims that it results in a bad version * exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cowrie has fixed this issue  in the meantime, and thus, it does not leak vulnerable information anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For the  experiment, the default Cowrie implementation version v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='04 of the T-Pot instance  is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3 outlines the connection attempt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Unambiguously, Cowrie results  in a bad packet length * exception, and thus, deviates fundamentally from an  OpenSSH response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The underlying off-the-shelf library TwistedConch checks if a  packet is within 1,048,576 bytes (1 MB) (Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Any packet that exceeds that  threshold causes this exception, which results in a loss of connection for the client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  This static check is performed when Cowrie tries to get the request packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It remains  dubious why TwistedConch has added it whenever a packet has to be returned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In  the RFC4253, the minimum packet size is 5 bytes whereas maximum packet size is  set to 32,768 bytes (256 KB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Debugging Cowrie shows that the exception occurs  during the version string validation (Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5, line 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The server validates  if the version string matches the allowed versions 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Any higher or  lower version will result in a Protocol major versions differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='\\n exception by  calling the function _unsupportedVersionReceived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This response would match  the behavior of OpenSSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Therefore, the version strings 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2 have been tested on Cowrie and  OpenSSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As a result, Cowrie’s bad packet length * exception occurs when the  version does not match the expected one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This result diverges from OpenSSH, as  only versions under 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99 lead to the same exception as Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For any higher ver-  sion, the connection can be established successfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It can be assumed that Cowrie  has an error in validating the version string.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Debugging Cowrie shows that the  method to return the Protocol major versions differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='\\n exception is called,  but the client does not receive this message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hence, the assumption is that the  underlying library TwistedConch is responsible for the incorrect message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Calculating the cosine similarity coefficient of both responses shows that the coeffi-  cient with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='46 is lower than the results from Vetterl [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In his study, the coeffi-  4Cowrie v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 on GitHub  57  cient between Cowrie and OpenSSH was on average 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Different implementation  approaches to reproduce his results have been considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The standard implemen-  tation to retrieve the coefficient returned the best result with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Moreover, a soft  cosine similarity with English word vectors from Mikolov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' [49] has been used;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  however, it did not improve the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In summary, the same response could not  be reproduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Nevertheless, it shows that both responses have similarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In conclusion, these are the protocol deviations that Vetterl [72] has presented in  his technical report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, this section could successfully recreate his findings by  detecting Cowrie on the transport level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Adversaries who modify their SSH client to  send the specific version string and key exchange initialization message could detect  Cowrie honeypots and stop further activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4: TwistedConch packet length validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Line 3 validates if the packet  length is not greater than 1 MB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If this check is not successful, the client  receives a bad packet length exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  def getPacket(self):  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  3  if packetLen > 1048576: # 1024 ** 2  4  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content="sendDisconnect(DISCONNECT_PROTOCOL_ERROR ,  5  'bad packet length %s' %  �→ packetLen)  6  return  7  ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 Attempt to Disguise Cowrie  Cowrie has to be tweaked to hide its generic weakness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Fixing the significant flaws  in Cowrie to avoid early detection remains an ephemeral patch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The continued use  of libraries that reimplement the behavior of OpenSSH leads attackers to try to  find subtle protocol differences and exclude any host machine that deviates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Such  approaches could be achieved by arbitrary Internet-wide scanning and calculating  the cosine similarity coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, the value of honeypots would decrease to  almost zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, a new solution is required to disguise SSH honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Vet-  terl [72] presented a solution to use OpenSSH as an intermediary instance between  the attacker and Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Unfortunately, this solution is outdated, and newer ver-  sions contain significant changes in structure and functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The concept is based  on Vetterl [72] solution, but due to newer versions available, the solution has to  be updated to the latest version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' By default, OpenSSH itself cannot act as an in-  termediary;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' therefore, it is necessary to customize the latest version to enable this  feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4 visualizes the flow of SSH packets between an attacker and  58  Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cowrie is hidden in the background, and it is only accessible via the loop-  back address 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1 on port 65522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The updated daemon is exposed to the  Internet, and it is accessible via 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='157 on port 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Each connection  to OpenSSH is forwarded to the honeypot through a network address translation  (NAT) rule5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accordingly, an attacker should not be able to detect Cowrie through  response deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  sshd  Internet  Cowrie  Gateway  127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1:65522  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='157:65522  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='4: Architecture of OpenSSH and Cowrie (derived from [72]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A NAT rule  forwards the communication from port 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only the SSH daemon is  accessible from extern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  For instance, the latest OpenSSH version 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P16 is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The implementation is  based on Vetterl [72] version 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As mentioned beforehand, due to major differ-  ences between both versions, a smooth transition is unattainable without modifica-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Fortunately, the basic idea to morph OpenSSH into an intermediary instance  stays the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In total, the connection and user authentication layer has to be modified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' These are  the following steps required to change the SSH daemon:  User authentication layer: permit any connection to communicate to Cowrie  without an authentication running in front of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Connection layer: create a separate channel to communicate with the attacker  that forwards the packets to Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Connection layer: handle the communication with Cowrie in a new channel  separated from others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The first step is to tweak the authentication to permit any session to forward an  incoming connection to Cowrie (Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Initially, it checks each session to see if  the chosen authentication method returns true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In order to skip the authentication  process, the server must return true for any client that tries to connect to the  honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, the authentication method has to be overridden in the main  method and the allowed user method that checks if the user is permitted to log  5iptables -t nat -A PREROUTING -p tcp –dport 22 -j REDIRECT –to-port 65222  6OpenSSH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 on GitHub  7sshd-honeypot on GitHub  59  in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The authentication process validates if a connection to Cowrie is successful and  returns true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In case of failure, the authentication would fail, resulting in a loss of  connection for the client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Next, the libssh library expects a different integer for a  successful authentication;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' therefore, the result is converted to the expected format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The allowed user method is changed to return true for any user trying to connect to  the honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cowrie continues the authentication process and communicates with  the attacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Second, the communication has to be forwarded to the honeypot (Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In  OpenSSH, communications are handled in channels as seen beforehand in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Technically, the daemon opens a SOCKS connection for each session to communicate  with the client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' SOCKS is a network protocol to exchange packets between servers  and clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The SSH daemon needs a separate channel to store the attacker’s session  and forward packets to communicate with Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The channel is implemented in  version 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P1 and can be used in 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 with minor adaptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The method validates  if the Cowrie channel is open and writes the new packets into the buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In the main  method, when the daemon is started, the channel is created, and a connection to the  running Cowrie instance is opened to forward a new session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' If Cowrie is unavailable,  the startup will fail;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' thus, it has to run prior to the SSH daemon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Lastly, the server loop responsible for connecting the client to the correct port  must be modified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It puts direct TCP/IP connections in the respective channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The connection layer handles multiple sessions simultaneously over a single user  authentication layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Without this adaption, Cowrie would not receive any packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The function in Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8 handles these connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' For instance, it checks if TCP  forwarding is allowed and if the port of Cowrie is defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Then, it connects the  current session to the respective port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The SSH daemon has to be adapted to start  and set up the channel in the main method at startup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, the configuration  has to be extended to configure the daemon to set the Cowrie IP address and the  port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  After compiling the version, a brief test proved a valid connection to the SSH dae-  mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5 Experiment 2: Avoid fingerprinting of Cowrie  The last experiment to conclude this chapter is to test if the concept helps to disguise  Cowrie and avoid fingerprint activities based on a custom local string version and  key exchange initialization message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  For instance, Vetterl [72] original 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P1 sshd-honeypot and the newly implemented  version 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 will be used for this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The forwarding communications are  handled by an unmodified Cowrie version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 running in a Docker environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The version 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P1 has been tested in heiCLOUD on a Debian 9 Jessie distribution,  60  whereas the version 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 with our latest adaption has been tested on a Debian 10  Buster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, both versions are validated locally in an encapsulated environ-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The clients to test the two concepts are a standard OpenSSH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='P1 and the  modified version with custom local version string and key exchange initialization  message to fingerprint honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  The standard client’s requests do not result in a bad packet length exception for  both servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This behavior reflects an original SSH daemon communication and  represents a successful test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The requests from the modified client are successful on  the latest version, whereas the older server 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P1 had problems with new encryption  and host key algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A successful connection to the original server from Vetterl  [72] could be recreated by using the 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3P1 version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This version has been used to  verify Cowrie beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The concept can forward any related packet to Cowrie  and hide the generic weakness of TwistedConch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Therefore, whether Cowrie can  be disguised to prevent any fingerprint activities with the help of OpenSSH has  been answered successfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  This section can confirm this assumption based on  the reproduction and implementation of the concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the other side, Cowrie  receives the connection and log information (Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, one downside is  the connection loss due to timeout restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This issue is a minor bug and could  be fixed in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In conclusion, this experiment has shown that the initial idea of hiding Cowrie in the  background and directing the communication through OpenSSH prevents fingerprint  activities of an adversary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, it has shown that protocol implementations  change rapidly to adapt to new security standards, leading to outdated honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6 Discussion  Depending on the interaction level, honeypots will always deviate from production  instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' As seen in the two experiments beforehand, detecting a generic weakness  is doable in a respective time, as well as mitigating it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Thus, finding and fixing  the weaknesses of honeypots becomes a continuous cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' However, this chapter  also outlined the importance of the libraries that were used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' TwistedConch is the  bottleneck of Cowrie, and it is updated8 frequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Libraries that reimplement  protocols have to be always up-to-date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In conclusion, such libraries should be  chosen carefully to avoid bugs that leave harmful information to attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  8Based on the lastest GitHub commit of the Python library  61  Client  Server  (KEX) SSH_MSG_KEXINIT  SSH_MSG_NEWKEYS  SSH_MSG_SERVICE_REQUEST  SSH_MSG_SERVICE_ACCEPT  SSH_MSG_USERAUTH_REQUEST  SSH_MSG_USERAUTH_SUCCESS  SSH_MSG_CHANNEL_OPEN  SSH_MSG_CHANNEL_OPEN_CONFIRMATION  SSH_MSG_CHANNEL_WINDOW_ADJUST  SSH_MSG_CHANNEL_DATA  SSH_MSG_CHANNEL_EXTENDED_DATA  SSH_MSG_CHANNEL_REQUEST  SSH_MSG_CHANNEL_REQUEST  SSH_MSG_GLOBAL_REQUEST  SSH_MSG_CHANNEL_OPEN  SSH_MSG_CHANNEL_OPEN_CONFIRMATION  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  SSH_MSG_CHANNEL_CLOSE  SSH_MSG_CHANNEL_CLOSE  ssh-transport  ssh-connection  ssh-userauth  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5: OpenSSH sample session flow diagram (derived from [70]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition,  the right side indicates the layers that are responsible for handling the  messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  62  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='5: Cowrie version string validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It tweaks the same results as OpenSSH  in line 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  def _unsupportedVersionReceived (self , remoteVersion:  �→ bytes) -> None:  2  """  3  Change message to be like OpenSSH  4  """  5  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='write(b"Protocol major versions differ  �→ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='\\n")  6  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='loseConnection ()  7  8  def dataReceived(self , data: bytes) -> None  9  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  10  if not self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='gotVersion:  11  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  12  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='otherVersionString = self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='buf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='split(b"\\n")  �→ [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' strip ()  13  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  14  # Checks if the version string has a correct  �→ format  15  m = re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='match(br"SSH -(\\d+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='\\d+) -(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' *)", self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ otherVersionString)  16  if m is None:  17  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  18  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='write(b"Invalid SSH  �→ identification  string .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='\\n")  19  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='loseConnection ()  20  return  21  else:  22  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  23  # Checks if version string is either 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='99 or  �→ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0  24  if remote_version not in self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ supportedVersions:  25  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' _unsupportedVersionReceived (self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ otherVersionString)  26  return  27  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  28  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  29  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  63  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6: Tweaked OpenSSH authentication to connect to Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only the essen-  tial code parts to change the authentication method have been added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  int  2  auth_password(struct ssh *ssh , const char *password)  3  {  4  Authctxt *authctxt = ssh ->authctxt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5  /* Send the request to Cowrie */  6  int rc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  7  rc = authenticate_password (authctxt ->user , password);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  8  authctxt ->valid = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  9  /* libssh returns  different  values compared to  �→ OpenSSH , for SSH_AUTH_SUCCESS =0 returns 1 */  10  if (rc == 0)  11  {  12  finish_connection_setup ();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  13  return 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  14  }  15  else  16  {  17  return 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  18  }  19  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  20  }  21  int authenticate_password(const char *username , const  �→ char *password)  22  {  23  int rc = -1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  24  /* No logins if we could not connect to Cowrie */  25  if (ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' error !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='= 1)  26  {  27  rc = ssh_userauth_password (ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ initial_session , username , password);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  28  }  29  return rc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  30  }  31  int  32  allowed_user(struct ssh *ssh , struct passwd * pw)  33  {  34  return 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  35  }  64  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='7: Tweaked OpenSSH channel to connect to Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only the essential  code parts to change the authentication method have been added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  static int  2  channel_handle_wfd(struct ssh *ssh , Channel *c,  3  fd_set *readset , fd_set *writeset)  4  {  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  6  // Implement  channel logic to forward data to Cowrie  7  int nbytes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  8  char buffer [65507] = {0};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  9  ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' rfd = c->rfd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  10  ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' wfd = c->wfd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  11  ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' efd = c->efd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  12  // Check the connection to Cowrie , if not , close the  �→ sshd -client connection  13  if (ssh_channel_is_open(channel_rw1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='channel_data) &&  14  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='ssh_channel_is_eof(channel_rw1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='channel_data))  15  {  16  // Read data from the channel (Cowrie)  17  nbytes = ssh_channel_read_nonblocking (channel_rw1  �→ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='channel_data , buffer , sizeof(buffer), 0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  18  if (nbytes > 0 && ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ got_command !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='= 1 && ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ subsystem_req !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='= 1)  19  {  20  write(ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='wfd , buffer ,  �→ nbytes);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  21  }  22  else if (nbytes > 0 && ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  �→ got_command == 1)  23  {  24  sshbuf_putf (&c->input , buffer , nbytes);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  25  }  26  } else  27  {  28  if (ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' counter_disconnect == 0)  29  {  30  ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' to_disconnect = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  31  }  32  }  33  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  34  }  65  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8: Tweaked OpenSSH server loop to connect to Cowrie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Only the essential  code parts to change the authentication method have been added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  static Channel *  2  server_request_direct_tcpip (struct ssh *ssh , int *reason ,  �→  const char ** errmsg)  3  {  4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  6  /* Implement direct -TCP/IP forwarding */  7  if (sshd_honey_options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='tcpForwardingPort !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='= 0)  8  {  9  /* Redirect to the host specified in  �→ sshd_config */  10  c = channel_connect_to_port (  11  ssh ,  12  sshd_honey_options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='tcpForwardingHost ,  13  sshd_honey_options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='tcpForwardingPort ,  14  "direct -tcpip",  15  "direct -tcpip",  16  reason ,  17  errmsg  18  );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  19  }  20  else  21  {  22  /* Redirect to any host */  23  c = channel_connect_to_port (ssh , target ,  �→ target_port , "direct -tcpip", "direct -  �→ tcpip", reason , errmsg);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  24  }  25  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  26  /* Make sure cowrie is aware of all requests (  �→ successful or not) */  27  ssh_channel_open_forward (channel_rw1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='channel_data_1 ,  28  target , target_port ,  29  originator , originator_port)  �→ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  30  31  sprintf(ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' target_ip , "%s", target)  �→ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  32  sprintf(ssh_client_conns1 [0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' target_port , "%d",  �→ target_port);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  33  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  34  }  66  Listing 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9: Cowrie log information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The new connection from this experiment has  been acquired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cowrie fetched information about the local string version  and kex message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  1  New connection: 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1:65522 [session: 2ca9a619ceb8]  2  Remote SSH version: SSH -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0- libssh_0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='6  3  SSH client hassh fingerprint: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=".  4  kex alg=b'curve25519 -sha256 ' key alg= b'ssh -ed25519 '  5  outgoing: b'aes256 -ctr ' b'hmac -sha2 -512' b'none '  6  incoming: b'aes256 -ctr ' b'hmac -sha2 -512' b'none '  67  Chapter 6  Conclusion  This thesis has shown that organizations can spot malicious activities using honeypot  solutions." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The result in this thesis successfully answered the original question of  whether honeypots contribute to a more secure infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It can confirm this  assumption based on its results in the cloud and in the university network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The first  approach was to collect data with the help of the T-Pot solution and compare them  to a previous study of similar cloud providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It has shown that these activities  increased significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The universitys’ cloud solution heiCLOUD has received more  attacks than ever, putting it in the first place compared to other cloud providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  It has seen various attacks in RDP, VoIP, and SSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The number of attacks related  to cryptocurrencies is particularly striking, reflecting the current situation of highly  traded GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition, the latest attacks like the Apache vulnerability in version  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 could be traced back to very early stages, showing how fast attackers adapt to  new vulnerabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It is assumed that most of the executed attacks on the instance  came from bots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Next, this thesis has focused on the university’s internal network and implemented  a new concept to detect every single packet sent to a host machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The MADCAT  solution, in conjunction with IDS tools, helped identify the open port 113 that has  been used to deploy attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It has shown that known attackers with an IP address  originating from Russia have probed the instance, and as an assumption, further  attacks would have been carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In retrospect, this helped remove the port from  the firewall’s permits, thus improving the security at the Heidelberg University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Any  other suspicious behavior in the eduroam network could not be registered, proving  that the firewall works as intented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Moreover, honeypots like Cowrie have a fundamental flaw because they rely on  off-the-shelf libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  These libraries often reimplement protocol behaviors like  OpenSSH and add a subtle difference to the response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' On the contrary, this devia-  tion of responses can be used to detect honeypots on the transport level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Adversaries  could spot honeypots before deploying any attack based on a cosine similarity coeffi-  cient, thus avoiding exposures to newly developed attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The findings Vetterl [72]  claims in his work have been recreated by adapting OpenSSH 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='8P1 and testing it  68  on different Debian instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Due to outdated algorithms, the key exchange initial-  ization message has been updated to work with the latest version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' It shows that the  latest Cowrie version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='0 results in a bad packet length because the local version  string does not match the expected ones of the underlying library TwistedConch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  This result deviates fundamentally from OpenSSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Lastly, an attempt to protect  Cowrie from early exposure has been made by hiding it in the background and tun-  neling requests through a customized OpenSSH daemon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' This has successfully fixed  the generic weakness of Cowrie so that connecting to Cowrie works without run-  ning into a bad packet length error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The last chapter shows that honeypots are not  flawless, and developers should be careful when deciding on additional libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  In conclusion, this thesis has presented concepts to catch attackers for different sce-  narios and shows that malicious activities have increased tremendously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In addition,  it has taken a deep dive into an edge-breaking study to detect honeypots on trans-  port level and has disguised Cowrie to block such activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' An interesting future  study could involve the development of a generic method to fingerprint honeypots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Future research could also examine other libraries that reimplement protocols to  find generic weaknesses and deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Ultimately, using honeypots as a security  parameter has been proven promising for further implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  69  Bibliography  [1] Fahim Abbasi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' 2020 trustwave global security report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Trustwave, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [2] John B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Althouse, Jeff Atkinson, and Josh Atkins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' JA3 - a method for profiling  ssl/tls clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/salesforce/ja3, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-  09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [3] Michael Armbrust, Armando Fox, Rean Griffith, Anthony D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Joseph, Randy  Katz, Andy Konwinski, Gunho Lee, David Patterson, Ariel Rabkin, Ion Stoica,  and Matei Zaharia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A view of cloud computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Communications of the ACM,  53(4):50–58, April 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1145/1721654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1721672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1145/1721654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1721672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [4] Vesselin Bontchev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Elasticpot: an elasticsearch honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://gitlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  com/bontchev/elasticpot, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [5] Vesselin Bontchev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Ipphoney: an internet printing protocol honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https:  //gitlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/bontchev/ipphoney, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [6] BSI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Die lage der it-sicherheit in deutschland 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Technical Report  BSI-LB21/510, Bundesamt für Sicherheit in der Informationstechnik, Sep  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='bsi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='bund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [7] Bill Cheswick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' An evening with berferd in which a cracker is lured, endured,  and studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Winter USENIX Conference, pages 163–174, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [8] Gabriel Cirlig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ADBHoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/huuck/ADBHoney, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Ac-  cessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [9] Theo Combe, Antony Martin, and Roberto Di Pietro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' To docker or not to  docker: A security perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' IEEE Cloud Computing, 3(5):54–62, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1109/MCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [10] CSEC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Information technology security guideline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Technical Report ITSG-  38, Communications Security Establishment Canada, May 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL https:  //cyber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='gc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [11] CVE-2001-0540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2001-0540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-2001-  0540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', March 09 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  name=CVE-2001-0540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  70  [12] CVE-2002-0013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2002-0013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-2002-  0013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', February 13 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='name=CVE-2002-0013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [13] CVE-2005-4050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2005-4050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-2005-  4050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', December 07 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='name=CVE-2005-4050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [14] CVE-2006-2369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2006-2369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-2006-  2369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', May 15 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  name=CVE-2006-2369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [15] CVE-2012-0152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2012-0152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-2012-  0152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', December 13 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='name=CVE-2012-0152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [16] CVE-2018-0101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2018-0101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-2018-  0101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', November 27 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='name=CVE-2018-0101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [17] CVE-2019-12263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2019-12263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-  2019-12263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', September 07 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/  cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='name=CVE-2019-12263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [18] CVE-2019-19781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2019-19781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-  2019-19781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', December 13 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/cgi-bin/  cvename.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='name=CVE-2019-19781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [19] CVE-2020-11899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2020-11899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-  2020-11899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', July 17 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' URL http://cve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='name=CVE-2020-11899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [20] CVE-2021-42013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' CVE-2021-42013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Available from MITRE, CVE-ID CVE-  2021-42013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=',  October 06 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='mitre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='cgi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='name=CVE-2021-42013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [21] Jeff Daniels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Server virtualization architecture and implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' XRDS,  16(1):8–12, September 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ISSN 1528-4972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='1145/1618588.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [22] ddosspot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='com/aelth/ddospot, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed:  2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [23] Tharam Dillon, Chen Wu, and Elizabeth Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cloud computing: Issues and  challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' In 2010 24th IEEE International Conference on Advanced Infor-  mation Networking and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' IEEE, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1109/aina.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1109/aina.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [24] dionaea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' dionaea - catches bugs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/DinoTools/dionaea,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  71  [25] Docker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Docker  overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='com/get-started/  overview/, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [26] elasticsearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' The Elastic Stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='co/elastic-stack/,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [27] Europol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Internet organised crime threat assessment (iocta).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' European Union  Agency for Law Enforcement Cooperation, 9(1), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [28] Europol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' About europol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='eu/about-europol,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [29] Maryam Feily, Alireza Shahrestani, and Sureswaran Ramadass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' In 2009 Third International Conference on Emerging  Security Information, Systems and Technologies, pages 268–273, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1109/SECURWARE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [30] Michael Flanders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' A simple and intuitive algorithm for preventing directory  traversal attacks, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [31] Federal Office for Information Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cert-bund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='bsi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [32] Martin Gallo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Honeysap: Sap low-interaction honeypot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  com/SecureAuthCorp/HoneySAP, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [33] Brian Hayes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Cloud computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ACM, 51(7):9–11, July 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' ISSN  0001-0782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1145/1364782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1145/  1364782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='1364786.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [34] Marcus Hutchins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Honepot for cve-2019-19781 (citrix adc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  com/MalwareTech/CitrixHoneypot, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [35] Yung Innanet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Hellpot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='com/yunginnanet/HellPot, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [36] Michael C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Johns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' Identification Protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' RFC 1413, RFC Editor, February  1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [37] Adel Karimi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  FATT /fingerprintAllTheThings - a pyshark based script for  extracting network metadata and fingerprints from pcap files and live network  traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' Accessed: 2021-09-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [38] Adel Karimi, Ben Reardson, John Althouse, Jeff Atkinson, and Josh Atkins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' Virtual Strategy Magazine,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [44] Sami Lehtinen and Chris Lonvick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' Datamation, 15(11):205, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content='  [46] mailoney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [47] P M Mell and T Grance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='06249, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' T-Pot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [53] Michel Oosterhof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [54] Sylvain Peyrefitte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [55] Niels Provos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', August 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [56] Antonio  Regalado.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [58] Lukas Rist, Johnny Vestergaard, Daniel Haslinger, Andrea Pasquale, and John  Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' Addison-Wesley, Amsterdam,  2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' ISBN 0743411463.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [68] University Computing Center Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content=' Linux J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
+page_content=', 2007  (156):6, apr 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [73] Lizhe Wang, Gregor von Laszewski, Andrew Younge, Xi He, Marcel Kunze, Jie  Tao, and Cheng Fu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+page_content='  [75] Tillmann Werner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtAyT4oBgHgl3EQfz_l6/content/2301.00710v1.pdf'}
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+Capturing the dynamics of Ti diffusion across TixW1−x/Cu
+heterostructures using X-ray photoelectron spectroscopy
+C. Kalha*
+P. K. Thakur T.-L. Lee M. Reisinger J. Zechner M. Nelhiebel A. Regoutz
+Curran Kalha, Anna Regoutz
+Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United
+Kingdom.
+Email Address: curran.kalha.19@ucl.ac.uk, a.regoutz@ucl.ac.uk
+Pardeep K. Thakur, Tien-Lin Lee
+Diamond Light Source Ltd., Diamond House, Harwell Science and Innovation Campus, Didcot, OX11
+0DE, United Kingdom.
+Michael Reisinger, Johannes Zechner, Michael Nelhiebel
+Kompetenzzentrum Automobil- und Industrie-Elektronik GmbH, Europastraße 8, 9524 Villach, Austria.
+Keywords: HAXPES, SXPS, XPS, power electronic device, diffusion barrier, metallisation, in-situ
+Interdiffusion phenomena between adjacent materials are highly prevalent in semiconductor device architectures and can present
+a major reliability challenge for the industry. To fully capture and better understand these phenomena, experimental approaches
+must go beyond static and post-mortem studies to include in-situ and in-operando setups. Here, soft and hard X-ray photoelec-
+tron spectroscopy (SXPS and HAXPES) is used to monitor diffusion in real-time across a proxy device. The device consists of a
+Si/SiO2/TixW1−x(300 nm)/Cu(25 nm) thin film material stack, with the TixW1−x film acting as a diffusion barrier between Si and
+Cu. The monitoring of diffusion is achieved through the continuous collection of spectra whilst in-situ annealing to 673 K. Ti within
+the TiW is found to be highly mobile during annealing, diffusing out of the barrier and accumulating at the Cu surface. Increasing
+the Ti concentration within the TixW1−x film increases the quantity of accumulated Ti, and Ti is first detected at the Cu surface at
+temperatures as low as 550 K. Surprisingly, at low Ti concentrations (x = 0.054), W is also mobile and diffuses alongside Ti. These
+results provide crucial evidence for the importance of diffusion barrier composition on their efficacy during device application, deliv-
+ering insights into the mechanisms underlying their effectiveness and limitations.
+1
+Introduction
+The binary pseudo-alloy of titanium-tungsten (TixW1−x, x ≤ 0.3) is a well-established, effective diffusion
+barrier and adhesion enhancer within silicon-based semiconductor devices. [1–3] It is designed to pre-
+vent the interdiffusion between adjacent metallisations and the underlying dielectric and semiconductor
+materials. TiW is compatible with various metallisations (Al, Au, Ag, In and Cu) and has remarkable
+thermal stability at elevated temperatures (≤850◦C). [4–19] Consequently, TiW diffusion barriers are
+now being widely implemented in next-generation SiC-based power semiconductor technologies with cop-
+per metallisation schemes, [20–22] and more recently within electrodes for GaAs photoconductive semi-
+conductor switches (PCSSs), [23] and gate metal stacks in GaN-based high electron mobility transistor
+(HEMT) devices. [24]
+Diffusion barriers are needed as Cu and Si readily react at relatively low temperatures to form inter-
+metallic copper-silicide compounds at the interface, which seriously hamper the performance and reli-
+ability of devices. [18, 25–29] Studies have shown that TiW films are capable of retarding and limiting
+this interdiffusion and subsequent reaction. [2, 18] However, when subjected to a high thermal budget,
+a depletion of Ti within the TiW grains has been observed, leading to the accumulation of Ti at grain
+boundaries. [30] The segregated Ti is then able to diffuse out of the barrier and through the metalli-
+sation via grain boundary diffusion. [8] This depletion of Ti is thought to lead to a greater defect den-
+sity within the TiW layer, consequently allowing for the potential of Cu and Si to bypass the barrier
+and react. Fugger et al. cite that this out-diffusion process is an “essential factor” in the failure of this
+barrier, [16] and others have also documented the segregation of Ti during high-temperature anneal-
+ing. [12,12,19,20,30,31]
+Given the importance of the TiW barrier to the overall device performance, reliability and its applica-
+tion in future SiC technologies and beyond, this Ti diffusion degradation process must be better under-
+stood, including how it impacts the stability of the TiW/Cu structure. The common thread across the
+1
+arXiv:2301.02577v1  [cond-mat.mtrl-sci]  6 Jan 2023
+
+vast majority of past experimental studies on TiW and diffusion barriers in general, including the present
+authors’ previous work, [19, 32] is that ex-situ samples are used to track the evolution of the diffusion
+process and to determine the temperature at which the barrier fails. Such studies also often focus on one
+Ti concentration and are therefore unable to address the effect of the titanium concentration of the film
+on the degradation mechanism.
+Figure 1: Schematic representation of the samples and experimental approach (not drawn to scale). (a) Device stack on
+a sample holder being annealed in-situ to 673 K and the expected Ti diffusion represented by grey vertical arrows. (b)
+A magnified view of the copper surface showing the Ti accumulation and the two photon energies used for SXPS and
+HAXPES measurements to excite the Ti 2p and Ti 1s electrons from the same depth. (c) SXPS laboratory-based Ar+
+sputtering depth profile used to quantify the elemental distribution across the TiW/Cu bilayer after in-situ annealing (i.e.
+post-mortem).
+Although ex-situ prepared samples give a good representation of the device after stress events, it is dif-
+ficult to correlate the results directly with what a device is experiencing during the applied stress. [8,20]
+Therefore, it is crucial to develop new characterisation strategies that can probe the degradation mecha-
+nism dynamically under realistic conditions while allowing for changes to the chemical states across the
+device stack to be monitored.
+To the best of our knowledge, only Le Priol et al. and Siol et al. provide in-situ monitoring measure-
+ments on TiW, both employing in-situ X-ray diffraction (XRD). Le Priol et al. studied the efficiency of
+a TiW barrier deposited from a 70:30 at.% W:Ti alloy target against indium diffusion at temperatures
+between 573-673 K under vacuum. [17] The authors could correlate the TiW barrier efficiency with its
+microstructure and determine the diffusion coefficient of In in TiW. Siol et al. were interested in under-
+standing the oxidation of TiW alloy precursors, and observed oxygen dissolution and the formation and
+decomposition of mixed (W,Ti)-oxide phases when ramping the temperature between 303 to 1073 K in
+air. [33]
+An explanation for the lack of in-situ/operando experiments in the field, which is in contrast to the im-
+portance of these material interfaces in both novel and commercial device applications, is the challenges
+associated with performing such experiments. These include extensive periods of time required to collect
+sufficient data, the availability of instruments with in-situ capability, and difficulties in sample prepara-
+tion and interfacing.
+The present work combines soft and hard X-ray photoelectron spectroscopies (SXPS and HAXPES) with
+in-situ annealing to study the effect of annealing temperature, annealing duration, and Ti:W ratio on
+the thermal stability of TiW/Cu bilayers in real-time, considerably expanding on the existing ex-situ
+work, including the present authors’ previous studies. [19, 32] Si/SiO2/TixW1−x(300 nm)/Cu(25 nm)
+device stacks (see Fig. 1(a) for a schematic of the stack) are annealed up to a maximum temperature of
+673 K (400◦C) and held there for 5 h. At the same time, soft and hard X-ray photoelectron spectra are
+continuously recorded to capture the Ti diffusion process and changes to the chemical state across the
+copper surface (see Fig. 1(b) for a schematic). The target temperature of 673 K is selected as it is in a
+common temperature regime employed during device fabrication to obtain desired grain growth and tex-
+2
+
+kev
+Ti 2p/1s e
+?
+25 nm
+Cu
+(b)
+Tiw
+300 nm
+Ti
+Cu
+Cu
+SiO2
+Tiw
+Tiw
+Si
+Heating to 673 KCture of the copper metallisation. [31, 34] Additionally, it is a temperature that can occur at short circuit
+events during the operation of potential devices. [35]
+A major benefit of combining the two variants of X-ray photoelectron spectroscopy (XPS) is that SXPS
+is more surface-sensitive, whereas HAXPES enables access to the Ti 1s core line. The Ti 1s offers an al-
+ternative to the commonly measured Ti 2p with soft X-ray sources. The Ti 1s compared to the Ti 2p
+has the added benefits of covering a smaller binding energy (BE) range and consequently necessitating
+a shorter collection time, the absence of spin-orbit splitting (SOS), no additional broadening to consider
+from the Coster-Kronig effect that influences the Ti 2p1/2 peak, and the absence of underlying satellites.
+For these reasons, the exploitation of the 1s core level over the 2p is becoming increasingly popular for
+transition metals, especially for the disentanglement of charge transfer satellite structures in the X-ray
+photoelectron spectra of metal oxides. [36–40]
+HAXPES is typically employed as it offers a larger probing depth than conventional SXPS. [40] How-
+ever, here, it is strategically used to obtain comparable probing depths of the Ti 2p and Ti 1s core lines,
+collected with SXPS and HAXPES, respectively. Using this combination, the more widely studied Ti 2p
+spectra can be used to understand the Ti 1s spectra better. In addition to the synchrotron-based XPS
+experiments, quantitative laboratory-based SXPS depth profiles were also conducted on the samples fol-
+lowing the in-situ experiment (i.e. post-mortem) to ascertain the quantitative distribution of Ti across
+the Cu metallisation (see Fig. 1(c) for a schematic of the depth profiling).
+2
+Methodology
+2.1
+Samples
+Three as-deposited Si/SiO2/TixW1−x/Cu thin film stacks with varying Ti:W composition were prepared
+through an established industrial route. The stack consists of a 50 nm SiO2 layer on an un-patterned Si
+(100) substrate, above which a 300 nm thick TiW layer was deposited via magnetron sputtering. The
+TiW films were deposited from composite targets with a nominal atomic concentration of 30:70 Ti:W,
+determined by X-ray fluorescence spectroscopy (XRF). By varying the deposition parameters, three sam-
+ples with an average Ti concentration, x across the entire film thickness of 5.4±0.3, 11.4±0.5, and 14.8±0.6
+at.% relative to W were realised (e.g (Ti/(Ti+W))×100). These concentrations were determined using
+laboratory-based SXPS and depth profiling across the entire film thickness (further details regarding the
+quantification of the TiW films can be found in Supplementary Information I). These samples will be re-
+ferred to as 5Ti, 10Ti and 15Ti, respectively, for the remainder of the manuscript. Finally, a 25 nm Cu
+capping layer was deposited via magnetron sputtering on top of the TiW barrier. Deposition of both
+TiW and Cu was conducted in an argon discharge with no active substrate heating or vacuum break be-
+tween successive depositions. The deposition chamber operated under a base pressure of 10-8-10-7 mbar.
+Further details regarding the deposition process have been reported in Refs. [31,41].
+2.2
+Dynamic synchrotron-based SXPS/HAXPES
+2.2.1
+Beamline optics and end station details
+SXPS and HAXPES measurements were conducted at beamline I09 of the Diamond Light Source, UK, [42]
+at photon energies of 1.415 keV and 5.927 keV, respectively (these will be abbreviated as 1.4 keV and
+5.9 keV throughout the remaining manuscript). 1.4 keV was selected using a 400 lines/mm plane grating
+monochromator, achieving a final energy resolution of 330 meV at room temperature. 5.9 keV was se-
+lected using a double-crystal Si (111) monochromator (DCM) in combination with a post-monochromator
+Si (004) channel-cut crystal, achieving a final energy resolution of 290 meV at room temperature. The
+total energy resolution was determined by extracting the 16/84% width of the Fermi edge of a clean poly-
+crystalline gold foil (see Supplementary Information II for further information on determining the resolu-
+tion). [43] The end station of beamline I09 is equipped with an EW4000 Scienta Omicron hemispherical
+analyser, with a ±28◦ acceptance angle. The base pressure of the analysis chamber was 3.5×10-10 mbar.
+3
+
+2.2
+Dynamic synchrotron-based SXPS/HAXPES
+To maximise the efficiency in the collection of spectra, the measurements were conducted in grazing inci-
+dence and at near-normal emission geometry.
+2.2.2
+Annealing
+Samples were individually annealed in-situ to a sample target temperature of 673 K (400◦C) using a tung-
+sten filament heater, and held at the temperature for approximately 5 h. The sample plate used for the
+experiment consisted of a copper disk (3 mm thick, 8 mm diameter) fixed to the centre of a flat tanta-
+lum plate, on which the sample was placed and secured using clips. Good thermal contact was made be-
+tween the copper disk and the sample using a thin silver foil. This allowed the sample temperature to be
+inferred by attaching an N-type thermocouple to the centre of the copper disc. The thermocouple was
+also connected to a Lakeshore temperature controller, which was programmed to ramp the sample tem-
+perature at a constant rate under a closed-loop control (see Supplementary Information III for an image
+of the sample plate holder).
+Prior to in-situ annealing, all samples were gently sputter cleaned in-situ for 10 minutes using a 0.5 keV
+de-focused argon ion (Ar+) source, operating with a 6 mA emission current and 5×10-5 mbar pressure.
+This was necessary to remove the native copper oxide that had formed on the sample surface during sam-
+ple transport.
+The process of in-situ annealing encourages the purging of adsorbed gases and organic species within the
+sample and on the sample surface (i.e. degassing). Therefore, annealing in a UHV environment will in-
+crease the chamber pressure, which is undesired, especially during the collection of photoelectron spec-
+tra. To account for sample degassing, the annealing process was conducted step-wise to ensure a good
+analysis chamber pressure was maintained throughout the measurements. Fig. 2 displays a represen-
+tative temperature profile acquired for sample 5Ti and the related pressure profile within the analysis
+chamber (see Supplementary Information IV for the temperature profiles collected for all three samples).
+The temperature profile consists of three stages. Additionally, as seen in the pressure profile in Fig. 2,
+with every increasing step in temperature, a temporary increase in pressure resulted due to the degassing
+of the sample.
+Prior to annealing in the analysis chamber, the samples were first heated in a subsidiary sample prepara-
+tion chamber to remove the majority of adsorbed molecules. This stage of annealing involves a fast ramp
+from room temperature to 523 K and will be referred to as Stage 1 of the annealing process. The Ti dif-
+fusion process was assumed to be insignificant in this temperature range. Next, the sample was moved
+to the main analysis chamber, where the temperature was ramped step-wise from 523 to the target tem-
+perature of 673 K while maintaining on average a pressure of 7×10-10 mbar (referred to as Stage 2). The
+temperature was then held at the 673 K target temperature for 5 h (referred to as Stage 3). The spectra
+were continuously collected using SXPS and HAXPES from the start of Stage 2 until the end of Stage 3
+of the annealing process. The period where the spectra were collected will be referred to as the “mea-
+surement window”. Across the measurement window, the same group of spectra were collected itera-
+tively, which will be referred to as the “spectral cycle”. Each spectral cycle took approximately 15 min-
+utes to collect, and details on which spectra were selected will be discussed in the following section. Dur-
+ing Stage 2, the temperature was increased once a spectral cycle was completed, which coincidentally
+allows sufficient time for the analysis chamber pressure to recover below 8×10-10 mbar.
+For completeness, we note that during the initial stages of annealing, sample 10Ti degassed more than
+samples 5Ti and 15Ti, and therefore the temperature ramp of Stage 2 for sample 10Ti was paused to al-
+low the pressure to recuperate. This meant that sample 10Ti was held at 543 K for four spectral cycles
+rather than one. Therefore, the total time of annealing of sample 10Ti was extended by approximately
+1 h compared to the annealing time of samples 5Ti and 15Ti. This is not expected to affect the diffu-
+sion process significantly or the resultant accumulation profiles, as the Ti diffusion at this temperature is
+minimal.
+4
+
+2.3
+Laboratory-based SXPS
+Figure 2: Representative temperature profile acquired from the Lakeshore temperature controller during the measurements
+on sample 5Ti. The temperature profile consists of three stages. Stage 1: a quick ramp to 523 K in a subsidiary chamber.
+Stage 2: a 10 K/[spectral cycle] ramp in the main analysis chamber, which was then decreased to a 5 K/[spectral cycle]
+ramp once 653 K was reached. The temperature was ramped step-wise in Stage 2 to allow the pressure in the analysis
+chamber to recover to <7×10-10 mbar after each temperature step (see inset for the pressure profile). Stage 3: holding
+period at 673 K for 5 h. The dotted line at t = 0 h indicates the start of the measurement window.
+2.2.3
+Core level selection
+The spectral cycle, which was run in an iterative loop during the experiment, included the following core
+level spectra: Cu 2p3/2, Ti 2p and W 4d collected with SXPS, and Ti 1s collected with HAXPES. The
+W 4d core level was selected over the commonly measured W 4f line as the former does not overlap with
+the core levels of Cu or Ti in this region, whereas the latter overlaps with the Ti 3p core level. The Cu
+Fermi edge was also included in the spectral cycle and was collected with both SXPS and HAXPES through-
+out the measurement window to (a) provide an intrinsic method of calibrating the BE scale and (b) mon-
+itor any change to the total energy resolution as a consequence of raising the sample temperature. Based
+on 16/84% fits of the collected Fermi edges across all measurements, the effect of thermal broadening is
+negligible under the experimental conditions used, and further information can be found in Supplemen-
+tary Information V. All spectra were aligned to the intrinsic Cu Fermi energy (EF) and the spectral ar-
+eas were obtained using the Thermo Avantage v5.9925 software package. The BE values quoted in this
+work are considered to have an estimated error of ±0.1 eV.
+The SXPS photon energy was set to 1.4 keV so that the kinetic energy (KE) of excited Ti 2p electrons
+at this photon energy matches the KE of Ti 1s electrons excited with the HAXPES photon energy (KETi 1s
+≈ KETi 2p3/2 ≈ 961 eV). Using the QUASES software package, [44] the inelastic mean free path (IMFP)
+of Ti 2p and Ti 1s electrons in Cu metal at the SXPS and HAXPES photon energies were calculated.
+The IMFP for the Ti 1s and Ti 2p3/2 is approximately 1.50 nm, and so the estimated probing depth
+(3λ) is 4.50 nm. Therefore, a direct comparison between the two Ti core levels will be possible as they
+originate from very similar probing depths.
+2.3
+Laboratory-based SXPS
+SXPS depth profile measurements were conducted on the samples that were annealed at I09 using a laboratory-
+based Thermo K-Alpha+ instrument (i.e. the in-situ annealed samples were removed and kept for a post-
+mortem analysis). The instrument operates with a monochromated Al Kα photon source (hν = 1.4867 keV)
+and consists of a 180◦ double-focusing hemispherical analyser, a two-dimensional detector that integrates
+intensity across the entire angular distribution range, and operates at a base pressure of 2×10-9 mbar.
+A 400 µm spot size was used for all measurements, achieved using an X-ray anode emission current of
+6 mA and a cathode voltage of 12 kV. A flood gun with an emission current of 100 µA was used to achieve
+5
+
+Stage 3
+700 -
+600 -
+Stage
+Stage 1
+Temperature / K
+1.6
+Temperature
+620
+Pressure
+500
+1.4
+610
+Temperature / K
+600
+1.0
+400 -
+0.8
+590
+580
+300 -
+............
+1.4
+1.6
+1.8
+2.0
+2.2
+t / h
+-2
+0
+2
+4
+6
+8
+10
+t / hthe desired level of charge compensation. The total energy resolution of the spectrometer was determined
+to be 400 meV. Survey and core level (W 4f, Ti 2p, O 1s and Cu 2p3/2) spectra were collected with pass
+energies of 200 and 20 eV, respectively. Depth profiles were conducted using a focused Ar+ ion source,
+operating at 500 eV energy and 10 mA current, rastering over a 2×2 mm2 area with a 30◦ sputtering an-
+gle. A total of 17 sputter or etch cycles, each lasting 180 s, was carried out with survey and core level
+spectra collected after each etch cycle. The data were analysed using the Thermo Avantage v5.9925 soft-
+ware package. The error associated with the quantification values is estimated to be ±0.3 at.% owing to
+the complexity of the W 4f core level and the low quantities of Cu and Ti/W in the TiW and Cu layers,
+respectively.
+3
+Results and Discussion
+Reference room temperature survey and core level spectra (Ti 1s, Cu 2p, Ti 2p and W 4d) were col-
+lected for the three samples after the in-situ sputter cleaning process, and prior to annealing, with the
+results displayed in Supplementary Information VI. From the survey spectra, the sample surfaces appear
+clean and are dominated by signals from Cu. Virtually no carbon is detected, and only a trace quantity
+of oxygen is present when measured with SXPS. The Cu 2p3/2 core level spectra are near identical for
+the three samples, and the position and line shape are commensurate with metallic copper. [45–47] A
+low-intensity satellite is observed between 943-948 eV in the Cu 2p3/2 core level spectra, but comparing
+the spectra to reference measurements of a polycrystalline Cu foil and an anhydrous Cu2O powder, the
+satellite intensity is in agreement with the Cu foil. This confirms that the Cu surface of these samples
+can be considered metallic and the native oxide contribution is minimised after in-situ sputtering.
+Importantly no Ti or W is observed in these room temperature measurements. This confirms both that
+the Cu layer is sufficiently thick so that even with SXPS the underlying TiW cannot be probed, and
+that the surfaces are consistent across all samples. The reference measurements show that the Cu L1M1M4,5
+Auger line overlaps with the Ti 1s core line but its intensity is vanishingly small. [48, 49] Nevertheless,
+care was taken to remove this contribution when we quantified the Ti 1s region to accurately determine
+the relative change in Ti concentration at the surface.
+The following sections present the Cu, Ti and W core level spectra and associated accumulation pro-
+files as a function of annealing duration/temperature across the three samples, with a focus on the initial
+stages of annealing and the 673 K holding period.
+3.1
+In-situ annealing profiles
+3.1.1
+Copper
+Fig. 3 displays the Cu 2p3/2 core level spectra collected over the 5 h holding period at 673 K for all three
+samples, i.e. Stage 3 (with t = 0 h in Fig. 3 referring to the start of the 5 h holding period). The spec-
+tra across all samples confirm that Cu still remains in its metallic state during annealing, with a BE po-
+sition of approximately 932.5 eV. Additionally, the narrow full width at half maximum (FWHM), found
+to be 0.8 eV, and the lack of significant satellite features in the 943-948 eV region give further confirma-
+tion of the metallic nature of the Cu surface. [45–47] From Fig. 3 it can be observed that after annealing
+and within the 673 K holding period, sample 5Ti has the highest Cu 2p3/2 signal intensity (Fig. 3(a)),
+followed by samples 10Ti (Fig. 3(b)) and 15Ti (Fig. 3(c)). Moreover, within the 5 h holding period, the
+signal intensity is continually decreasing with annealing duration and this effect is most notable in Fig. 3(c)
+for the sample with the highest Ti concentration.
+To determine the change in concentration of Cu at the sample surface across the measurement window,
+peak fit analysis of the Cu 2p3/2 core level was conducted to determine the change in area, with the re-
+sultant profile displayed in Fig. 4(a). In Fig. 4, time, t = 0 h is redefined as the first measurement point
+of the measurement window (i.e. at the start of Stage 2 at a temperature of 523 K (250◦C)). Note, t
+= 0 h in the context of Fig. 4 is not the same as t = 0 h in Fig. 3. The same is also true for Fig. 5 and
+Fig. 7, which present the equivalent spectra to Fig. 3 for the Ti 1s and W 4d core levels, respectively.
+6
+
+3.1
+In-situ annealing profiles
+Figure 3: Cu 2p3/2 core level spectra collected during the 673 K holding period (Stage 3) for sample (a) 5Ti, (b) 10Ti,
+and (c) 15Ti. Spectra for each sample are plotted over the same y-axis scale to show the differences in intensity across
+the three samples. The spectra have not been normalised but a constant linear background has been removed. To avoid
+congestion of this figure, spectra collected every other spectral cycle are presented (i.e. ≈30 minutes) rather than at every
+spectral cycle (i.e. ≈15 minutes). The legend displayed in (b) also applies to (a) and (c). Here, t = 0 h refers to the start
+of the 5 h holding period.
+The Cu 2p3/2 intensity profile in Fig. 4(a) reflects what is observed in the core level spectra collected
+across the 673 K holding period shown in Fig. 3, in that the Cu 2p3/2 signal intensity decreases as a func-
+tion of time and annealing temperature across both Stages 2 and 3 of the annealing process. The de-
+crease in intensity of the Cu 2p3/2 signal with time is a consequence of the diffusion of Ti out of the TiW
+layer during annealing. The accumulation of Ti leads to a displacement of Cu atoms and the formation
+of a Ti-rich surface layer, consequently attenuating the Cu signal. Additionally, when the TiW is more
+Ti-rich, Fig. 4(a) shows that the Cu signal diminishes more extensively suggesting a greater out-diffusion
+of Ti. As expected based on this interpretation, sample 15Ti shows the largest decay rate in the Cu 2p3/2
+signal, followed by sample 10Ti and then 5Ti. At the end of the measurement window, the Cu 2p3/2 sig-
+nal intensity has depreciated by approximately 2.8, 8.8 and 32.3 %, for sample 5Ti, 10Ti and 15Ti, re-
+spectively.
+3.1.2
+Titanium
+The Ti 1s core level spectra collected across the 5 h 673 K holding period (Stage 3) are displayed in Fig. 5,
+with the BE positions of the main signals annotated (see Supplementary Information VII and VIII for
+the equivalent Ti 2p core level spectra and heat maps of the Ti 1s spectra collected across the measure-
+ment window, respectively).
+Fig. 5 shows that by the time the 673 K holding period starts, a Ti 1s peak is observed across all three
+samples and the intensity continually increases during the 5 h holding period. This confirms that the on-
+set of diffusion occurs prior to Stage 3 of the annealing process as assumed during the discussion of the
+Cu profile. Significant differences in intensity of the Ti 1s spectra as a function of Ti concentration are
+observed, with sample 15Ti showing a considerably more intense peak than sample 10Ti and 5Ti (note
+the ×30 magnification of the 5Ti spectra). Notably, the spectral line shape also appears different across
+the samples indicating a change in the chemical state of the accumulated Ti.
+All spectra exhibit a lower BE feature at BEs of 4964.2-4965.1 eV, corresponding to metallic Ti in vary-
+ing environments (labelled as Ti(0)). As the Ti 1s core level is not as widely studied as Ti 2p due to the
+need for hard X-ray sources, only a handful of publications exist, with reported BEs varying consider-
+ably. [36,50–57] The BE positions of the Ti(0) 1s peak observed in the present work fall within the liter-
+ature range of metallic Ti, and the asymmetric line shape of the peak, which can be clearly observed in
+Fig. 5(b) and (c), is commensurate with this assignment. An asymmetric line shape is a hallmark of the
+core level spectra of many transition metals. [58]
+7
+
+(a) Cu 2p3/2, 5Ti @ 673 K
+(b) Cu 2p3/2, 10Ti @ 673 K
+(c) Cu 2p3/2, 15Ti @ 673 K
+932.5
+t=Oh
+t = 0.5 h
+5
+t=1h
+t = 1.5 h
+ziedzr
+ev
+Rel. Intensity I arb. units
+t=2h
+932.6
+t = 2.5 h
+Cu
+t=3h
+t = 3.5 h
+t=4h
+-t = 4.5 h
+-t=5h
+945
+940
+935
+930
+945
+940
+935
+930
+945
+940
+935
+930
+Binding Energy / eV
+Binding Energy / eV
+Binding Energy / eV3.1
+In-situ annealing profiles
+Figure 4: Relative area intensities measured as a function of time, t collected across the measurement window for all three
+samples, including (a) Cu, (b) Ti, and (c) W profiles, determined from peak fitting the Cu 2p3/2, Ti 1s and W 4d core
+level spectra, respectively, at each spectral cycle. Here, t = 0 h refers to the start of the measurement window. The yellow-
+filled marker for each dataset refers to the time when the 673 K holding period commences (i.e. data points before and
+after the marker refer to Stage 2 and Stage 3 of the annealing process). Vertical guidelines are also in place to mark this
+point for each sample. For Cu, the measured total Cu 2p3/2 areas are normalised relative to the initial raw area (I0) of
+their respective sample (i.e. I/I0). For Ti, the measured total raw Ti 1s signal area for each sample is first normalised rel-
+ative to the raw area of the Cu 2p3/2 core level measured during the same spectral cycle and then afterwards the resultant
+Ti 1s/Cu 2p3/2 area is normalised relative to the final raw intensity of sample 15Ti (i.e. I/IF). The W accumulation pro-
+file was determined by normalising the measured total raw W 4d spectral areas following the method used for the Ti 1s
+normalisation (i.e. I/IF).
+The 10Ti and 15Ti samples show a small BE difference of 0.2 eV, which could be attributed to the dif-
+ferences in the Ti:Cu and/or Ti:O ratio at the evolving surface. In contrast, the BE position in the 5Ti
+spectra is considerably lower, with a -0.9 eV shift relative to the BE position observed in the spectra of
+sample 10Ti. This shift can be attributed to the distinctly different surface configuration of this sam-
+ple due to the dominance of Ti-O environments and the co-diffusion of tungsten, both of which will be
+discussed later. Moreover, the quantity of Ti diffused to the surface is incredibly small for sample 5Ti,
+and therefore, the shift could be due to strong surface effects, with far fewer nearest neighbours being Ti
+leading to a negative shift in BE position. [59,60]
+During the 673 K holding period, the nature of the accumulated Ti for samples 10Ti and 15Ti is pre-
+dominately metallic, given that a single asymmetric peak is visible (see Figs. 5(b) and (c)). The accumu-
+lated Ti for sample 5Ti, shown in Fig. 5(a) is strikingly different as the intensity of the lower BE metal-
+lic peak is overshadowed by a large, fairly symmetric peak at approximately +4.5 eV from the Ti(0) 1s
+peak. This peak, labelled as Ti(IV) 1s, is attributed to Ti-O environments in the Ti 4+ oxidation state
+(i.e. TiO2 like). Renault et al. report the Ti 1s BE position of the TiO2 environment on a TiN film at
+4968.8 eV, [55] which agrees well with the value reported here. Therefore, unlike samples 10Ti and 15Ti,
+the Ti accumulated at the surface of sample 5Ti is not predominately metallic but oxidic. Additionally,
+there is a shoulder on the lower BE side of this Ti(IV) 1s peak (marked with an asterisk, *), which is
+attributed to lower valence states of Ti (i.e. 2+, 3+) that may also form due to the limited quantity of
+oxygen expected to be present (see Supplementary Information IX for a peak fit analysis of the spectra
+highlighting the presence of such environments). This shoulder increases in intensity with increasing an-
+nealing duration, and at the end of the 5 h period, a distinct Ti(0) 1s peak is difficult to observe.
+To aid with the interpretation of the Ti 1s spectra, as well as validate the chemical state assignments
+made so far, the Ti 2p spectra are used in parallel (see Supplementary Information VII). The Ti 2p spec-
+tra for samples 10Ti and 15Ti show a doublet peak with an asymmetric line shape at 454.5 and 460.6 eV
+(SOS = 6.1 eV), in agreement with metallic Ti. [61, 62] For sample 5Ti, three peaks are identified at
+453.8, 459.0, and 464.8 eV. The lowest BE peak corresponds to Ti 2p3/2 of Ti(0), whereas the other two
+correspond to the doublet of Ti oxide in the 4+ oxidation state (SOS = 5.8 eV), labelled as Ti(IV) (with
+the Ti(IV) 2p3/2 peak overlapping the Ti(0) 2p1/2 peak). These BE positions and the SOS of the Ti(IV)
+8
+
+100 -
+100
+130 -
+(b) Ti 1s
+06
+- 06
+5Ti
+120 -
+10Ti
+110-
+80 -
+%
+80 -
+%
+-15Ti
+%
+I rel.
+100
+70 -
+, Area / rel.
+70 -
+Area / r
+90 .
+Area /
+- 09
+60 -
+80 -
+ 2P3/2 A
+W 4d/Cu 2p3/2 A
+70 -
+50 -
+50 -
+2p3/2 
+Stage 2
+Stage 3
+Stage 2
+Stage 3
+60 
+Stage 2
+Stage 3
+1s/Cu 2
+40 -
+40 -
+Cu
+50 
+KI
+10Ti 673 K.
+30 -
+Ve29
+30
+40 -
+Rel.
+(c) W 4d
+Rel.
+Rel.
+30
+5Ti
+20 -
+20
+(a) Cu 2p3/2
+673 K
+20 -
+10 -
+5Ti
+10 -
+— 15Ti
+10 
+10Ti
+&:
+10Ti
+Fit
+-0
+15Ti
+·F0
+3
+4
+6
+2
+5
+7
+0
+1
+2
+5
+7
+8
+9
+0
+2
+3
+5
+6
+8
+9
+0
+1
+3
+4 
+6
+8
+9
+t / h
+t / h
+t / h3.1
+In-situ annealing profiles
+Figure 5: Ti 1s core level spectra collected during the 673 K holding period (Stage 3) for sample (a) 5Ti, (b) 10Ti, and (c)
+15Ti. Spectra for each core level are plotted over the same y-axis scale to show the differences in intensity across the three
+samples. The spectra have not been normalised, but a constant linear background has been removed. Additionally, spectra
+recorded every other spectral cycle are displayed to aid with the interpretation of the data. For sample 5Ti, the spectra are
+also shown magnified by ×30 to aid with viewing. The legend displayed in (b) also applies to (a) and (c). Here, t = 0 h
+refers to the start of the 5 h holding period.
+oxide doublet match well with literature values. [63,64]
+A shift of the lower BE Ti(0) 2p3/2 peak between the three samples is observed, with the peak positioned
+at 453.8, 454.7 and 454.4 eV for sample 5Ti, 10Ti and 15Ti, respectively. The relative shifts are similar
+to those observed in the Ti 1s spectra. Moreover, the Ti 2p spectra recorded for sample 5Ti also display
+a shoulder on the lower BE side of the main Ti(IV) 2p3/2, again reflecting what has been observed in the
+Ti 1s spectra, suggesting the presence of lower valence oxidation states that may form during the reac-
+tion between Ti and oxygen. [65, 66] Overall, this confirms the peak assignments made using the Ti 1s
+core level are valid and shows the importance of using multiple core levels to have confidence in the as-
+signment of chemical states.
+The observation of almost completely oxidised Ti on the surface of sample 5Ti is of interest, given that
+these measurements were conducted under ultra-high vacuum (UHV) conditions and annealed in-situ.
+The level of observed oxidation cannot be explained by Ti gettering residual oxygen from the analysis
+chamber as the quantity present in the chamber is insufficient to promote oxidation of Ti to the extent
+observed. Furthermore, as the sample is heated during the measurement, the sticking coefficients for ad-
+sorbed gases are greatly reduced. An alternative source of oxygen is residual oxygen within the Cu film,
+whether that be intrinsic to the film (i.e. incorporated during deposition) or that the sputtering pro-
+cess prior to annealing did not fully remove the native oxide layer that formed during the exposure of
+the samples to the atmosphere. From the room temperature reference survey spectra found in Supple-
+mentary Information VI, a small intensity O 1s signal is present. Laboratory-based SXPS depth profil-
+ing on the as-deposited samples was conducted to determine the oxygen level within the starting (i.e.
+pre-annealed) films and to validate this assumption further. Three sputter cycles (or etch steps) were
+completed before the underlying TiW signal became strong (see Supplementary Information X for the
+collected spectra). The profiles showed that within the Cu bulk, less than 2 rel. at.% of O is present,
+i.e., <2 at.% O, >98 at.% Cu. Within the errors of the performed quantification, this amount would be
+enough to facilitate the observed Ti oxidation.
+Overall it is apparent that the oxidation of Ti is dependent on both the quantity and rate of accumu-
+lation of Ti metal at the surface. Given the significant Ti oxidation observed for sample 5Ti, owing to
+the low concentration of accumulated Ti, it would be expected that during the early stages of annealing
+for the higher concentration samples, when an equally low concentration of Ti is expected to accumu-
+late, oxidation should also occur. To confirm this and explore the oxidation of accumulated Ti further,
+Fig. 6 displays the Ti 1s core level spectra collected across the measurement window for sample 10Ti
+9
+
+(a) Ti 1s, 5Ti @ 673 K
+(b) Ti 1s, 10Ti @ 673 K
+(c) Ti 1s, 15Ti @ 673 K
+t=0h
+t = 0.5 h
+t=1h
+t = 1.5 h
+Rel. Intensity I arb. units
+t=2h
+t = 2.5 h
+t=3h
+t = 3.5 h
+'SL(A)!!
+4964.2 ev
+t=4h
+Ti(0).1s..
+t = 4.5 h
+t=5h
+4965.1 eV
+Ti(0) 1s
+x30
+.9ev
+S
+4964.
+(0)!1
+4972
+4970
+4968
+4966
+4964
+4962
+4972
+4970
+4968
+4966
+4964
+4962
+4972
+4970
+4968
+4966
+4964
+4962
+Binding Energy / eV
+Binding Energy / eV
+Binding Energy / eV3.1
+In-situ annealing profiles
+(equivalent figures for sample 5Ti and 15Ti can be viewed in Supplementary Information XI and XII, re-
+spectively). Fig. 6(a) shows that during the initial stages of annealing sample 10Ti (≤603 K), the inten-
+sity first increases within the region of 4966-4970 eV. After 603 K the intensity increases below 4966 eV,
+where the metallic Ti(0) 1s peak is located, and this peak quickly becomes the dominant contribution
+to the total line shape and consequently masks the intensity of the environments seen on the higher BE
+side.
+Figure 6: Initial stages of annealing (523-673 K) described by the Cu 2p3/2 and Ti 1s core level spectra. (a) Raw Ti 1s
+core level spectra collected (i.e. with no intensity normalisation) at each temperature increment, with +5 h referring to
+the data collected at the end of the 5 h 673 K holding period. (b) A magnified view of the raw Ti 1s core level spectra
+collected between 523-623 K and a room temperature reference measurement on the same sample (i.e. before annealing) to
+highlight the Cu Auger contribution. (c) Normalised (0-1) Ti 1s core level spectra to emphasise the change in line shape as
+a function of temperature. (d) Normalised (0-1) Cu 2p3/2 spectra taken at selected temperatures. (a) and (b), and (c) and
+(d) are plotted on the same y-axis scale, respectively (note the ×12.5 magnification of the y-axis scale of (b)).
+From Fig. 5(a), we know that the 4966-4970 eV region corresponds to Ti-O environments, namely the
+Ti(IV) oxidation environment, suggesting that even for sample 10Ti, during the initial stages of anneal-
+ing when the accumulated Ti concentration is low, oxidation of Ti metal occurs. This region will be re-
+ferred to as Ti-O environments in the following discussion. Fig. 6(b) further emphasises the develop-
+ment of Ti-O environments by focusing on the spectra collected between 523-623 K. From this, it is clear
+that Ti-O environments evolve first and then after 603 K, the Ti(0) 1s peak appears due to the contin-
+uing diffusion of Ti metal from the TiW layer. It should be noted that the Cu LMM Auger peak is also
+present in this region, however, given that the main Cu 2p3/2 core level peak decreases with annealing
+duration and temperature, the observed increase in spectral intensity in this region cannot be explained
+10
+
+(a) Ti 1s - 10Ti
+(b) Initial Stage
+x12.5
+523 K
+Room T. Ref.
+(0)!1
+Ti(0) 1s
+543 K
+523 K
+563 K
+563 K
+583 K
+583 K
+units
+603 K
+603 K
+623 K
+623 K
+643 K
+653 K
+Ti-O
+663 K
+673 K
++5 h
+4972
+4970
+4968
+4966
+4964
+4962
+4972
+4970
+4968
+4966
+4964
+4962
+Binding Energy / eV
+Binding Energy / eV
+(c) BE Shift
+(d) Cu 2p3/2 - 10Ti
+ 2p3/2
+S
+932.5 eV
+623 K
+523 K
+Ti(O)
+633 K
+ (o)n
+603 K
+643 K
+673 K
+653 K
++5h
+units
+663 K
+673 K
+ +5 h
+Ti-O
+4972
+4970
+4968
+4966
+4964
+4962
+936
+934
+932
+930
+Binding Energy / eV
+Binding Energy / eV3.1
+In-situ annealing profiles
+by any interference from the Auger peak.
+The transition from predominantly Ti oxide to metal is evident in Fig. 6(c), showing the Ti 1s spectra
+normalised to the maximum peak height. This figure shows that the main intensity peak signal shifts
+towards lower BEs across the temperature range of 623-673 K (highlighted with an arrow), and this is
+accompanied by a decrease in the relative intensity of the Ti-O region. The observed shift is due to the
+emergence of the Ti(0) 1s metal peak and the overall reduction of the Ti-O contribution to the total
+spectral line shape. Lastly, Fig. 6(d) displays the Cu 2p3/2 spectrum recorded at different temperatures
+across the measurement window, and no discernible change is observed in the spectra. Additionally, Sup-
+plementary Information XIII shows that the same observation is true when comparing the Cu 2p3/2 line
+shape across all three samples. This indicates that only the Ti, not the Cu, is undergoing changes to its
+chemical state at the developing interface.
+Therefore, oxidation of the surface accumulated Ti is also observed in sample 10Ti but is more evident
+during the initial stages of annealing where the rate of metal Ti diffusion and quantity of accumulated
+Ti is small. The same holds true for sample 15Ti as seen in Supplementary Information XII. Beyond
+the qualitative analysis of the Ti 1s/2p spectra, an accumulation profile of Ti at the Cu surface across
+the measurement window can be obtained. The Ti accumulation profiles for the samples were extracted
+from the Ti 1s core level spectral areas and are displayed in Fig. 4(b) (the equivalent Ti 2p profile can
+be found in Supplementary Information XIV). Before discussing these profiles, it is important to reiter-
+ate that they represent changes in the quantity of surface-accumulated Ti with respect to time and not
+temperature, but with increasing time, the temperature also rises.
+The temperature at which Ti is first observed at the Cu surface (i.e. the onset), is difficult to identify
+with full confidence as the signal is very small, especially for samples 5Ti and 10Ti. For these two sam-
+ples, the temperature range between 553-563 K (i.e. within the first two hours of Stage 2) is when a Ti
+signal is clearly detectable. The detection of these small Ti signals was only possible through analysing
+the Ti 1s core level as it was much more intense and sharper than the Ti 2p (Supplementary Informa-
+tion XV provides a comparison of the Ti 2p and Ti 1s measured at the same point to highlight this is-
+sue). In contrast, for sample 15Ti, it is obvious from Fig. S15(b) in Supplementary Information XII, that
+Ti is observed from the start of the measurement window (i.e. 523 K) and may have even begun to accu-
+mulate during Stage 1 of the annealing process.
+The Ti profile displayed in Fig. 4(b) shows that with increasing the concentration of Ti within the TiW
+film, a greater out-diffusion of Ti is observed and thus, a greater accumulation of Ti on the Cu surface
+occurs. From the profile, it is apparent that the rate of diffusion and the quantity of accumulated Ti dif-
+fers significantly across the three samples. Focusing on the last data point in the Ti profile at the end
+of the 673 K holding period, the Ti 1s/Cu 2p3/2 area ratios of samples 5Ti and 10Ti are 3.7±0.5 and
+18.2±0.5 %, respectively of that of sample 15Ti. This indicates that a linear relationship between the Ti
+concentration in the film and the quantity of accumulated Ti on the Cu surface does not exist (i.e. they
+do not scale proportionally).
+Sinojiya et al. studied similar TixW1−x films across a composition range and observed that above a cer-
+tain Ti concentration threshold, segregation of Ti toward the grain boundaries was favoured, and this
+enrichment increased with increasing Ti concentration. [67] Additionally, they observed that the change
+in Ti concentration not only enhances the segregation of Ti but is also accompanied by a change in stress,
+microstructure, and grain boundary density within the TiW films. A columnar grain boundary structure
+was also observed at higher concentrations with a relatively higher grain boundary density. Therefore,
+in our case, for sample 15Ti it is possible that a greater quantity of Ti was already segregated from the
+TiW grains within the as-deposited films or that annealing promoted a greater segregation compared to
+samples 5Ti and 10Ti, and consequently that this led to the differences observed in the Ti accumulation
+profile between the three samples. Furthermore, based on the work of Sinojiya et al., the expected differ-
+ences in the microstructure across samples 5, 10 and 15Ti will also contribute to the changes observed in
+the Ti diffusion profile as properties such as grain boundary density will affect the rate of diffusion.
+The Ti accumulation profile displayed in Fig. 4(b), collected across the measurement window of all three
+samples, exhibit two different diffusion regimes. The first regime occurs before the 673 K target is reached
+11
+
+3.1
+In-situ annealing profiles
+Figure 7: W 4d core level spectra collected during the 673 K holding period (Stage 3) for samples (a) 5Ti, (b) 10Ti, and
+(c) 15Ti. Spectra for each core level are plotted over the same y-axis scale to show the differences in intensity across the
+three samples. Note the ×10 magnification of the spectra for sample 5Ti in (a). The spectra have not been normalised, but
+a constant linear background has been removed. Additionally, spectra recorded every other spectral cycle are displayed to
+aid with the interpretation of the data. For sample 5Ti (a), the inset shows a ×10 magnification of the spectra to aid with
+viewing. The legend is the same as that used in Fig. 3(b) and Fig. 5(b). Here, t = 0 h refers to the start of the 5 h holding
+period.
+(i.e. during Stage 2), wherein a rapid exponential increase in intensity occurs when ramping the temper-
+ature. Once the 673 K target is reached (i.e. during Stage 3), the second regime occurs wherein the dif-
+fusion rate begins to decelerate and starts to plateau. A plateau is observed for sample 5Ti, and signs
+of a plateau are present for sample 10Ti by the end of the measurement window. In contrast, the pro-
+file for sample 15Ti does not show signs of plateauing, indicating that Ti continues to accumulate at
+the Cu surface under the temperature and measurement window tested in this experiment. By fitting
+the linear portions of the Ti 1s profile collected during Stages 2 and 3 of annealing, the rate of increase
+in the Ti 1s signal intensity relative to sample 15Ti can be determined. The results of the linear fits of
+Stage 2 for samples 5Ti, 10Ti and 15Ti were found to be 0.7, 4.9 and 16.5, respectively, and for Stage
+3 were found to be 0.2, 1.4 and 9.7, respectively (error estimated to be ±20%). These values highlight
+the dramatic decrease in the Ti accumulation rate during Stage 3 of annealing. Multiple processes could
+be responsible for these changes in the accumulation rate. For instance, only a finite quantity of Ti may
+be available to segregate from the TiW grains, therefore, after annealing for several hours, a plateau is
+reached as no more Ti is available to diffuse. [19] Additionally, the accumulation appears to decelerate
+after the 673 K mark is reached. This deceleration may imply that when subjected to a constant tem-
+perature rather than a temperature ramp, the rate of diffusion levels off as a steady-state system is reached
+due to the thermal input remaining at a constant rate.
+3.1.3
+Tungsten
+Fig. 7 displays the collected W 4d core level spectra for all samples during the 5 h 673 K holding period
+(Stage 3). W is not observed within this period for the 10Ti and 15Ti samples, however, it is detected
+for sample 5Ti, whose TiW film contains the lowest Ti concentration. This confirms that W co-diffuses
+to the surface only for sample 5Ti, and given that it is already detected at t = 0 h of the holding period,
+the diffusion likely occurred prior to Stage 3. The BE position of the W 4d 5/2 peak is at 243.2 eV, in
+good agreement with metallic W. [68] Within the 5 h period, the concentration of surface accumulated
+W does not increase in intensity with increasing annealing duration, suggesting that the accumulation
+has plateaued and the diffusion has subsided. The presence of W at the Cu surface may also influence
+the oxidation behaviour of the accumulated Ti as observed in the previous section.
+Fig. 4(c) displays the relative accumulation profile of W at the Cu surface across the measurement win-
+12
+
+(a) 5Ti @ 673 K
+x10
+Rel. Intensity I arb. units
+(b) 10Ti @ 673 K
+W(0) 4d3/2.
+255.6 eV
+243.2 eV
+(c) 15Ti @ 673 K
+265
+260
+255
+250
+245
+240
+235
+Binding Energy / eV3.2
+Elemental distribution across the in-situ annealed TiW/Cu bilayer
+dow for all three samples. Due to the poor signal-to-noise ratio (SNR) of the W 4d spectra, it is diffi-
+cult to have complete confidence in determining the exact temperature at which W is first observed for
+sample 5Ti. However, the signal becomes apparent at 553-563 K, similar to when Ti was observed at the
+surface of the same sample. The poor SNR is also responsible for the large scatter in the accumulation
+profile, leading to an area change greater than 100 rel.%. Fitting the data points with an asymptotic
+curve shows that a plateau is reached when crossing from Stage 2 to Stage 3 of the annealing process,
+with the 673 K holding period profile flattening, similar to what was observed for the Ti profile. The ob-
+served plateau indicates that a finite quantity of W is able to migrate from the barrier and that a steady
+state is reached within the measurement window explored.
+The diffusion of W is surprising as the vast majority of studies on TiW only report the out-diffusion of
+Ti. For example, even studies on pure W diffusion barriers, [69–72] or on a TiW barrier with a relatively
+low Ti concentration (4.9 at.%) [73] do not report any mobility of W. However, some studies observe W
+diffusion from a W or TiW barrier within thin film stacks at temperatures below 600◦C, although no de-
+tails are given on a possible reason as to why this occurs. [74–76]
+Based on the present results, it is hypothesised that the Ti concentration of the TiW film dictates the
+overall stability of the diffusion barrier. If it is too low (i.e. in the 5Ti sample), a small amount of W be-
+comes mobile and is free to migrate through the Cu overlayer alongside Ti and accumulate at the sur-
+face. This suggests that Ti plays an active role in stabilising the barrier and achieving the desired mi-
+crostructure necessary for good barrier performance. Therefore, tuning the Ti concentration to an opti-
+mum value can significantly improve the barrier performance.
+3.2
+Elemental distribution across the in-situ annealed TiW/Cu bilayer
+From the in-situ annealing results, it is clear that under the conditions tested, the out-diffusion of Ti
+from TiW and through the Cu metallisation is observed for the two samples with the higher Ti concen-
+tration - 10Ti and 15Ti. Whereas, for the lowest Ti concentration sample (5Ti), both Ti and W diffuse
+through the copper metallisation. To quantify the elemental ratio of Cu, Ti, and W across the metalli-
+sation, depth profiling using laboratory-based SXPS was conducted on the in-situ annealed samples (i.e.
+post-mortem). Survey spectra collected at each etch cycle for all three samples can be found in Supple-
+mentary Information XVI, showing the change in composition and transition between the Cu overlayer
+and TiW sublayer.
+Figure 8: Post-mortem laboratory-based SXPS sputter depth profiles collected across samples (a) 5Ti, (b) 10Ti and (c)
+15Ti after in-situ annealing at beamline I09. Etch Cycle 0 refers to the spectra collected on the as-received sample (i.e.
+before any sputtering). Horizontal guidelines are added to show the final Ti at.% for each sample, with the dotted, dashed
+and solid orange lines referring to samples 5, 10 and 15Ti, respectively.
+The depth profiles for the three samples displayed in Fig. 8 highlight the distribution of Ti across the Cu
+13
+
+Etch time / min
+Etch time / min
+Etch time / min
+0
+6
+12
+18
+24
+30
+36
+42
+48
+0
+6
+12
+18
+24
+30
+36
+42
+48
+0
+6
+12
+18
+24
+30
+36
+42
+48
+100 (a)
+[(b)
+100 (c)
+W
+100 .
+Cu
+Cu
+Cu
+W
+06
+06
+06 
+W
+at.%
+80-
+80 -
+80 -
+Interface
+Interface
+Interface
+ percentage / rel.
+70 -
+70 -
+70 -
+60 -
+60 -
+60 -
+Cu Surface
+Cu Surface
+ Surface
+F09
+50 -
+TiW
+50 -
+Tiw
+TiW
+40 -
+40 -
+40 -
+Cu
+. atomic
+30 -
+30 -
+30 -
+Rel.
+20 -
+20 -
+20 -
+Ti
+Ti
+10 
+10 -
+10 -
+F0
+0
+2
+4
+6
+8
+10
+12
+14
+16
+0
+2
+4
+6
+8
+10
+12
+14
+16
+0
+2
+4
+6
+8
+10
+12
+14
+16
+Etch Cycle
+Etch Cycle
+Etch Cycle3.2
+Elemental distribution across the in-situ annealed TiW/Cu bilayer
+layer and confirm what was observed in the in-situ measurements, in that at the Cu surface, the quan-
+tity of accumulated Ti increases in intensity as the Ti concentration of the film increases. The profiles
+further confirm that Ti is found throughout the Cu film after annealing. However, its distribution is not
+uniform, with more Ti observed at the Cu/air and TiW/Cu interfaces. Despite the strong out-diffusion,
+distinct Cu and TiW zones are still observable in the depth profiles, showing that the TiW/Cu bilayer
+has not failed when stressed under these conditions.
+Several studies on Cu/Ti bilayer films have identified that a reaction between the two films can occur as
+low as 325◦C, leading to the formation of intermetallic CuTi and Cu3Ti compounds at the interface. [77–
+79] As shown in Fig. 6(c), the shifts observed for the Ti 1s core line are representative of a changing ox-
+ide to metal ratio rather than the formation of an intermetallic compound, whereas the Cu 2p3/2 spectra
+displayed in Fig. 6(d) show no change in the line shape. If an intermetallic compound were to form, one
+would expect some systematic change to the spectra with increasing annealing duration and temperature
+or for samples with a higher Ti concentration in the TiW film, as these will cause the greatest surface
+enrichment of Ti on the Cu. The possibility of such a reaction is difficult to answer from the core level
+spectra alone. The depth profiles can aid with this discussion. At etch cycle 0 (i.e. as-received surface),
+the Ti:Cu ratio for sample 15Ti is 7.5:92.5. Of course, this may be slightly skewed as the surface is oxi-
+dised, and so there may be additional diffusion of Ti across the metal/oxide interface, but also a carbon
+surface layer is present which will affect the quantification. Nevertheless, this ratio is insufficient to form
+stoichiometric CuTi or Cu3Ti intermetallic phases that were reported in previous studies on the Ti/Cu
+interface. [77] Therefore, based on this literature, the presented spectra and the quantified Ti:Cu ratio, a
+reaction between Cu and Ti at the developing Cu/Ti interface does not occur due to the relatively small
+amount of diffused Ti, which again may explain why no systematic shifts in the core level spectra com-
+mensurate with a Cu-Ti reaction were observed. However, it should be noted that it may not be possible
+to observe intermetallic compounds as (a) the quantity of diffused Ti is very small, and (b) the Cu 2p3/2
+core line is known to have small chemical shifts. [80]
+In terms of W, the depth profiles shown in Fig. 8 confirm that W is only observed at the Cu surface for
+sample 5Ti and is not present at the surface or within the Cu bulk for samples 10Ti and 15Ti. Fig. 8(a)
+shows that for sample 5Ti, the W profile is fairly constant across etch cycles 0-3, suggesting that W is
+homogeneously distributed throughout the Cu metallisation and is not accumulated at the Cu/air inter-
+face like Ti. Quantification of the Cu, Ti and W signals reveals that at the surface of sample 5Ti (etch
+cycle 0), the composition is 97.9 (Cu), 0.9 (Ti), and 1.2 (W) rel. at.%, showing that significant W diffu-
+sion has occurred.
+Fig. 8 shows that the Cu signal tends towards 0 rel. at.% for all samples when the interface is reached.
+However, Cu is still detected at the deepest point of the depth profile, with a composition at etch cycle
+17 calculated to be 0.1 (Cu) 99.9 (Ti + W), 0.7 (Cu) 99.3 (Ti + W), and 1.4 (Cu) 98.6 (Ti + W) rel.
+at.%, for samples 5Ti, 10Ti and 15Ti, respectively. Moreover, with increasing Ti concentration, the el-
+ement profiles broaden, and their gradients toward the “interface” labelled zone reduce. This provides
+evidence that there is a degree of intermixing at the TiW/Cu interface, and for films with higher Ti con-
+centrations, a greater intermixing is observed due to the larger rate of atomic flux of Ti across the inter-
+face during annealing. Therefore, the out-diffusion of Ti from the TiW also promotes the down diffusion
+of Cu into the TiW layer, and consequently, the TiW and Cu layers bleed into each other.
+To summarise, the depth profiles show that clear TiW and Cu zones remain across all samples despite
+the diffusion and intermixing that occurs during annealing. Although the concentration of Cu observed
+at the deepest point of the depth profiles increases when the concentration of Ti in the TiW increases,
+it is difficult to determine how deep the Cu diffuses, as the measurement point of the last depth profile
+etch cycle is still very much at the surface of the 300 nm thick TiW film. However, given the low con-
+centration of Cu detected at this point (≤1.4 at.%), and the fact that distinct Cu and TiW zones still
+remain, one can be confident that under the conditions tested, the TiW barrier has not failed, and the
+majority of Cu is held above the barrier.
+14
+
+4
+Conclusion
+The thermal stability of the TiW barrier in conjunction with a Cu metallisation overlayer was evaluated
+in real-time using a combination of SXPS and HAXPES, and annealing the sample in-situ to a target
+temperature of 673 K. The primary mode of degradation was the segregation of Ti from the TiW barrier
+and its diffusion to the copper surface to form a surface overlayer. The concentration of Ti in TiW was
+shown to have a significant influence on the thermal stability of the TiW barrier. Two thresholds are
+observed when moving across the TiW composition window tested here: (I) below a certain concentra-
+tion of Ti, W gains mobility, suggesting that the incorporation of Ti stabilises W, and (II) above a cer-
+tain concentration of Ti the diffusion drastically increases, suggesting that at higher concentrations grain
+boundary segregation of Ti from the TiW grains is favoured, resulting in significantly more out-diffusion
+of Ti. The post-mortem depth profiles validate the effectiveness of TiW diffusion barriers as despite the
+degradation observed during annealing, the Ti depletion is not significant enough to lead to the failure
+of the barrier, as distinct Cu and TiW zones are still present. Overall, it is clear that the composition
+heavily dictates the stability of TiW, but under the conditions tested, all three barrier compositions re-
+main effective at suppressing the permeation of copper. Based on this, the TiW alloy can cement itself
+as an excellent diffusion barrier to incorporate into future device technologies.
+Supporting Information
+The Supplementary Information includes room temperature reference spectra, heat maps of the Ti 1s
+spectra collected across the measurement window, and the Ti 2p spectra collected for all samples dur-
+ing the 673 K holding period. Additionally, core level spectra collected for samples 5Ti and 15Ti during
+the 523-673 K annealing period, survey spectra from the laboratory-based SXPS depth profile, informa-
+tion on the residual level of oxygen within the Cu films from laboratory-based SXPS, and a comparison
+of the Ti 2p and Ti 1s core levels can be found in the Supplementary Information. Information on the
+peak fitting procedures used, and the method to determine and monitor the thermal broadening is also
+available in the Supplementary Information.
+Acknowledgements
+C.K. acknowledges the support from the Department of Chemistry, UCL. A.R. acknowledges the support
+from the Analytical Chemistry Trust Fund for her CAMS-UK Fellowship. This work was carried out
+with the support of Diamond Light Source, instrument I09 (proposal NT29451-1 and NT29451-2). The
+authors would like to thank Dave McCue, I09 beamline technician, for his support of the experiments.
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+Table of Contents
+The binary alloy of TiW is an attractive diffusion barrier for Si- and SiC-based power semiconductor devices that imple-
+ment a copper metallisation scheme. However, at high temperatures, the barrier is found to degrade via the out-diffusion
+of Ti. This work explores the degradation mechanism using an in-situ X-ray photoelectron spectroscopy approach to moni-
+tor the diffusion in real-time.
+20
+
+Ti 2p/1s e
+SXPS
+HAXPES
+UHV
+Cu
+Ti
+TiW
+LIVE
+SiO2
+Si
+Heating to 673 KCapturing the dynamics of Ti diffusion across TixW1−x/Cu
+heterostructures using X-ray photoelectron spectroscopy
+C. Kalha,1, a) P. K. Thakur,2 T.-L. Lee,2 M. Reisinger,3 J. Zechner,3 M. Nelhiebel,3 and A. Regoutz1, b)
+1)Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ,
+United Kingdom.
+2)Diamond Light Source Ltd., Diamond House, Harwell Science and Innovation Campus, Didcot, OX11 0DE,
+United Kingdom.
+3)Kompetenzzentrum Automobil- und Industrie-Elektronik GmbH, Europastraße 8, 9524 Villach,
+Austria.
+(Dated: 9 January 2023)
+a)Electronic mail: curran.kalha.19@ucl.ac.uk
+b)Electronic mail: a.regoutz@ucl.ac.uk
+arXiv:2301.02577v1  [cond-mat.mtrl-sci]  6 Jan 2023
+
+2
+CONTENTS
+I. Peak fit analysis of as-deposited TiW spectra
+3
+II. Room temperature energy resolution
+7
+III. Sample Plate Holder
+8
+IV. Temperature Profiles
+9
+V. Energy resolution as a function of temperature
+10
+VI. Room temperature reference spectra
+12
+VII. In-situ annealing Ti 2p core level spectra
+14
+VIII. Heat map of Ti 1s spectra collected over the measurement window
+15
+IX. 5Ti Ti 1s peak fit analysis
+16
+X. Residual oxygen within the as-deposited Cu film
+17
+XI. Early Stages of Annealing for Sample 5Ti
+18
+XII. Early Stages of Annealing for Sample 15Ti
+19
+XIII. Cu 2p3/2 line shape changes
+20
+XIV. In-situ annealing Ti 2p concentration profile
+21
+XV. Ti 2p/1s comparison
+22
+XVI. Depth Profile Survey Spectra
+23
+XVII. References
+24
+
+3
+I.
+PEAK FIT ANALYSIS OF AS-DEPOSITED TIW SPECTRA
+To determine the Ti:W ratio of the as-deposited samples the Ti 2p and W 4f core level spectra were collected with
+laboratory-based SXPS, after both ex-situ and in-situ preparation of the Si/SiO2/TiW/Cu samples. Samples were first cleaved to
+5×5 mm2 pieces using a diamond-tipped pen, after which they were submerged in a dilute solution of HNO3 (5:1 65 % conc.
+HNO3: Milli-Q water) for 10 min. This was carried out to selectively remove the copper metallisation layer without affecting
+the TiW layer. The samples were then sputter cleaned in-situ to remove contamination during the ex-situ preparation stages and
+any oxide formation. The survey spectra collected after the in-situ preparation are displayed in Fig. 1.
+FIG. 1. SXP survey spectra collected before and after in-situ preparation of samples, including (a) survey spectra collected for sample 10Ti
+after each etch step, and (b) survey spectra collected for all three samples at the end of the in-situ preparation method. Spectra are normalised
+(0-1) to the height of the most intense peak and are vertically offset. VB = valence band.
+Once the sputter cleaning was performed, a depth profile using a focused Ar+ source was then conducted for each sample to
+determine the Ti:W concentration profile across the film. The depth profile consisted of six sputter (or etch) steps, each lasting
+for 30 min while the Ar+ ion gun operated at a 500 eV accelerating voltage and 10 mA emission current. After six etch steps,
+the SiO2 layer was detectable. The Ti 2p and W 4f core level spectra were collected at each etch step. Representative Ti 2p and
+W 4f spectra along with representative peak fits are displayed in Fig 2. Spectra were aligned to the intrinsic Fermi energy (EF)
+of the respective sample. A systematic shift toward higher binding energy (BE) is observed in the W 4f spectra with decreasing
+Ti, a trend that is also observed in the Ti 2p spectra.
+To determine the Ti:W ratio the Ti 2p core level spectra collected across the entire depth profile were first fitted with the
+Smart-type background implemented in the Avantage software package, which is a Shirley-type background with the additional
+
+(a)
+1s
+As recieved
+0
+W 4d3/2
+W 4f
+Etch 1
+Norm. Intensity I arb. units
+W 4d5/2
+Etch 2
+Etch 3
+ 4p3/2
+Cu 2p3/2
+C
+Cu 2p1/2
+4s
+2
+W
+ KLL
+S
+F
+1s
+L
+N.
+0
+5s
+2
+F
+*0 2s
+1000
+800
+600
+400
+200
+0
+Binding Energy / eV
+(b)
+5Ti
+W 4f
+10Ti
+Norm. Intensity I arb. units
+15Ti
+W 4d5/2
+1 4p3/2
+W 4d3/2
+W 4p1/2
+i2p
+W4s
+2
+O KLL
+W5s
+VB
+1000
+800
+600
+400
+200
+0
+Binding Energy / eV4
+FIG. 2. SXP core level spectra collected for all samples after the in-situ removal of the copper capping layer and oxide layer, and representative
+peak fits of the (a) W 4f and (b) Ti 2p core level spectra. Spectra are normalised to the W 4f 7/2 peak height of the respective sample. Peak fits
+of the W 4f and Ti 2p core levels for spectra collected on the 10Ti sample are displayed in (c) and (d), respectively.
+constraint that the background should not be greater than the data points. The smart background was chosen because at lower Ti
+concentrations, the background on the lower binding energy (BE) side of the Ti 2p begins to rise due to the increase in intensity
+of the close neighbouring W 4p3/2 plasmon and this hampers the effective use of the Shirley-type background, as it would cut the
+data points. Due to the complexity of the Ti 2p core level, the total area was fitted rather than to isolate the contributions from the
+two spin states. The average Ti 2p relative atomic sensitivity factor (RASF) was applied to the resultant fitted area to quantify
+the region. For W 4f the Shirley-type background was implemented and three peaks were added for the W 4f 7/2, W 4f 5/2 and
+W 5p3/2 core lines. It is assumed that after sputtering only the metallic tungsten environment is present. The W 4f peaks were
+given asymmetry to account for the core-hole coupling with conduction band states and constrained to have the same full width
+at half maximum (FWHM) and line shape as each other.1 The Avantage software package uses a least square fitting procedure
+to determine a suitable Lorentzian/Gaussian (L/G) mix, tail mix, full width at half maximum (FWHM), and tail exponent of the
+peaks. Additionally, the area ratio of the 4f doublet peaks was set so that the lower spin state peak had an area that was 0.75 that
+of the higher spin state peak (i.e. 3:4 area ratio). The same line shape (FWHM, L/G mix, tail mix, tail exponent and area ratio)
+was applied to all W 4f spectra across the depth profile. Additionally, the W 5p3/2 peak was fitted with a psuedo-Voigt profile
+peak with a fixed L/G mix of 30% Lorentzian and a variable FWHM constraint. The BE range of the backgrounds, the line
+shapes, and FWHM constraints of the peaks were then applied to all spectra to be consistent across the sample set and the depth
+profiles. However, if the line shape was not constrained the same value within error (±0.3 at.%) was achieved. To determine the
+relative Ti:W ratio in at.% the RASF corrected Ti 2p spectral area was compared to the RASF corrected W 4f 7/2 spectral area.
+Fig. 3 displays the quantification results from the depth profiles along with a standard deviation across the film thickness. The
+three samples have an average Ti at.% relative to W of 5.4±0.3 (5Ti), 11.4±0.3 (10Ti) and 14.8±0.6 at.% (15Ti). Furthermore,
+Fig. 4 displays the spectra collected across the depth profile of sample 10Ti, and it can be seen that the W 4f line shape remains
+fairly constant across the first five etch steps, and subtle changes are observed in the W 4f/Ti 2p area ratio, reflecting what is
+observed with the values from the quantification. Furthermore, the survey spectra displayed in Fig. 4(a) nicely show how the
+depth profile penetrates across the TiW and into the substrate, as in the last three etches, Si-O peaks first emerge followed by Si
+
+(a) W 4f
+(b) Ti 2p
+ 2p3/2 
+5Ti
+5Ti
+10Ti
+10Ti
+15Ti
+15Ti
+Norm. Intensity I arb. units
+W
+2p1/2
+一
+W 5p3/2
+38
+36
+34
+32
+30
+464
+462
+460
+458
+456
+454
+452
+Binding Energy / eV
+Binding Energy / eV
+(c) W 4f peak fit
+(d) Ti 2p peak fit 
+Counts
+·Counts
+W 4f
+Total Area
+W 5p3/2
+Background
+Envelope
+Background
+Envelope
+units
+Intensity I arb.
+38
+36
+34
+32
+30
+464
+462
+460
+458
+456
+454
+452
+Binding Energy / eV
+Binding Energy / eV5
+peaks.
+FIG. 3. Ti:W relative quantification as a function of sputtering duration across the three TiW films. The depth of profile of sample 5Ti, 10Ti
+and 15Ti is displayed in (a), (b), and (c), respectively. 0 min etch time refers to the first measured point in the depth profile. This was collected
+after the sample surface was in-situ sputter cleaned to remove the remnants from the ex-situ cleaning process but before the first etching cycle
+of the depth profile. This measurement point is referred to as Etch 0.
+
+100 -
+100.
+100
+::
+06
+94.6 at.% ± 0.3
+ 06 
+- 06
+.O..
+?
+::
+Q
+88.6 at.% ± 0.4
+80 -
+80 -
+80 -
+85.2 at.% ± 0.6
+(a)
+ (b)
+(c)
+%
+0
+W
+W
+W
+FOL
+70 -
+0
+Ti
+Ti
+Ti
+nc.
+09
+ 09 
+- 09
+: Con
+!S/O!S
+Atomic (
+1←
+50 -
+50
+50 -
+*O!S
+S
+40 -
+40 -
+40 -
+Relative
+30 -
+30 -
+30 -
+20 -
+20 -
+20 -
+14.8 at.% ± 0.6
+11.4 at.% ± 0.5
+0
+C
+5.4 at.% ± 0.3
+10 -
+10 }
+10 -
+70
+-0
+0
+20
+40
+60
+80
+100
+120
+140
+0
+20
+40
+60
+80
+100
+120
+140
+0
+20
+40
+60
+80
+100
+120
+140
+Etch Time / min
+Etch Time / min
+Etch Time / min6
+FIG. 4. Spectra collected during the first five etch steps of the depth profile for sample 10Ti, including (a) survey, (b) W 4f, and (c) Ti 2p
+spectra. The survey spectra are normalised to the height of the maximum intensity peak, whereas the W 4f and Ti 2p spectra are normalised to
+the sum of the total W 4f/5p3/2 and Ti 2p areas. The dotted grey line in the survey spectra refers to the Etch 0 spectrum, and the survey spectra
+have been offset vertically. Etch 0 refers to the first measurement at sputtering time 0 min (i.e. after the in-situ cleaning but before the first
+depth profile etching cycle). As no Fermi edge or C 1s was measured during the depth profiles, the BE scale is not calibrated and is plotted as
+recorded.
+
+(a)
+Etch 0
+Norm. Intensity I arb. units 
+S
+4
+4d
+Final Etch
+S
+S
+0
+W
+W 4p3/2
+1 4p1/2
+2p
+4s
+2
+2
+Ar 
+600
+500
+400
+300
+200
+100
+0
+Binding Energy / eV
+(b) W 4f/5p + Ti 3p
+W(0) 4f/2 
+(c) Ti 2p
+Etch 0
+Etch 0
+Ti(0) 2p3/2 
+Etch 1
+Etch 1
+Etch 2
+Etch 2
+Etch 3
+Etch 3
+ Intensity I arb. units
+Etch 4
+Etch 4
+Ti(0) 2p1/2
+Norm. I
+W(0) 5p3/2
+38
+36
+34
+32
+30
+464
+462
+460
+458
+456
+454
+452
+Binding Energy / ev
+Binding Energy / e7
+II.
+ROOM TEMPERATURE ENERGY RESOLUTION
+The room temperature total energy resolution of the SXPS and HAXPES experiments at the synchrotron was determined
+by determining the 16/84% width of the Fermi edge of a polycrystalline gold foil. Fig. 5 displays the Fermi edges of the foil
+measured with SXPS and HAXPES at room temperature and fitted with a Boltzmann curve.
+FIG. 5. Fermi edge (EF) spectra collected with (a) SXPS and (b) HAXPES on a polycrystalline gold foil at room temperature. The energy
+resolution is determined by extracting the 16/84% width (i.e. one standard deviation on either side of the Fermi energy.
+
+(a) hv= 1.4 keV
+Raw Data
+BoltzmannFit
+Norm. Intensity / arb. units
+16/84 width
+=330meV
+0.50
+0.25
+0.00
+-0.25
+-0.50
+Binding Energy / eV
+(b) hv= 5.9 keV
+Raw Data
+Boltzmann Fit
+Norm. Intensity / arb. units
+16/84 width
+=290meV
+0.50
+0.25
+0.00
+-0.25
+-0.50
+BindingEnergy/ev8
+III.
+SAMPLE PLATE HOLDER
+FIG. 6. Annotated image of the sample plate holder used for the in-situ annealing experiment at beamline I09.
+
+Thermo-
+couple
+sample9
+IV.
+TEMPERATURE PROFILES
+FIG. 7. Temperature profiles for all three samples. The start of the measurement window is indicated by the vertically dotted grey line, whereas
+the red dotted and dashed lines indicate the end of the measurement cycle for samples 5Ti/15Ti and 10Ti, respectively. The temperature profile
+for samples 5Ti and 10Ti are near-identical and so overlap.
+
+750.
+5Ti
+10Ti
+700-
+15Ti
+650 .
+600
+Start
+/ K
+Temperature /
+550
+500
+450
+400
+350
+300
+1
+-2
+0
+1
+2
+3
+4
+5
+6
+7
+8
+-1
+9
+10
+t / h10
+V.
+ENERGY RESOLUTION AS A FUNCTION OF TEMPERATURE
+In order to assess the effect of temperature on the thermal broadening of the collected spectra, the intrinsic Fermi edge of the
+sample (i.e. copper) was captured with SXPS and HAXPES at each spectral cycle. By extracting the 16/84% width of the Fermi
+edge (as shown in Fig. 5), the change in total energy resolution could be monitored with respect to temperature. According to
+Mähl et al. the thermal broadening (γf ) of a Fermi edge at temperature T measured with XPS can be described by:
+γf = 4ln(
+√
+2+1)kbT ≈ 7
+2kbT,
+(1)
+where kb is the Boltzmann constant and approximating kbT to
+T
+11600
+eV
+K gives a value of 90 meV and 200 meV for the thermal
+broadening at 300 K and 673 K, respectively.2 Therefore, a change of 110 meV in the total energy resolution of this experiment
+is expected. Fig. 8(a) displays the change in Fermi edge width with respect to annealing temperature and duration during
+preliminary test measurements.
+It can be seen in Fig. 8(a) that across the measured temperature range, on average the change in 16/84% Fermi edge width
+is less than 60 meV. Considering everything remains constant during the measurement (i.e. pass energy, dwell time, analyser,
+geometry, sample) except for temperature, this change is representative of the thermal broadening. This value is slightly lower
+than the theoretical value, but this can be attributed to the assumptions made in the theoretical model and the error associated
+with the 16/84% method. Additionally, Fig. 8(c) and (d) display the Fermi edge spectra at key temperatures measured in this
+experiment for sample 15Ti. The changes observed are minimal, with the hard X-ray-collected Fermi edges appearing more
+sensitive to temperature than the soft X-ray-collected edges.
+Overall, the change in resolution is insignificant for the core level spectra as it falls below the energy resolution of the
+spectrometer. Therefore, when analysing the changes to the core level spectra for all samples, thermal broadening effects
+are negligible. Moreover, Fig. 8(b) displays the Cu 2p3/2 core level spectrum collected at selected temperatures. The room
+temperature spectrum is slightly broader than the higher temperature spectra, but the high-temperature spectra FWHM remain
+reasonably constant, falling in line with the changes observed when tracking the Fermi edge width. The reason for the broader
+room temperature spectrum and slight asymmetry on the lower binding energy side can be attributed to surface contamination
+(i.e. remnant oxide contributions) but when heated, the surface is cleaned, leading to a narrowing of the FWHM.
+
+11
+FIG. 8. Energy resolution measurements as a function of annealing temperature and duration, including (a) the Fermi edge width collected
+with both soft (SX) and hard (HX) X-rays for sample 10Ti as a function of temperature during preliminary measurements, (b) selected Cu 2p3/2
+core level spectra collected with SXPS on sample 15Ti as a function of annealing temperature, collected during this experiment, plotted on
+a relative BE scale and normalised to the maximum intensity to emphasis the change in peak FWHM as a function of annealing temperature
+and duration. (c) and (d) display the selected Fermi edge spectra collected as a function of annealing temperature measured with soft and hard
+X-rays, respectively. (c) and (d) are normalised to the maximum height (accounting for noise) of the Fermi edge and plotted on the same y-axis
+scale. RT Ref. refers to the room temperature reference spectrum.
+
+(b) Cu 2p3/2, 15Ti
+(a)
+2 hr Hold @ 673 K-:
+RT Ref.
+1.5 keV △E Linear Fit
+Increased
+650
+probe fix*
+523 K
+5.9 keV △E Linear Fit
+acquistion time
+0.45
+623 K
+EXP down
+- Avg. Temperature
+600
+673 K, t = 0 h
+FWHM / ev
+End of Day 1
+ units
+RT Ref.
+0.82
+ev
+673 K, t = 5 h
+%
+523 K
+0.73
+0.40
+550
+H
+Norm. Intensity I arb.
+Width
+623 K
+0.78
+Temperature / 1
+0o
+673 K, t = 0 h
+0.76
+500
+673 K, t = 5 h
+0.76
+Fermi Edge I
+0.35
+0
+450
+000
+0.30
+400
+00
+Day 2 Ramp Start 、
+000
+-350
+0.25
+J. Room T (298 K) ref.
+*Temperature readings before this point are 15-20 K lower
+300
+0
+100
+200
+300
+400
+500
+600
+700
+4
+3
+2
+1
+0
+-1
+-2
+-3
+-4
+Duration / min
+Rel. Binding Energy / eV
+(c) Eε, 1.4 keV
+(d) Eε, 5.9 keV
+RT Ref.
+RT Ref.
+523 K
+523 K
+623 K
+623 K
+673 K+5 h
+673 K+5 h
+Norm Intensity / arb. units 
+△RT = 340 meV
+ART = 290 meV
+△673K + 5h = 390 meV
+△673K + 5h = 330 meV
+0.6
+0.4
+0.2
+0.0
+-0.2
+-0.4
+-0.6
+0.6
+0.4
+0.2
+0.0
+-0.2
+-0.4
+-0.6
+Binding Energy / eV
+Binding Energy / eV12
+VI.
+ROOM TEMPERATURE REFERENCE SPECTRA
+FIG. 9. SXPS and HAXPES room-temperature reference spectra collected for as-deposited samples 5Ti, 10Ti and 15Ti after the surface was
+in-situ cleaned via argon sputtering, including (a) survey, (b) Cu 2p3/2, (c) W 4d, (d) Ti 2p and (e) Ti 1s, with the Ti 1s collected with HAXPES
+and the others with SXPS. Spectra are normalised to the maximum height of the Cu 2p3/2 signal. Spectra collected on reference copper
+compounds (Cu, Cu2O) are also included, which were measured using the laboratory-based SXPS instrument.
+To have confidence in the interpretation of the Cu 2p2/3 spectra, reference measurements were conducted using laboratory-based
+SXPS instrument (hν = 1.4867 keV) on a polycrystalline Cu foil (Alfa Aesar, 99.9985% metals basis, 0.25 mm thick) and an
+anhydrous Cu2O powder (Cu2O, Sigma Aldrich, >=99.99% metals basis). The foil reference was sputter cleaned in-situ using
+
+ 2p3/2 
+(a) Survey
+5Ti
+10Ti
+no
+ units
+15Ti
+Cu 2p1/2
+. Intensity I arb.
+Cu LsM2.3M4.5
+Cu L2M4.5 M4.5 
+Norm.
+3
+01s
+3
+3d
+3
+Cu
+900
+800
+700
+600
+500
+400
+300
+200
+100
+0
+Binding Energy / eV
+[(b) Cu 2p3/2, Room T ref.
+[(c) W 4d, Room T ref.
+5Ti
+5Ti
+10Ti
+10Ti
+15Ti
+15Ti
+Cu polycrystalline foil ref
+Norm. Intensity / arb. units
+Anhydrous Cu,O ref.
+Ar 2p
+945
+940
+935
+930
+260
+255
+250
+245
+240
+Binding Energy / eV
+Binding Energy / eV
+(d) Ti 2p, Room T ref.
+(e) Ti 1s, Room T ref.
+5Ti
+5Ti
+10Ti
+10Ti
+15Ti
+15Ti
+Norm. Intensity I arb. units
+Cu L,M,M4.5
+Cu L,M,M4.5
+人
+468 466464462460 458456454452
+4972
+4970
+ 49684966
+4964
+4962
+Binding Energy / eV
+Binding Energy / eV13
+a focused argon ion beam and sputtering for 10 min, with the ion gun operating at 2 keV voltage. The Cu2O powder was
+received in a sealed ampule under an argon atmosphere, and to minimise further oxidation (i.e. the formation of CuO) the
+sample was prepared in a glovebag under argon. The recorded Cu 2p3/2 spectra of these reference materials are overlaid on the
+room temperature reference spectra of samples 5, 10 and 15Ti, displayed in Fig. 9(b). The binding energy scale was calibrated
+to the intrinsic Fermi energy for the TiW/Cu samples and the Cu foil reference, whereas for Cu2O the scale was calibrated to
+adventitious carbon (284.8 eV).
+It can be observed, that there is good agreement between the Cu foil reference and the spectra recorded for the TiW/Cu
+samples. A very weak satellite is observed between 942-948 eV for the TiW/Cu samples, however, this is also present in the
+Cu foil reference, therefore indicating that the native oxide contribution has been minimised as much as possible. The slight
+differences in Cu 2p3/2 FWHM between the foil reference and TiW/Cu samples can be explained by the differences in total
+energy resolution between the synchrotron (hν = 1.4 keV) and laboratory-based measurements, which were determined to be
+330 meV and 600 meV, respectively. The laboratory-based SXPS instrument used for the collection of reference spectra was not
+the same used for the depth profiles described in the manuscript, hence the different energy resolution.
+Cu Auger peaks are identified to overlap with the measured Ti 2p and Ti 1s core levels when measured with hν = 1.4 and
+5.9 keV, respectively. The Auger peak appears at a BE position of ≈4967.0 eV in the Ti 1s region and ≈457.0 eV in the Ti 2p
+region, equating to a kinetic energy (KE) of ≈959.0 eV for both the Auger peaks. The reason why they both have the same
+kinetic energy is due to the strategic decision to tune the photon energies so that the Ti 1s and Ti 2p probing depths match.
+Possible Auger transition energies have been calculated and tabulated by Coghlan et al.,3 and the position of the Auger in the
+Ti 1s spectra correlates with the Auger Cu L1M1M4,5 transition calculated at 962 eV (KE). It is clear that these peaks are not
+due to titanium as they do not possess the attributes of a core level peak nor the expected BE position of titanium metal/oxide
+in either the 2p or 1s spectrum. Aside from the Cu Auger peaks, the Ar 2p core level peak is visible in the W 4d region at
+approximately 241.0 eV corresponding to implanted argon from the sputtering process. However, this peak is again incredibly
+small and does not affect the analysis of the W 4d spectrum that may develop during annealing.
+
+14
+VII.
+IN-SITU ANNEALING TI 2P CORE LEVEL SPECTRA
+FIG. 10. Ti 2p core level spectra collected during the 673 K holding period (Stage 3) for sample (a) 5Ti, (b) 10Ti, and (c) 15Ti. Spectra for
+each core level are plotted over the same y-axis scale to show the differences in intensity across the three samples. The spectra have not been
+normalised but a constant linear background has been removed. Additionally, spectra recorded every other spectral cycle are displayed to aid
+with the interpretation of the data. The 5Ti spectra have been magnified by ×15 to aid with viewing. The legend displayed in (b) also applies
+to (a) and (c). Ti(0) and Ti(IV) refers to metallic Ti and titanium oxide in the 4+ oxidation state, respectively.
+
+Ti(0) 2p3/2
+(a) Ti 2p, 5Ti @ 673 K
+(b) Ti 2p, 10Ti @ 673 K
+(c) Ti 2p, 15Ti @ 673 K
+454.4 eV
+zisdz (o)1
+t=0h
+453.8 eV
+t = 0.5 h
+Ti(IV) 2p1....
+t=1h
+454.8 eV
+t = 1.5 h
+. units
+t=2h
+t = 2.5 h
+Ti(0) 2P12..
+Rel. Intensity I arb. t
+460.5 eV
+t=3h
+t = 3.5 h
+x15
+t=4h
+t = 4.5 h
+Ti(0) 2p3/2.
+454.7 eV
+t=5h
+2p112.
+Ti(IV) 2p3/2.
+459.0 eV
+ (0)!
+468466 
+464
+462
+ 460
+458
+456
+454452468
+466
+464462460458456454452468
+466
+464462460458
+456454
+452
+Binding Energy / eV
+Binding Energy / eV
+Binding Energy / eV15
+VIII.
+HEAT MAP OF TI 1S SPECTRA COLLECTED OVER THE MEASUREMENT WINDOW
+FIG. 11. HAXPES maps of the Ti 1s core level collected across the entire measurement window, for sample (a) 5Ti, (b) 10Ti and (c) 15Ti. The
+spectra are aligned to the intrinsic Fermi energy of the respective sample, and their intensity is not normalised but plotted as-collected (after
+the subtraction of a constant linear background). The top panel displays the median spectrum collected across the measurement window and
+the right panel displays the point-by-point temperature profile as a function of time. Due to the large variation in spectral intensity between
+sample 5Ti and 15Ti, the spectra displayed here are on independent intensity scales and so the intensities should not be directly compared.
+Ti(0) and Ti(IV) refers to metallic Ti and titanium oxide in the 4+ oxidation state, respectively.
+
+(a) 5Ti
+Intensity I arb. units
+(b) 10Ti
+Intensity I arb. units
+suun
+Ti(IV
+[(c) 15Ti
+Intensity / arb. I
+(0)!
+4972
+4970
+4968
+4966
+4964
+4962
+4972　497049684966　49644962
+4972　49704968　4966　49644962
+8.
+8
+8-
+6.
+6.
+6-
+/1
+4 .
+Intensity I arb. units
+ma
+Intensity / arb. units
+max
+max
+2 
+2
+--673 ....
+2 -
+-673 K...
+.673 K....
+min
+mir
+min
+497249704968
+496649644962
+497249704968496649644962
+4972
+497049684966
+ 49644962
+Binding Energy / eV
+Binding Energy / eV
+Binding Energy / eV
+Temperature / K
+Temperature / K
+Temperature / K16
+IX.
+5TI TI 1S PEAK FIT ANALYSIS
+FIG. 12. Peak fit analysis of the Ti 1s core level for sample 5Ti. The oxide peaks are constrained to have the same FWHM (2.2 eV) and
+Lorentzian/Gaussian mix (50), whereas the metal peak line shape was derived from peak fitting the 673 K spectra of sample 30Ti with one
+asymmetric line shape. A Shirley-type background was used, and the Cu L1M1M4,5 contribution was not removed.
+
+Ti 1s peak fit, 5Ti, 673 K
+iV
+Intensity / arb. units
+Ti(II)+Ti(I)
+Ti(O)
+4972
+4970
+4968
+4966
+4964
+4962
+Binding Energy / eV17
+X.
+RESIDUAL OXYGEN WITHIN THE AS-DEPOSITED CU FILM
+FIG. 13. Depth profile results across the three as-deposited TiW/Cu samples to determine the level of O within the bulk Cu film. Samples
+were sputtered using a focused 500 eV Ar+ ion-beam gun energy for 6 min, rastering over a 2×2 mm2 area and measuring at the centre of
+the sputter crater. Three cycles of sputtering were conducted equating to 18 min total sputtering time. (a) and (b) show the Cu 2p3/2 and O 1s
+spectra collected after the first, second and third etch steps for sample 5Ti only, respectively. Etch 0 refers to the as-received measurement (i.e.
+before any sputtering) and is not included here as the samples were stored and handled in air so a thin native oxide and adventitious carbon
+layer were present. The quantification results of the O/(Cu+O) ratio at each of the three etch steps for all three samples are shown in (c). The
+spectra are aligned to the ISO standard BE value of metallic Cu 2p3/2 (932.62 eV)4 and normalised to the Cu 2p3/2 total spectral area. After
+Etch 3, the TiW layer is reached and the Ti and W signals become dominant.
+
+(a) Cu 2p3/2, 5Ti
+(b) O 1s, 5Ti
+(c)
+Etch 1
+Etch 1
+5TI
+1.75-
+nd
+Etch 2
+— 10Ti
+Etch 2
+Etch 3
+Etch 3
+— 15Ti
+1.50-
+I arb. units
+O / at.
+Norm. Intensity I
+1.00-
+at.%
+0.50 -
+0.25 -
+0.00
+940
+938
+936
+934
+932
+930
+928
+536
+534
+532
+530
+528
+526
+1
+2
+3
+Binding Energy / eV
+Binding Energy / eV
+Etch Cycle18
+XI.
+EARLY STAGES OF ANNEALING FOR SAMPLE 5TI
+FIG. 14. Initial stages of annealing (523-673 K) described by the Cu 2p3/2 and Ti 1s core level spectra for sample 5Ti. (a) Ti 1s core level
+spectra collected (with no intensity normalisation) at each temperature increment, with +5 h referring to the data collected at the end of the
+5 h 673 K holding period. (b) A magnified view of the Ti 1s core level spectra collected between 523-623 K as well as a room temperature
+reference measurement on the same sample (prior to annealing) to highlight the Cu Auger contribution. (c) Normalised (0-1) Ti 1s core level
+spectra to emphasise the change in line shape. (d) Normalised (0-1) Cu 2p3/2 spectra taken at selected temperatures. All data have been aligned
+to the intrinsic Fermi energy. (a) and (b), and (c) and (d) are plotted on the same y-axis scale.
+
+(a) Ti 1s - 5Ti
+1s
+(b) Initial Stage
+x2
+523 K
+Room T. Ref.
+543 K
+523 K
+563 K
+543 K
+583 K
+563 K
+. units
+603 K
+583 K
+I-O
+623 K
+623 K
+/arb.
+643 K
+653 K
+Intensity /
+663 K
+) 1s
+673 K
+(0)!1
+Ti(0) 1s
++5 h
+Rel. I
+4972
+4970
+4968
+4966
+4964
+4962
+4972
+4970
+4968
+4966
+4964
+4962
+Binding Energy / eV
+Binding Energy / eV
+4968.7 eV
+(c) BE Shift
+(d) Cu 2p3/2 - 5Ti
+Ti(IV) 1s
+932.5 ev
+623 K
+523 K
+633 K
+603 K
+643 K
+673 K
+653 K
+- +5 h
+. units
+663 K
+673 K
+Norm. Intensity I arb.
++5 h
+4964.2 eV
+Ti(0)
+4972
+4970
+4968
+4966
+4964
+4962
+936
+934
+932
+930
+Binding Energy / ev
+Binding Energy / ev19
+XII.
+EARLY STAGES OF ANNEALING FOR SAMPLE 15TI
+FIG. 15. Initial stages of annealing (523-673 K) described by the Cu 2p3/2 and Ti 1s core level spectra for sample 15Ti. (a) Ti 1s core level
+spectra collected (with no intensity normalisation) at each temperature increment, with +5 h referring to the data collected at the end of the
+5 h 673 K holding period. (b) A magnified view of the Ti 1s core level spectra collected between 523-623 K as well as a room temperature
+reference measurement on the same sample (prior to annealing) to highlight the Cu Auger contribution. (c) Normalised (0-1) Ti 1s core level
+spectra to emphasise the change in line shape. (d) Normalised (0-1) Cu 2p3/2 spectra taken at selected temperatures. All data have been aligned
+to the intrinsic Fermi energy. (a) and (b), and (c) and (d) are plotted on the same y-axis scale.
+
+(a) Ti 1s - 15Ti
+Ti(0) 1s
+(b) Initial Stage
+x64
+523 K
+Room T. Ref.
+543 K
+523 K
+563 K
+543 K
+Ti(0) 1s
+583 K
+563 K
+units
+603 K
+623 K
+arb.
+643 K
+653 K
+Ti-O
+Rel. Intensity I
+663 K
+673 K
+- +5 h
+4968
+4966
+4964
+4962
+4972
+4968
+4966
+4962
+4972
+4970
+4970
+4964
+Binding Energy / eV
+Binding Energy / eV
+(c) BE Shift
+4964.9 eV
+(d) Cu 2p3/2 - 15Ti
+Ti(0) 1s
+932.6 eV
+623 K
+523 K
+633 K
+(o)ng
+603 K
+643 K
+673 K
+653 K
+ +5h
+units
+663 K
+673 K
+arb.
+-- +5 h
+Norm. Intensity I
+4972
+4970
+4968
+4966
+4964
+4962
+936
+934
+932
+930
+Binding Energy / eV
+Binding Energy / ev20
+XIII.
+CU 2P3/2 LINE SHAPE CHANGES
+FIG. 16. Comparison of the Cu 2p3/2 spectral line shape of the three samples. The spectra presented were captured at the end of the 673 K
+holding period (i.e. 673 K + 5 h). The spectra are normalised 0-1 and aligned to the main intensity to make it easier to observe changes in the
+line shape.
+
+Cu 2p3/2
+Cu(0) 2p3/2
+5Ti
+10Ti
+15Ti
+4
+3
+2
+1
+0
+-1
+-2
+-3
+Rel. 
+Binding Energy / eV21
+XIV.
+IN-SITU ANNEALING TI 2P CONCENTRATION PROFILE
+FIG. 17. Relative Ti concentration profile as a function of time, t collected across the measurement window for all three samples, determined
+from peak fitting the Ti 2p core level spectra. The yellow-filled marker for each dataset refers to the time when the 673 K holding period
+commences. Vertical guidelines are also in place to mark this point for each sample. The measured Ti 2p signal intensity for each sample
+is first normalised relative to the area of the Cu 2p3/2 core level measured during the same spectral cycle and then afterwards the resultant
+Ti 2p/Cu 2p3/2 area is normalised relative to the final intensity of sample 15Ti (IF).
+
+100
+Ti 2p
+K
+K
+673
+673
+90
+—5Ti
+ 10Ti
+5Ti&15Ti
+LOI
+%
+80
+15Ti
+70-
+60 
+50 -
+Stage 2
+Stage 3
+40-
+30.
+20 -
+10-
+0
+0
+1
+2
+3
+4
+5
+6
+7
+8
+9
+t /h22
+XV.
+TI 2P/1S COMPARISON
+FIG. 18. A comparison of the (a) Ti 1s, and (b) Ti 2p core level spectra recorded at 573 K (t = 2 h) for sample 10Ti. Spectra are normalised to
+the signal-to-noise ratio. Guidelines are marked for the positions of the expected peaks. It is clear that the Ti 1s is more sensitive to smaller
+concentrations of titanium than the Ti 2p. Additionally, the nature of the secondary background for the Ti 2p region means that quantification
+of this area is incredibly difficult and cannot be done reliably, whereas a standard XPS background can easily be applied to the Ti 1s region.
+
+(a) Ti 1s, 10Ti, 573 K
+(b) Ti 2p, 10Ti, 573 K
+Norm. Intensity I arb. units
+Ti(IV) 2p1/2 
+Ti(IV) 1s
+Ti(IV) 2p3/2
+ 2p1/2
+Ti(0) 2p3/2
+Ti(0) 1s
+Ti(0)
+4972
+4970
+4968
+4966
+4964
+4962
+468 
+466
+464 462 460 458 456 454 452
+Binding Energy / eV
+Binding Energy / eV23
+XVI.
+DEPTH PROFILE SURVEY SPECTRA
+FIG. 19. Survey spectra collected after each etch cycle during the post-mortem depth profile measurements for (a) 5Ti, (b) 10Ti, and (c) 15Ti
+samples. The top spectrum displayed in each sub-figure is taken on the as-received sample (i.e. no etch) and then the spectra collected after
+each cycle are stacked vertically below (going from blue to grey to black). Spectra coloured in blue are Cu-rich, black are W-rich and red is
+termed the “interface” as it marks the point where the Cu and W signals cross over in the depth profiles.
+
+(a)
+Etch 0
+Ti 3p / W 4f
+Cu 2p 1/2 
+Cu 2p3/2
+Cu 3p / W 5s
+Cu Surface
+W 4d5/2
+Interface
+Intensity I arb. units
+Cu 2s
+Cu LMM
+TiW Bulk
+Cu3s
+S
+1s
+-VB
+0
+c
+S
+F
+Z
+Norm.
+Ti LMM
+W 5p1/2
+1000
+800
+600
+400
+200
+0
+Binding Energy / eV
+(b)
+>Cu 2p1/2
+Etch 0
+Ti 3p / W 4f
+Cu 2p3/2
+Cu Surface
+>Cu2s
+ Cu 3p / W 5s
+Cu LMM
+Interface
+. units
+2
+TiW Bulk
+S
+S
+3s
+ Intensity I arb.
+1s
+dz!
+N1s
+ 2p
+C
+-VB
+1
+S
+Norm.
+Ti LMM
+W 5p1/2
+1000
+800
+600
+400
+200
+0
+Binding Energy / eV
+(c)
+Etch 0
+Ti 3p / W 4f
+Cu 2p1/2
+Cu 2p3/2
+Cu Surface
+Cu 3p / W 5s
+ Cu 2s
+Interface
+. units
+Cu LMM
+TiW Bulk
+S
+Cu 3s
+ Intensity I arb.
+S
+S
+S
+C.
+-VB
+F
+Z
+S
+4
+Norm.
+Ti LMM
+W 5p1/2
+1000
+800
+600
+400
+200
+0
+Binding Energy / eV24
+XVII.
+REFERENCES
+1S. Hüfner, G. Wertheim, and J. Wernick, Solid State Communications 17, 417 (1975).
+2S. Mähl, M. Neumann, S. Dieckhoff, V. Schlett, and A. Baalmann, Journal of Electron Spectroscopy and Related Phenomena 85, 197 (1997).
+3W. Coghlan and R. Clausing, Atomic Data and Nuclear Data Tables 5, 317 (1973).
+4S. Siol, J. Mann, J. Newman, T. Miyayama, K. Watanabe, P. Schmutz, C. Cancellieri, and L. P. Jeurgens, Surface and Interface Analysis 52, 802 (2020).
+
diff --git a/u9E0T4oBgHgl3EQfsQGm/content/tmp_files/load_file.txt b/u9E0T4oBgHgl3EQfsQGm/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d091b54fc784ab81904b3afe61c0da5fc7bf77f5
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+page_content='Capturing the dynamics of Ti diffusion across TixW1−x/Cu  heterostructures using X-ray photoelectron spectroscopy  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Kalha*  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Thakur T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Lee M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Reisinger J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Zechner M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Nelhiebel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Regoutz  Curran Kalha, Anna Regoutz  Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United  Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Email Address: curran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='kalha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='19@ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='uk, a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='regoutz@ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='uk  Pardeep K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Thakur, Tien-Lin Lee  Diamond Light Source Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=', Diamond House, Harwell Science and Innovation Campus, Didcot, OX11  0DE, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Michael Reisinger, Johannes Zechner, Michael Nelhiebel  Kompetenzzentrum Automobil- und Industrie-Elektronik GmbH, Europastraße 8, 9524 Villach, Austria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Keywords: HAXPES, SXPS, XPS, power electronic device, diffusion barrier, metallisation, in-situ  Interdiffusion phenomena between adjacent materials are highly prevalent in semiconductor device architectures and can present  a major reliability challenge for the industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' To fully capture and better understand these phenomena, experimental approaches  must go beyond static and post-mortem studies to include in-situ and in-operando setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Here, soft and hard X-ray photoelec-  tron spectroscopy (SXPS and HAXPES) is used to monitor diffusion in real-time across a proxy device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The device consists of a  Si/SiO2/TixW1−x(300 nm)/Cu(25 nm) thin film material stack, with the TixW1−x film acting as a diffusion barrier between Si and  Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The monitoring of diffusion is achieved through the continuous collection of spectra whilst in-situ annealing to 673 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ti within  the TiW is found to be highly mobile during annealing, diffusing out of the barrier and accumulating at the Cu surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Increasing  the Ti concentration within the TixW1−x film increases the quantity of accumulated Ti, and Ti is first detected at the Cu surface at  temperatures as low as 550 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Surprisingly, at low Ti concentrations (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='054), W is also mobile and diffuses alongside Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' These  results provide crucial evidence for the importance of diffusion barrier composition on their efficacy during device application, deliv-  ering insights into the mechanisms underlying their effectiveness and limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  1  Introduction  The binary pseudo-alloy of titanium-tungsten (TixW1−x, x ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3) is a well-established, effective diffusion  barrier and adhesion enhancer within silicon-based semiconductor devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [1–3] It is designed to pre-  vent the interdiffusion between adjacent metallisations and the underlying dielectric and semiconductor  materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' TiW is compatible with various metallisations (Al, Au, Ag, In and Cu) and has remarkable  thermal stability at elevated temperatures (≤850◦C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [4–19] Consequently, TiW diffusion barriers are  now being widely implemented in next-generation SiC-based power semiconductor technologies with cop-  per metallisation schemes, [20–22] and more recently within electrodes for GaAs photoconductive semi-  conductor switches (PCSSs), [23] and gate metal stacks in GaN-based high electron mobility transistor  (HEMT) devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [24]  Diffusion barriers are needed as Cu and Si readily react at relatively low temperatures to form inter-  metallic copper-silicide compounds at the interface, which seriously hamper the performance and reli-  ability of devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [18, 25–29] Studies have shown that TiW films are capable of retarding and limiting  this interdiffusion and subsequent reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [2, 18] However, when subjected to a high thermal budget,  a depletion of Ti within the TiW grains has been observed, leading to the accumulation of Ti at grain  boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [30] The segregated Ti is then able to diffuse out of the barrier and through the metalli-  sation via grain boundary diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [8] This depletion of Ti is thought to lead to a greater defect den-  sity within the TiW layer, consequently allowing for the potential of Cu and Si to bypass the barrier  and react.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fugger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' cite that this out-diffusion process is an “essential factor” in the failure of this  barrier, [16] and others have also documented the segregation of Ti during high-temperature anneal-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [12,12,19,20,30,31]  Given the importance of the TiW barrier to the overall device performance, reliability and its applica-  tion in future SiC technologies and beyond, this Ti diffusion degradation process must be better under-  stood, including how it impacts the stability of the TiW/Cu structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The common thread across the  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='02577v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='mtrl-sci]  6 Jan 2023  vast majority of past experimental studies on TiW and diffusion barriers in general, including the present  authors’ previous work, [19, 32] is that ex-situ samples are used to track the evolution of the diffusion  process and to determine the temperature at which the barrier fails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Such studies also often focus on one  Ti concentration and are therefore unable to address the effect of the titanium concentration of the film  on the degradation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Figure 1: Schematic representation of the samples and experimental approach (not drawn to scale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) Device stack on  a sample holder being annealed in-situ to 673 K and the expected Ti diffusion represented by grey vertical arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (b)  A magnified view of the copper surface showing the Ti accumulation and the two photon energies used for SXPS and  HAXPES measurements to excite the Ti 2p and Ti 1s electrons from the same depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (c) SXPS laboratory-based Ar+  sputtering depth profile used to quantify the elemental distribution across the TiW/Cu bilayer after in-situ annealing (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  post-mortem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Although ex-situ prepared samples give a good representation of the device after stress events, it is dif-  ficult to correlate the results directly with what a device is experiencing during the applied stress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [8,20]  Therefore, it is crucial to develop new characterisation strategies that can probe the degradation mecha-  nism dynamically under realistic conditions while allowing for changes to the chemical states across the  device stack to be monitored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  To the best of our knowledge, only Le Priol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' and Siol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' provide in-situ monitoring measure-  ments on TiW, both employing in-situ X-ray diffraction (XRD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Le Priol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' studied the efficiency of  a TiW barrier deposited from a 70:30 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% W:Ti alloy target against indium diffusion at temperatures  between 573-673 K under vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [17] The authors could correlate the TiW barrier efficiency with its  microstructure and determine the diffusion coefficient of In in TiW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Siol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' were interested in under-  standing the oxidation of TiW alloy precursors, and observed oxygen dissolution and the formation and  decomposition of mixed (W,Ti)-oxide phases when ramping the temperature between 303 to 1073 K in  air.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [33]  An explanation for the lack of in-situ/operando experiments in the field, which is in contrast to the im-  portance of these material interfaces in both novel and commercial device applications, is the challenges  associated with performing such experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' These include extensive periods of time required to collect  sufficient data, the availability of instruments with in-situ capability, and difficulties in sample prepara-  tion and interfacing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The present work combines soft and hard X-ray photoelectron spectroscopies (SXPS and HAXPES) with  in-situ annealing to study the effect of annealing temperature, annealing duration, and Ti:W ratio on  the thermal stability of TiW/Cu bilayers in real-time, considerably expanding on the existing ex-situ  work, including the present authors’ previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [19, 32] Si/SiO2/TixW1−x(300 nm)/Cu(25 nm)  device stacks (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 1(a) for a schematic of the stack) are annealed up to a maximum temperature of  673 K (400◦C) and held there for 5 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' At the same time, soft and hard X-ray photoelectron spectra are  continuously recorded to capture the Ti diffusion process and changes to the chemical state across the  copper surface (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 1(b) for a schematic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The target temperature of 673 K is selected as it is in a  common temperature regime employed during device fabrication to obtain desired grain growth and tex-  2  kev  Ti 2p/1s e  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  25 nm  Cu  (b)  Tiw  300 nm  Ti  Cu  Cu  SiO2  Tiw  Tiw  Si  Heating to 673 KCture of the copper metallisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [31, 34] Additionally, it is a temperature that can occur at short circuit  events during the operation of potential devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [35]  A major benefit of combining the two variants of X-ray photoelectron spectroscopy (XPS) is that SXPS  is more surface-sensitive, whereas HAXPES enables access to the Ti 1s core line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Ti 1s offers an al-  ternative to the commonly measured Ti 2p with soft X-ray sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Ti 1s compared to the Ti 2p  has the added benefits of covering a smaller binding energy (BE) range and consequently necessitating  a shorter collection time, the absence of spin-orbit splitting (SOS), no additional broadening to consider  from the Coster-Kronig effect that influences the Ti 2p1/2 peak, and the absence of underlying satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  For these reasons, the exploitation of the 1s core level over the 2p is becoming increasingly popular for  transition metals, especially for the disentanglement of charge transfer satellite structures in the X-ray  photoelectron spectra of metal oxides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [36–40]  HAXPES is typically employed as it offers a larger probing depth than conventional SXPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [40] How-  ever, here, it is strategically used to obtain comparable probing depths of the Ti 2p and Ti 1s core lines,  collected with SXPS and HAXPES, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Using this combination, the more widely studied Ti 2p  spectra can be used to understand the Ti 1s spectra better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In addition to the synchrotron-based XPS  experiments, quantitative laboratory-based SXPS depth profiles were also conducted on the samples fol-  lowing the in-situ experiment (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' post-mortem) to ascertain the quantitative distribution of Ti across  the Cu metallisation (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 1(c) for a schematic of the depth profiling).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  2  Methodology  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  Samples  Three as-deposited Si/SiO2/TixW1−x/Cu thin film stacks with varying Ti:W composition were prepared  through an established industrial route.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The stack consists of a 50 nm SiO2 layer on an un-patterned Si  (100) substrate, above which a 300 nm thick TiW layer was deposited via magnetron sputtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  TiW films were deposited from composite targets with a nominal atomic concentration of 30:70 Ti:W,  determined by X-ray fluorescence spectroscopy (XRF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' By varying the deposition parameters, three sam-  ples with an average Ti concentration, x across the entire film thickness of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5, and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% relative to W were realised (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='g (Ti/(Ti+W))×100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' These concentrations were determined using  laboratory-based SXPS and depth profiling across the entire film thickness (further details regarding the  quantification of the TiW films can be found in Supplementary Information I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' These samples will be re-  ferred to as 5Ti, 10Ti and 15Ti, respectively, for the remainder of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Finally, a 25 nm Cu  capping layer was deposited via magnetron sputtering on top of the TiW barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Deposition of both  TiW and Cu was conducted in an argon discharge with no active substrate heating or vacuum break be-  tween successive depositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The deposition chamber operated under a base pressure of 10-8-10-7 mbar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Further details regarding the deposition process have been reported in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [31,41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Dynamic synchrotron-based SXPS/HAXPES  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  Beamline optics and end station details  SXPS and HAXPES measurements were conducted at beamline I09 of the Diamond Light Source, UK, [42]  at photon energies of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='415 keV and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='927 keV, respectively (these will be abbreviated as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 keV and  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 keV throughout the remaining manuscript).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 keV was selected using a 400 lines/mm plane grating  monochromator, achieving a final energy resolution of 330 meV at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 keV was se-  lected using a double-crystal Si (111) monochromator (DCM) in combination with a post-monochromator  Si (004) channel-cut crystal, achieving a final energy resolution of 290 meV at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  total energy resolution was determined by extracting the 16/84% width of the Fermi edge of a clean poly-  crystalline gold foil (see Supplementary Information II for further information on determining the resolu-  tion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [43] The end station of beamline I09 is equipped with an EW4000 Scienta Omicron hemispherical  analyser, with a ±28◦ acceptance angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The base pressure of the analysis chamber was 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5×10-10 mbar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Dynamic synchrotron-based SXPS/HAXPES  To maximise the efficiency in the collection of spectra, the measurements were conducted in grazing inci-  dence and at near-normal emission geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Annealing  Samples were individually annealed in-situ to a sample target temperature of 673 K (400◦C) using a tung-  sten filament heater, and held at the temperature for approximately 5 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The sample plate used for the  experiment consisted of a copper disk (3 mm thick, 8 mm diameter) fixed to the centre of a flat tanta-  lum plate, on which the sample was placed and secured using clips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Good thermal contact was made be-  tween the copper disk and the sample using a thin silver foil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This allowed the sample temperature to be  inferred by attaching an N-type thermocouple to the centre of the copper disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The thermocouple was  also connected to a Lakeshore temperature controller, which was programmed to ramp the sample tem-  perature at a constant rate under a closed-loop control (see Supplementary Information III for an image  of the sample plate holder).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Prior to in-situ annealing, all samples were gently sputter cleaned in-situ for 10 minutes using a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 keV  de-focused argon ion (Ar+) source, operating with a 6 mA emission current and 5×10-5 mbar pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  This was necessary to remove the native copper oxide that had formed on the sample surface during sam-  ple transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The process of in-situ annealing encourages the purging of adsorbed gases and organic species within the  sample and on the sample surface (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' degassing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, annealing in a UHV environment will in-  crease the chamber pressure, which is undesired, especially during the collection of photoelectron spec-  tra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' To account for sample degassing, the annealing process was conducted step-wise to ensure a good  analysis chamber pressure was maintained throughout the measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 2 displays a represen-  tative temperature profile acquired for sample 5Ti and the related pressure profile within the analysis  chamber (see Supplementary Information IV for the temperature profiles collected for all three samples).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The temperature profile consists of three stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, as seen in the pressure profile in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 2,  with every increasing step in temperature, a temporary increase in pressure resulted due to the degassing  of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Prior to annealing in the analysis chamber, the samples were first heated in a subsidiary sample prepara-  tion chamber to remove the majority of adsorbed molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This stage of annealing involves a fast ramp  from room temperature to 523 K and will be referred to as Stage 1 of the annealing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Ti dif-  fusion process was assumed to be insignificant in this temperature range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Next, the sample was moved  to the main analysis chamber, where the temperature was ramped step-wise from 523 to the target tem-  perature of 673 K while maintaining on average a pressure of 7×10-10 mbar (referred to as Stage 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  temperature was then held at the 673 K target temperature for 5 h (referred to as Stage 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra  were continuously collected using SXPS and HAXPES from the start of Stage 2 until the end of Stage 3  of the annealing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The period where the spectra were collected will be referred to as the “mea-  surement window”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Across the measurement window, the same group of spectra were collected itera-  tively, which will be referred to as the “spectral cycle”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Each spectral cycle took approximately 15 min-  utes to collect, and details on which spectra were selected will be discussed in the following section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Dur-  ing Stage 2, the temperature was increased once a spectral cycle was completed, which coincidentally  allows sufficient time for the analysis chamber pressure to recover below 8×10-10 mbar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  For completeness, we note that during the initial stages of annealing, sample 10Ti degassed more than  samples 5Ti and 15Ti, and therefore the temperature ramp of Stage 2 for sample 10Ti was paused to al-  low the pressure to recuperate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This meant that sample 10Ti was held at 543 K for four spectral cycles  rather than one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, the total time of annealing of sample 10Ti was extended by approximately  1 h compared to the annealing time of samples 5Ti and 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This is not expected to affect the diffu-  sion process significantly or the resultant accumulation profiles, as the Ti diffusion at this temperature is  minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3  Laboratory-based SXPS  Figure 2: Representative temperature profile acquired from the Lakeshore temperature controller during the measurements  on sample 5Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The temperature profile consists of three stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Stage 1: a quick ramp to 523 K in a subsidiary chamber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Stage 2: a 10 K/[spectral cycle] ramp in the main analysis chamber, which was then decreased to a 5 K/[spectral cycle]  ramp once 653 K was reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The temperature was ramped step-wise in Stage 2 to allow the pressure in the analysis  chamber to recover to <7×10-10 mbar after each temperature step (see inset for the pressure profile).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Stage 3: holding  period at 673 K for 5 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The dotted line at t = 0 h indicates the start of the measurement window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3  Core level selection  The spectral cycle, which was run in an iterative loop during the experiment, included the following core  level spectra: Cu 2p3/2, Ti 2p and W 4d collected with SXPS, and Ti 1s collected with HAXPES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  W 4d core level was selected over the commonly measured W 4f line as the former does not overlap with  the core levels of Cu or Ti in this region, whereas the latter overlaps with the Ti 3p core level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Cu  Fermi edge was also included in the spectral cycle and was collected with both SXPS and HAXPES through-  out the measurement window to (a) provide an intrinsic method of calibrating the BE scale and (b) mon-  itor any change to the total energy resolution as a consequence of raising the sample temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Based  on 16/84% fits of the collected Fermi edges across all measurements, the effect of thermal broadening is  negligible under the experimental conditions used, and further information can be found in Supplemen-  tary Information V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' All spectra were aligned to the intrinsic Cu Fermi energy (EF) and the spectral ar-  eas were obtained using the Thermo Avantage v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9925 software package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The BE values quoted in this  work are considered to have an estimated error of ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The SXPS photon energy was set to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 keV so that the kinetic energy (KE) of excited Ti 2p electrons  at this photon energy matches the KE of Ti 1s electrons excited with the HAXPES photon energy (KETi 1s  ≈ KETi 2p3/2 ≈ 961 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Using the QUASES software package, [44] the inelastic mean free path (IMFP)  of Ti 2p and Ti 1s electrons in Cu metal at the SXPS and HAXPES photon energies were calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The IMFP for the Ti 1s and Ti 2p3/2 is approximately 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50 nm, and so the estimated probing depth  (3λ) is 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, a direct comparison between the two Ti core levels will be possible as they  originate from very similar probing depths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3  Laboratory-based SXPS  SXPS depth profile measurements were conducted on the samples that were annealed at I09 using a laboratory-  based Thermo K-Alpha+ instrument (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' the in-situ annealed samples were removed and kept for a post-  mortem analysis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The instrument operates with a monochromated Al Kα photon source (hν = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4867 keV)  and consists of a 180◦ double-focusing hemispherical analyser, a two-dimensional detector that integrates  intensity across the entire angular distribution range, and operates at a base pressure of 2×10-9 mbar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  A 400 µm spot size was used for all measurements, achieved using an X-ray anode emission current of  6 mA and a cathode voltage of 12 kV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A flood gun with an emission current of 100 µA was used to achieve  5  Stage 3  700 -  600 -  Stage  Stage 1  Temperature / K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  Temperature  620  Pressure  500  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  610  Temperature / K  600  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0  400 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8  590  580  300 -  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  t / h  2  0  2  4  6  8  10  t / hthe desired level of charge compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The total energy resolution of the spectrometer was determined  to be 400 meV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Survey and core level (W 4f, Ti 2p, O 1s and Cu 2p3/2) spectra were collected with pass  energies of 200 and 20 eV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Depth profiles were conducted using a focused Ar+ ion source,  operating at 500 eV energy and 10 mA current, rastering over a 2×2 mm2 area with a 30◦ sputtering an-  gle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A total of 17 sputter or etch cycles, each lasting 180 s, was carried out with survey and core level  spectra collected after each etch cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The data were analysed using the Thermo Avantage v5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9925 soft-  ware package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The error associated with the quantification values is estimated to be ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% owing to  the complexity of the W 4f core level and the low quantities of Cu and Ti/W in the TiW and Cu layers,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3  Results and Discussion  Reference room temperature survey and core level spectra (Ti 1s, Cu 2p, Ti 2p and W 4d) were col-  lected for the three samples after the in-situ sputter cleaning process, and prior to annealing, with the  results displayed in Supplementary Information VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' From the survey spectra, the sample surfaces appear  clean and are dominated by signals from Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Virtually no carbon is detected, and only a trace quantity  of oxygen is present when measured with SXPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Cu 2p3/2 core level spectra are near identical for  the three samples, and the position and line shape are commensurate with metallic copper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [45–47] A  low-intensity satellite is observed between 943-948 eV in the Cu 2p3/2 core level spectra, but comparing  the spectra to reference measurements of a polycrystalline Cu foil and an anhydrous Cu2O powder, the  satellite intensity is in agreement with the Cu foil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This confirms that the Cu surface of these samples  can be considered metallic and the native oxide contribution is minimised after in-situ sputtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Importantly no Ti or W is observed in these room temperature measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This confirms both that  the Cu layer is sufficiently thick so that even with SXPS the underlying TiW cannot be probed, and  that the surfaces are consistent across all samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The reference measurements show that the Cu L1M1M4,5  Auger line overlaps with the Ti 1s core line but its intensity is vanishingly small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [48, 49] Nevertheless,  care was taken to remove this contribution when we quantified the Ti 1s region to accurately determine  the relative change in Ti concentration at the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The following sections present the Cu, Ti and W core level spectra and associated accumulation pro-  files as a function of annealing duration/temperature across the three samples, with a focus on the initial  stages of annealing and the 673 K holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  Copper  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3 displays the Cu 2p3/2 core level spectra collected over the 5 h holding period at 673 K for all three  samples, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Stage 3 (with t = 0 h in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3 referring to the start of the 5 h holding period).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spec-  tra across all samples confirm that Cu still remains in its metallic state during annealing, with a BE po-  sition of approximately 932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, the narrow full width at half maximum (FWHM), found  to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV, and the lack of significant satellite features in the 943-948 eV region give further confirma-  tion of the metallic nature of the Cu surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [45–47] From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3 it can be observed that after annealing  and within the 673 K holding period, sample 5Ti has the highest Cu 2p3/2 signal intensity (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3(a)),  followed by samples 10Ti (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3(b)) and 15Ti (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Moreover, within the 5 h holding period, the  signal intensity is continually decreasing with annealing duration and this effect is most notable in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3(c)  for the sample with the highest Ti concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  To determine the change in concentration of Cu at the sample surface across the measurement window,  peak fit analysis of the Cu 2p3/2 core level was conducted to determine the change in area, with the re-  sultant profile displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4, time, t = 0 h is redefined as the first measurement point  of the measurement window (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' at the start of Stage 2 at a temperature of 523 K (250◦C)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Note, t  = 0 h in the context of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4 is not the same as t = 0 h in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The same is also true for Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 7, which present the equivalent spectra to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3 for the Ti 1s and W 4d core levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  Figure 3: Cu 2p3/2 core level spectra collected during the 673 K holding period (Stage 3) for sample (a) 5Ti, (b) 10Ti,  and (c) 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra for each sample are plotted over the same y-axis scale to show the differences in intensity across  the three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra have not been normalised but a constant linear background has been removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' To avoid  congestion of this figure, spectra collected every other spectral cycle are presented (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' ≈30 minutes) rather than at every  spectral cycle (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' ≈15 minutes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The legend displayed in (b) also applies to (a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Here, t = 0 h refers to the start  of the 5 h holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The Cu 2p3/2 intensity profile in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(a) reflects what is observed in the core level spectra collected  across the 673 K holding period shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3, in that the Cu 2p3/2 signal intensity decreases as a func-  tion of time and annealing temperature across both Stages 2 and 3 of the annealing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The de-  crease in intensity of the Cu 2p3/2 signal with time is a consequence of the diffusion of Ti out of the TiW  layer during annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The accumulation of Ti leads to a displacement of Cu atoms and the formation  of a Ti-rich surface layer, consequently attenuating the Cu signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, when the TiW is more  Ti-rich, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(a) shows that the Cu signal diminishes more extensively suggesting a greater out-diffusion  of Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' As expected based on this interpretation, sample 15Ti shows the largest decay rate in the Cu 2p3/2  signal, followed by sample 10Ti and then 5Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' At the end of the measurement window, the Cu 2p3/2 sig-  nal intensity has depreciated by approximately 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 and 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3 %, for sample 5Ti, 10Ti and 15Ti, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Titanium  The Ti 1s core level spectra collected across the 5 h 673 K holding period (Stage 3) are displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5,  with the BE positions of the main signals annotated (see Supplementary Information VII and VIII for  the equivalent Ti 2p core level spectra and heat maps of the Ti 1s spectra collected across the measure-  ment window, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5 shows that by the time the 673 K holding period starts, a Ti 1s peak is observed across all three  samples and the intensity continually increases during the 5 h holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This confirms that the on-  set of diffusion occurs prior to Stage 3 of the annealing process as assumed during the discussion of the  Cu profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Significant differences in intensity of the Ti 1s spectra as a function of Ti concentration are  observed, with sample 15Ti showing a considerably more intense peak than sample 10Ti and 5Ti (note  the ×30 magnification of the 5Ti spectra).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Notably, the spectral line shape also appears different across  the samples indicating a change in the chemical state of the accumulated Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  All spectra exhibit a lower BE feature at BEs of 4964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2-4965.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1 eV, corresponding to metallic Ti in vary-  ing environments (labelled as Ti(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' As the Ti 1s core level is not as widely studied as Ti 2p due to the  need for hard X-ray sources, only a handful of publications exist, with reported BEs varying consider-  ably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [36,50–57] The BE positions of the Ti(0) 1s peak observed in the present work fall within the liter-  ature range of metallic Ti, and the asymmetric line shape of the peak, which can be clearly observed in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5(b) and (c), is commensurate with this assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' An asymmetric line shape is a hallmark of the  core level spectra of many transition metals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [58]  7  (a) Cu 2p3/2, 5Ti @ 673 K  (b) Cu 2p3/2, 10Ti @ 673 K  (c) Cu 2p3/2, 15Ti @ 673 K  932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  t=Oh  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  5  t=1h  t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  ziedzr  ev  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  t=2h  932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  t = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  Cu  t=3h  t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  t=4h  t = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  t=5h  945  940  935  930  945  940  935  930  945  940  935  930  Binding Energy / eV  Binding Energy / eV  Binding Energy / eV3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  Figure 4: Relative area intensities measured as a function of time, t collected across the measurement window for all three  samples, including (a) Cu, (b) Ti, and (c) W profiles, determined from peak fitting the Cu 2p3/2, Ti 1s and W 4d core  level spectra, respectively, at each spectral cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Here, t = 0 h refers to the start of the measurement window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The yellow-  filled marker for each dataset refers to the time when the 673 K holding period commences (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' data points before and  after the marker refer to Stage 2 and Stage 3 of the annealing process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Vertical guidelines are also in place to mark this  point for each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For Cu, the measured total Cu 2p3/2 areas are normalised relative to the initial raw area (I0) of  their respective sample (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' I/I0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For Ti, the measured total raw Ti 1s signal area for each sample is first normalised rel-  ative to the raw area of the Cu 2p3/2 core level measured during the same spectral cycle and then afterwards the resultant  Ti 1s/Cu 2p3/2 area is normalised relative to the final raw intensity of sample 15Ti (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' I/IF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The W accumulation pro-  file was determined by normalising the measured total raw W 4d spectral areas following the method used for the Ti 1s  normalisation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' I/IF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The 10Ti and 15Ti samples show a small BE difference of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 eV, which could be attributed to the dif-  ferences in the Ti:Cu and/or Ti:O ratio at the evolving surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In contrast, the BE position in the 5Ti  spectra is considerably lower, with a -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 eV shift relative to the BE position observed in the spectra of  sample 10Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This shift can be attributed to the distinctly different surface configuration of this sam-  ple due to the dominance of Ti-O environments and the co-diffusion of tungsten, both of which will be  discussed later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Moreover, the quantity of Ti diffused to the surface is incredibly small for sample 5Ti,  and therefore, the shift could be due to strong surface effects, with far fewer nearest neighbours being Ti  leading to a negative shift in BE position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [59,60]  During the 673 K holding period, the nature of the accumulated Ti for samples 10Ti and 15Ti is pre-  dominately metallic, given that a single asymmetric peak is visible (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5(b) and (c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The accumu-  lated Ti for sample 5Ti, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5(a) is strikingly different as the intensity of the lower BE metal-  lic peak is overshadowed by a large, fairly symmetric peak at approximately +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 eV from the Ti(0) 1s  peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This peak, labelled as Ti(IV) 1s, is attributed to Ti-O environments in the Ti 4+ oxidation state  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' TiO2 like).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Renault et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' report the Ti 1s BE position of the TiO2 environment on a TiN film at  4968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV, [55] which agrees well with the value reported here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, unlike samples 10Ti and 15Ti,  the Ti accumulated at the surface of sample 5Ti is not predominately metallic but oxidic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally,  there is a shoulder on the lower BE side of this Ti(IV) 1s peak (marked with an asterisk, *), which is  attributed to lower valence states of Ti (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 2+, 3+) that may also form due to the limited quantity of  oxygen expected to be present (see Supplementary Information IX for a peak fit analysis of the spectra  highlighting the presence of such environments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This shoulder increases in intensity with increasing an-  nealing duration, and at the end of the 5 h period, a distinct Ti(0) 1s peak is difficult to observe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  To aid with the interpretation of the Ti 1s spectra, as well as validate the chemical state assignments  made so far, the Ti 2p spectra are used in parallel (see Supplementary Information VII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Ti 2p spec-  tra for samples 10Ti and 15Ti show a doublet peak with an asymmetric line shape at 454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 and 460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 eV  (SOS = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1 eV), in agreement with metallic Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [61, 62] For sample 5Ti, three peaks are identified at  453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8, 459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0, and 464.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The lowest BE peak corresponds to Ti 2p3/2 of Ti(0), whereas the other two  correspond to the doublet of Ti oxide in the 4+ oxidation state (SOS = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV), labelled as Ti(IV) (with  the Ti(IV) 2p3/2 peak overlapping the Ti(0) 2p1/2 peak).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' These BE positions and the SOS of the Ti(IV)  8  100 -  100  130 -  (b) Ti 1s  06  06  5Ti  120 -  10Ti  110-  80 -  %  80 -  %  15Ti  %  I rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  100  70 -  , Area / rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  70 -  Area / r  90 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Area /  09  60 -  80 -  2P3/2 A  W 4d/Cu 2p3/2 A  70 -  50 -  50 -  2p3/2  Stage 2  Stage 3  Stage 2  Stage 3  60  Stage 2  Stage 3  1s/Cu 2  40 -  40 -  Cu  50  KI  10Ti 673 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  30 -  Ve29  30  40 -  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (c) W 4d  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  30  5Ti  20 -  20  (a) Cu 2p3/2  673 K  20 -  10 -  5Ti  10 -  — 15Ti  10  10Ti  &:  10Ti  Fit  0  15Ti  F0  3  4  6  2  5  7  0  1  2  5  7  8  9  0  2  3  5  6  8  9  0  1  3  4  6  8  9  t / h  t / h  t / h3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  Figure 5: Ti 1s core level spectra collected during the 673 K holding period (Stage 3) for sample (a) 5Ti, (b) 10Ti, and (c)  15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra for each core level are plotted over the same y-axis scale to show the differences in intensity across the three  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra have not been normalised, but a constant linear background has been removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, spectra  recorded every other spectral cycle are displayed to aid with the interpretation of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For sample 5Ti, the spectra are  also shown magnified by ×30 to aid with viewing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The legend displayed in (b) also applies to (a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Here, t = 0 h  refers to the start of the 5 h holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  oxide doublet match well with literature values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [63,64]  A shift of the lower BE Ti(0) 2p3/2 peak between the three samples is observed, with the peak positioned  at 453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8, 454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7 and 454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 eV for sample 5Ti, 10Ti and 15Ti, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The relative shifts are similar  to those observed in the Ti 1s spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Moreover, the Ti 2p spectra recorded for sample 5Ti also display  a shoulder on the lower BE side of the main Ti(IV) 2p3/2, again reflecting what has been observed in the  Ti 1s spectra, suggesting the presence of lower valence oxidation states that may form during the reac-  tion between Ti and oxygen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [65, 66] Overall, this confirms the peak assignments made using the Ti 1s  core level are valid and shows the importance of using multiple core levels to have confidence in the as-  signment of chemical states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The observation of almost completely oxidised Ti on the surface of sample 5Ti is of interest, given that  these measurements were conducted under ultra-high vacuum (UHV) conditions and annealed in-situ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The level of observed oxidation cannot be explained by Ti gettering residual oxygen from the analysis  chamber as the quantity present in the chamber is insufficient to promote oxidation of Ti to the extent  observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Furthermore, as the sample is heated during the measurement, the sticking coefficients for ad-  sorbed gases are greatly reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' An alternative source of oxygen is residual oxygen within the Cu film,  whether that be intrinsic to the film (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' incorporated during deposition) or that the sputtering pro-  cess prior to annealing did not fully remove the native oxide layer that formed during the exposure of  the samples to the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' From the room temperature reference survey spectra found in Supple-  mentary Information VI, a small intensity O 1s signal is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Laboratory-based SXPS depth profil-  ing on the as-deposited samples was conducted to determine the oxygen level within the starting (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  pre-annealed) films and to validate this assumption further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Three sputter cycles (or etch steps) were  completed before the underlying TiW signal became strong (see Supplementary Information X for the  collected spectra).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The profiles showed that within the Cu bulk, less than 2 rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% of O is present,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=', <2 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% O, >98 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Within the errors of the performed quantification, this amount would be  enough to facilitate the observed Ti oxidation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Overall it is apparent that the oxidation of Ti is dependent on both the quantity and rate of accumu-  lation of Ti metal at the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Given the significant Ti oxidation observed for sample 5Ti, owing to  the low concentration of accumulated Ti, it would be expected that during the early stages of annealing  for the higher concentration samples, when an equally low concentration of Ti is expected to accumu-  late, oxidation should also occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' To confirm this and explore the oxidation of accumulated Ti further,  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6 displays the Ti 1s core level spectra collected across the measurement window for sample 10Ti  9  (a) Ti 1s, 5Ti @ 673 K  (b) Ti 1s, 10Ti @ 673 K  (c) Ti 1s, 15Ti @ 673 K  t=0h  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  t=1h  t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  t=2h  t = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  t=3h  t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content="5 h  'SL(A)!" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  4964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 ev  t=4h  Ti(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  t = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  t=5h  4965.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1 eV  Ti(0) 1s  x30  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9ev  S  4964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (0)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  4972  4970  4968  4966  4964  4962  4972  4970  4968  4966  4964  4962  4972  4970  4968  4966  4964  4962  Binding Energy / eV  Binding Energy / eV  Binding Energy / eV3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  (equivalent figures for sample 5Ti and 15Ti can be viewed in Supplementary Information XI and XII, re-  spectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6(a) shows that during the initial stages of annealing sample 10Ti (≤603 K), the inten-  sity first increases within the region of 4966-4970 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' After 603 K the intensity increases below 4966 eV,  where the metallic Ti(0) 1s peak is located, and this peak quickly becomes the dominant contribution  to the total line shape and consequently masks the intensity of the environments seen on the higher BE  side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Figure 6: Initial stages of annealing (523-673 K) described by the Cu 2p3/2 and Ti 1s core level spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) Raw Ti 1s  core level spectra collected (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' with no intensity normalisation) at each temperature increment, with +5 h referring to  the data collected at the end of the 5 h 673 K holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (b) A magnified view of the raw Ti 1s core level spectra  collected between 523-623 K and a room temperature reference measurement on the same sample (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' before annealing) to  highlight the Cu Auger contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (c) Normalised (0-1) Ti 1s core level spectra to emphasise the change in line shape as  a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (d) Normalised (0-1) Cu 2p3/2 spectra taken at selected temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) and (b), and (c) and  (d) are plotted on the same y-axis scale, respectively (note the ×12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 magnification of the y-axis scale of (b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5(a), we know that the 4966-4970 eV region corresponds to Ti-O environments, namely the  Ti(IV) oxidation environment, suggesting that even for sample 10Ti, during the initial stages of anneal-  ing when the accumulated Ti concentration is low, oxidation of Ti metal occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This region will be re-  ferred to as Ti-O environments in the following discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6(b) further emphasises the develop-  ment of Ti-O environments by focusing on the spectra collected between 523-623 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' From this, it is clear  that Ti-O environments evolve first and then after 603 K, the Ti(0) 1s peak appears due to the contin-  uing diffusion of Ti metal from the TiW layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' It should be noted that the Cu LMM Auger peak is also  present in this region, however, given that the main Cu 2p3/2 core level peak decreases with annealing  duration and temperature, the observed increase in spectral intensity in this region cannot be explained  10  (a) Ti 1s - 10Ti  (b) Initial Stage  x12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  523 K  Room T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (0)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  Ti(0) 1s  543 K  523 K  563 K  563 K  583 K  583 K  units  603 K  603 K  623 K  623 K  643 K  653 K  Ti-O  663 K  673 K  +5 h  4972  4970  4968  4966  4964  4962  4972  4970  4968  4966  4964  4962  Binding Energy / eV  Binding Energy / eV  (c) BE Shift  (d) Cu 2p3/2 - 10Ti  2p3/2  S  932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 eV  623 K  523 K  Ti(O)  633 K  (o)n  603 K  643 K  673 K  653 K  +5h  units  663 K  673 K  +5 h  Ti-O  4972  4970  4968  4966  4964  4962  936  934  932  930  Binding Energy / eV  Binding Energy / eV3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  by any interference from the Auger peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The transition from predominantly Ti oxide to metal is evident in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6(c), showing the Ti 1s spectra  normalised to the maximum peak height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This figure shows that the main intensity peak signal shifts  towards lower BEs across the temperature range of 623-673 K (highlighted with an arrow), and this is  accompanied by a decrease in the relative intensity of the Ti-O region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The observed shift is due to the  emergence of the Ti(0) 1s metal peak and the overall reduction of the Ti-O contribution to the total  spectral line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Lastly, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6(d) displays the Cu 2p3/2 spectrum recorded at different temperatures  across the measurement window, and no discernible change is observed in the spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, Sup-  plementary Information XIII shows that the same observation is true when comparing the Cu 2p3/2 line  shape across all three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This indicates that only the Ti, not the Cu, is undergoing changes to its  chemical state at the developing interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Therefore, oxidation of the surface accumulated Ti is also observed in sample 10Ti but is more evident  during the initial stages of annealing where the rate of metal Ti diffusion and quantity of accumulated  Ti is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The same holds true for sample 15Ti as seen in Supplementary Information XII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Beyond  the qualitative analysis of the Ti 1s/2p spectra, an accumulation profile of Ti at the Cu surface across  the measurement window can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Ti accumulation profiles for the samples were extracted  from the Ti 1s core level spectral areas and are displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(b) (the equivalent Ti 2p profile can  be found in Supplementary Information XIV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Before discussing these profiles, it is important to reiter-  ate that they represent changes in the quantity of surface-accumulated Ti with respect to time and not  temperature, but with increasing time, the temperature also rises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The temperature at which Ti is first observed at the Cu surface (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' the onset), is difficult to identify  with full confidence as the signal is very small, especially for samples 5Ti and 10Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For these two sam-  ples, the temperature range between 553-563 K (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' within the first two hours of Stage 2) is when a Ti  signal is clearly detectable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The detection of these small Ti signals was only possible through analysing  the Ti 1s core level as it was much more intense and sharper than the Ti 2p (Supplementary Informa-  tion XV provides a comparison of the Ti 2p and Ti 1s measured at the same point to highlight this is-  sue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In contrast, for sample 15Ti, it is obvious from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' S15(b) in Supplementary Information XII, that  Ti is observed from the start of the measurement window (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 523 K) and may have even begun to accu-  mulate during Stage 1 of the annealing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The Ti profile displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(b) shows that with increasing the concentration of Ti within the TiW  film, a greater out-diffusion of Ti is observed and thus, a greater accumulation of Ti on the Cu surface  occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' From the profile, it is apparent that the rate of diffusion and the quantity of accumulated Ti dif-  fers significantly across the three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Focusing on the last data point in the Ti profile at the end  of the 673 K holding period, the Ti 1s/Cu 2p3/2 area ratios of samples 5Ti and 10Ti are 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 and  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 %, respectively of that of sample 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This indicates that a linear relationship between the Ti  concentration in the film and the quantity of accumulated Ti on the Cu surface does not exist (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' they  do not scale proportionally).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Sinojiya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' studied similar TixW1−x films across a composition range and observed that above a cer-  tain Ti concentration threshold, segregation of Ti toward the grain boundaries was favoured, and this  enrichment increased with increasing Ti concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [67] Additionally, they observed that the change  in Ti concentration not only enhances the segregation of Ti but is also accompanied by a change in stress,  microstructure, and grain boundary density within the TiW films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A columnar grain boundary structure  was also observed at higher concentrations with a relatively higher grain boundary density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore,  in our case, for sample 15Ti it is possible that a greater quantity of Ti was already segregated from the  TiW grains within the as-deposited films or that annealing promoted a greater segregation compared to  samples 5Ti and 10Ti, and consequently that this led to the differences observed in the Ti accumulation  profile between the three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Furthermore, based on the work of Sinojiya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=', the expected differ-  ences in the microstructure across samples 5, 10 and 15Ti will also contribute to the changes observed in  the Ti diffusion profile as properties such as grain boundary density will affect the rate of diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The Ti accumulation profile displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(b), collected across the measurement window of all three  samples, exhibit two different diffusion regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The first regime occurs before the 673 K target is reached  11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  In-situ annealing profiles  Figure 7: W 4d core level spectra collected during the 673 K holding period (Stage 3) for samples (a) 5Ti, (b) 10Ti, and  (c) 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra for each core level are plotted over the same y-axis scale to show the differences in intensity across the  three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Note the ×10 magnification of the spectra for sample 5Ti in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra have not been normalised, but  a constant linear background has been removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, spectra recorded every other spectral cycle are displayed to  aid with the interpretation of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For sample 5Ti (a), the inset shows a ×10 magnification of the spectra to aid with  viewing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The legend is the same as that used in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3(b) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Here, t = 0 h refers to the start of the 5 h holding  period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' during Stage 2), wherein a rapid exponential increase in intensity occurs when ramping the temper-  ature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Once the 673 K target is reached (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' during Stage 3), the second regime occurs wherein the dif-  fusion rate begins to decelerate and starts to plateau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A plateau is observed for sample 5Ti, and signs  of a plateau are present for sample 10Ti by the end of the measurement window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In contrast, the pro-  file for sample 15Ti does not show signs of plateauing, indicating that Ti continues to accumulate at  the Cu surface under the temperature and measurement window tested in this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' By fitting  the linear portions of the Ti 1s profile collected during Stages 2 and 3 of annealing, the rate of increase  in the Ti 1s signal intensity relative to sample 15Ti can be determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The results of the linear fits of  Stage 2 for samples 5Ti, 10Ti and 15Ti were found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 and 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5, respectively, and for Stage  3 were found to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 and 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7, respectively (error estimated to be ±20%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' These values highlight  the dramatic decrease in the Ti accumulation rate during Stage 3 of annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Multiple processes could  be responsible for these changes in the accumulation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For instance, only a finite quantity of Ti may  be available to segregate from the TiW grains, therefore, after annealing for several hours, a plateau is  reached as no more Ti is available to diffuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [19] Additionally, the accumulation appears to decelerate  after the 673 K mark is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This deceleration may imply that when subjected to a constant tem-  perature rather than a temperature ramp, the rate of diffusion levels off as a steady-state system is reached  due to the thermal input remaining at a constant rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3  Tungsten  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 7 displays the collected W 4d core level spectra for all samples during the 5 h 673 K holding period  (Stage 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' W is not observed within this period for the 10Ti and 15Ti samples, however, it is detected  for sample 5Ti, whose TiW film contains the lowest Ti concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This confirms that W co-diffuses  to the surface only for sample 5Ti, and given that it is already detected at t = 0 h of the holding period,  the diffusion likely occurred prior to Stage 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The BE position of the W 4d 5/2 peak is at 243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 eV, in  good agreement with metallic W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [68] Within the 5 h period, the concentration of surface accumulated  W does not increase in intensity with increasing annealing duration, suggesting that the accumulation  has plateaued and the diffusion has subsided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The presence of W at the Cu surface may also influence  the oxidation behaviour of the accumulated Ti as observed in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(c) displays the relative accumulation profile of W at the Cu surface across the measurement win-  12  (a) 5Ti @ 673 K  x10  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  (b) 10Ti @ 673 K  W(0) 4d3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 eV  243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 eV  (c) 15Ti @ 673 K  265  260  255  250  245  240  235  Binding Energy / eV3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Elemental distribution across the in-situ annealed TiW/Cu bilayer  dow for all three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Due to the poor signal-to-noise ratio (SNR) of the W 4d spectra, it is diffi-  cult to have complete confidence in determining the exact temperature at which W is first observed for  sample 5Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, the signal becomes apparent at 553-563 K, similar to when Ti was observed at the  surface of the same sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The poor SNR is also responsible for the large scatter in the accumulation  profile, leading to an area change greater than 100 rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fitting the data points with an asymptotic  curve shows that a plateau is reached when crossing from Stage 2 to Stage 3 of the annealing process,  with the 673 K holding period profile flattening, similar to what was observed for the Ti profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The ob-  served plateau indicates that a finite quantity of W is able to migrate from the barrier and that a steady  state is reached within the measurement window explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The diffusion of W is surprising as the vast majority of studies on TiW only report the out-diffusion of  Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For example, even studies on pure W diffusion barriers, [69–72] or on a TiW barrier with a relatively  low Ti concentration (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%) [73] do not report any mobility of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, some studies observe W  diffusion from a W or TiW barrier within thin film stacks at temperatures below 600◦C, although no de-  tails are given on a possible reason as to why this occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [74–76]  Based on the present results, it is hypothesised that the Ti concentration of the TiW film dictates the  overall stability of the diffusion barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' If it is too low (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' in the 5Ti sample), a small amount of W be-  comes mobile and is free to migrate through the Cu overlayer alongside Ti and accumulate at the sur-  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This suggests that Ti plays an active role in stabilising the barrier and achieving the desired mi-  crostructure necessary for good barrier performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, tuning the Ti concentration to an opti-  mum value can significantly improve the barrier performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Elemental distribution across the in-situ annealed TiW/Cu bilayer  From the in-situ annealing results, it is clear that under the conditions tested, the out-diffusion of Ti  from TiW and through the Cu metallisation is observed for the two samples with the higher Ti concen-  tration - 10Ti and 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Whereas, for the lowest Ti concentration sample (5Ti), both Ti and W diffuse  through the copper metallisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' To quantify the elemental ratio of Cu, Ti, and W across the metalli-  sation, depth profiling using laboratory-based SXPS was conducted on the in-situ annealed samples (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  post-mortem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Survey spectra collected at each etch cycle for all three samples can be found in Supple-  mentary Information XVI, showing the change in composition and transition between the Cu overlayer  and TiW sublayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Figure 8: Post-mortem laboratory-based SXPS sputter depth profiles collected across samples (a) 5Ti, (b) 10Ti and (c)  15Ti after in-situ annealing at beamline I09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Etch Cycle 0 refers to the spectra collected on the as-received sample (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  before any sputtering).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Horizontal guidelines are added to show the final Ti at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% for each sample, with the dotted, dashed  and solid orange lines referring to samples 5, 10 and 15Ti, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  The depth profiles for the three samples displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8 highlight the distribution of Ti across the Cu  13  Etch time / min  Etch time / min  Etch time / min  0  6  12  18  24  30  36  42  48  0  6  12  18  24  30  36  42  48  0  6  12  18  24  30  36  42  48  100 (a)  [(b)  100 (c)  W  100 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Cu  Cu  Cu  W  06  06  06  W  at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%  80-  80 -  80 -  Interface  Interface  Interface  percentage / rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  70 -  70 -  70 -  60 -  60 -  60 -  Cu Surface  Cu Surface  Surface  F09  50 -  TiW  50 -  Tiw  TiW  40 -  40 -  40 -  Cu  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' atomic  30 -  30 -  30 -  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  20 -  20 -  20 -  Ti  Ti  10  10 -  10 -  F0  0  2  4  6  8  10  12  14  16  0  2  4  6  8  10  12  14  16  0  2  4  6  8  10  12  14  16  Etch Cycle  Etch Cycle  Etch Cycle3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  Elemental distribution across the in-situ annealed TiW/Cu bilayer  layer and confirm what was observed in the in-situ measurements, in that at the Cu surface, the quan-  tity of accumulated Ti increases in intensity as the Ti concentration of the film increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The profiles  further confirm that Ti is found throughout the Cu film after annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, its distribution is not  uniform, with more Ti observed at the Cu/air and TiW/Cu interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Despite the strong out-diffusion,  distinct Cu and TiW zones are still observable in the depth profiles, showing that the TiW/Cu bilayer  has not failed when stressed under these conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Several studies on Cu/Ti bilayer films have identified that a reaction between the two films can occur as  low as 325◦C, leading to the formation of intermetallic CuTi and Cu3Ti compounds at the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [77–  79] As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6(c), the shifts observed for the Ti 1s core line are representative of a changing ox-  ide to metal ratio rather than the formation of an intermetallic compound, whereas the Cu 2p3/2 spectra  displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6(d) show no change in the line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' If an intermetallic compound were to form, one  would expect some systematic change to the spectra with increasing annealing duration and temperature  or for samples with a higher Ti concentration in the TiW film, as these will cause the greatest surface  enrichment of Ti on the Cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The possibility of such a reaction is difficult to answer from the core level  spectra alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The depth profiles can aid with this discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' At etch cycle 0 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' as-received surface),  the Ti:Cu ratio for sample 15Ti is 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5:92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Of course, this may be slightly skewed as the surface is oxi-  dised, and so there may be additional diffusion of Ti across the metal/oxide interface, but also a carbon  surface layer is present which will affect the quantification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Nevertheless, this ratio is insufficient to form  stoichiometric CuTi or Cu3Ti intermetallic phases that were reported in previous studies on the Ti/Cu  interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [77] Therefore, based on this literature, the presented spectra and the quantified Ti:Cu ratio, a  reaction between Cu and Ti at the developing Cu/Ti interface does not occur due to the relatively small  amount of diffused Ti, which again may explain why no systematic shifts in the core level spectra com-  mensurate with a Cu-Ti reaction were observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, it should be noted that it may not be possible  to observe intermetallic compounds as (a) the quantity of diffused Ti is very small, and (b) the Cu 2p3/2  core line is known to have small chemical shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' [80]  In terms of W, the depth profiles shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8 confirm that W is only observed at the Cu surface for  sample 5Ti and is not present at the surface or within the Cu bulk for samples 10Ti and 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8(a)  shows that for sample 5Ti, the W profile is fairly constant across etch cycles 0-3, suggesting that W is  homogeneously distributed throughout the Cu metallisation and is not accumulated at the Cu/air inter-  face like Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Quantification of the Cu, Ti and W signals reveals that at the surface of sample 5Ti (etch  cycle 0), the composition is 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 (Cu), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 (Ti), and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 (W) rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%, showing that significant W diffu-  sion has occurred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8 shows that the Cu signal tends towards 0 rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% for all samples when the interface is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  However, Cu is still detected at the deepest point of the depth profile, with a composition at etch cycle  17 calculated to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1 (Cu) 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 (Ti + W), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7 (Cu) 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3 (Ti + W), and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 (Cu) 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 (Ti + W) rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%, for samples 5Ti, 10Ti and 15Ti, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Moreover, with increasing Ti concentration, the el-  ement profiles broaden, and their gradients toward the “interface” labelled zone reduce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This provides  evidence that there is a degree of intermixing at the TiW/Cu interface, and for films with higher Ti con-  centrations, a greater intermixing is observed due to the larger rate of atomic flux of Ti across the inter-  face during annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, the out-diffusion of Ti from the TiW also promotes the down diffusion  of Cu into the TiW layer, and consequently, the TiW and Cu layers bleed into each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  To summarise, the depth profiles show that clear TiW and Cu zones remain across all samples despite  the diffusion and intermixing that occurs during annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Although the concentration of Cu observed  at the deepest point of the depth profiles increases when the concentration of Ti in the TiW increases,  it is difficult to determine how deep the Cu diffuses, as the measurement point of the last depth profile  etch cycle is still very much at the surface of the 300 nm thick TiW film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, given the low con-  centration of Cu detected at this point (≤1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%), and the fact that distinct Cu and TiW zones still  remain, one can be confident that under the conditions tested, the TiW barrier has not failed, and the  majority of Cu is held above the barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  14  4  Conclusion  The thermal stability of the TiW barrier in conjunction with a Cu metallisation overlayer was evaluated  in real-time using a combination of SXPS and HAXPES, and annealing the sample in-situ to a target  temperature of 673 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The primary mode of degradation was the segregation of Ti from the TiW barrier  and its diffusion to the copper surface to form a surface overlayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The concentration of Ti in TiW was  shown to have a significant influence on the thermal stability of the TiW barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Two thresholds are  observed when moving across the TiW composition window tested here: (I) below a certain concentra-  tion of Ti, W gains mobility, suggesting that the incorporation of Ti stabilises W, and (II) above a cer-  tain concentration of Ti the diffusion drastically increases, suggesting that at higher concentrations grain  boundary segregation of Ti from the TiW grains is favoured, resulting in significantly more out-diffusion  of Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The post-mortem depth profiles validate the effectiveness of TiW diffusion barriers as despite the  degradation observed during annealing, the Ti depletion is not significant enough to lead to the failure  of the barrier, as distinct Cu and TiW zones are still present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Overall, it is clear that the composition  heavily dictates the stability of TiW, but under the conditions tested, all three barrier compositions re-  main effective at suppressing the permeation of copper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Based on this, the TiW alloy can cement itself  as an excellent diffusion barrier to incorporate into future device technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Supporting Information  The Supplementary Information includes room temperature reference spectra, heat maps of the Ti 1s  spectra collected across the measurement window, and the Ti 2p spectra collected for all samples dur-  ing the 673 K holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, core level spectra collected for samples 5Ti and 15Ti during  the 523-673 K annealing period, survey spectra from the laboratory-based SXPS depth profile, informa-  tion on the residual level of oxygen within the Cu films from laboratory-based SXPS, and a comparison  of the Ti 2p and Ti 1s core levels can be found in the Supplementary Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Information on the  peak fitting procedures used, and the method to determine and monitor the thermal broadening is also  available in the Supplementary Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Acknowledgements  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' acknowledges the support from the Department of Chemistry, UCL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' acknowledges the support  from the Analytical Chemistry Trust Fund for her CAMS-UK Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This work was carried out  with the support of Diamond Light Source, instrument I09 (proposal NT29451-1 and NT29451-2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  authors would like to thank Dave McCue, I09 beamline technician, for his support of the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
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+page_content=' Chawla, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Sankarraman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Payer, Journal of Electron Spectroscopy and Related Phenom-  ena 1992, 61 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  19  REFERENCES  Table of Contents  The binary alloy of TiW is an attractive diffusion barrier for Si- and SiC-based power semiconductor devices that imple-  ment a copper metallisation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, at high temperatures, the barrier is found to degrade via the out-diffusion  of Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This work explores the degradation mechanism using an in-situ X-ray photoelectron spectroscopy approach to moni-  tor the diffusion in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  20  Ti 2p/1s e  SXPS  HAXPES  UHV  Cu  Ti  TiW  LIVE  SiO2  Si  Heating to 673 KCapturing the dynamics of Ti diffusion across TixW1−x/Cu  heterostructures using X-ray photoelectron spectroscopy  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Kalha,1, a) P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Thakur,2 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Lee,2 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Reisinger,3 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Zechner,3 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Nelhiebel,3 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Regoutz1, b)  1)Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ,  United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  2)Diamond Light Source Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=', Diamond House, Harwell Science and Innovation Campus, Didcot, OX11 0DE,  United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3)Kompetenzzentrum Automobil- und Industrie-Elektronik GmbH, Europastraße 8, 9524 Villach,  Austria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (Dated: 9 January 2023)  a)Electronic mail: curran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='kalha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='19@ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='uk  b)Electronic mail: a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='regoutz@ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='uk  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='02577v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='mtrl-sci]  6 Jan 2023  2  CONTENTS  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Peak fit analysis of as-deposited TiW spectra  3  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Room temperature energy resolution  7  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Sample Plate Holder  8  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Temperature Profiles  9  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Energy resolution as a function of temperature  10  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Room temperature reference spectra  12  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In-situ annealing Ti 2p core level spectra  14  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Heat map of Ti 1s spectra collected over the measurement window  15  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5Ti Ti 1s peak fit analysis  16  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Residual oxygen within the as-deposited Cu film  17  XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Early Stages of Annealing for Sample 5Ti  18  XII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Early Stages of Annealing for Sample 15Ti  19  XIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Cu 2p3/2 line shape changes  20  XIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' In-situ annealing Ti 2p concentration profile  21  XV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ti 2p/1s comparison  22  XVI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Depth Profile Survey Spectra  23  XVII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' References  24  3  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  PEAK FIT ANALYSIS OF AS-DEPOSITED TIW SPECTRA  To determine the Ti:W ratio of the as-deposited samples the Ti 2p and W 4f core level spectra were collected with  laboratory-based SXPS, after both ex-situ and in-situ preparation of the Si/SiO2/TiW/Cu samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Samples were first cleaved to  5×5 mm2 pieces using a diamond-tipped pen, after which they were submerged in a dilute solution of HNO3 (5:1 65 % conc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  HNO3: Milli-Q water) for 10 min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This was carried out to selectively remove the copper metallisation layer without affecting  the TiW layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The samples were then sputter cleaned in-situ to remove contamination during the ex-situ preparation stages and  any oxide formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The survey spectra collected after the in-situ preparation are displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' SXP survey spectra collected before and after in-situ preparation of samples, including (a) survey spectra collected for sample 10Ti  after each etch step, and (b) survey spectra collected for all three samples at the end of the in-situ preparation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra are normalised  (0-1) to the height of the most intense peak and are vertically offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' VB = valence band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Once the sputter cleaning was performed, a depth profile using a focused Ar+ source was then conducted for each sample to  determine the Ti:W concentration profile across the film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The depth profile consisted of six sputter (or etch) steps, each lasting  for 30 min while the Ar+ ion gun operated at a 500 eV accelerating voltage and 10 mA emission current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' After six etch steps,  the SiO2 layer was detectable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Ti 2p and W 4f core level spectra were collected at each etch step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Representative Ti 2p and  W 4f spectra along with representative peak fits are displayed in Fig 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra were aligned to the intrinsic Fermi energy (EF)  of the respective sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A systematic shift toward higher binding energy (BE) is observed in the W 4f spectra with decreasing  Ti, a trend that is also observed in the Ti 2p spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  To determine the Ti:W ratio the Ti 2p core level spectra collected across the entire depth profile were first fitted with the  Smart-type background implemented in the Avantage software package, which is a Shirley-type background with the additional  (a)  1s  As recieved  0  W 4d3/2  W 4f  Etch 1  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  W 4d5/2  Etch 2  Etch 3  4p3/2  Cu 2p3/2  C  Cu 2p1/2  4s  2  W  KLL  S  F  1s  L  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  0  5s  2  F  0 2s  1000  800  600  400  200  0  Binding Energy / eV  (b)  5Ti  W 4f  10Ti  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  15Ti  W 4d5/2  1 4p3/2  W 4d3/2  W 4p1/2  i2p  W4s  2  O KLL  W5s  VB  1000  800  600  400  200  0  Binding Energy / eV4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' SXP core level spectra collected for all samples after the in-situ removal of the copper capping layer and oxide layer, and representative  peak fits of the (a) W 4f and (b) Ti 2p core level spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra are normalised to the W 4f 7/2 peak height of the respective sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Peak fits  of the W 4f and Ti 2p core levels for spectra collected on the 10Ti sample are displayed in (c) and (d), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  constraint that the background should not be greater than the data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The smart background was chosen because at lower Ti  concentrations, the background on the lower binding energy (BE) side of the Ti 2p begins to rise due to the increase in intensity  of the close neighbouring W 4p3/2 plasmon and this hampers the effective use of the Shirley-type background, as it would cut the  data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Due to the complexity of the Ti 2p core level, the total area was fitted rather than to isolate the contributions from the  two spin states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The average Ti 2p relative atomic sensitivity factor (RASF) was applied to the resultant fitted area to quantify  the region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' For W 4f the Shirley-type background was implemented and three peaks were added for the W 4f 7/2, W 4f 5/2 and  W 5p3/2 core lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' It is assumed that after sputtering only the metallic tungsten environment is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The W 4f peaks were  given asymmetry to account for the core-hole coupling with conduction band states and constrained to have the same full width  at half maximum (FWHM) and line shape as each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1 The Avantage software package uses a least square fitting procedure  to determine a suitable Lorentzian/Gaussian (L/G) mix, tail mix, full width at half maximum (FWHM), and tail exponent of the  peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, the area ratio of the 4f doublet peaks was set so that the lower spin state peak had an area that was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='75 that  of the higher spin state peak (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3:4 area ratio).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The same line shape (FWHM, L/G mix, tail mix, tail exponent and area ratio)  was applied to all W 4f spectra across the depth profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, the W 5p3/2 peak was fitted with a psuedo-Voigt profile  peak with a fixed L/G mix of 30% Lorentzian and a variable FWHM constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The BE range of the backgrounds, the line  shapes, and FWHM constraints of the peaks were then applied to all spectra to be consistent across the sample set and the depth  profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, if the line shape was not constrained the same value within error (±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%) was achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' To determine the  relative Ti:W ratio in at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% the RASF corrected Ti 2p spectral area was compared to the RASF corrected W 4f 7/2 spectral area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3 displays the quantification results from the depth profiles along with a standard deviation across the film thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  three samples have an average Ti at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% relative to W of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3 (5Ti), 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3 (10Ti) and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% (15Ti).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Furthermore,  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4 displays the spectra collected across the depth profile of sample 10Ti, and it can be seen that the W 4f line shape remains  fairly constant across the first five etch steps, and subtle changes are observed in the W 4f/Ti 2p area ratio, reflecting what is  observed with the values from the quantification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Furthermore, the survey spectra displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4(a) nicely show how the  depth profile penetrates across the TiW and into the substrate, as in the last three etches, Si-O peaks first emerge followed by Si  (a) W 4f  (b) Ti 2p  2p3/2  5Ti  5Ti  10Ti  10Ti  15Ti  15Ti  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  W  2p1/2  一  W 5p3/2  38  36  34  32  30  464  462  460  458  456  454  452  Binding Energy / eV  Binding Energy / eV  (c) W 4f peak fit  (d) Ti 2p peak fit  Counts  Counts  W 4f  Total Area  W 5p3/2  Background  Envelope  Background  Envelope  units  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  38  36  34  32  30  464  462  460  458  456  454  452  Binding Energy / eV  Binding Energy / eV5  peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ti:W relative quantification as a function of sputtering duration across the three TiW films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The depth of profile of sample 5Ti, 10Ti  and 15Ti is displayed in (a), (b), and (c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 0 min etch time refers to the first measured point in the depth profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This was collected  after the sample surface was in-situ sputter cleaned to remove the remnants from the ex-situ cleaning process but before the first etching cycle  of the depth profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This measurement point is referred to as Etch 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  100 -  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  100  ::  06  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3  06  06  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  ::  Q  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  80 -  80 -  80 -  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  (a)  (b)  (c)  %  0  W  W  W  FOL  70 -  0  Ti  Ti  Ti  nc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  09  09  09  : Con  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='S/O!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='S  Atomic (  1←  50 -  50  50 -  O!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='S  S  40 -  40 -  40 -  Relative  30 -  30 -  30 -  20 -  20 -  20 -  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  0  C  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3  10 -  10 }  10 -  70  0  0  20  40  60  80  100  120  140  0  20  40  60  80  100  120  140  0  20  40  60  80  100  120  140  Etch Time / min  Etch Time / min  Etch Time / min6  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra collected during the first five etch steps of the depth profile for sample 10Ti, including (a) survey, (b) W 4f, and (c) Ti 2p  spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The survey spectra are normalised to the height of the maximum intensity peak, whereas the W 4f and Ti 2p spectra are normalised to  the sum of the total W 4f/5p3/2 and Ti 2p areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The dotted grey line in the survey spectra refers to the Etch 0 spectrum, and the survey spectra  have been offset vertically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Etch 0 refers to the first measurement at sputtering time 0 min (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' after the in-situ cleaning but before the first  depth profile etching cycle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' As no Fermi edge or C 1s was measured during the depth profiles, the BE scale is not calibrated and is plotted as  recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a)  Etch 0  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  S  4  4d  Final Etch  S  S  0  W  W 4p3/2  1 4p1/2  2p  4s  2  2  Ar  600  500  400  300  200  100  0  Binding Energy / eV  (b) W 4f/5p + Ti 3p  W(0) 4f/2  (c) Ti 2p  Etch 0  Etch 0  Ti(0) 2p3/2  Etch 1  Etch 1  Etch 2  Etch 2  Etch 3  Etch 3  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Etch 4  Etch 4  Ti(0) 2p1/2  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' I  W(0) 5p3/2  38  36  34  32  30  464  462  460  458  456  454  452  Binding Energy / ev  Binding Energy / e7  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  ROOM TEMPERATURE ENERGY RESOLUTION  The room temperature total energy resolution of the SXPS and HAXPES experiments at the synchrotron was determined  by determining the 16/84% width of the Fermi edge of a polycrystalline gold foil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5 displays the Fermi edges of the foil  measured with SXPS and HAXPES at room temperature and fitted with a Boltzmann curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fermi edge (EF) spectra collected with (a) SXPS and (b) HAXPES on a polycrystalline gold foil at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The energy  resolution is determined by extracting the 16/84% width (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' one standard deviation on either side of the Fermi energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a) hv= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 keV  Raw Data  BoltzmannFit  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  16/84 width  =330meV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50  Binding Energy / eV  (b) hv= 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 keV  Raw Data  Boltzmann Fit  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  16/84 width  =290meV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50  BindingEnergy/ev8  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  SAMPLE PLATE HOLDER  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Annotated image of the sample plate holder used for the in-situ annealing experiment at beamline I09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Thermo-  couple  sample9  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  TEMPERATURE PROFILES  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Temperature profiles for all three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The start of the measurement window is indicated by the vertically dotted grey line, whereas  the red dotted and dashed lines indicate the end of the measurement cycle for samples 5Ti/15Ti and 10Ti, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The temperature profile  for samples 5Ti and 10Ti are near-identical and so overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  750.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  5Ti  10Ti  700-  15Ti  650 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  600  Start  / K  Temperature /  550  500  450  400  350  300  1  2  0  1  2  3  4  5  6  7  8  1  9  10  t / h10  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  ENERGY RESOLUTION AS A FUNCTION OF TEMPERATURE  In order to assess the effect of temperature on the thermal broadening of the collected spectra, the intrinsic Fermi edge of the  sample (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' copper) was captured with SXPS and HAXPES at each spectral cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' By extracting the 16/84% width of the Fermi  edge (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 5), the change in total energy resolution could be monitored with respect to temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' According to  Mähl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' the thermal broadening (γf ) of a Fermi edge at temperature T measured with XPS can be described by:  γf = 4ln(  √  2+1)kbT ≈ 7  2kbT,  (1)  where kb is the Boltzmann constant and approximating kbT to  T  11600  eV  K gives a value of 90 meV and 200 meV for the thermal  broadening at 300 K and 673 K, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 Therefore, a change of 110 meV in the total energy resolution of this experiment  is expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8(a) displays the change in Fermi edge width with respect to annealing temperature and duration during  preliminary test measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  It can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8(a) that across the measured temperature range, on average the change in 16/84% Fermi edge width  is less than 60 meV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Considering everything remains constant during the measurement (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' pass energy, dwell time, analyser,  geometry, sample) except for temperature, this change is representative of the thermal broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' This value is slightly lower  than the theoretical value, but this can be attributed to the assumptions made in the theoretical model and the error associated  with the 16/84% method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8(c) and (d) display the Fermi edge spectra at key temperatures measured in this  experiment for sample 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The changes observed are minimal, with the hard X-ray-collected Fermi edges appearing more  sensitive to temperature than the soft X-ray-collected edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Overall, the change in resolution is insignificant for the core level spectra as it falls below the energy resolution of the  spectrometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Therefore, when analysing the changes to the core level spectra for all samples, thermal broadening effects  are negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Moreover, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8(b) displays the Cu 2p3/2 core level spectrum collected at selected temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The room  temperature spectrum is slightly broader than the higher temperature spectra, but the high-temperature spectra FWHM remain  reasonably constant, falling in line with the changes observed when tracking the Fermi edge width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The reason for the broader  room temperature spectrum and slight asymmetry on the lower binding energy side can be attributed to surface contamination  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' remnant oxide contributions) but when heated, the surface is cleaned, leading to a narrowing of the FWHM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  11  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Energy resolution measurements as a function of annealing temperature and duration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' including (a) the Fermi edge width collected  with both soft (SX) and hard (HX) X-rays for sample 10Ti as a function of temperature during preliminary measurements,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (b) selected Cu 2p3/2  core level spectra collected with SXPS on sample 15Ti as a function of annealing temperature,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' collected during this experiment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' plotted on  a relative BE scale and normalised to the maximum intensity to emphasis the change in peak FWHM as a function of annealing temperature  and duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (c) and (d) display the selected Fermi edge spectra collected as a function of annealing temperature measured with soft and hard  X-rays, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (c) and (d) are normalised to the maximum height (accounting for noise) of the Fermi edge and plotted on the same y-axis  scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' RT Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' refers to the room temperature reference spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (b) Cu 2p3/2, 15Ti  (a)  2 hr Hold @ 673 K-:  RT Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 keV △E Linear Fit  Increased  650  probe fix*  523 K  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 keV △E Linear Fit  acquistion time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='45  623 K  EXP down  Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Temperature  600  673 K, t = 0 h  FWHM / ev  End of Day 1  units  RT Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='82  ev  673 K, t = 5 h  %  523 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='73  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='40  550  H  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Width  623 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='78  Temperature / 1  0o  673 K, t = 0 h  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='76  500  673 K, t = 5 h  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='76  Fermi Edge I  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='35  0  450  000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='30  400  00  Day 2 Ramp Start 、  000  350  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Room T (298 K) ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Temperature readings before this point are 15-20 K lower  300  0  100  200  300  400  500  600  700  4  3  2  1  0  1  2  3  4  Duration / min  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Binding Energy / eV  (c) Eε, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 keV  (d) Eε, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 keV  RT Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  RT Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  523 K  523 K  623 K  623 K  673 K+5 h  673 K+5 h  Norm Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  △RT = 340 meV  ART = 290 meV  △673K + 5h = 390 meV  △673K + 5h = 330 meV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6  Binding Energy / eV  Binding Energy / eV12  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  ROOM TEMPERATURE REFERENCE SPECTRA  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' SXPS and HAXPES room-temperature reference spectra collected for as-deposited samples 5Ti, 10Ti and 15Ti after the surface was  in-situ cleaned via argon sputtering, including (a) survey, (b) Cu 2p3/2, (c) W 4d, (d) Ti 2p and (e) Ti 1s, with the Ti 1s collected with HAXPES  and the others with SXPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra are normalised to the maximum height of the Cu 2p3/2 signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra collected on reference copper  compounds (Cu, Cu2O) are also included, which were measured using the laboratory-based SXPS instrument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  To have confidence in the interpretation of the Cu 2p2/3 spectra, reference measurements were conducted using laboratory-based  SXPS instrument (hν = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4867 keV) on a polycrystalline Cu foil (Alfa Aesar, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9985% metals basis, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25 mm thick) and an  anhydrous Cu2O powder (Cu2O, Sigma Aldrich, >=99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='99% metals basis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The foil reference was sputter cleaned in-situ using  2p3/2  (a) Survey  5Ti  10Ti  no  units  15Ti  Cu 2p1/2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Cu LsM2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='3M4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  Cu L2M4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 M4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  3  01s  3  3d  3  Cu  900  800  700  600  500  400  300  200  100  0  Binding Energy / eV  [(b) Cu 2p3/2, Room T ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  [(c) W 4d, Room T ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  5Ti  5Ti  10Ti  10Ti  15Ti  15Ti  Cu polycrystalline foil ref  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Anhydrous Cu,O ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ar 2p  945  940  935  930  260  255  250  245  240  Binding Energy / eV  Binding Energy / eV  (d) Ti 2p, Room T ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (e) Ti 1s, Room T ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  5Ti  5Ti  10Ti  10Ti  15Ti  15Ti  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Cu L,M,M4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  Cu L,M,M4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5  人  468 466464462460 458456454452  4972  4970  49684966  4964  4962  Binding Energy / eV  Binding Energy / eV13  a focused argon ion beam and sputtering for 10 min, with the ion gun operating at 2 keV voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Cu2O powder was  received in a sealed ampule under an argon atmosphere, and to minimise further oxidation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' the formation of CuO) the  sample was prepared in a glovebag under argon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The recorded Cu 2p3/2 spectra of these reference materials are overlaid on the  room temperature reference spectra of samples 5, 10 and 15Ti, displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 9(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The binding energy scale was calibrated  to the intrinsic Fermi energy for the TiW/Cu samples and the Cu foil reference, whereas for Cu2O the scale was calibrated to  adventitious carbon (284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  It can be observed, that there is good agreement between the Cu foil reference and the spectra recorded for the TiW/Cu  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A very weak satellite is observed between 942-948 eV for the TiW/Cu samples, however, this is also present in the  Cu foil reference, therefore indicating that the native oxide contribution has been minimised as much as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The slight  differences in Cu 2p3/2 FWHM between the foil reference and TiW/Cu samples can be explained by the differences in total  energy resolution between the synchrotron (hν = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 keV) and laboratory-based measurements, which were determined to be  330 meV and 600 meV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The laboratory-based SXPS instrument used for the collection of reference spectra was not  the same used for the depth profiles described in the manuscript, hence the different energy resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Cu Auger peaks are identified to overlap with the measured Ti 2p and Ti 1s core levels when measured with hν = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 and  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 keV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The Auger peak appears at a BE position of ≈4967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0 eV in the Ti 1s region and ≈457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0 eV in the Ti 2p  region, equating to a kinetic energy (KE) of ≈959.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0 eV for both the Auger peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The reason why they both have the same  kinetic energy is due to the strategic decision to tune the photon energies so that the Ti 1s and Ti 2p probing depths match.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Possible Auger transition energies have been calculated and tabulated by Coghlan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=',3 and the position of the Auger in the  Ti 1s spectra correlates with the Auger Cu L1M1M4,5 transition calculated at 962 eV (KE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' It is clear that these peaks are not  due to titanium as they do not possess the attributes of a core level peak nor the expected BE position of titanium metal/oxide  in either the 2p or 1s spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Aside from the Cu Auger peaks, the Ar 2p core level peak is visible in the W 4d region at  approximately 241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0 eV corresponding to implanted argon from the sputtering process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' However, this peak is again incredibly  small and does not affect the analysis of the W 4d spectrum that may develop during annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  14  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  IN-SITU ANNEALING TI 2P CORE LEVEL SPECTRA  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ti 2p core level spectra collected during the 673 K holding period (Stage 3) for sample (a) 5Ti, (b) 10Ti, and (c) 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra for  each core level are plotted over the same y-axis scale to show the differences in intensity across the three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra have not been  normalised but a constant linear background has been removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, spectra recorded every other spectral cycle are displayed to aid  with the interpretation of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The 5Ti spectra have been magnified by ×15 to aid with viewing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The legend displayed in (b) also applies  to (a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ti(0) and Ti(IV) refers to metallic Ti and titanium oxide in the 4+ oxidation state, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti(0) 2p3/2  (a) Ti 2p, 5Ti @ 673 K  (b) Ti 2p, 10Ti @ 673 K  (c) Ti 2p, 15Ti @ 673 K  454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='4 eV  zisdz (o)1  t=0h  453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  Ti(IV) 2p1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  t=1h  454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='8 eV  t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  t=2h  t = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  Ti(0) 2P12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' t  460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 eV  t=3h  t = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  x15  t=4h  t = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 h  Ti(0) 2p3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7 eV  t=5h  2p112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti(IV) 2p3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='0 eV  (0)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  468466  464  462  460  458  456  454452468  466  464462460458456454452468  466  464462460458  456454  452  Binding Energy / eV  Binding Energy / eV  Binding Energy / eV15  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  HEAT MAP OF TI 1S SPECTRA COLLECTED OVER THE MEASUREMENT WINDOW  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' HAXPES maps of the Ti 1s core level collected across the entire measurement window, for sample (a) 5Ti, (b) 10Ti and (c) 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  spectra are aligned to the intrinsic Fermi energy of the respective sample, and their intensity is not normalised but plotted as-collected (after  the subtraction of a constant linear background).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The top panel displays the median spectrum collected across the measurement window and  the right panel displays the point-by-point temperature profile as a function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Due to the large variation in spectral intensity between  sample 5Ti and 15Ti, the spectra displayed here are on independent intensity scales and so the intensities should not be directly compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti(0) and Ti(IV) refers to metallic Ti and titanium oxide in the 4+ oxidation state, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a) 5Ti  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  (b) 10Ti  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  suun  Ti(IV  [(c) 15Ti  Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' I  (0)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  4972  4970  4968  4966  4964  4962  4972 497049684966 49644962  4972 49704968 4966 49644962  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  8  8-  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  6-  /1  4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  ma  Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  max  max  2  2  --673 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  2 -  673 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='673 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='.  min  mir  min  497249704968  496649644962  497249704968496649644962  4972  497049684966  49644962  Binding Energy / eV  Binding Energy / eV  Binding Energy / eV  Temperature / K  Temperature / K  Temperature / K16  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  5TI TI 1S PEAK FIT ANALYSIS  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Peak fit analysis of the Ti 1s core level for sample 5Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The oxide peaks are constrained to have the same FWHM (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 eV) and  Lorentzian/Gaussian mix (50), whereas the metal peak line shape was derived from peak fitting the 673 K spectra of sample 30Ti with one  asymmetric line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A Shirley-type background was used, and the Cu L1M1M4,5 contribution was not removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti 1s peak fit, 5Ti, 673 K  iV  Intensity / arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Ti(II)+Ti(I)  Ti(O)  4972  4970  4968  4966  4964  4962  Binding Energy / eV17  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  RESIDUAL OXYGEN WITHIN THE AS-DEPOSITED CU FILM  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Depth profile results across the three as-deposited TiW/Cu samples to determine the level of O within the bulk Cu film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Samples  were sputtered using a focused 500 eV Ar+ ion-beam gun energy for 6 min, rastering over a 2×2 mm2 area and measuring at the centre of  the sputter crater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Three cycles of sputtering were conducted equating to 18 min total sputtering time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) and (b) show the Cu 2p3/2 and O 1s  spectra collected after the first, second and third etch steps for sample 5Ti only, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Etch 0 refers to the as-received measurement (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  before any sputtering) and is not included here as the samples were stored and handled in air so a thin native oxide and adventitious carbon  layer were present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The quantification results of the O/(Cu+O) ratio at each of the three etch steps for all three samples are shown in (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The  spectra are aligned to the ISO standard BE value of metallic Cu 2p3/2 (932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='62 eV)4 and normalised to the Cu 2p3/2 total spectral area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' After  Etch 3, the TiW layer is reached and the Ti and W signals become dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a) Cu 2p3/2, 5Ti  (b) O 1s, 5Ti  (c)  Etch 1  Etch 1  5TI  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='75-  nd  Etch 2  — 10Ti  Etch 2  Etch 3  Etch 3  — 15Ti  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50-  I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  O / at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='00-  at.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='%  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='50 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='25 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='00  940  938  936  934  932  930  928  536  534  532  530  528  526  1  2  3  Binding Energy / eV  Binding Energy / eV  Etch Cycle18  XI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  EARLY STAGES OF ANNEALING FOR SAMPLE 5TI  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Initial stages of annealing (523-673 K) described by the Cu 2p3/2 and Ti 1s core level spectra for sample 5Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) Ti 1s core level  spectra collected (with no intensity normalisation) at each temperature increment, with +5 h referring to the data collected at the end of the  5 h 673 K holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (b) A magnified view of the Ti 1s core level spectra collected between 523-623 K as well as a room temperature  reference measurement on the same sample (prior to annealing) to highlight the Cu Auger contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (c) Normalised (0-1) Ti 1s core level  spectra to emphasise the change in line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (d) Normalised (0-1) Cu 2p3/2 spectra taken at selected temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' All data have been aligned  to the intrinsic Fermi energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) and (b), and (c) and (d) are plotted on the same y-axis scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a) Ti 1s - 5Ti  1s  (b) Initial Stage  x2  523 K  Room T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  543 K  523 K  563 K  543 K  583 K  563 K  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  603 K  583 K  I-O  623 K  623 K  /arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  643 K  653 K  Intensity /  663 K  ) 1s  673 K  (0)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='1  Ti(0) 1s  +5 h  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' I  4972  4970  4968  4966  4964  4962  4972  4970  4968  4966  4964  4962  Binding Energy / eV  Binding Energy / eV  4968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='7 eV  (c) BE Shift  (d) Cu 2p3/2 - 5Ti  Ti(IV) 1s  932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='5 ev  623 K  523 K  633 K  603 K  643 K  673 K  653 K  +5 h  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  663 K  673 K  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  +5 h  4964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='2 eV  Ti(0)  4972  4970  4968  4966  4964  4962  936  934  932  930  Binding Energy / ev  Binding Energy / ev19  XII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  EARLY STAGES OF ANNEALING FOR SAMPLE 15TI  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Initial stages of annealing (523-673 K) described by the Cu 2p3/2 and Ti 1s core level spectra for sample 15Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) Ti 1s core level  spectra collected (with no intensity normalisation) at each temperature increment, with +5 h referring to the data collected at the end of the  5 h 673 K holding period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (b) A magnified view of the Ti 1s core level spectra collected between 523-623 K as well as a room temperature  reference measurement on the same sample (prior to annealing) to highlight the Cu Auger contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (c) Normalised (0-1) Ti 1s core level  spectra to emphasise the change in line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (d) Normalised (0-1) Cu 2p3/2 spectra taken at selected temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' All data have been aligned  to the intrinsic Fermi energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' (a) and (b), and (c) and (d) are plotted on the same y-axis scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a) Ti 1s - 15Ti  Ti(0) 1s  (b) Initial Stage  x64  523 K  Room T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  543 K  523 K  563 K  543 K  Ti(0) 1s  583 K  563 K  units  603 K  623 K  arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  643 K  653 K  Ti-O  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I  663 K  673 K  +5 h  4968  4966  4964  4962  4972  4968  4966  4962  4972  4970  4970  4964  Binding Energy / eV  Binding Energy / eV  (c) BE Shift  4964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='9 eV  (d) Cu 2p3/2 - 15Ti  Ti(0) 1s  932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='6 eV  623 K  523 K  633 K  (o)ng  603 K  643 K  673 K  653 K  +5h  units  663 K  673 K  arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  -- +5 h  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I  4972  4970  4968  4966  4964  4962  936  934  932  930  Binding Energy / eV  Binding Energy / ev20  XIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  CU 2P3/2 LINE SHAPE CHANGES  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Comparison of the Cu 2p3/2 spectral line shape of the three samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra presented were captured at the end of the 673 K  holding period (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 673 K + 5 h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The spectra are normalised 0-1 and aligned to the main intensity to make it easier to observe changes in the  line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Cu 2p3/2  Cu(0) 2p3/2  5Ti  10Ti  15Ti  4  3  2  1  0  1  2  3  Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Binding Energy / eV21  XIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  IN-SITU ANNEALING TI 2P CONCENTRATION PROFILE  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Relative Ti concentration profile as a function of time, t collected across the measurement window for all three samples, determined  from peak fitting the Ti 2p core level spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The yellow-filled marker for each dataset refers to the time when the 673 K holding period  commences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Vertical guidelines are also in place to mark this point for each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The measured Ti 2p signal intensity for each sample  is first normalised relative to the area of the Cu 2p3/2 core level measured during the same spectral cycle and then afterwards the resultant  Ti 2p/Cu 2p3/2 area is normalised relative to the final intensity of sample 15Ti (IF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  100  Ti 2p  K  K  673  673  90  —5Ti  10Ti  5Ti&15Ti  LOI  %  80  15Ti  70-  60  50 -  Stage 2  Stage 3  40-  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  20 -  10-  0  0  1  2  3  4  5  6  7  8  9  t /h22  XV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  TI 2P/1S COMPARISON  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' A comparison of the (a) Ti 1s, and (b) Ti 2p core level spectra recorded at 573 K (t = 2 h) for sample 10Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra are normalised to  the signal-to-noise ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Guidelines are marked for the positions of the expected peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' It is clear that the Ti 1s is more sensitive to smaller  concentrations of titanium than the Ti 2p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Additionally, the nature of the secondary background for the Ti 2p region means that quantification  of this area is incredibly difficult and cannot be done reliably, whereas a standard XPS background can easily be applied to the Ti 1s region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a) Ti 1s, 10Ti, 573 K  (b) Ti 2p, 10Ti, 573 K  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Ti(IV) 2p1/2  Ti(IV) 1s  Ti(IV) 2p3/2  2p1/2  Ti(0) 2p3/2  Ti(0) 1s  Ti(0)  4972  4970  4968  4966  4964  4962  468  466  464 462 460 458 456 454 452  Binding Energy / eV  Binding Energy / eV23  XVI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  DEPTH PROFILE SURVEY SPECTRA  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Survey spectra collected after each etch cycle during the post-mortem depth profile measurements for (a) 5Ti, (b) 10Ti, and (c) 15Ti  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' The top spectrum displayed in each sub-figure is taken on the as-received sample (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' no etch) and then the spectra collected after  each cycle are stacked vertically below (going from blue to grey to black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' Spectra coloured in blue are Cu-rich, black are W-rich and red is  termed the “interface” as it marks the point where the Cu and W signals cross over in the depth profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  (a)  Etch 0  Ti 3p / W 4f  Cu 2p 1/2  Cu 2p3/2  Cu 3p / W 5s  Cu Surface  W 4d5/2  Interface  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Cu 2s  Cu LMM  TiW Bulk  Cu3s  S  1s  VB  0  c  S  F  Z  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti LMM  W 5p1/2  1000  800  600  400  200  0  Binding Energy / eV  (b)  >Cu 2p1/2  Etch 0  Ti 3p / W 4f  Cu 2p3/2  Cu Surface  >Cu2s  Cu 3p / W 5s  Cu LMM  Interface  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  2  TiW Bulk  S  S  3s  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  1s  dz!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  N1s  2p  C  VB  1  S  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti LMM  W 5p1/2  1000  800  600  400  200  0  Binding Energy / eV  (c)  Etch 0  Ti 3p / W 4f  Cu 2p1/2  Cu 2p3/2  Cu Surface  Cu 3p / W 5s  Cu 2s  Interface  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content=' units  Cu LMM  TiW Bulk  S  Cu 3s  Intensity I arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  S  S  S  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  VB  F  Z  S  4  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
+page_content='  Ti LMM  W 5p1/2  1000  800  600  400  200  0  Binding Energy / eV24  XVII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
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+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/u9E0T4oBgHgl3EQfsQGm/content/2301.02577v1.pdf'}
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diff --git a/uNE0T4oBgHgl3EQfsAG-/content/tmp_files/2301.02574v1.pdf.txt b/uNE0T4oBgHgl3EQfsAG-/content/tmp_files/2301.02574v1.pdf.txt
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+Draft version January 9, 2023
+Typeset using LATEX default style in AASTeX631
+Gamma-ray Emission from Galaxies Hosting Molecular Outflows
+Alex McDaniel
+,1 Marco Ajello
+,1 and Chris Karwin
+1
+1Department of Physics and Astronomy, Clemson University, Clemson, SC, 29631
+ABSTRACT
+Many star-forming galaxies and those hosting active galactic nuclei (AGN) show evidence of massive
+outflows of material in a variety of phases including ionized, neutral atomic, and molecular. Molecular
+outflows in particular have been the focus of recent interest as they may be responsible for removing
+gas from the galaxy, thereby suppressing star formation.
+As material is ejected from the cores of
+galaxies, interactions of the outflowing material with the interstellar medium can accelerate cosmic
+rays and produce high-energy gamma rays. In this work, we search for gamma-ray emission from a
+sample of local galaxies known to host molecular outflows using data collected by the Fermi Large
+Area Telescope. We employ a stacking technique in order to search for and characterize the average
+gamma-ray emission properties of the sample. Gamma-ray emission is detected from the galaxies in
+our sample at the 4.4 σ level with a power-law photon index of Γ ≈ 2 in the 1-800 GeV energy range.
+The emission is found to correlate with tracers of star formation activity, namely the 8 − 1000 µm
+infrared luminosity. We also find that the observed signal can be predominantly attributed to H ii
+galaxies hosting energy-driven outflows. While we do not find evidence suggesting that the outflows
+are accelerating charged particles directly, galaxies with molecular outflows may produce more gamma
+rays than galaxies without outflows. In particular, the set consisting of gamma-ray-detected galaxies
+with molecular outflows are nearly perfect calorimeters and may be future targets for searches of
+high-energy neutrinos.
+Keywords: Ultraluminous infrared galaxies (1735), Gamma rays (637), Molecular gas (1073), Galactic
+winds (572), Galaxy winds (626), AGN host galaxies (2017)
+1. INTRODUCTION
+The presence of galactic outflows and winds is well documented in galaxies over a wide range of distances and physical
+scales. Whether powered by starburst activity or active galactic nuclei, these winds are able to drive large amounts of
+material from their host galaxies, injecting energy into their surrounding medium (Veilleux et al. 2005; Cicone et al.
+2018; Veilleux et al. 2020). Galactic outflows manifest in a variety of different phases and with observational evidence
+spanning a wide range of frequencies. The sub-pc highly-ionized outflows are primarily measured by X-ray absorption
+lines (Reeves et al. 2009; Tombesi et al. 2012, 2013; Gofford et al. 2013; Nardini et al. 2015), whereas the neutral atomic
+phase is primarily measured by observations of the sodium doublet (Heckman et al. 2000; Rupke et al. 2005; Cazzoli
+et al. 2016; Roberts-Borsani & Saintonge 2019), and the molecular phase is measured through various radio, infrared,
+and optical observations (Fischer et al. 2010; Feruglio et al. 2010; Sturm et al. 2011; Combes et al. 2013; Spoon et al.
+2013; Veilleux et al. 2013; Cicone et al. 2014; Garc´ıa-Burillo et al. 2015; Stone et al. 2016; Gonz´alez-Alfonso et al.
+2017; Bolatto et al. 2021; Stuber et al. 2021). Together, understanding the details of the various phases of galactic
+outflows helps to shed light on galactic structure and feedback in galaxies.
+Among the different outflow phases, the molecular phase is particularly interesting. For one, the molecular phase
+dominates the mass of the outflowing material and extends to the largest physical scales (Cicone et al. 2014; Carniani
+et al. 2015; Garc´ıa-Burillo et al. 2015). Furthermore, the molecular gas driven in the wind is also the fuel for star
+Corresponding author: Alex McDaniel
+armcdan@clemson.edu
+arXiv:2301.02574v1  [astro-ph.HE]  6 Jan 2023
+
+ID2
+McDaniel et al.
+formation, creating a direct link between the molecular outflow and star formation properties of the galaxy with
+potential effects on galaxy evolution. Detailed studies of molecular outflows have recently gained interest due in part
+to the capabilities of instruments such as Herschel in infrared (IR) or the Atacama Large Millimeter/submillimeter
+Array (ALMA) and the NOrthern Extended Millimeter Array (NOEMA) at millimeter wavelengths, which allow for
+several methods of detecting molecular outflows (see also Veilleux et al. 2020; Stuber et al. 2021). In infrared, P
+Cygni profiles of OH transitions have yielded multiple detections (Fischer et al. 2010; Sturm et al. 2011; Spoon et al.
+2013; Veilleux et al. 2013; Stone et al. 2016; Gonz´alez-Alfonso et al. 2017), while CO line transitions (as well as other
+molecular tracers, e.g. HCN; Aalto et al. 2012) with instruments such as ALMA, NOEMA, or the IRAM Plateau de
+Bure Interferometer (PdBI) have also provided an effective method for detecting molecular outflows and characterizing
+their properties (Feruglio et al. 2010; Combes et al. 2013; Cicone et al. 2014; Garc´ıa-Burillo et al. 2015; Bolatto et al.
+2021). Molecular outflows are the dominant component of the total outflow mass, have mass-loss rates on the order
+of a few hundred M⊙ yr−1, and extend to scales of 0.1 − 10 kpc with wind velocities on the order of 102 − 103 km s−1
+(Sturm et al. 2011; Cicone et al. 2014; Fluetsch et al. 2019; Lutz et al. 2020; Fluetsch et al. 2021). They are found
+throughout the universe, from nearby systems out to as far as redshift of z ∼ 6 (Jones et al. 2019; Spilker et al. 2020).
+Commonly – though not exclusively – they are found associated with (ultra)-luminous infrared galaxies ((U)LIRGs)
+(Pereira-Santaella et al. 2021; Chen et al. 2010; Veilleux et al. 2013; Pereira-Santaella et al. 2018). In a recent study
+by Fluetsch et al. (2019), a collection of local (z < 0.2) molecular outflows has been compiled from the literature and
+archival data in order to analyze their properties and examine the relations between them in a systematic manner.
+While studies of galactic outflows have primarily been limited to the energy regimes of X-rays and below, theoretical
+models suggest that the interactions of the outflowing gas with the interstellar medium can create shocks in which
+cosmic rays can be accelerated. The cosmic rays can then interact with the ambient material and interstellar radiation
+fields to produce gamma rays through both hadronic and leptonic processes (Lamastra et al. 2016; Wang & Loeb
+2016). The efficiency of cosmic-ray acceleration in outflows is predicted to be comparable to or in excess of other
+acceleration sites such as supernova remnants (SNRs, Faucher-Gigu`ere & Quataert 2012; Nims et al. 2015). Recently,
+the detection of gamma rays from highly-ionized, ultra-fast outflows (UFOs) using Fermi-LAT data has been reported
+(Ajello et al. 2021), and it is possible that molecular outflows may also be observed in gamma rays (Lamastra et al.
+2016). In fact, several of the galaxies that are known to host powerful outflows are also gamma-ray emitters with
+significant detections by Fermi-LAT (Lenain et al. 2010; Abdo et al. 2010a; Ackermann et al. 2012; Hayashida et al.
+2013; Tang et al. 2014; Ajello et al. 2020), as well as by other higher-energy gamma-ray telescopes (Acero et al. 2009;
+VERITAS Collaboration et al. 2009). These include some notable and particularly well-studied systems, such as M 82,
+NGC 253, and NGC 1068. In some cases, the emission from gamma-ray-detected galaxies hosting molecular outflows
+exceeds that expected from Lγ − LIR relations (Ajello et al. 2020).
+Despite the theoretical basis for gamma-ray emission from molecular outflows and the gamma-ray detection of several
+galaxies hosting molecular outflows, thus far no concrete detection that can be directly attributed to the molecular
+outflow exists. Models of the gamma-ray emission from molecular outflows predict a relatively faint signal, which can
+be difficult to distinguish from other sources of gamma-ray emission such as starburst activity (Lamastra et al. 2016).
+It is also unclear what the interplay may be between star formation activity and the molecular outflow. These two
+phenomena are intrinsically linked to the molecular gas of the galaxy (Feldmann 2020) - in some cases, it has even
+been shown that enhanced star formation may take place within the outflow itself (Maiolino et al. 2017; Gallagher
+et al. 2019; Perna et al. 2020).
+The primary goal of this paper is to study the potential gamma-ray emission from a well-selected sample of galaxies
+that are known to host molecular outflows and that have not yet been individually resolved by current gamma-ray
+instruments. To do this we use ∼ 11 years of Fermi-LAT data and employ a stacking technique designed to detect
+faint sources and characterize their emission. We then aim to determine the origin of the gamma-ray emission and
+how its properties relate to the properties of the molecular outflow and whether it can be disentangled from star-
+formation—induced gamma rays.
+The remainder of the paper is as follows: in Section 2, we describe the sample of molecular outflows, while we
+describe the gamma-ray data selection and the analysis procedure in Section 3. In Section 4, we present the results of
+the gamma-ray analysis and study the relationship between the gamma-ray emission and galaxy properties. In Section
+5, we provide a discussion of these results. Throughout this work, we adopt cosmological values of H0 = 70 km s−1
+Mpc−1, ΩM = 0.27 and ΩΛ = 0.73.
+
+3
+2. SAMPLE SELECTION
+The initial sample of molecular outflows in our analysis is taken from (Fluetsch et al. (2019), hereafter F19). In
+their work, they collect a sample of 45 galaxies with evidence of molecular outflows within the local universe (z < 0.2).
+The sample includes 31 galaxies taken from the literature with outflow properties obtained through the analysis of the
+CO(1-0) and CO(2-1) emission lines using observations from either the IRAM PdBI (Cicone et al. 2014; Dasyra et al.
+2014; Leroy et al. 2015; Garc´ıa-Burillo et al. 2015; Querejeta et al. 2016) or ALMA (Combes et al. 2013; Sun et al.
+2014; Pereira-Santaella et al. 2016; Salak et al. 2016; Veilleux et al. 2017). An additional 10 outflows were identified
+from archival ALMA CO data by the authors of F19. However, five of the 31 outflows taken from the literature and
+three of those from the ALMA archival data only include upper limits on the outflow properties. Also included in the
+sample of F19 are four outflows observed with far-infrared transitions of OH with the Herschel/PACS spectrometer
+(Gonz´alez-Alfonso et al. 2017).
+From this sample we remove a number of galaxies based on the following criteria: first, we remove the 8 non-
+detections wherein only upper limit estimates were provided by F19, after which 37 outflows remain. We then proceed
+to make cuts based on spatial coincidence with sources in the 4FGL (Abdollahi et al. 2020) by removing all galaxies
+that fall within the 95% confidence radius of a 4FGL source1. This criterion removes 5 galaxies from the sample, each
+of which has been directly studied and detected by Fermi. Specifically, these are NGC 2146 (Tang et al. 2014), NGC
+1068 (Ackermann et al. 2012), the Circinus Galaxy (Hayashida et al. 2013), NGC 253, and M82 (Abdo et al. 2010a).
+Although we exclude these from the stacking of unresolved sources, they are used in the later analysis (see Section
+4), and the Fermi data for these sources are analyzed following the same procedure described in Section 3.1 that is
+applied to the benchmark sample. We additionally check for spatial coincidences with known gamma-ray blazars from
+the Roma-BZCAT catalog (Massaro et al. 2015) and remove bright radio galaxies included in the 3C/4C catalogs
+(Bennett 1962; Pilkington & Scott 1996) or in Yuan & Wang (2012). For the BZCAT and radio sources, we remove
+any targets that lie within 0.1◦ of the sources. This value is chosen as it is roughly similar to the mean 4FGL 95%
+confidence radius. These criteria remove only one additional source – the radio galaxy 4C 12.50. In all, the spatial
+coincidence cuts remove 6 galaxies from our sample. In addition, we identify two galaxies that have nearby, extremely
+bright 4FGL sources (although outside the 95% confidence radius). Specifically, IRAS 05189-2524 is ∼ 0.5◦ away from
+4FGL J0523.3-2527 (classified as a binary), and IRAS 15115+0208 is ∼ 0.45◦ away from 4FGL J1512.2+0202, which
+is associated with the flat-spectrum radio quasar PKS 1509+022. The nearby 4FGL sources contribute relatively high
+counts and comprise the majority of the background within the 68% containment radius of the point-spread-function
+(PSF) centered at the target. To avoid any potential impacts from these nearby, bright 4FGL sources, we remove the
+two targets from our sample.
+Our final benchmark sample consists of 29 galaxies. A selection of properties of the host galaxies and the molecular
+outflows are reported in Table 1. Several of these properties, such as optical classification, the AGN luminosity, and
+the AGN contribution to the bolometric luminosity (αbol = LAGN/Lbol), are taken directly from F19 and references
+therein. Properties of the outflows such as mass-loss rates and kinetic power are derived from the line observations of
+the molecular outflows reported in F19. To calculate the total 8 µm − 1000 µm IR luminosity (LIR), we use the four
+IR flux bands (f12µm, f25µm, f60µm, f100µm) from the Infrared Astronomical Satellite (IRAS) Faint Source Catalog
+(FSC, Moshir et al. 1992) and the prescription of Sanders & Mirabel (1996). Luminosity distances are taken from the
+NASA Extragalactic Database2 (NED).
+To summarize, the general composition of our final sample includes 8 H ii galaxies, 3 Seyfert 1 galaxies, 11 Seyfert
+2 galaxies, and 7 LINERs (for simplicity, we will categorize all the LINERs and Seyferts as AGN galaxies throughout
+the remainder of the text, though it should be noted that αbol is the more descriptive indicator of the role of the AGN
+contribution). The galaxies extend out to redshift z ≲ 0.2, range in luminosity from 109.5L⊙ < LIR < 1012.7L⊙, and
+include 7 LIRGs and 15 ULIRGs.
+python check
+3. DATA SELECTION AND ANALYSIS
+3.1. Data
+1 The spatial coincidence cuts are performed using the first 4FGL data release (Abdollahi et al. 2020) to be consistent with the point-source
+modeling. More recent 4FGL data releases do not detect additional galaxies from our benchmark sample, therefore the spatial coincidence
+cuts are the same for the subsequent 4FGL-DR2 (Ballet et al. 2020) and 4FGL-DR3 (Fermi-LAT collaboration et al. 2022) data releases.
+2 https://ned.ipac.caltech.edu/cgi-bin/objsearch?search type=Search&refcode=2019MNRAS.483.4586F
+
+4
+McDaniel et al.
+Name
+Type
+DL
+SFR
+log LIR
+log LAGN
+αbol
+˙Mout
+log Pk
+Pk/LAGN
+qIR
+[Mpc]
+[M⊙/yr]
+[L⊙]
+[ergs/s]
+[M⊙/yr]
+[ergs/s]
+PG 0157+001
+Sy1
+777.0
+209.0
+12.6
+45.3
+0.18
+93.0
+42.3
+1.1 × 10−3
+2.13
+NGC 1266
+LINER
+28.6
+1.6
+10.5
+43.3
+0.25
+11.0
+41.0
+5.3 × 10−3
+2.36
+IRAS F03158+4227
+Sy2
+632.0
+220.0
+12.6
+45.9
+0.55
+1500.0
+44.7
+0.054
+–
+NGC 1377
+LINER
+23.9
+0.9
+10.1
+42.9
+0.2
+5.0
+40.3
+2.2 × 10−3
+3.53
+NGC 1433
+Sy2
+14.5
+0.2
+9.5
+42.2
+0.2
+0.7
+39.3
+1.3 × 10−3
+–
+NGC 1614
+H ii
+68.3
+45.0
+11.6
+≤ 42.1
+6.0 × 10−4
+21.0
+41.9
+≥ 0.731
+2.77
+NGC 1808
+H ii
+10.8
+5.1
+10.7
+≤ 41.0
+5.0 × 10−4
+3.0
+40.0
+≥ 0.095
+2.82
+IRAS F08572+3915
+Sy2
+265.0
+20.0
+12.1
+45.7
+0.86
+403.0
+43.9
+0.016
+3.57
+NGC 3256
+H ii
+44.6
+36.0
+11.6
+≤ 42.0
+7.0 × 10−4
+4.0
+40.9
+≥ 0.085
+2.37
+IRAS F10565+2448
+Sy2
+196.0
+95.0
+12.0
+44.8
+0.17
+100.0
+42.8
+9.9 × 10−3
+2.64
+IRAS F11119+3257
+Sy1
+929.0
+144.0
+12.7
+46.2
+0.689
+203.0
+43.8
+4.0 × 10−3
+1.62
+NGC 3628
+H ii
+17.1
+1.8
+10.2
+≤ 40.8
+9.0 × 10−4
+1.5
+39.1
+≥ 0.019
+2.00
+ESO 320-G030
+H ii
+51.1
+20.0
+11.1
+≤ 41.1
+1.0 × 10−4
+1.2
+40.9
+≥ 0.637
+2.77
+NGC 4418
+Sy2
+36.4
+14.5
+11.2
+43.8
+5.0 × 10−4
+19.0
+41.0
+1.7 × 10−3
+3.35
+Mrk 231
+Sy1
+189.0
+234.0
+12.5
+45.7
+0.34
+350.0
+43.7
+0.01
+2.44
+IRAS 13120-5453
+Sy2
+138.0
+157.0
+12.3
+44.4
+0.173
+1115.0
+44.0
+0.474
+2.78
+M 51
+Sy2
+11.1
+2.6
+10.4
+43.8
+0.61
+11.0
+40.5
+5.6 × 10−4
+2.11
+Mrk 273
+Sy2
+169.0
+139.0
+12.1
+44.2
+0.08
+200.0
+43.4
+0.168
+2.49
+SDSS J1356+1026
+Sy2
+579.0
+20.0
+11.9
+46.0
+0.43
+118.0
+43.0
+9.3 × 10−4
+2.32
+IRAS F14348-1447
+LINER
+382.0
+169.0
+12.3
+44.6
+0.17
+420.0
+43.4
+0.069
+–
+IRAS F14378-3651
+LINER
+308.0
+112.0
+12.2
+45.1
+0.21
+180.0
+43.0
+7.8 × 10−3
+2.27
+NGC 6240
+Sy2
+107.0
+16.0
+11.8
+45.4
+0.78
+267.0
+43.1
+5.6 × 10−3
+2.10
+IRAS 17208-0014
+H ii
+189.0
+200.0
+12.4
+≤ 43.7
+0.24
+176.0
+43.3
+≥ 0.427
+2.79
+NGC 6764
+LINER
+32.6
+2.6
+10.4
+42.2
+0.017
+1.0
+40.0
+5.4 × 10−3
+2.25
+IRAS 20100-4156
+H ii
+605.0
+330.0
+12.7
+≤ 42.9
+7.0 × 10−4
+1457.0
+44.0
+≥ 11.23
+2.93
+IC 5063
+Sy2
+47.2
+0.6
+10.8
+44.3
+0.9
+8.0
+41.4
+1.1 × 10−3
+1.11
+IRAS F20551-4250
+LINER
+187.0
+43.0
+12.0
+44.8
+0.13
+200.0
+43.1
+0.023
+2.89
+IRAS 22491-1808
+H ii
+348.0
+145.0
+12.1
+≤ 41.6
+0.06
+654.0
+43.1
+≥ 27.454
+3.26
+IRAS 23365+3604
+LINER
+285.0
+137.0
+12.1
+44.7
+0.072
+57.0
+42.6
+7.8 × 10−3
+2.73
+Table 1. Galaxy and outflow properties for targets in the benchmark sample. For more detail see F19. Luminosity distances
+are taken from NED, and the infrared luminosities (LIR) are computed from the IRAS fluxes. The SFR is computed using LIR,
+the AGN contribution to the total bolometric luminosity, and the relation of Sturm et al. (2011). The AGN contribution to the
+total bolometric luminosity is given by αbol = LAGN/Lbol. Pk is the kinetic power of the outflow, defined as Pk = 0.5 ˙Moutv2
+out.
+The values for αbol, LAGN, mass loss rate, and outflow velocity are taken from F19. qIR is the ratio of IR and 1.4 GHz radio
+fluxes, as defined in Helou et al. (1985); Ivison et al. (2010); Harrison et al. (2014), with radio fluxes taken from NED when
+available. Logarithmic values for LIR, LAGN, and Pk are base 10 (i.e. log10).
+The data used in this analysis was collected over 11.1 years by the Fermi-LAT between August 4, 2008 and Septem-
+ber 10, 2019. We use events with energies in the range 1-800 GeV binned into 8 bins per decade and a pixel size of
+0.08◦. To reduce contamination from the Earth’s limb, we use a maximum zenith angle of 105◦. We define a 10◦ × 10◦
+region of interest (ROI) centered at the position of each galaxy in the sample using RA and Dec values taken from
+NED. We use the standard data filters (DATA QUAL> 0 and LAT CONFIG==1) and select photons correspond-
+ing to the P8R3 SOURCE V2 class. The analysis is performed using Fermipy (v0.19.0, Wood et al. 2017), which
+utilizes the underlying Fermitools (v1.2.23). The Galactic diffuse emission is modeled using the standard interstellar
+emission model (gll iem v07.fits). For the extragalactic emission and residual instrumental background we use
+iso P8R3 SOURCE V2 v1.txt, and the point source emission is modeled using the 4FGL catalog (gll psc v20.fits).
+In order to account for photon leakage from sources outside of the ROI due to the PSF of the detector, the model
+
+5
+Figure 1. Gamma-ray SED for the molecular outflow model of NGC 1068 from Lamastra et al. (2016) (red). The blue line
+and band show the predicted median and 50% containment band of our sample when applying the same model scaled to the
+characteristics of each source. Data points for NGC 1068 from the Lamastra et al. (2016) analysis are shown as green crosses.
+We also show in grey the Fermi-LAT broadband sensitivity for a power-law source using 10 years of Fermi data.
+includes all 4FGL sources within a 15◦ × 15◦ region. The energy dispersion correction (edisp bins=-1) is enabled for
+all sources except the isotropic component.
+3.2. Stacking Analysis
+While a number of galaxies hosting molecular outflows have also been observed in gamma rays by the Fermi-LAT,
+it is not currently known to what extent the molecular outflow contributes to this emission. In most galaxies, it is
+likely that any potential molecular-outflow induced gamma-ray emission would fall under the detection threshold of
+the Fermi-LAT. To illustrate this, we consider the analysis of Lamastra et al. (2016) wherein the gamma-ray emission
+of an AGN-driven molecular outflow is estimated for the gamma-ray detected galaxy NGC 1068 – a relatively close
+(DL = 14.4 Mpc), bright, and particularly well-studied galaxy. Based on models that assume typical parameter values
+for LAGN and outflow characteristics of NGC 1068, as well as adopting conventions of SNR shock efficiencies for energy
+injection to cosmic ray protons and electrons, their results yield flux values at the level of roughly ∼ 2 − 5 × 10−13
+ergs cm−2 s−1 in the 1-800 GeV energy range.
+Making use of the Lamastra et al. (2016) results and adopting
+their model wherein the gamma-ray emission from an outflow is directly related to the kinetic power of the outflow
+(Pk = 0.5 ˙Moutv2
+out), we can produce a rough estimate for gamma-ray emission from our sample. For each outflow, we
+scale the gamma-ray luminosity found in Lamastra et al. (2016) by the kinetic power of the outflow, then calculate
+the flux from using the distance to the outflow. This gives a median expected flux on the order of ∼ 2 − 4 × 10−14
+ergs cm−2 s−1 (corresponding to a photon flux of 2.8 − 5.6 × 10−12 ph cm−2 s−1 for a power law index of 2.2). This is
+illustrated in Figure 1. We emphasize that the Lamastra et al. (2016) model represents the predicted contribution from
+only the molecular outflow. Their work finds that this is not sufficient to fully account for the gamma-ray detection of
+NGC 1068 (see Figure 1), assuming the standard cosmic-ray acceleration efficiency parameters. Rather, a comparable
+contribution from starburst activity would be required to account for the gamma-ray emission. For comparison, we
+also show the Fermi-LAT broadband sensitivity3 for a point source located at intermediate latitudes (ℓ = 0◦, b = 30◦)
+using 10 years of Fermi-LAT data.
+The above estimates serve as an indication that the emission from individual molecular outflows is likely below the
+sensitivity of the Fermi-LAT, and therefore motivates the use of a stacking technique in order to detect emission from
+the overall population. The method employed is the same as that applied successfully in a number of previous studies
+(e.g. Fermi-LAT Collaboration et al. 2018; Paliya et al. 2019; Ajello et al. 2020, 2021). For this procedure, we work
+3 https://www.slac.stanford.edu/exp/glast/groups/canda/lat Performance.htm
+
+10-11
+NGC1068
+(Lamastra+2016)
+Fermi-LAT
+10-12
+E2dN/dE[ergs 
+10-13
+10-14
+NGC1068(Lamastra+2016)
+Median
+10-15
+50%Containment
+10-1
+100
+101
+102
+103
+E[GeV]6
+McDaniel et al.
+under the assumption that the sample population can be characterized by average quantities such as flux, luminosity,
+or photon index. We begin the analysis by optimizing the model components for the ROI of each target using a
+maximum likelihood fit and evaluate the significance of each source in the ROI using the TS defined by:
+TS = −2 log(L0/L),
+(1)
+where L0 is the likelihood for the null hypothesis (i.e. all sources except for molecular outflow), and L is the likelihood
+for the alternative hypothesis (all sources including the molecular outflow).
+Here, the spectral parameters of the
+Galactic diffuse component (index and normalization) and the normalization of the isotropic component are left free.
+We also leave free the normalizations of all 4FGL sources with TS ≥ 25 that are within 5◦ of the ROI center, as well as
+sources with TS ≥ 500 and within 7◦. The fitting of the molecular outflow source assumes a power-law spectral model
+with the normalization and index left free. At this stage, we also use the Fermipy function find sources to search for
+new point sources. The find sources function generates TS maps and identifies new sources based on peaks in the
+TS. The maps are generated using a power-law spectral model ( dN
+dE ∝ E−Γ) with an index of Γ = 2.0. The minimum
+separation between two point sources is set to 0.5◦, and the minimum TS for including a source in the model is set to
+16.
+After these processing steps, we then create a bi-dimensional TS array in flux-index space for each target. The
+flux-index stacking method employed here has been validated a number of previous times through simulations (see
+e.g. Paliya et al. 2019; Ajello et al. 2020, 2021), and has been shown to be a reliable technique. Underpinning this
+approach is the assumption that if the gamma-ray emission in each target comes from the same emission mechanism,
+the average index will be broadly representative of the population. Similarly, the flux of the sample population is
+assumed to be roughly concentrated around the average, which is motivated by the fact that most Fermi sources are
+detected in flux near the threshold (Abdollahi et al. 2020). Furthermore, sources with particularly high fluxes are
+more likely to have already been individually detected. Some other stacking analysis studies have chosen to instead
+test alternative hypotheses, such as for example stacking one dimensional TS profiles as a function of only index (de
+Menezes et al. 2021). However, we elect to follow the approach of generating the two dimensional TS profiles, which
+has been both successfully employed in previous studies as well as validated through several simulations.
+With the isotropic and galactic diffuse background models left free, we scan photon indices from 1 to 3.3 with a
+spacing of 0.1 and total integrated photon fluxes from 10−13 to 10−9 ph cm−2 s−1 with 40 logarithmically spaced
+bins over the 1-800 GeV energy range. This choice of energy range is consistent with that used in the most recent
+application of this stacking analysis studying ultra-fast outflows (Ajello et al. 2021). Since the TS is an additive
+quantity, the stacked profile is merely the sum of the arrays for either the given sample or any desired sub-sample.
+4. RESULTS
+4.1. Stacked TS for the Benchmark Sample
+In Figure 2, we show the stacked TS array for the full benchmark sample of 29 molecular outflows that have not
+previously been detected by gamma-ray observations. The best-fit photon flux is 1.3+0.7
+−0.6 × 10−11 ph cm−2 s−1 with
+photon index Γ = 2.0+0.3
+−0.2. The maximal TS value is 22.8, corresponding to roughly a 4.4 σ detection for 2 degrees of
+freedom. From the benchmark sample, we check for any galaxies in the sample that may be individually detected at
+a significant level. We note that none of the individual targets have significant (TS > 25) detections; furthermore, all
+are below the 3σ level with a median TS value at the best-fit parameters of 2.2.
+4.2. Scientific Control Sample
+In order to understand to what extent the purported signal from the benchmark sample can be attributed to the
+presence of the molecular outflows, we repeat our analysis on a control sample consisting of galaxies where no molecular
+outflow has been detected. In compiling the sample of molecular outflows in F19, the authors analyzed ALMA archival
+data for ∼ 100 galaxies in order to search for evidence of outflows. As discussed earlier (cf. Section 2), the authors
+were able to detect or even constrain outflow properties in only 10 galaxies. For our control sample, we therefore
+make use of a sub-sample of the galaxies for which no outflow was detected. However, it is important to note that
+most of these galaxies lack ALMA observations that are sensitive enough to detect the outflows, and non-detections
+do not necessarily imply the absence of outflowing molecular gas. We thus use the subset of galaxies with the most
+sensitive ALMA observations that were examined by the authors of F19. The distribution of ALMA line sensitivities
+
+7
+Figure 2. Stacked TS profile for the benchmark sample. Overlaid are the 1, 2, and 3 σ contours for 2 degrees of freedom.
+as presented in the ALMA Science Archive4 is shown in Figure 3 along with the most sensitive observations for the
+galaxies in the benchmark sample that were detected with ALMA observations. We note that all the galaxies selected
+for our control sample of ALMA non-detections have estimated sensitivities less than ∼ 0.62 mJy beam−1, better than
+for most of the detected galaxies. We therefore treat this as a reasonable selection of galaxies lacking a prominent
+molecular outflow.
+In constructing the control sample, our aim is to match the characteristics of the benchmark sample, particularly
+their distributions in distance and LIR. However, the control sample obtained from the ALMA archival data poorly
+samples higher IR luminosities. For instance, only one galaxy from the ALMA archival control sample (IRAS 07251-
+0248) has an IR luminosity greater than 1012L⊙, whereas almost half our benchmark sample has IR luminosities above
+this level. To address this, we searched the literature for known (U)LIRGs (i.e. LIR ≳ 1012L⊙) for which a search for
+a molecular outflow has been performed. We found no evidence of molecular outflows for these galaxies reported in
+the literature.
+Previous studies – particularly ones interested in the multi-phase nature of outflows – have similarly searched the
+literature for evidence of the presence of various outflows in galaxies. Such searches have identified several candidates
+that lack any significant evidence of molecular outflows using a variety of detection techniques. Of these, we select IRAS
+06259-4708N, IRAS 13156+0435N, and IRAS 19542+1110 (Fluetsch et al. 2021), as well as IRAS 06035-7102, IRAS
+00198-7926, and IRAS 20414-1651 (Westmoquette et al. 2012). Additionally, in Veilleux et al. (2013), non-detections
+of an outflow in the molecular phase using Herschel/PACS observations of the OH 119 µm line were reported for PG
+2130+099, IRAS F23128-5919, IRAS F15206+3342, IRAS F13305-1739. Finally, we also include the galaxy I Zw 1,
+which has been observed to have outflows in the neutral atomic and ionized phases, though the molecular outflow
+phase has not been directly constrained. I Zw 1 was reported as a non-detection using CO emission lines in Cicone
+et al. (2014) and is listed as lacking evidence of a molecular outflow in Fluetsch et al. (2021) (though the properties of
+the other phases were used to place limits on the molecular outflow in F19). A search for more recent studies of the
+presence of molecular outflows in the systems listed above yields no definitive evidence.
+We note that while these galaxies form one of the best control samples of ULIRGs lacking direct evidence of molecular
+outflows available, it is not necessarily the case that the presence of outflowing molecular gas can be explicitly excluded.
+In fact, when searching through catalogs of local known (U)LIRGs (e.g. in the IRAS Revised Bright Galaxy Survey
+(RBGS) or Great Observatories All-sky LIRG Survey (GOALS) catalogs (Sanders et al. 2003; Armus et al. 2009)), most
+candidates that have been studied tend to show some evidence of a molecular outflow. Furthermore, although the exact
+prevalence is not known, there is increasing evidence that molecular outflows are widely ubiquitous in these systems
+4 https://almascience.nrao.edu/aq/
+
+TS
+3.0
+20
+Photon Index 
+2.5
+15
+2.0
++
+10
+1.5
+5
+1.0
+-13
+-12
+-11
+-10
+-9
+log(Flux [ph cm-2 s-1j)8
+McDaniel et al.
+(Chen et al. 2010; Veilleux et al. 2013; Pereira-Santaella et al. 2018, 2021). Therefore, we caution that this subset
+of the control sample should be thought of as a collection of galaxies where the molecular outflow is not prominent
+enough to be detected with standard techniques, rather than claiming that they are concretely excluded.
+The control test analysis is performed following an identical procedure to the benchmark sample, including all spatial
+coincidence cuts discussed in Section 2. In total, this sample comprises 19 from the ALMA archival observations and
+11 (U)LIRGS from the literature. The TS array for the control is shown in the left panel of Figure 3, with a peak
+value of TS = 1.3 at index of Γ = 2.6 and 95% upper limit of 1.6×10−11 ph cm−2 s−1. Given the relatively low TS for
+the control sample in comparison with the results for the benchmark sample, the conclusion that the observed signal
+is related to the presence of the outflow is supported.
+Figure 3. Left: TS profile for control sample galaxies where no outflow has been successfully detected. Right: Distribution of
+estimated line sensitivities from the ALMA archive for the best observations of the molecular outflows in our benchmark sample
+(orange) and those used in the scientific control sample (blue).
+4.3. Technical Control Sample
+As an additional test to the scientific control sample using galaxies without detected molecular outflows, we run
+a separate technical control analysis to account for systematic effects of the Fermi analysis, such as the underlying
+background intensity and the effects of nearby gamma-ray sources in our model. This is performed in the following
+manner. For each galaxy in our benchmark sample of galaxies hosting molecular outflows (i.e. Table 1), we randomly
+select a set of coordinates located between 1◦ − 2◦ from the galaxy coordinates and run these through the analysis
+pipeline. As in the previous cases, a bi-dimensional TS profile is created for each set of coordinates. We then stack
+the TS profiles to obtain an estimate of the background TS. This process is repeated five times, yielding in maximum
+TS values of TS = [2.04, 5.86, 3.67, 0.86, 0.08]. Figure 4 shows the TS profiles for the iterations yielding the highest
+and lowest TS values. Although the fluctuations in the technical control TS can vary as high as TS ≈ 6, the generally
+low TS values found in the control analysis indicate that our ROIs are well modeled.
+4.4. Radio Emission and the Role of Jets
+Another potential contribution to the gamma-ray emission may be from jets. Particularly, the presence of radio jets
+has been shown to be important for detecting a gamma-ray counterpart, e.g. in radio galaxies (Abdo et al. 2010b) and
+low-luminosity AGN (de Menezes et al. 2020). One way to infer the presence of a radio jet is based on the ratio of the
+8 − 1000 µm IR flux to the 1.4 GHz monochromatic radio flux (Ivison et al. 2010; Harrison et al. 2014). Specifically,
+ratio values of qIR ≲ 1.8 are indicative of a radio excess and the likely presence of a radio jet, whereas values of ∼ 2.4
+are consistent with radio emission due to star-formation (Helou et al. 1985; Ivison et al. 2010; Harrison et al. 2014).
+In Table 1, the qIR values for our sample are listed (see also Figure 13 of F19). Two of the galaxies in the sample
+
+TS
+1.2
+3.0
+Photon Index 
+1.0
+2.5
+0.8
+2.0
+0.6
+0.4
+1.5
+0.2
+1.0
+0.0
+-13
+-12
+-11
+-10
+-9
+log(Flux [ph cm-2 s-1j)10
+Control
+MOs
+8
+6
+4
+2
+0
+100
+Line Sens. [mJy beam-1 (10 km s-1)]9
+Figure 4. TS profiles for the iterations of the technical control sample with the highest maximum TS value (left) and the
+lowest maximum TS value (right). Note that for visualization purposes the minimum of the color scale for the right panel is set
+to −1.
+exhibit a radio excess, however for the majority of the sample there is little evidence for the presence of radio jets
+as indicated by these values. Given the relationship between radio and gamma-ray jets and the lack of evidence for
+jets in our sample, we expect any gamma-ray contributions from jet emission to be minimal. Furthermore, the lack
+of radio excess in these targets may indicate that the outflows are not accelerating large amounts of cosmic rays as
+cosmic-ray electrons would produce radio emission.
+4.5. Gamma Rays in Energy or Momentum Conserving Outflows
+The mechanisms by which the outflows are driven in AGN galaxies can be summarized by three theoretical paradigms.
+Two of the paradigms are directly related to the dynamics of the shock blast. In the energy-driven case, the shock
+expands in an adiabatic, energy conserving fashion due to inefficient cooling. In the momentum-driven case, the cooling
+of the shocked gas is more efficient, and the full energy of the wind is injected into the ambient medium. These two
+models are also often referred to as “energy-conserving” and “momentum-conserving,” respectively (King 2010; King
+et al. 2011; Faucher-Gigu`ere & Quataert 2012; King & Pounds 2015). A third class of models for driving the outflow
+invokes the radiation-pressure—driven scenario in which the outflows can be driven by the direct pressure of IR, UV,
+and optical photons on the ISM (Fabian 2012; Ishibashi et al. 2018). For star-formation-driven outflows, the canonical
+paradigm is an energy-driven scenario (Chevalier & Clegg 1985; Heckman et al. 1990; Cicone et al. 2016). An alternate
+scenario where radiation pressure drives the outflow may also play a meaningful role (Murray et al. 2005; Thompson
+et al. 2015). However, for this to be the primary driver, a ratio of outflow momentum rate to the radiation momentum
+(
+˙
+Moutvout
+Lbol/c ) near unity would be expected (Murray et al. 2005; Davies et al. 2019), whereas for most of the star-forming
+galaxies this ratio is ∼ 0.1 − 0.5 (F19).
+A useful distinction between the various AGN outflow models is the relation between the kinetic properties of the
+outflow and their host AGN. Specifically, the ratio of kinetic power (Pk = 0.5 ˙Moutv2
+out) to the AGN luminosity LAGN
+in the energy-driven scenario is around 0.05 or greater (King et al. 2011; Costa et al. 2014; King & Pounds 2015).
+However, in momentum-driven models, the wind is less efficient at removing material from the inner regions of the
+galaxy, and a lower fraction of the AGN luminosity is transferred to the outflow, with Pk/LAGN values typically
+below ∼ 0.1% (Costa et al. 2014; King & Pounds 2015; F19). Additionally, radiation-pressure models show power
+fractions up to ∼ 1% or even superlinear scaling between the kinetic power and AGN luminosity (Ishibashi et al.
+2018). Typically, models favor the energy-driven mechanism for observations of large scale outflows, largely because
+the influence of the momentum-driven outflows is expected to be confined to the inner 0.1-1 kpc regime (King et al.
+2011; King & Pounds 2015).
+
+TS
+3.0
+5
+2.5
+4
+3
+2.0
++
+2
+1.5
+1
+1.0
+-13
+-12
+-11
+-10
+6-
+log(Flux [ph cm-2 s-1])TS
+0.0
+3.0
+-0.2
+2.5
+-0.4
+2.0
+-0.6
+1.5
+-0.8
+1.0
+-1.0
+-12
+-10
+log(Flux [ph cm-2 s-1])10
+McDaniel et al.
+Figure 5. Left: Distribution of the benchmark sample in the Pk −LAGN plane. The shaded area is the region corresponding to
+the energy-driven regime above the Pk/LAGN = 5% line. The shaded region contains 11 of the outflows, while the remaining 18
+fall into the Pk/LAGN < 5% region. Points with star markers are the H ii galaxies, while the triangles represent AGN galaxies.
+Colors correspond to the log of the AGN contribution to the bolometric luminosity (αbol = LAGN/Lbol). Right: Stacked TS
+array for the galaxies in the energy-driven (i.e. Pk/LAGN > 5%) regime. The max TS is 25.8 and the best-fit flux and index
+are 2.5+1.4
+−1.3 × 10−11 ph cm−2 s−1 and Γ = 2.0+0.3
+−0.3, respectively.
+Here, we explore whether there is any connection between the adopted driving mechanism and the observed gamma-
+ray emission. To do this, we separate the galaxies in our sample at the 5% value for the ratio of the outflow kinetic
+power to the AGN luminosity, roughly grouping the sample into galaxies that fall into the energy-driven regime from
+those that do not (i.e. they are more consistent with momentum-driven or radiation-pressure models). In the left
+panel of Figure 5, we show the distribution of our sample in the Pk − LAGN space along with the 5% line. In the right
+panel of Figure 5, we show the stacked TS profile for the subsample of energy-driven outflows, which yields a max TS
+of 25.8 at a flux and index of 2.5+1.4
+−1.3 × 10−11 ph cm−2 s−1 and Γ = 2.0+0.3
+−0.3, respectively. On the other hand, in the
+non-energy-driven regime, the maximum TS value is only TS = 3.6. Thus, we see that any signal from our sample
+coincides with the energy-driven subset and even slightly improves upon the signal of the full benchmark sample.
+Since the production of gamma rays from molecular outflows relies on cosmic ray interactions in the ISM, it appears
+consistent that the signal would most coincide with energy-driven outflows. In this paradigm, the outward expanding
+gas propagates more quickly and imparts greater momentum to the ISM, in comparison to momentum-driven outflows
+where most of the energy is lost in cooling processes within ∼ 1 kpc scales from the launched winds.
+As can be seen in Figure 5, the subsets created by the Pk/LAGN = 5% division also subdivide the sample into
+groups containing either mostly H ii or mostly AGN galaxies. For comparison, we compute the signal from the explicit
+subgrouping based on H ii or AGN classification of the galaxy. We find that the subset of only H ii galaxies has TS =
+22.45, while the subset of only AGN galaxies have TS = 6.65.
+4.6. Gamma-ray Luminosity Scaling Relations
+In the following section, we investigate the scaling relationship between the gamma-ray luminosity and the properties
+of the outflow sample. As a recent example, Ajello et al. (2021) found that the gamma-ray emission from ultra-fast
+outflows scales with both the bolometric luminosity of the host and the kinetic power of the outflow. In star-forming
+galaxies, strong correlations exist with radio and IR luminosities (Ackermann et al. 2012; Ajello et al. 2020). For our
+approach, we assume a simple log-linear relation of the form:
+log10
+�
+Lγ
+ergs/s
+�
+= β + α log10
+� X
+X0
+�
+,
+(2)
+
+log(αbol)
+45
+44
+D
+-1
+43
+log(Pk [ergs s
+42
+-2
+41
+/LAGN
+A
+40
+-3
+39
+38.
+40
+42
+44
+46
+log(LAGN [ergs s-1])TS
+25
+3.0
+Photon Index 
+20
+2.5
+15
+2.0
+10
+1.5
+5
+1.0
+0
+-13
+-12
+-11
+-10
+-9
+log(Flux [ph cm-2 s-1j)11
+where X is some parameter of interest normalized to X0. For each target, we convert the flux-index plane to α − β
+space using the known distance and adopting the best-fit photon index found in the stacked flux-index TS profile
+(i.e. Γ = 2, see Figure 2). We then combine the individual α − β TS profiles to obtain the stacked TS profile in
+the α − β plane. We investigated possible trends with a number of different properties of the host galaxy and the
+outflow itself. F19 provides several characteristics of the host galaxies and the outflows, either aggregated from the
+literature or (in the case of the outflow parameters in their archival ALMA outflows) calculated from the data directly.
+We explored several parameters of interest using the relation above (particularly, the AGN bolometric luminosity, the
+outflow kinetic power, and the mass outflow rate); however, in most cases the relation found was not significant and/or
+provided a lower TS than the simple flux stacking shown in Figure 2. Of the parameters considered, the IR luminosity
+provided the strongest correlation and the only one showing improvement over the benchmark flux-index TS of 22.8
+(with the exception of the AGN corrected SFR, see the end of section 4.6.2).
+4.6.1. The Lγ − LIR Correlation
+From the various relations explored, the strongest correlation found was between the gamma-ray emission and the
+infrared luminosity, stated explicitly as:
+log10
+�
+Lγ
+ergs/s
+�
+= β + α log10
+�
+LIR
+1010L⊙
+�
+.
+(3)
+For this relation, we find best fit values of α = 1.36+0.08
+−0.12 and β = 38.7+0.16
+−0.20 with a TS = 25.9, a ∆TS = 3.1 improvement
+over the flux-index stacking. This suggests that there is a significant relationship between the gamma-ray and infrared
+luminosities for this sample. The resulting TS profiles in the α—β space for the benchmark and scientific control
+samples are shown in the left and right panels of Figure 6. Numerous previous studies have established the connection
+between a galaxy’s infrared and gamma-ray luminosities (Ackermann et al. 2012; Ajello et al. 2020). The standard
+interpretation for this is that both emission types can be traced to star-formation activity. The infrared is a result
+of the UV light of massive stars being absorbed and re-emitted by the interstellar dust (Lonsdale Persson & Helou
+1987; Buat & Xu 1996), whereas the gamma rays are produced from cosmic rays accelerated by the core collapse
+supernovae of massive stars. A number of star-forming galaxies have been directly detected at gamma-ray energies by
+Fermi-LAT (see e.g. Ackermann et al. 2012; Ajello et al. 2020; Kornecki et al. 2020); however, there are many more
+that have yet to be detected. In Ajello et al. (2020, hereafter A20), a stacking analysis similar to the one performed
+here was conducted on a sample of star-forming galaxies with the goal of characterizing the gamma-ray emission in
+both detected galaxies and undetected star-forming galaxies. In the following section, we employ a similar approach
+on a sample of star-forming galaxies (as a comparison to the molecular outflow sample) in order to better understand
+the role star formation plays in the gamma-ray emission of our sample vs the outflow itself.
+4.6.2. Star-forming Galaxy Comparison Sample
+Many of the galaxies in our sample have significant star formation activity. The LIR − Lγ relation has been well
+established in previous studies of star-forming galaxies (SFGs, Ackermann et al. 2012; A20). In order to compare the
+gamma-ray signal in our sample with that of the previous works, we reanalyze a subset of the SFGs studied in A20 using
+our analysis pipeline as described in Section 3. Beginning with the full sample used in that analysis, we employ the
+same catalog cross matching selection criteria as for our original sample, removing targets that are spatially coincident
+with 4FGL, BZCAT, and radio galaxy sources and removing any molecular outflows in our analysis. Furthermore, we
+limit the galaxies to those that are roughly compatible with the LIR − DL distribution of our sample. Specifically,
+we keep only galaxies with 10 Mpc < DL < 1000 Mpc and 106.5 (DL/Mpc)2 < LIR/L⊙ < 108.8 (DL/Mpc)2. This
+ultimately leaves us with a sample of 515 star-forming galaxies as a comparison sample (hereafter referred to as the
+SFG sample). The IR luminosities and distances used for the SFG sample are taken from A20. We briefly note that
+the A20 sample primarily consists of a subset of the IRAS RBGS (Sanders et al. 2003). The range of distances and
+IR luminosities used in the selection is shown as the shaded region in the left panel of Figure 8. Also shown in this
+figure are the LIR −DL values for the star-forming galaxies, our benchmark molecular outflow sample, and the control
+sample (see Section 4.2). The analysis of the SFG sample yields a total TS of 42.9, with best fit index of Γ = 2.5+0.4
+−0.2
+and flux of 6.31+1.6
+−3.7 × 10−12 ph cm−2 s−1. The TS profile for the SFG sample is shown in Figure 7.
+This analysis yields a significant detection of gamma rays from SFGs consistent with previous work (A20). However,
+it is worth considering why no signal is detected in the control sample while there is in the SFGs, since presumably
+
+12
+McDaniel et al.
+Figure 6. TS profiles in the α—β plane, characterizing the Lγ—LIR relation (see Equation 3) for the benchmark sample (left
+panel) and for the scientific control sample (right panel). Contours show the 1, 2, and 3 σ levels for 2 degrees of freedom.
+Figure 7. Stacked TS profile for the sample of star-forming galaxies. Overlaid are the 1, 2, and 3 σ contours for 2 degrees of
+freedom.
+the control sample would also produce some gamma rays from star formation. One factor is that the difference in
+the sizes of the control and the SFG samples affects the detection significance. We demonstrate this by repeatedly
+sampling a random subset of 30 galaxies from the SFG sample and computing the TS. We find that there is a roughly
+30% chance of obtaining a TS at or below the level of the control sample (TS ≲ 2). In contrast, we find a < 0.5%
+chance of obtaining a TS near the level of the benchmark sample (TS > 20). Another important consideration is that
+the flux limit of the control sample is appreciably lower than the SFGs, as can be seen in the left panel of Figure
+8 by comparing the lower edge of the blue shaded region with the distribution of SFGs (grey dots). The SFGs are
+based primarily on the flux-limited sample of the RBGS (Sanders et al. 2003) and are therefore selected for bright IR
+
+TS
+2.5
+25
+2.0
+20
+15
+α
+1.5
++
+10
+1.0
+5
+0.5 +
+0
+36
+37
+38
+39
+40
+βTS
+2.5
+5
+4
+2.0
+3
+α
+1.5
+2
+1.0
+1
+0.5
+0
+36
+37
+38
+39
+40
+βTS
+40
+3.0
+Photon Index 
+30
+2.5
+2.0
+20
+1.5
+10
+1.0
+-13
+-12
+-11
+-10
+-9
+log(Flux [ph cm-2 s-1j)13
+galaxies, whereas the control sample is selected for galaxies with a flux limit based on the benchmark sample5. A final
+consideration is that in constructing the control sample we were careful to select galaxies that do not have molecular
+outflows. While we remove known molecular outflows from the SFG sample, it is possible that this sample contains
+galaxies hosting molecular outflows that have not been detected due to lack of direct observations and analysis.
+We also analyze a number of galaxies that have been detected in gamma rays and have also been observed to contain
+molecular outflows. These include the five gamma-ray-detected outflows from the F19 sample (NGC 253, NGC 1068,
+Circinus, M 82, and NGC 2146), as well as NGC 4945 (Lenain et al. 2010; Ackermann et al. 2012; Bolatto et al.
+2021) and Arp 220 (Peng et al. 2016; A20; Perna et al. 2020). Properties of these galaxies and their outflows are
+listed in Table 2. Each of these galaxies has been analyzed following the same procedures as the SFG and benchmark
+samples (see Section 3.1). Since the detected galaxies often have larger uncertainties in log(LIR) than log(Lγ), we
+employ an orthogonal distance regression (ODR) method (Boggs & Rogers 1990). This method takes into account the
+two-dimensional uncertainties, which are not incorporated in the stacking method. The fit is evaluated using the ODR
+equivalent version of the χ2 metric. This yields best-fit values of α = 1.11+0.08
+−0.06 and β = 39.37+0.07
+−0.05 with a reduced
+χ2 of χ2/(d.o.f.) = 16.03/5 = 3.21. While the reduced χ2 value does not indicate a good fit, this is likely due to the
+uncertainties in distance which have not been accounted for here, and which range in value from ∼ 5 − 15%, and some
+intrinsic scatter is to be expected based on previous results (Ajello et al. 2020). The resulting best-fit α − β values for
+the SFG sample, the undetected molecular outflows, and the individually-detected galaxies with outflows are provided
+in Table 3. In this table, we also show the best-fit α − β values for the subsample of undetected molecular outflows
+with LIR > 1011L⊙. In Figure 9, we show the 1σ bands for the Lγ − LIR relation for the undetected and detected
+molecular outflow samples as well as the sample of SFGs. We also show the data points for the seven detected galaxies
+with molecular outflows and data points for the undetected molecular outflows stacked in bins of LIR. Additionally,
+we include the calorimetric limit wherein the cosmic rays in the galaxy lose most of their energy to pion production of
+gamma rays, assuming a conversion efficiency of supernova energy to cosmic rays of 10% (cf. Thompson et al. 2007;
+Lacki et al. 2011; Ackermann et al. 2012). The dark blue outlined region in Figure 9 shows the 1 σ band for only
+undetected galaxies in our sample that have LIR > 1011L⊙. These targets dominate the signal and are consistent with
+both the calorimetric limit and the 1σ band of the detected galaxies.
+Name
+Type
+DL
+SFR
+log LIR
+log LAGN
+αbol
+˙Mout
+log Pk
+Pk/LAGN
+qIR
+[Mpc]
+[M⊙/yr]
+[L⊙]
+[ergs/s]
+[M⊙/yr]
+[ergs/s]
+NGC 253
+H ii
+3.30
+2.8
+10.44
+≤ 40.66
+≤ 4 × 10−4
+1.4
+39.04
+≥ 0.024
+3.01
+NGC 1068
+Sy2
+13.10
+16.8
+11.27
+43.94
+0.097
+28.0
+41.30
+0.0023
+2.32
+NGC 2146
+H ii
+18.00
+11.7
+11.07
+≤ 41.09
+≤ 3 × 10−4
+5.0
+40.52
+≥ 0.27
+2.83
+M 82
+H ii
+3.70
+5.9
+10.77
+≤ 41.54
+≤ 9 × 10−4
+4.0
+40.09
+≥ 0.036
+2.62
+Circinus
+Sy2
+4.21
+0.7
+10.22
+43.57
+0.59
+1.0
+39.87
+2 × 10−4
+2.07
+NGC 4945
+Sy2
+3.80
+2.2
+10.48
+43.54
+0.26
+20.0
+41.56
+0.01
+2.48
+Arp 220
+LINER
+79.90
+134.6
+12.21
+45.08
+0.17
+100.0
+43.31
+0.017
+2.99
+Table 2. Galaxy and outflow properties for the individually detected galaxies. Luminosity distances are taken from NED, and
+the infrared luminosities (LIR) are computed from the IRAS fluxes. The SFR is computed using LIR, the AGN contribution
+to the total bolometric luminosity, and the relation of Sturm et al. (2011). The AGN contribution to the total bolometric
+luminosity is given by αbol = LAGN/Lbol. Pk is the kinetic power of the outflow, defined as Pk = 0.5 ˙Moutv2
+out. The αbol, LAGN,
+mass-loss rates, outflow velocities, and type classifications are taken from F19 for galaxies included in that study (i.e. all except
+NGC 4945 and Arp 220). LIR values are taken from A20 except for Circinus, which is taken from Kornecki et al. (2020). qIR
+is the ratio between the IR and 1.4 GHz radio fluxes (as defined in Helou et al. 1985; Ivison et al. 2010; Harrison et al. 2014)
+with radio fluxes taken from NED. Logarithmic values for LIR, LAGN, and Pk are base 10 (i.e. log10). The outflow mass-loss
+rate and velocity for NGC 4945 are taken from Bolatto et al. (2021), the AGN luminosity is from Marconi et al. (2000), and the
+classification is from Baumgartner et al. (2013). For Arp 220, the outflow mass-loss rate and velocity are from Barcos-Mu˜noz
+et al. (2018), and the classification, αbol, and AGN luminosity are from Nardini et al. (2010).
+5 We note that a more stringent flux limit (e.g. ∼3 times higher than that of Figure 8) has negligible impact on the results for the control
+or benchmark samples.
+
+14
+McDaniel et al.
+Figure 8. Left: Distribution in LIR − DL space of our benchmark sample (blue stars for H ii and magenta triangles for AGN
+galaxies), control sample (orange dots), and the SFG sample (grey dots). The shaded region shows our LIR − DL selection
+criteria. Right: 1, 2, and 3 σ α − β contours characterizing the Lγ − LIR correlation for the benchmark sample of undetected
+molecular outflows (blue), the detected outflows (orange), the SFG sample (green), and the 95% upper limits for the Control
+sample (grey). Best-fit values are shown for the SFG and molecular outflow sample as white dots.
+Γγ
+α
+β
+TSmax(α, β)
+SFGs
+2.5+0.4
+−0.2
+1.15+0.09
+−0.12
+38.73+0.10
+−0.10
+52.5
+Undetected MOs
+2.0+0.3
+−0.3
+1.36+0.08
+−0.12
+38.71+0.16
+−0.20
+25.9
+Und. MOs (LIR > 1011L⊙)
+2.0+0.3
+−0.2
+1.18+0.09
+−0.13
+39.20+0.16
+−0.25
+20.2
+Detected MOs
+2.33+0.07
+−0.06
+1.11+0.08
+−0.06
+39.37+0.07
+−0.05
+χ2
+red = 3.21
+Table 3.
+Best-fit α − β values and corresponding TS (in the α − β plane) for the different samples, following the Lγ − LIR
+relation of Equation 3. We also show the best-fit photon index (Γγ) from the flux-index stack for each sample. In the bottom
+row, we show the best-fit parameters for the gamma-ray-detected sample obtained using the χ2 metric.
+The right panel of Figure 8 shows the 1, 2, and 3 σ contours for the SFG sample, the undetected molecular outflow
+sample, and the detected outflow sample. For the control sample, we show the 95% upper limit on the β parameter
+computed using the “delta-log-likelihood” method by finding 2∆ log L = −2.71 for each α value (see e.g. Ackermann
+et al. 2014, 2015; MAGIC Collaboration et al. 2016). The contours of the undetected molecular outflow sample are
+consistent with those of the SFG comparison sample, although the undetected molecular outflow sample has a greater
+best-fit α dependence. The results for the control sample are also compatible with the undetected molecular outflow
+and SFG contours, in particular noting that the SFG contours are essentially fully enclosed up to the 3 σ level within
+the control sample upper limit region. The blue molecular outflow contours are largely contained within the grey
+control region; however, the best-fit point and most of the 1 σ contour are outside of this region, indicating that there
+may be some level of gamma-ray emission due to the presence of the outflow. Furthermore, the complete compatibility
+of the SFG contours with the control sample upper limits suggests that the SFG sample is likely comprised of galaxies
+that lack prominent molecular outflows.
+In many cases, particularly for highly star-forming galaxies, the IR luminosity of a galaxy can be considered a direct
+proxy for the SFR in a galaxy (Kennicutt 1998; Bell 2003; Kennicutt & Evans 2012). However, in some cases the
+central AGN can be a significant contributor to the total IR luminosity. We account for this by using the estimated
+AGN contribution to the total luminosity as provided in F19 by the parameter αbol = LAGN/Lbol. Making use of the
+
+13
+12
+log(LIR [Lol)
+11
+10
+Control
+9
+SFGs
+MOs-HII
+8
+MOs-AGN
+101
+102
+103
+Dt.[Mpc]2.5
+2.0
+1.5
+α
+1.0
+Und. MOs
+Det. MOs - x?
+SFGs
+0.5
+Control
+36
+37
+38
+39
+40
+β15
+Figure 9. Plot of Lγ vs LIR. Our molecular outflow sample is divided into 4 quantile bins based on LIR, shown with the black
+crosses. The abscissa is set at the mean LIR of each bin. For the lowest LIR bin we show the 95% upper limit. The grey dashed
+line is the calorimetric limit. Gamma-ray-detected galaxies known to host molecular outflows are plotted individually. We also
+show the 1 σ band for the undetected molecular outflows (blue), the SFG comparison sample (green), and the detected molecular
+outflows (orange). The dark blue contour shows the 1 σ band for the undetected molecular outflows with LIR > 1011L⊙.
+LIR is helpful in comparing our results to previous studies of gamma rays from star-forming galaxies; however, by
+accounting for the AGN contribution, we can obtain a more realistic estimate of the SFR and a better understanding
+of the role of star formation in our molecular outflow sample. We adopt the AGN-corrected star-formation rate from
+Sturm et al. (2011), which is of the form
+SFR
+�
+M⊙ yr−1�
+= (1 − α) × 10−10LIR.
+(4)
+Using the relation
+log10
+�
+Lγ
+ergs/s
+�
+= β + α log10
+�
+SFR
+M⊙ yr−1
+�
+,
+(5)
+we find α = 1.43+0.09
+−0.11 and β = 38.71+0.17
+−0.23 with a TS value of TS = 28.8. We note that the overall α − β dependence is
+compatible with the Lγ − LIR relation, though we see a slight improvement in the TS when comparing the Lγ with
+the SFR when accounting for the AGN contribution.
+5. CONCLUSIONS
+In this work, we have performed a stacked gamma-ray analysis of a sample of nearby galaxies known to host molecular
+outflows. The results of this analysis provide evidence of gamma-ray emission from this population, particularly in
+
+43
+42
+41
+40
+Calorimetric Limit
+Und. MOs
+-1T)601
+Und. MOs, LIR > 1011Lo
+Det. MOs - x?
+39
+SFGs
+NGC 1068
+NGC 2146
+Circinus
+38
+Arp 220
+NGC 253
+M 82
+NGC 4945
+37
+9.0
+9.5
+10.0
+10.5
+11.0
+11.5
+12.0
+12.5
+13.0
+log(LIR [LoJ)16
+McDaniel et al.
+contrast to the lack of signal seen in the control sample of galaxies without molecular outflows.
+In the analysis
+of only those targets in our sample that are not individually resolved, we find a detection of gamma-ray emission
+at a significance of 4.4 σ with an average photon flux for the sample of 1.3+0.7
+−0.6 × 10−11 ph cm−2 s−1 with photon
+index Γ = 2.0+0.3
+−0.2 in the 1 − 800 GeV range. The bulk of this signal can be attributed to H ii galaxies and other
+AGN galaxies consistent with an “energy-conserving” driving mechanism as indicated by high kinetic power to AGN
+luminosity ratios.
+We do not find strong evidence for direct scaling of the gamma-ray luminosity with properties intrinsic to the outflows
+themselves (e.g. outflow mass rate and kinetic power). In other words, there is no evidence that the outflow is directly
+accelerating cosmic rays. Rather, the most prominent scaling with the gamma-ray luminosity is with properties of the
+host galaxy – namely, the infrared luminosity (and in turn the related SFR). In comparison with the SFG sample,
+galaxies hosting molecular outflows tend to exhibit somewhat different Lγ −LIR properties. In the case of the detected
+outflow-hosting galaxies, the distinction is highly pronounced as this sample occupies an entirely different region of
+the Lγ − LIR plane. For the sample of undetected galaxies with molecular outflows, the distinction is not as stark.
+While the SFGs and undetected galaxies hosting outflows are mostly compatible, there is deviation in the Lγ − LIR
+scaling relation parameter α that can be seen in both the α − β contour plot (Figure 8) and the Lγ − LIR relations
+(Figure 9). In fact, as can be seen in Figure 9, the differences in these parameters result in compatibility between the
+undetected galaxies hosting outflows and several of the individually detected galaxies (especially M 82, NGC 1068,
+and Arp 220), whereas these are still outliers from the SFG band. Figure 9 also shows that the sample of gamma-ray
+detected galaxies with an outflow are on average near perfect calorimeters, in contrast to the full sample of undetected
+molecular outflows or SFGs. Although, as demonstrated in Table 3 and Figure 9, the subsample of undetected galaxies
+with molecular outflows classified as LIRGs or ULIRGs (i.e. L⊙ > 1011 or L⊙ > 1012) are also compatible with the
+calorimetric limit. Additionally, the galaxies in our sample have radio-infrared ratios (as indicated by qIR) compatible
+with typical star-forming galaxies.
+This suggests that the galaxies in our sample are not accelerating cosmic ray
+electrons to a greater extent than other star-forming galaxies and that any cosmic-ray protons present are efficiently
+converted into gamma rays, consistent with the observed calorimetry.
+In a number of galaxies, recent observational evidence has been found for star formation triggered within the outflow
+itself (Maiolino et al. 2017; Gallagher et al. 2019; Perna et al. 2020). The triggering of star formation in outflows
+is a consequence of higher density regions caused by compression of the cold gas swept up in the expanding shock.
+Within these local density enhancements, the rate of proton-proton interactions could potentially increase, which may
+in turn produce additional gamma rays. Thus, it is possible that the molecular outflow enhances a galaxy’s gamma-ray
+emission in these regions.
+In addition, the observed calorimetry of the gamma-ray-detected sample and the sample of undetected high-LIR
+galaxies suggests that galaxies hosting molecular outflows may be bright sources of high-energy neutrinos, as evidenced
+by the marginal detection of NGC 1068 by IceCube (Aartsen et al. 2020). Indeed, starburst galaxies are expected to
+accelerate protons and produce neutrinos up to high TeV and PeV energies (Tamborra et al. 2014; Yoast-Hull et al.
+2015; Peretti et al. 2020; Ha et al. 2021), and the presence of molecular outflows may play a meaningful role in the
+neutrino production given the near calorimetric nature of the detected population.
+Increasingly, it appears that molecular outflows are a common feature in galaxies, and in particular molecular
+outflows seem to be highly common in ULIRGs (Chen et al. 2010; Veilleux et al. 2013; Pereira-Santaella et al. 2018,
+2021). For instance, nearly all of the ULIRGs in the GOALS (Armus et al. 2009) and IRAS RBGS (Sanders et al.
+2003) catalogs have detected or tentative evidence of a molecular outflow. It may be the case that molecular outflows
+are a commonality in gamma-ray-emitting SFGs, particularly those detected in gamma rays at greater distances. In
+fact, several of the SFGs detected by Fermi also have well observed molecular outflows (e.g. NGC 253, NGC 1068,
+NGC 2146, NGC 4945, Circinus, M82, Arp 220). While our analysis suggests the outflow itself may not be responsible
+for the direct acceleration of cosmic rays, it may enable an environment favorable to efficient conversion of cosmic rays
+to gamma-ray emission, for example by way of enhanced star formation in the outflow.
+Future studies may be able to probe molecular outflows and their gamma-ray emission more carefully through
+increased sample sizes and more in depth studies of their outflow properties. Ongoing and planned surveys as well
+as dedicated studies continue to discover new evidence of molecular outflows in both local and more distant galaxies
+(Lutz et al. 2020; Salak et al. 2020; May et al. 2020; Stuber et al. 2021; Bolatto et al. 2021). Additionally, studies
+of more distant molecular outflows (see e.g. Stuber et al. 2021) and explorations of trends between their gamma-ray
+and infrared luminosities in conjunction with SFGs and ULIRGs at these larger redshifts can also perhaps clarify the
+
+17
+relationship between the molecular outflows, star formation, and the gamma-ray emission. The presence of gamma-ray
+emission in the molecular outflows studied in this paper sets up an intriguing path for determining to what extent the
+molecular outflow itself plays a role in the production of gamma rays, and the results here can aid in the development
+of theoretical modeling to disentangle contributions from star formation and from the molecular outflow.
+The authors acknowledge support from NASA grant 80NSSC21K1915. Clemson University is acknowledged for gen-
+erous allotment of compute time on Palmetto cluster.
+1
+2
+The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes
+that have supported both the development and the operation of the LAT as well as scientific data analysis. These
+include the National Aeronautics and Space Administration and the Department of Energy in the United States,
+the Commissariat `a l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de
+Physique Nucl´eaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale
+di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy
+Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the
+K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden.
+3
+4
+5
+6
+7
+8
+9
+10
+Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto
+Nazionale di Astrofisica in Italy and the Centre National d’´Etudes Spatiales in France. This work performed in part
+under DOE Contract DE-AC02-76SF00515.
+11
+12
+13
+This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propul-
+sion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Admin-
+istration..
+14
+15
+16
+Facilities: Fermi-LAT (Atwood et al. 2009)
+Software: astropy (Astropy Collaboration et al. 2013), Fermipy (Wood et al. 2017)
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@@ -0,0 +1,2058 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf,len=2057
+page_content='Draft version January 9, 2023  Typeset using LATEX default style in AASTeX631  Gamma-ray Emission from Galaxies Hosting Molecular Outflows  Alex McDaniel  ,1 Marco Ajello  ,1 and Chris Karwin  1  1Department of Physics and Astronomy, Clemson University, Clemson, SC, 29631  ABSTRACT  Many star-forming galaxies and those hosting active galactic nuclei (AGN) show evidence of massive  outflows of material in a variety of phases including ionized, neutral atomic, and molecular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Molecular  outflows in particular have been the focus of recent interest as they may be responsible for removing  gas from the galaxy, thereby suppressing star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  As material is ejected from the cores of  galaxies, interactions of the outflowing material with the interstellar medium can accelerate cosmic  rays and produce high-energy gamma rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In this work, we search for gamma-ray emission from a  sample of local galaxies known to host molecular outflows using data collected by the Fermi Large  Area Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We employ a stacking technique in order to search for and characterize the average  gamma-ray emission properties of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gamma-ray emission is detected from the galaxies in  our sample at the 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 σ level with a power-law photon index of Γ ≈ 2 in the 1-800 GeV energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The emission is found to correlate with tracers of star formation activity, namely the 8 − 1000 µm  infrared luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We also find that the observed signal can be predominantly attributed to H ii  galaxies hosting energy-driven outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' While we do not find evidence suggesting that the outflows  are accelerating charged particles directly, galaxies with molecular outflows may produce more gamma  rays than galaxies without outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In particular, the set consisting of gamma-ray-detected galaxies  with molecular outflows are nearly perfect calorimeters and may be future targets for searches of  high-energy neutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Keywords: Ultraluminous infrared galaxies (1735), Gamma rays (637), Molecular gas (1073), Galactic  winds (572), Galaxy winds (626), AGN host galaxies (2017)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' INTRODUCTION  The presence of galactic outflows and winds is well documented in galaxies over a wide range of distances and physical  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Whether powered by starburst activity or active galactic nuclei, these winds are able to drive large amounts of  material from their host galaxies, injecting energy into their surrounding medium (Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Galactic outflows manifest in a variety of different phases and with observational evidence  spanning a wide range of frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The sub-pc highly-ionized outflows are primarily measured by X-ray absorption  lines (Reeves et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Tombesi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gofford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Nardini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015), whereas the neutral atomic  phase is primarily measured by observations of the sodium doublet (Heckman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Rupke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Cazzoli  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Roberts-Borsani & Saintonge 2019), and the molecular phase is measured through various radio, infrared,  and optical observations (Fischer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Feruglio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Combes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Spoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Garc´ıa-Burillo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gonz´alez-Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Bolatto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stuber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Together, understanding the details of the various phases of galactic  outflows helps to shed light on galactic structure and feedback in galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Among the different outflow phases, the molecular phase is particularly interesting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For one, the molecular phase  dominates the mass of the outflowing material and extends to the largest physical scales (Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Carniani  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Garc´ıa-Burillo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Furthermore, the molecular gas driven in the wind is also the fuel for star  Corresponding author: Alex McDaniel  armcdan@clemson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='edu  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='02574v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='HE]  6 Jan 2023  ID2  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  formation, creating a direct link between the molecular outflow and star formation properties of the galaxy with  potential effects on galaxy evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Detailed studies of molecular outflows have recently gained interest due in part  to the capabilities of instruments such as Herschel in infrared (IR) or the Atacama Large Millimeter/submillimeter  Array (ALMA) and the NOrthern Extended Millimeter Array (NOEMA) at millimeter wavelengths, which allow for  several methods of detecting molecular outflows (see also Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stuber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In infrared, P  Cygni profiles of OH transitions have yielded multiple detections (Fischer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Spoon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gonz´alez-Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2017), while CO line transitions (as well as other  molecular tracers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' HCN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Aalto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012) with instruments such as ALMA, NOEMA, or the IRAM Plateau de  Bure Interferometer (PdBI) have also provided an effective method for detecting molecular outflows and characterizing  their properties (Feruglio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Combes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Garc´ıa-Burillo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Bolatto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Molecular outflows are the dominant component of the total outflow mass, have mass-loss rates on the order  of a few hundred M⊙ yr−1, and extend to scales of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 − 10 kpc with wind velocities on the order of 102 − 103 km s−1  (Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Lutz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' They are found  throughout the universe, from nearby systems out to as far as redshift of z ∼ 6 (Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Spilker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Commonly – though not exclusively – they are found associated with (ultra)-luminous infrared galaxies ((U)LIRGs)  (Pereira-Santaella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pereira-Santaella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In a recent study  by Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2019), a collection of local (z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2) molecular outflows has been compiled from the literature and  archival data in order to analyze their properties and examine the relations between them in a systematic manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  While studies of galactic outflows have primarily been limited to the energy regimes of X-rays and below, theoretical  models suggest that the interactions of the outflowing gas with the interstellar medium can create shocks in which  cosmic rays can be accelerated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The cosmic rays can then interact with the ambient material and interstellar radiation  fields to produce gamma rays through both hadronic and leptonic processes (Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Wang & Loeb  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The efficiency of cosmic-ray acceleration in outflows is predicted to be comparable to or in excess of other  acceleration sites such as supernova remnants (SNRs, Faucher-Gigu`ere & Quataert 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Nims et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Recently,  the detection of gamma rays from highly-ionized, ultra-fast outflows (UFOs) using Fermi-LAT data has been reported  (Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021), and it is possible that molecular outflows may also be observed in gamma rays (Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In fact, several of the galaxies that are known to host powerful outflows are also gamma-ray emitters with  significant detections by Fermi-LAT (Lenain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Hayashida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020), as well as by other higher-energy gamma-ray telescopes (Acero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  VERITAS Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These include some notable and particularly well-studied systems, such as M 82,  NGC 253, and NGC 1068.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In some cases, the emission from gamma-ray-detected galaxies hosting molecular outflows  exceeds that expected from Lγ − LIR relations (Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Despite the theoretical basis for gamma-ray emission from molecular outflows and the gamma-ray detection of several  galaxies hosting molecular outflows, thus far no concrete detection that can be directly attributed to the molecular  outflow exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Models of the gamma-ray emission from molecular outflows predict a relatively faint signal, which can  be difficult to distinguish from other sources of gamma-ray emission such as starburst activity (Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  It is also unclear what the interplay may be between star formation activity and the molecular outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These two  phenomena are intrinsically linked to the molecular gas of the galaxy (Feldmann 2020) - in some cases, it has even  been shown that enhanced star formation may take place within the outflow itself (Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gallagher  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Perna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The primary goal of this paper is to study the potential gamma-ray emission from a well-selected sample of galaxies  that are known to host molecular outflows and that have not yet been individually resolved by current gamma-ray  instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To do this we use ∼ 11 years of Fermi-LAT data and employ a stacking technique designed to detect  faint sources and characterize their emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We then aim to determine the origin of the gamma-ray emission and  how its properties relate to the properties of the molecular outflow and whether it can be disentangled from star-  formation—induced gamma rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The remainder of the paper is as follows: in Section 2, we describe the sample of molecular outflows, while we  describe the gamma-ray data selection and the analysis procedure in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In Section 4, we present the results of  the gamma-ray analysis and study the relationship between the gamma-ray emission and galaxy properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In Section  5, we provide a discussion of these results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Throughout this work, we adopt cosmological values of H0 = 70 km s−1  Mpc−1, ΩM = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='27 and ΩΛ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' SAMPLE SELECTION  The initial sample of molecular outflows in our analysis is taken from (Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2019), hereafter F19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In  their work, they collect a sample of 45 galaxies with evidence of molecular outflows within the local universe (z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The sample includes 31 galaxies taken from the literature with outflow properties obtained through the analysis of the  CO(1-0) and CO(2-1) emission lines using observations from either the IRAM PdBI (Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Dasyra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Garc´ıa-Burillo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Querejeta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016) or ALMA (Combes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pereira-Santaella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Salak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' An additional 10 outflows were identified  from archival ALMA CO data by the authors of F19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However, five of the 31 outflows taken from the literature and  three of those from the ALMA archival data only include upper limits on the outflow properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Also included in the  sample of F19 are four outflows observed with far-infrared transitions of OH with the Herschel/PACS spectrometer  (Gonz´alez-Alfonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  From this sample we remove a number of galaxies based on the following criteria: first, we remove the 8 non-  detections wherein only upper limit estimates were provided by F19, after which 37 outflows remain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We then proceed  to make cuts based on spatial coincidence with sources in the 4FGL (Abdollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020) by removing all galaxies  that fall within the 95% confidence radius of a 4FGL source1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This criterion removes 5 galaxies from the sample, each  of which has been directly studied and detected by Fermi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Specifically, these are NGC 2146 (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014), NGC  1068 (Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012), the Circinus Galaxy (Hayashida et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013), NGC 253, and M82 (Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Although we exclude these from the stacking of unresolved sources, they are used in the later analysis (see Section  4), and the Fermi data for these sources are analyzed following the same procedure described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 that is  applied to the benchmark sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We additionally check for spatial coincidences with known gamma-ray blazars from  the Roma-BZCAT catalog (Massaro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015) and remove bright radio galaxies included in the 3C/4C catalogs  (Bennett 1962;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pilkington & Scott 1996) or in Yuan & Wang (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For the BZCAT and radio sources, we remove  any targets that lie within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1◦ of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This value is chosen as it is roughly similar to the mean 4FGL 95%  confidence radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These criteria remove only one additional source – the radio galaxy 4C 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In all, the spatial  coincidence cuts remove 6 galaxies from our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In addition, we identify two galaxies that have nearby, extremely  bright 4FGL sources (although outside the 95% confidence radius).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Specifically, IRAS 05189-2524 is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5◦ away from  4FGL J0523.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3-2527 (classified as a binary), and IRAS 15115+0208 is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='45◦ away from 4FGL J1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2+0202, which  is associated with the flat-spectrum radio quasar PKS 1509+022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The nearby 4FGL sources contribute relatively high  counts and comprise the majority of the background within the 68% containment radius of the point-spread-function  (PSF) centered at the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To avoid any potential impacts from these nearby, bright 4FGL sources, we remove the  two targets from our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Our final benchmark sample consists of 29 galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A selection of properties of the host galaxies and the molecular  outflows are reported in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Several of these properties, such as optical classification, the AGN luminosity, and  the AGN contribution to the bolometric luminosity (αbol = LAGN/Lbol), are taken directly from F19 and references  therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Properties of the outflows such as mass-loss rates and kinetic power are derived from the line observations of  the molecular outflows reported in F19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To calculate the total 8 µm − 1000 µm IR luminosity (LIR), we use the four  IR flux bands (f12µm, f25µm, f60µm, f100µm) from the Infrared Astronomical Satellite (IRAS) Faint Source Catalog  (FSC, Moshir et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 1992) and the prescription of Sanders & Mirabel (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Luminosity distances are taken from the  NASA Extragalactic Database2 (NED).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  To summarize, the general composition of our final sample includes 8 H ii galaxies, 3 Seyfert 1 galaxies, 11 Seyfert  2 galaxies, and 7 LINERs (for simplicity, we will categorize all the LINERs and Seyferts as AGN galaxies throughout  the remainder of the text, though it should be noted that αbol is the more descriptive indicator of the role of the AGN  contribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The galaxies extend out to redshift z ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2, range in luminosity from 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5L⊙ < LIR < 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7L⊙, and  include 7 LIRGs and 15 ULIRGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  python check  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' DATA SELECTION AND ANALYSIS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Data  1 The spatial coincidence cuts are performed using the first 4FGL data release (Abdollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020) to be consistent with the point-source  modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' More recent 4FGL data releases do not detect additional galaxies from our benchmark sample, therefore the spatial coincidence  cuts are the same for the subsequent 4FGL-DR2 (Ballet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020) and 4FGL-DR3 (Fermi-LAT collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2022) data releases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2 https://ned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='ipac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='edu/cgi-bin/objsearch?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='search type=Search&refcode=2019MNRAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='483.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4586F  4  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Name  Type  DL  SFR  log LIR  log LAGN  αbol  ˙Mout  log Pk  Pk/LAGN  qIR  [Mpc]  [M⊙/yr]  [L⊙]  [ergs/s]  [M⊙/yr]  [ergs/s]  PG 0157+001  Sy1  777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='18  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='13  NGC 1266  LINER  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='25  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='36  IRAS F03158+4227  Sy2  632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='55  1500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='054  –  NGC 1377  LINER  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2 × 10−3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='53  NGC 1433  Sy2  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3 × 10−3  –  NGC 1614  H ii  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  ≤ 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0 × 10−4  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='731  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='77  NGC 1808  H ii  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  ≤ 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0 × 10−4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='095  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='82  IRAS F08572+3915  Sy2  265.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
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+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='27  NGC 6240  Sy2  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='78  267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='10  IRAS 17208-0014  H ii  189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  ≤ 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='24  176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='427  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='79  NGC 6764  LINER  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='017  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='25  IRAS 20100-4156  H ii  605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  ≤ 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0 × 10−4  1457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  ≥ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='23  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='93  IC 5063  Sy2  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='11  IRAS F20551-4250  LINER  187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='13  200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='023  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='89  IRAS 22491-1808  H ii  348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  ≤ 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='06  654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  ≥ 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='454  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='26  IRAS 23365+3604  LINER  285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='072  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 × 10−3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='73  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Galaxy and outflow properties for targets in the benchmark sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For more detail see F19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Luminosity distances  are taken from NED, and the infrared luminosities (LIR) are computed from the IRAS fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The SFR is computed using LIR,  the AGN contribution to the total bolometric luminosity, and the relation of Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The AGN contribution to the  total bolometric luminosity is given by αbol = LAGN/Lbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pk is the kinetic power of the outflow, defined as Pk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 ˙Moutv2  out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The values for αbol, LAGN, mass loss rate, and outflow velocity are taken from F19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' qIR is the ratio of IR and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 GHz radio  fluxes, as defined in Helou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (1985);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ivison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2010);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Harrison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2014), with radio fluxes taken from NED when  available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Logarithmic values for LIR, LAGN, and Pk are base 10 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' log10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The data used in this analysis was collected over 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 years by the Fermi-LAT between August 4, 2008 and Septem-  ber 10, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We use events with energies in the range 1-800 GeV binned into 8 bins per decade and a pixel size of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To reduce contamination from the Earth’s limb, we use a maximum zenith angle of 105◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We define a 10◦ × 10◦  region of interest (ROI) centered at the position of each galaxy in the sample using RA and Dec values taken from  NED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We use the standard data filters (DATA QUAL> 0 and LAT CONFIG==1) and select photons correspond-  ing to the P8R3 SOURCE V2 class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The analysis is performed using Fermipy (v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0, Wood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2017), which  utilizes the underlying Fermitools (v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The Galactic diffuse emission is modeled using the standard interstellar  emission model (gll iem v07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='fits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For the extragalactic emission and residual instrumental background we use  iso P8R3 SOURCE V2 v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='txt, and the point source emission is modeled using the 4FGL catalog (gll psc v20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='fits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In order to account for photon leakage from sources outside of the ROI due to the PSF of the detector, the model  5  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gamma-ray SED for the molecular outflow model of NGC 1068 from Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2016) (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The blue line  and band show the predicted median and 50% containment band of our sample when applying the same model scaled to the  characteristics of each source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Data points for NGC 1068 from the Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2016) analysis are shown as green crosses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  We also show in grey the Fermi-LAT broadband sensitivity for a power-law source using 10 years of Fermi data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  includes all 4FGL sources within a 15◦ × 15◦ region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The energy dispersion correction (edisp bins=-1) is enabled for  all sources except the isotropic component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stacking Analysis  While a number of galaxies hosting molecular outflows have also been observed in gamma rays by the Fermi-LAT,  it is not currently known to what extent the molecular outflow contributes to this emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In most galaxies, it is  likely that any potential molecular-outflow induced gamma-ray emission would fall under the detection threshold of  the Fermi-LAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To illustrate this, we consider the analysis of Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2016) wherein the gamma-ray emission  of an AGN-driven molecular outflow is estimated for the gamma-ray detected galaxy NGC 1068 – a relatively close  (DL = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 Mpc), bright, and particularly well-studied galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Based on models that assume typical parameter values  for LAGN and outflow characteristics of NGC 1068, as well as adopting conventions of SNR shock efficiencies for energy  injection to cosmic ray protons and electrons, their results yield flux values at the level of roughly ∼ 2 − 5 × 10−13  ergs cm−2 s−1 in the 1-800 GeV energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Making use of the Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2016) results and adopting  their model wherein the gamma-ray emission from an outflow is directly related to the kinetic power of the outflow  (Pk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 ˙Moutv2  out), we can produce a rough estimate for gamma-ray emission from our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For each outflow, we  scale the gamma-ray luminosity found in Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2016) by the kinetic power of the outflow, then calculate  the flux from using the distance to the outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This gives a median expected flux on the order of ∼ 2 − 4 × 10−14  ergs cm−2 s−1 (corresponding to a photon flux of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6 × 10−12 ph cm−2 s−1 for a power law index of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This is  illustrated in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We emphasize that the Lamastra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2016) model represents the predicted contribution from  only the molecular outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Their work finds that this is not sufficient to fully account for the gamma-ray detection of  NGC 1068 (see Figure 1), assuming the standard cosmic-ray acceleration efficiency parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Rather, a comparable  contribution from starburst activity would be required to account for the gamma-ray emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For comparison, we  also show the Fermi-LAT broadband sensitivity3 for a point source located at intermediate latitudes (ℓ = 0◦, b = 30◦)  using 10 years of Fermi-LAT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The above estimates serve as an indication that the emission from individual molecular outflows is likely below the  sensitivity of the Fermi-LAT, and therefore motivates the use of a stacking technique in order to detect emission from  the overall population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The method employed is the same as that applied successfully in a number of previous studies  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Fermi-LAT Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Paliya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For this procedure, we work  3 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='slac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='stanford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='edu/exp/glast/groups/canda/lat Performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='htm  10-11  NGC1068  (Lamastra+2016)  Fermi-LAT  10-12  E2dN/dE[ergs  10-13  10-14  NGC1068(Lamastra+2016)  Median  10-15  50%Containment  10-1  100  101  102  103  E[GeV]6  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  under the assumption that the sample population can be characterized by average quantities such as flux, luminosity,  or photon index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We begin the analysis by optimizing the model components for the ROI of each target using a  maximum likelihood fit and evaluate the significance of each source in the ROI using the TS defined by:  TS = −2 log(L0/L),  (1)  where L0 is the likelihood for the null hypothesis (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' all sources except for molecular outflow), and L is the likelihood  for the alternative hypothesis (all sources including the molecular outflow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Here, the spectral parameters of the  Galactic diffuse component (index and normalization) and the normalization of the isotropic component are left free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  We also leave free the normalizations of all 4FGL sources with TS ≥ 25 that are within 5◦ of the ROI center, as well as  sources with TS ≥ 500 and within 7◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The fitting of the molecular outflow source assumes a power-law spectral model  with the normalization and index left free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' At this stage, we also use the Fermipy function find sources to search for  new point sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The find sources function generates TS maps and identifies new sources based on peaks in the  TS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The maps are generated using a power-law spectral model ( dN  dE ∝ E−Γ) with an index of Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The minimum  separation between two point sources is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5◦, and the minimum TS for including a source in the model is set to  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  After these processing steps, we then create a bi-dimensional TS array in flux-index space for each target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The  flux-index stacking method employed here has been validated a number of previous times through simulations (see  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Paliya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020, 2021), and has been shown to be a reliable technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Underpinning this  approach is the assumption that if the gamma-ray emission in each target comes from the same emission mechanism,  the average index will be broadly representative of the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Similarly, the flux of the sample population is  assumed to be roughly concentrated around the average, which is motivated by the fact that most Fermi sources are  detected in flux near the threshold (Abdollahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Furthermore, sources with particularly high fluxes are  more likely to have already been individually detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Some other stacking analysis studies have chosen to instead  test alternative hypotheses, such as for example stacking one dimensional TS profiles as a function of only index (de  Menezes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However, we elect to follow the approach of generating the two dimensional TS profiles, which  has been both successfully employed in previous studies as well as validated through several simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  With the isotropic and galactic diffuse background models left free, we scan photon indices from 1 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3 with a  spacing of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 and total integrated photon fluxes from 10−13 to 10−9 ph cm−2 s−1 with 40 logarithmically spaced  bins over the 1-800 GeV energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This choice of energy range is consistent with that used in the most recent  application of this stacking analysis studying ultra-fast outflows (Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Since the TS is an additive  quantity, the stacked profile is merely the sum of the arrays for either the given sample or any desired sub-sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' RESULTS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stacked TS for the Benchmark Sample  In Figure 2, we show the stacked TS array for the full benchmark sample of 29 molecular outflows that have not  previously been detected by gamma-ray observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The best-fit photon flux is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6 × 10−11 ph cm−2 s−1 with  photon index Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The maximal TS value is 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8, corresponding to roughly a 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 σ detection for 2 degrees of  freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' From the benchmark sample, we check for any galaxies in the sample that may be individually detected at  a significant level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We note that none of the individual targets have significant (TS > 25) detections;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' furthermore, all  are below the 3σ level with a median TS value at the best-fit parameters of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Scientific Control Sample  In order to understand to what extent the purported signal from the benchmark sample can be attributed to the  presence of the molecular outflows, we repeat our analysis on a control sample consisting of galaxies where no molecular  outflow has been detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In compiling the sample of molecular outflows in F19, the authors analyzed ALMA archival  data for ∼ 100 galaxies in order to search for evidence of outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' As discussed earlier (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Section 2), the authors  were able to detect or even constrain outflow properties in only 10 galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For our control sample, we therefore  make use of a sub-sample of the galaxies for which no outflow was detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However, it is important to note that  most of these galaxies lack ALMA observations that are sensitive enough to detect the outflows, and non-detections  do not necessarily imply the absence of outflowing molecular gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We thus use the subset of galaxies with the most  sensitive ALMA observations that were examined by the authors of F19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The distribution of ALMA line sensitivities  7  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stacked TS profile for the benchmark sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Overlaid are the 1, 2, and 3 σ contours for 2 degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  as presented in the ALMA Science Archive4 is shown in Figure 3 along with the most sensitive observations for the  galaxies in the benchmark sample that were detected with ALMA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We note that all the galaxies selected  for our control sample of ALMA non-detections have estimated sensitivities less than ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='62 mJy beam−1, better than  for most of the detected galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We therefore treat this as a reasonable selection of galaxies lacking a prominent  molecular outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In constructing the control sample, our aim is to match the characteristics of the benchmark sample, particularly  their distributions in distance and LIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However, the control sample obtained from the ALMA archival data poorly  samples higher IR luminosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For instance, only one galaxy from the ALMA archival control sample (IRAS 07251-  0248) has an IR luminosity greater than 1012L⊙, whereas almost half our benchmark sample has IR luminosities above  this level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To address this, we searched the literature for known (U)LIRGs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' LIR ≳ 1012L⊙) for which a search for  a molecular outflow has been performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We found no evidence of molecular outflows for these galaxies reported in  the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Previous studies – particularly ones interested in the multi-phase nature of outflows – have similarly searched the  literature for evidence of the presence of various outflows in galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Such searches have identified several candidates  that lack any significant evidence of molecular outflows using a variety of detection techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Of these, we select IRAS  06259-4708N, IRAS 13156+0435N, and IRAS 19542+1110 (Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021), as well as IRAS 06035-7102, IRAS  00198-7926, and IRAS 20414-1651 (Westmoquette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Additionally, in Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2013), non-detections  of an outflow in the molecular phase using Herschel/PACS observations of the OH 119 µm line were reported for PG  2130+099, IRAS F23128-5919, IRAS F15206+3342, IRAS F13305-1739.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Finally, we also include the galaxy I Zw 1,  which has been observed to have outflows in the neutral atomic and ionized phases, though the molecular outflow  phase has not been directly constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' I Zw 1 was reported as a non-detection using CO emission lines in Cicone  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2014) and is listed as lacking evidence of a molecular outflow in Fluetsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2021) (though the properties of  the other phases were used to place limits on the molecular outflow in F19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A search for more recent studies of the  presence of molecular outflows in the systems listed above yields no definitive evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  We note that while these galaxies form one of the best control samples of ULIRGs lacking direct evidence of molecular  outflows available, it is not necessarily the case that the presence of outflowing molecular gas can be explicitly excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In fact, when searching through catalogs of local known (U)LIRGs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' in the IRAS Revised Bright Galaxy Survey  (RBGS) or Great Observatories All-sky LIRG Survey (GOALS) catalogs (Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Armus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2009)), most  candidates that have been studied tend to show some evidence of a molecular outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Furthermore, although the exact  prevalence is not known, there is increasing evidence that molecular outflows are widely ubiquitous in these systems  4 https://almascience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='nrao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='edu/aq/  TS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  20  Photon Index  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  15  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  +  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  13  12  11  10  9  log(Flux [ph cm-2 s-1j)8  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pereira-Santaella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2018, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Therefore, we caution that this subset  of the control sample should be thought of as a collection of galaxies where the molecular outflow is not prominent  enough to be detected with standard techniques, rather than claiming that they are concretely excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The control test analysis is performed following an identical procedure to the benchmark sample, including all spatial  coincidence cuts discussed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In total, this sample comprises 19 from the ALMA archival observations and  11 (U)LIRGS from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The TS array for the control is shown in the left panel of Figure 3, with a peak  value of TS = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3 at index of Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6 and 95% upper limit of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6×10−11 ph cm−2 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Given the relatively low TS for  the control sample in comparison with the results for the benchmark sample, the conclusion that the observed signal  is related to the presence of the outflow is supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Left: TS profile for control sample galaxies where no outflow has been successfully detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Right: Distribution of  estimated line sensitivities from the ALMA archive for the best observations of the molecular outflows in our benchmark sample  (orange) and those used in the scientific control sample (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Technical Control Sample  As an additional test to the scientific control sample using galaxies without detected molecular outflows, we run  a separate technical control analysis to account for systematic effects of the Fermi analysis, such as the underlying  background intensity and the effects of nearby gamma-ray sources in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This is performed in the following  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For each galaxy in our benchmark sample of galaxies hosting molecular outflows (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Table 1), we randomly  select a set of coordinates located between 1◦ − 2◦ from the galaxy coordinates and run these through the analysis  pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' As in the previous cases, a bi-dimensional TS profile is created for each set of coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We then stack  the TS profiles to obtain an estimate of the background TS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This process is repeated five times, yielding in maximum  TS values of TS = [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='04, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='86, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='67, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='86, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Figure 4 shows the TS profiles for the iterations yielding the highest  and lowest TS values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Although the fluctuations in the technical control TS can vary as high as TS ≈ 6, the generally  low TS values found in the control analysis indicate that our ROIs are well modeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Radio Emission and the Role of Jets  Another potential contribution to the gamma-ray emission may be from jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Particularly, the presence of radio jets  has been shown to be important for detecting a gamma-ray counterpart, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' in radio galaxies (Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010b) and  low-luminosity AGN (de Menezes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' One way to infer the presence of a radio jet is based on the ratio of the  8 − 1000 µm IR flux to the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 GHz monochromatic radio flux (Ivison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Harrison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Specifically,  ratio values of qIR ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 are indicative of a radio excess and the likely presence of a radio jet, whereas values of ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  are consistent with radio emission due to star-formation (Helou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ivison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Harrison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In Table 1, the qIR values for our sample are listed (see also Figure 13 of F19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Two of the galaxies in the sample  TS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  Photon Index  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  13  12  11  10  9  log(Flux [ph cm-2 s-1j)10  Control  MOs  8  6  4  2  0  100  Line Sens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' [mJy beam-1 (10 km s-1)]9  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' TS profiles for the iterations of the technical control sample with the highest maximum TS value (left) and the  lowest maximum TS value (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Note that for visualization purposes the minimum of the color scale for the right panel is set  to −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  exhibit a radio excess, however for the majority of the sample there is little evidence for the presence of radio jets  as indicated by these values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Given the relationship between radio and gamma-ray jets and the lack of evidence for  jets in our sample, we expect any gamma-ray contributions from jet emission to be minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Furthermore, the lack  of radio excess in these targets may indicate that the outflows are not accelerating large amounts of cosmic rays as  cosmic-ray electrons would produce radio emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gamma Rays in Energy or Momentum Conserving Outflows  The mechanisms by which the outflows are driven in AGN galaxies can be summarized by three theoretical paradigms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Two of the paradigms are directly related to the dynamics of the shock blast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the energy-driven case, the shock  expands in an adiabatic, energy conserving fashion due to inefficient cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the momentum-driven case, the cooling  of the shocked gas is more efficient, and the full energy of the wind is injected into the ambient medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These two  models are also often referred to as “energy-conserving” and “momentum-conserving,” respectively (King 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' King  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Faucher-Gigu`ere & Quataert 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' King & Pounds 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A third class of models for driving the outflow  invokes the radiation-pressure—driven scenario in which the outflows can be driven by the direct pressure of IR, UV,  and optical photons on the ISM (Fabian 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ishibashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For star-formation-driven outflows, the canonical  paradigm is an energy-driven scenario (Chevalier & Clegg 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Heckman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Cicone et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' An alternate  scenario where radiation pressure drives the outflow may also play a meaningful role (Murray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Thompson  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However, for this to be the primary driver, a ratio of outflow momentum rate to the radiation momentum  (  ˙  Moutvout  Lbol/c ) near unity would be expected (Murray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Davies et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019), whereas for most of the star-forming  galaxies this ratio is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 (F19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  A useful distinction between the various AGN outflow models is the relation between the kinetic properties of the  outflow and their host AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Specifically, the ratio of kinetic power (Pk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 ˙Moutv2  out) to the AGN luminosity LAGN  in the energy-driven scenario is around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='05 or greater (King et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Costa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' King & Pounds 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  However, in momentum-driven models, the wind is less efficient at removing material from the inner regions of the  galaxy, and a lower fraction of the AGN luminosity is transferred to the outflow, with Pk/LAGN values typically  below ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1% (Costa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' King & Pounds 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' F19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Additionally, radiation-pressure models show power  fractions up to ∼ 1% or even superlinear scaling between the kinetic power and AGN luminosity (Ishibashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Typically, models favor the energy-driven mechanism for observations of large scale outflows, largely because  the influence of the momentum-driven outflows is expected to be confined to the inner 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1-1 kpc regime (King et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' King & Pounds 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  TS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  4  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  +  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  13  12  11  10  6-  log(Flux [ph cm-2 s-1])TS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12  10  log(Flux [ph cm-2 s-1])10  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Left: Distribution of the benchmark sample in the Pk −LAGN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The shaded area is the region corresponding to  the energy-driven regime above the Pk/LAGN = 5% line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The shaded region contains 11 of the outflows, while the remaining 18  fall into the Pk/LAGN < 5% region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Points with star markers are the H ii galaxies, while the triangles represent AGN galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Colors correspond to the log of the AGN contribution to the bolometric luminosity (αbol = LAGN/Lbol).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Right: Stacked TS  array for the galaxies in the energy-driven (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pk/LAGN > 5%) regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The max TS is 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 and the best-fit flux and index  are 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3 × 10−11 ph cm−2 s−1 and Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Here, we explore whether there is any connection between the adopted driving mechanism and the observed gamma-  ray emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' To do this, we separate the galaxies in our sample at the 5% value for the ratio of the outflow kinetic  power to the AGN luminosity, roughly grouping the sample into galaxies that fall into the energy-driven regime from  those that do not (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' they are more consistent with momentum-driven or radiation-pressure models).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the left  panel of Figure 5, we show the distribution of our sample in the Pk − LAGN space along with the 5% line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the right  panel of Figure 5, we show the stacked TS profile for the subsample of energy-driven outflows, which yields a max TS  of 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 at a flux and index of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3 × 10−11 ph cm−2 s−1 and Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' On the other hand, in the  non-energy-driven regime, the maximum TS value is only TS = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Thus, we see that any signal from our sample  coincides with the energy-driven subset and even slightly improves upon the signal of the full benchmark sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Since the production of gamma rays from molecular outflows relies on cosmic ray interactions in the ISM, it appears  consistent that the signal would most coincide with energy-driven outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In this paradigm, the outward expanding  gas propagates more quickly and imparts greater momentum to the ISM, in comparison to momentum-driven outflows  where most of the energy is lost in cooling processes within ∼ 1 kpc scales from the launched winds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  As can be seen in Figure 5, the subsets created by the Pk/LAGN = 5% division also subdivide the sample into  groups containing either mostly H ii or mostly AGN galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For comparison, we compute the signal from the explicit  subgrouping based on H ii or AGN classification of the galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We find that the subset of only H ii galaxies has TS =  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='45, while the subset of only AGN galaxies have TS = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gamma-ray Luminosity Scaling Relations  In the following section, we investigate the scaling relationship between the gamma-ray luminosity and the properties  of the outflow sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' As a recent example, Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2021) found that the gamma-ray emission from ultra-fast  outflows scales with both the bolometric luminosity of the host and the kinetic power of the outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In star-forming  galaxies, strong correlations exist with radio and IR luminosities (Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For our  approach, we assume a simple log-linear relation of the form:  log10  �  Lγ  ergs/s  �  = β + α log10  � X  X0  �  ,  (2)  log(αbol)  45  44  D  1  43  log(Pk [ergs s  42  2  41  /LAGN  A  40  3  39  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  40  42  44  46  log(LAGN [ergs s-1])TS  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  Photon Index  20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  15  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  0  13  12  11  10  9  log(Flux [ph cm-2 s-1j)11  where X is some parameter of interest normalized to X0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For each target, we convert the flux-index plane to α − β  space using the known distance and adopting the best-fit photon index found in the stacked flux-index TS profile  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Γ = 2, see Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We then combine the individual α − β TS profiles to obtain the stacked TS profile in  the α − β plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We investigated possible trends with a number of different properties of the host galaxy and the  outflow itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' F19 provides several characteristics of the host galaxies and the outflows, either aggregated from the  literature or (in the case of the outflow parameters in their archival ALMA outflows) calculated from the data directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  We explored several parameters of interest using the relation above (particularly, the AGN bolometric luminosity, the  outflow kinetic power, and the mass outflow rate);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' however, in most cases the relation found was not significant and/or  provided a lower TS than the simple flux stacking shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Of the parameters considered, the IR luminosity  provided the strongest correlation and the only one showing improvement over the benchmark flux-index TS of 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  (with the exception of the AGN corrected SFR, see the end of section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The Lγ − LIR Correlation  From the various relations explored, the strongest correlation found was between the gamma-ray emission and the  infrared luminosity, stated explicitly as:  log10  �  Lγ  ergs/s  �  = β + α log10  �  LIR  1010L⊙  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  (3)  For this relation, we find best fit values of α = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='36+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='12 and β = 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='16  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='20 with a TS = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9, a ∆TS = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1 improvement  over the flux-index stacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This suggests that there is a significant relationship between the gamma-ray and infrared  luminosities for this sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The resulting TS profiles in the α—β space for the benchmark and scientific control  samples are shown in the left and right panels of Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Numerous previous studies have established the connection  between a galaxy’s infrared and gamma-ray luminosities (Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The standard  interpretation for this is that both emission types can be traced to star-formation activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The infrared is a result  of the UV light of massive stars being absorbed and re-emitted by the interstellar dust (Lonsdale Persson & Helou  1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Buat & Xu 1996), whereas the gamma rays are produced from cosmic rays accelerated by the core collapse  supernovae of massive stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A number of star-forming galaxies have been directly detected at gamma-ray energies by  Fermi-LAT (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Kornecki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' however, there are many more  that have yet to be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2020, hereafter A20), a stacking analysis similar to the one performed  here was conducted on a sample of star-forming galaxies with the goal of characterizing the gamma-ray emission in  both detected galaxies and undetected star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the following section, we employ a similar approach  on a sample of star-forming galaxies (as a comparison to the molecular outflow sample) in order to better understand  the role star formation plays in the gamma-ray emission of our sample vs the outflow itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Star-forming Galaxy Comparison Sample  Many of the galaxies in our sample have significant star formation activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The LIR − Lγ relation has been well  established in previous studies of star-forming galaxies (SFGs, Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In order to compare the  gamma-ray signal in our sample with that of the previous works, we reanalyze a subset of the SFGs studied in A20 using  our analysis pipeline as described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Beginning with the full sample used in that analysis, we employ the  same catalog cross matching selection criteria as for our original sample, removing targets that are spatially coincident  with 4FGL, BZCAT, and radio galaxy sources and removing any molecular outflows in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Furthermore, we  limit the galaxies to those that are roughly compatible with the LIR − DL distribution of our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Specifically,  we keep only galaxies with 10 Mpc < DL < 1000 Mpc and 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 (DL/Mpc)2 < LIR/L⊙ < 108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8 (DL/Mpc)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This  ultimately leaves us with a sample of 515 star-forming galaxies as a comparison sample (hereafter referred to as the  SFG sample).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The IR luminosities and distances used for the SFG sample are taken from A20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We briefly note that  the A20 sample primarily consists of a subset of the IRAS RBGS (Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The range of distances and  IR luminosities used in the selection is shown as the shaded region in the left panel of Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Also shown in this  figure are the LIR −DL values for the star-forming galaxies, our benchmark molecular outflow sample, and the control  sample (see Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The analysis of the SFG sample yields a total TS of 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9, with best fit index of Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  and flux of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='31+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7 × 10−12 ph cm−2 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The TS profile for the SFG sample is shown in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  This analysis yields a significant detection of gamma rays from SFGs consistent with previous work (A20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However,  it is worth considering why no signal is detected in the control sample while there is in the SFGs, since presumably  12  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' TS profiles in the α—β plane, characterizing the Lγ—LIR relation (see Equation 3) for the benchmark sample (left  panel) and for the scientific control sample (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Contours show the 1, 2, and 3 σ levels for 2 degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stacked TS profile for the sample of star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Overlaid are the 1, 2, and 3 σ contours for 2 degrees of  freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  the control sample would also produce some gamma rays from star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' One factor is that the difference in  the sizes of the control and the SFG samples affects the detection significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We demonstrate this by repeatedly  sampling a random subset of 30 galaxies from the SFG sample and computing the TS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We find that there is a roughly  30% chance of obtaining a TS at or below the level of the control sample (TS ≲ 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In contrast, we find a < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5%  chance of obtaining a TS near the level of the benchmark sample (TS > 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Another important consideration is that  the flux limit of the control sample is appreciably lower than the SFGs, as can be seen in the left panel of Figure  8 by comparing the lower edge of the blue shaded region with the distribution of SFGs (grey dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The SFGs are  based primarily on the flux-limited sample of the RBGS (Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2003) and are therefore selected for bright IR  TS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  20  15  α  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  +  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 +  0  36  37  38  39  40  βTS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  5  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  3  α  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  0  36  37  38  39  40  βTS  40  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  Photon Index  30  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  13  12  11  10  9  log(Flux [ph cm-2 s-1j)13  galaxies, whereas the control sample is selected for galaxies with a flux limit based on the benchmark sample5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A final  consideration is that in constructing the control sample we were careful to select galaxies that do not have molecular  outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' While we remove known molecular outflows from the SFG sample, it is possible that this sample contains  galaxies hosting molecular outflows that have not been detected due to lack of direct observations and analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  We also analyze a number of galaxies that have been detected in gamma rays and have also been observed to contain  molecular outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These include the five gamma-ray-detected outflows from the F19 sample (NGC 253, NGC 1068,  Circinus, M 82, and NGC 2146), as well as NGC 4945 (Lenain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Bolatto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2021) and Arp 220 (Peng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Perna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Properties of these galaxies and their outflows are  listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Each of these galaxies has been analyzed following the same procedures as the SFG and benchmark  samples (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Since the detected galaxies often have larger uncertainties in log(LIR) than log(Lγ), we  employ an orthogonal distance regression (ODR) method (Boggs & Rogers 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This method takes into account the  two-dimensional uncertainties, which are not incorporated in the stacking method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The fit is evaluated using the ODR  equivalent version of the χ2 metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This yields best-fit values of α = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='06 and β = 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='37+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='05 with a reduced  χ2 of χ2/(d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=') = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='03/5 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' While the reduced χ2 value does not indicate a good fit, this is likely due to the  uncertainties in distance which have not been accounted for here, and which range in value from ∼ 5 − 15%, and some  intrinsic scatter is to be expected based on previous results (Ajello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The resulting best-fit α − β values for  the SFG sample, the undetected molecular outflows, and the individually-detected galaxies with outflows are provided  in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In this table, we also show the best-fit α − β values for the subsample of undetected molecular outflows  with LIR > 1011L⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In Figure 9, we show the 1σ bands for the Lγ − LIR relation for the undetected and detected  molecular outflow samples as well as the sample of SFGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We also show the data points for the seven detected galaxies  with molecular outflows and data points for the undetected molecular outflows stacked in bins of LIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Additionally,  we include the calorimetric limit wherein the cosmic rays in the galaxy lose most of their energy to pion production of  gamma rays, assuming a conversion efficiency of supernova energy to cosmic rays of 10% (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Thompson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Lacki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ackermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The dark blue outlined region in Figure 9 shows the 1 σ band for only  undetected galaxies in our sample that have LIR > 1011L⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These targets dominate the signal and are consistent with  both the calorimetric limit and the 1σ band of the detected galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Name  Type  DL  SFR  log LIR  log LAGN  αbol  ˙Mout  log Pk  Pk/LAGN  qIR  [Mpc]  [M⊙/yr]  [L⊙]  [ergs/s]  [M⊙/yr]  [ergs/s]  NGC 253  H ii  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='30  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='44  ≤ 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='66  ≤ 4 × 10−4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='04  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='024  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='01  NGC 1068  Sy2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='10  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='27  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='097  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0023  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='32  NGC 2146  H ii  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='00  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='07  ≤ 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='09  ≤ 3 × 10−4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='52  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='27  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='83  M 82  H ii  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='70  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='77  ≤ 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='54  ≤ 9 × 10−4  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='09  ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='036  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='62  Circinus  Sy2  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='22  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='59  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='87  2 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='07  NGC 4945  Sy2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='48  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='26  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='48  Arp 220  LINER  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='90  134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='21  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='17  100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='017  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='99  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Galaxy and outflow properties for the individually detected galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Luminosity distances are taken from NED, and  the infrared luminosities (LIR) are computed from the IRAS fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The SFR is computed using LIR, the AGN contribution  to the total bolometric luminosity, and the relation of Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The AGN contribution to the total bolometric  luminosity is given by αbol = LAGN/Lbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pk is the kinetic power of the outflow, defined as Pk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5 ˙Moutv2  out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The αbol, LAGN,  mass-loss rates, outflow velocities, and type classifications are taken from F19 for galaxies included in that study (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' all except  NGC 4945 and Arp 220).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' LIR values are taken from A20 except for Circinus, which is taken from Kornecki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' qIR  is the ratio between the IR and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 GHz radio fluxes (as defined in Helou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ivison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Harrison et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014)  with radio fluxes taken from NED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Logarithmic values for LIR, LAGN, and Pk are base 10 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' log10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The outflow mass-loss  rate and velocity for NGC 4945 are taken from Bolatto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2021), the AGN luminosity is from Marconi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2000), and the  classification is from Baumgartner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For Arp 220, the outflow mass-loss rate and velocity are from Barcos-Mu˜noz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2018), and the classification, αbol, and AGN luminosity are from Nardini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  5 We note that a more stringent flux limit (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' ∼3 times higher than that of Figure 8) has negligible impact on the results for the control  or benchmark samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  14  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Left: Distribution in LIR − DL space of our benchmark sample (blue stars for H ii and magenta triangles for AGN  galaxies), control sample (orange dots), and the SFG sample (grey dots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The shaded region shows our LIR − DL selection  criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Right: 1, 2, and 3 σ α − β contours characterizing the Lγ − LIR correlation for the benchmark sample of undetected  molecular outflows (blue), the detected outflows (orange), the SFG sample (green), and the 95% upper limits for the Control  sample (grey).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Best-fit values are shown for the SFG and molecular outflow sample as white dots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Γγ  α  β  TSmax(α, β)  SFGs  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='15+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='12  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='73+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='10  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='10  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  Undetected MOs  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='36+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='12  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='71+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='16  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='20  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='9  Und.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MOs (LIR > 1011L⊙)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='18+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='13  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='20+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='16  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='25  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2  Detected MOs  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='33+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='08  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='06  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='37+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='07  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='05  χ2  red = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='21  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Best-fit α − β values and corresponding TS (in the α − β plane) for the different samples, following the Lγ − LIR  relation of Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We also show the best-fit photon index (Γγ) from the flux-index stack for each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the bottom  row, we show the best-fit parameters for the gamma-ray-detected sample obtained using the χ2 metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The right panel of Figure 8 shows the 1, 2, and 3 σ contours for the SFG sample, the undetected molecular outflow  sample, and the detected outflow sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For the control sample, we show the 95% upper limit on the β parameter  computed using the “delta-log-likelihood” method by finding 2∆ log L = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='71 for each α value (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ackermann  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MAGIC Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The contours of the undetected molecular outflow sample are  consistent with those of the SFG comparison sample, although the undetected molecular outflow sample has a greater  best-fit α dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The results for the control sample are also compatible with the undetected molecular outflow  and SFG contours, in particular noting that the SFG contours are essentially fully enclosed up to the 3 σ level within  the control sample upper limit region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The blue molecular outflow contours are largely contained within the grey  control region;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' however, the best-fit point and most of the 1 σ contour are outside of this region, indicating that there  may be some level of gamma-ray emission due to the presence of the outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Furthermore, the complete compatibility  of the SFG contours with the control sample upper limits suggests that the SFG sample is likely comprised of galaxies  that lack prominent molecular outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In many cases, particularly for highly star-forming galaxies, the IR luminosity of a galaxy can be considered a direct  proxy for the SFR in a galaxy (Kennicutt 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Bell 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Kennicutt & Evans 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' However, in some cases the  central AGN can be a significant contributor to the total IR luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We account for this by using the estimated  AGN contribution to the total luminosity as provided in F19 by the parameter αbol = LAGN/Lbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Making use of the  13  12  log(LIR [Lol)  11  10  Control  9  SFGs  MOs-HII  8  MOs-AGN  101  102  103  Dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' [Mpc]2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  α  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  Und.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MOs  Det.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MOs - x?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  SFGs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  Control  36  37  38  39  40  β15  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Plot of Lγ vs LIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Our molecular outflow sample is divided into 4 quantile bins based on LIR, shown with the black  crosses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The abscissa is set at the mean LIR of each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For the lowest LIR bin we show the 95% upper limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The grey dashed  line is the calorimetric limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gamma-ray-detected galaxies known to host molecular outflows are plotted individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We also  show the 1 σ band for the undetected molecular outflows (blue), the SFG comparison sample (green), and the detected molecular  outflows (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The dark blue contour shows the 1 σ band for the undetected molecular outflows with LIR > 1011L⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  LIR is helpful in comparing our results to previous studies of gamma rays from star-forming galaxies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' however, by  accounting for the AGN contribution, we can obtain a more realistic estimate of the SFR and a better understanding  of the role of star formation in our molecular outflow sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We adopt the AGN-corrected star-formation rate from  Sturm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' (2011), which is of the form  SFR  �  M⊙ yr−1�  = (1 − α) × 10−10LIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  (4)  Using the relation  log10  �  Lγ  ergs/s  �  = β + α log10  �  SFR  M⊙ yr−1  �  ,  (5)  we find α = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='43+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='09  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='11 and β = 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='71+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='17  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='23 with a TS value of TS = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' We note that the overall α − β dependence is  compatible with the Lγ − LIR relation, though we see a slight improvement in the TS when comparing the Lγ with  the SFR when accounting for the AGN contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' CONCLUSIONS  In this work, we have performed a stacked gamma-ray analysis of a sample of nearby galaxies known to host molecular  outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The results of this analysis provide evidence of gamma-ray emission from this population, particularly in  43  42  41  40  Calorimetric Limit  Und.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MOs  1T)601  Und.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MOs, LIR > 1011Lo  Det.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' MOs - x?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  39  SFGs  NGC 1068  NGC 2146  Circinus  38  Arp 220  NGC 253  M 82  NGC 4945  37  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='5  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0  log(LIR [LoJ)16  McDaniel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  contrast to the lack of signal seen in the control sample of galaxies without molecular outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In the analysis  of only those targets in our sample that are not individually resolved, we find a detection of gamma-ray emission  at a significance of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='4 σ with an average photon flux for the sample of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='7  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='6 × 10−11 ph cm−2 s−1 with photon  index Γ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='0+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='2 in the 1 − 800 GeV range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The bulk of this signal can be attributed to H ii galaxies and other  AGN galaxies consistent with an “energy-conserving” driving mechanism as indicated by high kinetic power to AGN  luminosity ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  We do not find strong evidence for direct scaling of the gamma-ray luminosity with properties intrinsic to the outflows  themselves (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' outflow mass rate and kinetic power).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In other words, there is no evidence that the outflow is directly  accelerating cosmic rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Rather, the most prominent scaling with the gamma-ray luminosity is with properties of the  host galaxy – namely, the infrared luminosity (and in turn the related SFR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In comparison with the SFG sample,  galaxies hosting molecular outflows tend to exhibit somewhat different Lγ −LIR properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In the case of the detected  outflow-hosting galaxies, the distinction is highly pronounced as this sample occupies an entirely different region of  the Lγ − LIR plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For the sample of undetected galaxies with molecular outflows, the distinction is not as stark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  While the SFGs and undetected galaxies hosting outflows are mostly compatible, there is deviation in the Lγ − LIR  scaling relation parameter α that can be seen in both the α − β contour plot (Figure 8) and the Lγ − LIR relations  (Figure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In fact, as can be seen in Figure 9, the differences in these parameters result in compatibility between the  undetected galaxies hosting outflows and several of the individually detected galaxies (especially M 82, NGC 1068,  and Arp 220), whereas these are still outliers from the SFG band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Figure 9 also shows that the sample of gamma-ray  detected galaxies with an outflow are on average near perfect calorimeters, in contrast to the full sample of undetected  molecular outflows or SFGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Although, as demonstrated in Table 3 and Figure 9, the subsample of undetected galaxies  with molecular outflows classified as LIRGs or ULIRGs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' L⊙ > 1011 or L⊙ > 1012) are also compatible with the  calorimetric limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Additionally, the galaxies in our sample have radio-infrared ratios (as indicated by qIR) compatible  with typical star-forming galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  This suggests that the galaxies in our sample are not accelerating cosmic ray  electrons to a greater extent than other star-forming galaxies and that any cosmic-ray protons present are efficiently  converted into gamma rays, consistent with the observed calorimetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In a number of galaxies, recent observational evidence has been found for star formation triggered within the outflow  itself (Maiolino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Gallagher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Perna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The triggering of star formation in outflows  is a consequence of higher density regions caused by compression of the cold gas swept up in the expanding shock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Within these local density enhancements, the rate of proton-proton interactions could potentially increase, which may  in turn produce additional gamma rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Thus, it is possible that the molecular outflow enhances a galaxy’s gamma-ray  emission in these regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  In addition, the observed calorimetry of the gamma-ray-detected sample and the sample of undetected high-LIR  galaxies suggests that galaxies hosting molecular outflows may be bright sources of high-energy neutrinos, as evidenced  by the marginal detection of NGC 1068 by IceCube (Aartsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Indeed, starburst galaxies are expected to  accelerate protons and produce neutrinos up to high TeV and PeV energies (Tamborra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Yoast-Hull et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Peretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021), and the presence of molecular outflows may play a meaningful role in the  neutrino production given the near calorimetric nature of the detected population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Increasingly, it appears that molecular outflows are a common feature in galaxies, and in particular molecular  outflows seem to be highly common in ULIRGs (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Veilleux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Pereira-Santaella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2018,  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' For instance, nearly all of the ULIRGs in the GOALS (Armus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2009) and IRAS RBGS (Sanders et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  2003) catalogs have detected or tentative evidence of a molecular outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' It may be the case that molecular outflows  are a commonality in gamma-ray-emitting SFGs, particularly those detected in gamma rays at greater distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' In  fact, several of the SFGs detected by Fermi also have well observed molecular outflows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' NGC 253, NGC 1068,  NGC 2146, NGC 4945, Circinus, M82, Arp 220).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' While our analysis suggests the outflow itself may not be responsible  for the direct acceleration of cosmic rays, it may enable an environment favorable to efficient conversion of cosmic rays  to gamma-ray emission, for example by way of enhanced star formation in the outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  Future studies may be able to probe molecular outflows and their gamma-ray emission more carefully through  increased sample sizes and more in depth studies of their outflow properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Ongoing and planned surveys as well  as dedicated studies continue to discover new evidence of molecular outflows in both local and more distant galaxies  (Lutz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Salak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' May et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stuber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Bolatto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Additionally, studies  of more distant molecular outflows (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Stuber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2021) and explorations of trends between their gamma-ray  and infrared luminosities in conjunction with SFGs and ULIRGs at these larger redshifts can also perhaps clarify the  17  relationship between the molecular outflows, star formation, and the gamma-ray emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' The presence of gamma-ray  emission in the molecular outflows studied in this paper sets up an intriguing path for determining to what extent the  molecular outflow itself plays a role in the production of gamma rays, and the results here can aid in the development  of theoretical modeling to disentangle contributions from star formation and from the molecular outflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  The authors acknowledge support from NASA grant 80NSSC21K1915.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Clemson University is acknowledged for gen-  erous allotment of compute time on Palmetto cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  1  2  The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes  that have supported both the development and the operation of the LAT as well as scientific data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' These  include the National Aeronautics and Space Administration and the Department of Energy in the United States,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  the Commissariat `a l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de  Physique Nucl´eaire et de Physique des Particules in France,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' the Agenzia Spaziale Italiana and the Istituto Nazionale  di Fisica Nucleare in Italy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' the Ministry of Education,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Culture,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Sports,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Science and Technology (MEXT),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' High Energy  Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' and the  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  3  4  5  6  7  8  9  10  Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto  Nazionale di Astrofisica in Italy and the Centre National d’´Etudes Spatiales in France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' This work performed in part  under DOE Contract DE-AC02-76SF00515.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='  11  12  13  This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propul-  sion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Admin-  istration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='.  14  15  16  Facilities: Fermi-LAT (Atwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content=' 2009)  Software: astropy (Astropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
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+page_content=', Sturm, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
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+page_content='1088/0004-637X/776/1/27  VERITAS Collaboration, Acciari, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
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+page_content='1038/nature08557  Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
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+page_content=' 2016, Nature Physics, 12, 1116,  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
+page_content='1038/nphys3837  Westmoquette, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/uNE0T4oBgHgl3EQfsAG-/content/2301.02574v1.pdf'}
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+page_content='之江实验室' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='编辑' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='讨论1' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='上传视频' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='事业单位性质的新型研发机构' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='一分钟了解之江实验室' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='00:50' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='创新策源地 探访浙江省实验室 之江实验室：在智能计算的赛道上奔跑' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='03:38' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='智盘智慧食堂-之江实验室' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='01:05' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='之江实验室重大科研成果发布' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='01:50' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='之江实验室的“之江天枢”再升级 从停车管理到航空航天都能用到' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='01:56' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='收藏24' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='49' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='之江实验室（Zhejiang Lab），成立于2017年9月，坐落于杭州城西科创大走廊核心地带，是由浙江省人民政府主导举办、浙江大学等院校支撑、企业参与的事业单位性质的新型研发机构，是浙江深入实施创新驱动发展战略、探索新型举国体制浙江路径的重大科技创新平台  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2020年7月，之江实验室获批牵头建设智能科学与技术浙江省实验室。2021年6月，之江实验室纳入国家实验室体系  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='之江实验室以“打造国家战略科技力量”为使命，主攻智能感知、人工智能、智能计算、智能网络和智能系统五大科研方向，重点开展前沿基础研究、关键技术攻关和重大装备系统研发，致力于建设国际一流的智能感知研究与实验中心、国际一流的人工智能创新中心、国际一流的智能科学与技术研究中心和全球领先的智能计算基础研究与创新高地  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='中文名之江实验室外文名Zhejiang Lab成立时间2017年9月6日 机构地址杭州市余杭区中泰街道科创大道 主管部门浙江省人民政府 党委书记佟桂莉 主    任王坚 机构类型事业单位性质的新型研发机构 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='目录' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='1 研究方向' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2 发展历史' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='3 体系架构' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='4 科研条件' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='5 科研成就' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='▪ 学术期刊' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='▪ 荣誉表彰' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='6 机构领导' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='▪ 管理团队' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='▪ 学术咨询委员会' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='研究方向编辑 播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='该实验室以人工智能与网络信息为主要研究方向，开展重大前沿基础研究和关键技术攻关，推进前沿基础研究和应用技术研究的有机互动和深度融合  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='之江实验室瞄准国家实验室布局领域以及国家实施重大科技专项的重点领域，立足浙江现有科研基础与优势，聚焦网络信息技术前沿，以重大科技任务攻关和大型科技基础设施建设为主线，以大数据和云计算为基础，以泛智能、强实时、高安全为抓手，以未来网络计算和系统、泛化人工智能、泛在信息安全、无障感知互联、智能制造技术为方向，开展重大前沿基础研究和关键技术攻关，推进前沿基础研究和应用技术研究的有机互动和深度融合。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='《浙江省人民政府关于成立之江实验室的通知》要求省级有关部门和各市、县（市、区）政府积极支持之江实验室建设，做好政策配套、建设保障和创新资源集聚等工作。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='发展历史编辑 播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2017年8月，为认真贯彻落实习近平总书记科技创新思想，深入实施创新驱动发展战略，以科技创新为核心带动全面创新，加快推进网络信息国家实验室创建工作，积极探索一条从人才强、科技强到产业强、经济强、国家强的发展新路径，浙江省人民政府决定成立之江实验室  。之江实验室是开放协同、混合所有制的新型科研机构，按“一体、双核、多点”的架构组建，即建立以省政府、浙江大学、阿里巴巴集团共同出资成立的之江实验室为一体，以浙江大学、阿里巴巴集团为双核，以国内外高校院所、央企民企优质创新资源为多点的组织架构。将以国家目标和战略需求为导向，打造一批世界一流的基础学科群，整合一批重大科学基础设施，汇聚一批全球顶尖的研发团队，取得一批具有影响力的重大共性技术成果，支撑具有国际竞争力的创新型产业集群发展，积极争创网络信息国家实验室。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2017年9月6日上午，开放协同、混合所有制的新型科研机构——之江实验室在杭州未来科技城“人工智能小镇”正式挂牌成立。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年3月31日，由国内外院士、顶尖科学家等32名委员组成的之江实验室第一届学术咨询委员会正式成立并召开第一次会议。路甬祥院士担任首届咨询委员会主任。一批具有重要影响力的学术“大拿”将以战略科学家的眼界、求真务实的科学态度为实验室的未来发展谋划思路、指路引航。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年5月9日，之江实验室第一届理事会第二次会议在杭州召开。浙江省省长、之江实验室理事长袁家军在会上提出“以无我境界全力推进之江实验室建设，打造科技创新旗舰、数字浙江平台”，为实验室的发展奠定了主基调。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年7月12日，之江实验室举行首席科学家聘任仪式，中国工程院院士潘云鹤受聘之江实验室人工智能领域首席科学家，中国工程院院士邬江兴受聘之江实验室网络安全首席科学家  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年9月5日，之江实验室周年庆系列活动之趣味运动会暨一周年集体生日会举行，之江青年自己作词作曲的青春之歌《逐梦之江》同步发布。2018年，之江实验室不断探索内部文化建设，通过举办之江讲坛、之江沙龙等形式，增强团队凝聚力，激发创新活力。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年9月27日从浙江省科技厅联合浙江日报社组织的“创新驱动看浙江”活动中获悉，之江实验室的组织架构、建章立制及三年发展规划的编制已完成，首批5个重大攻关项目启动，分别是先进人工智能算法平台基础理论与关键技术研究、智能无障感知芯片与系统、多中心协同的生物医学智能信息技术平台、城市大脑科研与公共服务平台，以及工业互联网安全平台。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年8月至11月，之江实验室成功举办首届“之江杯全球人工智能大赛”，吸引全球39个国家和地区的4000余支队伍报名参赛。实验室将依托人工智能大赛平台，以赛引才、以赛促研、以赛兴业，引领人工智能发展潮流，打造浙江人工智能科技创新高地。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年10月17日，之江实验室理事会正式聘任浙江大学信息学部主任鲍虎军、阿里巴巴集团搜索事业部郑宇化博士为之江实验室专职副主任，浙江省副省长、之江实验室理事会副理事长王文序为两位副主任颁发聘书。浙大、阿里骨干力量的加入，将有效推动之江实验室“一体两核”深度融合。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年11月5日-10日，之江实验室携最新科研成果“以网络空间拟态防御技术理论为基础的成套设备和系统”亮相世界互联网大会，面向全世界展示了实验室成立一年多以来的建设进展与成果。实验室与阿里云、浙江中控共建的supET工业互联网平台项目入选大会15项全球领先科技成果。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年12月28日，之江实验室园区一期工程奠基动工。省委书记车俊、省长袁家军出席奠基活动。占地1358亩的实验室园区将在未来科技城南湖拔地而起，按照“智能、生态”的理念，打造世界一流的基础研究中心和“未来城市样本”。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年，之江实验室在工业互联网、人工智能芯片等领域布局启动了9大自主科研项目。这批重大项目的实施，标志着之江实验室在科研发展上迈出了关键的一步。经过科研人员的不懈努力，部分项目的科研成果已初步显现。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2018年，之江实验室共举办11期“之江讲坛”，中国工程院院士潘云鹤、方滨兴、杨小牛、吾守尔·斯拉木、图灵奖得主等顶级学术大咖分享最新研究成果，推动实验室形成浓郁的学习型文化氛围。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2019年11月2日，之江实验室牵头，联合浙江大学、阿里巴巴等多单位共同研发打造的“天枢”人工智能开源开放平台在浙江杭州正式发布。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2020年7月，之江实验室获批牵头建设智能科学与技术浙江省实验室  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2020年12月19日，从之江实验室获悉，之江实验室·AI莫干山基地正式开工建设。该基地位于湖州德清莫干山，是之江实验室的首个科研“飞地”  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2021年6月，之江实验室纳入国家实验室体系  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2022年11月6日，之江实验室发起并正式启动生物计算国际合作科学计划，携手伦敦大学、华盛顿大学、以色列理工学院等国际顶尖科研力量，共同开展生物计算创新探索研究，赋能生命健康、新材料、环境等多领域发展。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2022年11月11日，启动“杭州市新型研发机构联盟”建设。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2022年，之江实验室推出了“之江瑶光”智能计算操作系统。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2023年以来，之江实验室算力利用率增长了近50%。截至4月，在之江实验室，每天要完成超过200余项计算研发任务。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='体系架构编辑 播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='之江实验室体系架构：' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='科研条件编辑 播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='实验室选址杭州市余杭区南湖区块，位处杭州城西科创大走廊的核心区域  ，总规划用地约1358亩，秉持“人本化、生态化、数字化”建设理念，致力于打造布局合理、条件过硬、环境一流的未来社区模板和科学研究综合试验场。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='一期建设用地约613亩，分为科研办公区和生活配套区，主要包括主楼、计算与数据中心、大科学装置、实验平台、各研究院（研究中心）用楼、行政会议中心、文化设施（展厅）、食堂、体育设施、学术交流中心以及人才公寓等。一期已于2021年3月正式启用。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='二期建设规划总用地约745亩，其中科研区规划用地约577亩，主要建设内容包括数字反应堆功能区、融合创新区、未来大厦、之江讲堂、综合服务区等  。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='科研成就编辑 播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='学术期刊' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2021年11月16日，在之江实验室、美国科学促进会旗下期刊Science和Science Robotics共同主办的2021世界青年科学家峰会系列活动之“智能计算创新论坛”现场，之江实验室与美国科学促进会（AAAS）在中国杭州、美国华盛顿两地，以视频方式在线签署联合办刊协议，双方将共同创办科学伙伴期刊Intelligent Computing（《智能计算》）。之江实验室主任朱世强与《科学》系列期刊出版人比尔·莫兰代表双方签约。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='该期刊计划于2021年底前开发建设完成投审稿系统，在Science网站上搭建完成伙伴期刊网页。2022年1月开放投审稿系统，正式接收投稿。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='荣誉表彰' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2022年5月，之江实验室智能计算研究院智能超算研究中心被授予第26届“中国青年五四奖章”。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2022年5月，入选浙江省科学家精神教育基地名单。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2022年11月9日，在2022年世界互联网领先科技成果发布活动上，之江实验室的“基于高性能人工智能训练芯片的智算集群”科技成果，入选2022年世界互联网领先科技成果提名项目名单。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2023年3月，之江实验室深度参与的“FAST精细刻画活跃重复快速射电暴”入选“2022年度中国科学十大进展”，并位列第2位。 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='机构领导编辑 播报' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='管理团队' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='党委书记：佟桂莉 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='主任：王坚  ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='党委委员、副主任：袁继新' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='副主任：鲍虎军、郑宇化' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='党委副书记：赵新龙' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='纪委书记：韩常灿' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='党委委员、主任助理：李碧清、陈伟' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='党委委员、总工程师：赵志峰 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='学术咨询委员会' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='学术咨询委员会是之江实验室最高学术咨询机构，主要作用是为实验室出谋划策，指导和把握实验室科研方向，进行学术工作评估。第一届学术咨询委员会委员共33人，由国内外知名院士、科学家、特级专家组成。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='主任：路甬祥' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='副主任：潘云鹤、邬贺铨、邬江兴、吴曼青、徐惠彬' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='词条图册' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='更多图册' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='参考资料' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='1  之江实验室首个科研“飞地” AI莫干山基地开工建设-中新网   ．中新网[引用日期2020-12-20]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='2  之江实验室首批5大项目启动，将建先进人工智能算法平台   ．澎湃[引用日期2018-09-27]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='3  浙江成立之江实验室：混合所有制，将争创网络信息国家实验室   ．澎湃新闻网[引用日期2017-08-31]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='4  之江实验室挂牌成立   ．浙江在线[引用日期2017-09-14]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='5  “天枢”人工智能开源开放平台在杭州发布   ．新华社[引用日期2019-11-02]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='6  最新！余杭南湖畔 之江实验室园区打下第一桩   ．新蓝网．2019-05-10[引用日期2019-06-03]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='7  《智能计算》创刊—新闻—科学网   ．科学网．2021-11-20[引用日期2021-11-20]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='8  第26届“中国青年五四奖章”评选揭晓   ．中国政府网．2022-05-03[引用日期2022-05-05]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='9  23家入选！浙江首批科学家精神教育基地名单公布   ．微信[引用日期2022-05-28]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='10  之江实验室携手全球研究团队开展生物计算国际科学合作   ．中国新闻网[引用日期2022-11-07]' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='展开全部' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='学术论文内容来自' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
+page_content='None.    欢迎与之江实验室共成长． 《 信息技术与标准化 》 ， 2020  郑小洁.    实现国家科技发展的共建共享——"一体双核多点"之江实验室． 《 vip 》 ， 2018  朱世强.    之江实验室:志在高端突破． 《 cnki 》 ， 2018  刘娟.    之江实验室VS国家实验室、美国能源部下属国家实验室——探索新型研发机构模式． 《 cnki 》 ， 2017  刘娟.    之江实验室VS国家实验室,美国能源部下属国家实验室——探索新型研发机构模式． 《 cnki 》 ， 2017' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\zjlab\\content\\zjlab-baidu.txt'}
diff --git a/zjlab/content/zjlab-baidu.txt b/zjlab/content/zjlab-baidu.txt
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+之江实验室 
+播报
+编辑
+讨论1
+上传视频
+事业单位性质的新型研发机构
+
+一分钟了解之江实验室
+00:50
+
+创新策源地 探访浙江省实验室 之江实验室：在智能计算的赛道上奔跑
+03:38
+
+智盘智慧食堂-之江实验室
+01:05
+
+之江实验室重大科研成果发布
+01:50
+
+之江实验室的“之江天枢”再升级 从停车管理到航空航天都能用到
+01:56
+
+ 收藏24
+49
+之江实验室（Zhejiang Lab），成立于2017年9月，坐落于杭州城西科创大走廊核心地带，是由浙江省人民政府主导举办、浙江大学等院校支撑、企业参与的事业单位性质的新型研发机构，是浙江深入实施创新驱动发展战略、探索新型举国体制浙江路径的重大科技创新平台 [13] 。
+2020年7月，之江实验室获批牵头建设智能科学与技术浙江省实验室。2021年6月，之江实验室纳入国家实验室体系 [21] 。
+之江实验室以“打造国家战略科技力量”为使命，主攻智能感知、人工智能、智能计算、智能网络和智能系统五大科研方向，重点开展前沿基础研究、关键技术攻关和重大装备系统研发，致力于建设国际一流的智能感知研究与实验中心、国际一流的人工智能创新中心、国际一流的智能科学与技术研究中心和全球领先的智能计算基础研究与创新高地 [13] 。
+中文名之江实验室外文名Zhejiang Lab成立时间2017年9月6日 [4]机构地址杭州市余杭区中泰街道科创大道 [17]主管部门浙江省人民政府 [18]党委书记佟桂莉 [15]主    任王坚 [17-18]机构类型事业单位性质的新型研发机构 [13]
+目录
+1 研究方向
+2 发展历史
+3 体系架构
+4 科研条件
+5 科研成就
+▪ 学术期刊
+▪ 荣誉表彰
+6 机构领导
+▪ 管理团队
+▪ 学术咨询委员会
+研究方向编辑 播报
+该实验室以人工智能与网络信息为主要研究方向，开展重大前沿基础研究和关键技术攻关，推进前沿基础研究和应用技术研究的有机互动和深度融合 [1] 。
+之江实验室瞄准国家实验室布局领域以及国家实施重大科技专项的重点领域，立足浙江现有科研基础与优势，聚焦网络信息技术前沿，以重大科技任务攻关和大型科技基础设施建设为主线，以大数据和云计算为基础，以泛智能、强实时、高安全为抓手，以未来网络计算和系统、泛化人工智能、泛在信息安全、无障感知互联、智能制造技术为方向，开展重大前沿基础研究和关键技术攻关，推进前沿基础研究和应用技术研究的有机互动和深度融合。
+《浙江省人民政府关于成立之江实验室的通知》要求省级有关部门和各市、县（市、区）政府积极支持之江实验室建设，做好政策配套、建设保障和创新资源集聚等工作。 [3]
+发展历史编辑 播报
+2017年8月，为认真贯彻落实习近平总书记科技创新思想，深入实施创新驱动发展战略，以科技创新为核心带动全面创新，加快推进网络信息国家实验室创建工作，积极探索一条从人才强、科技强到产业强、经济强、国家强的发展新路径，浙江省人民政府决定成立之江实验室 [18] 。之江实验室是开放协同、混合所有制的新型科研机构，按“一体、双核、多点”的架构组建，即建立以省政府、浙江大学、阿里巴巴集团共同出资成立的之江实验室为一体，以浙江大学、阿里巴巴集团为双核，以国内外高校院所、央企民企优质创新资源为多点的组织架构。将以国家目标和战略需求为导向，打造一批世界一流的基础学科群，整合一批重大科学基础设施，汇聚一批全球顶尖的研发团队，取得一批具有影响力的重大共性技术成果，支撑具有国际竞争力的创新型产业集群发展，积极争创网络信息国家实验室。 [3]
+2017年9月6日上午，开放协同、混合所有制的新型科研机构——之江实验室在杭州未来科技城“人工智能小镇”正式挂牌成立。 [4]
+2018年3月31日，由国内外院士、顶尖科学家等32名委员组成的之江实验室第一届学术咨询委员会正式成立并召开第一次会议。路甬祥院士担任首届咨询委员会主任。一批具有重要影响力的学术“大拿”将以战略科学家的眼界、求真务实的科学态度为实验室的未来发展谋划思路、指路引航。
+2018年5月9日，之江实验室第一届理事会第二次会议在杭州召开。浙江省省长、之江实验室理事长袁家军在会上提出“以无我境界全力推进之江实验室建设，打造科技创新旗舰、数字浙江平台”，为实验室的发展奠定了主基调。
+2018年7月12日，之江实验室举行首席科学家聘任仪式，中国工程院院士潘云鹤受聘之江实验室人工智能领域首席科学家，中国工程院院士邬江兴受聘之江实验室网络安全首席科学家 [19] 。
+2018年9月5日，之江实验室周年庆系列活动之趣味运动会暨一周年集体生日会举行，之江青年自己作词作曲的青春之歌《逐梦之江》同步发布。2018年，之江实验室不断探索内部文化建设，通过举办之江讲坛、之江沙龙等形式，增强团队凝聚力，激发创新活力。
+2018年9月27日从浙江省科技厅联合浙江日报社组织的“创新驱动看浙江”活动中获悉，之江实验室的组织架构、建章立制及三年发展规划的编制已完成，首批5个重大攻关项目启动，分别是先进人工智能算法平台基础理论与关键技术研究、智能无障感知芯片与系统、多中心协同的生物医学智能信息技术平台、城市大脑科研与公共服务平台，以及工业互联网安全平台。 [2]
+2018年8月至11月，之江实验室成功举办首届“之江杯全球人工智能大赛”，吸引全球39个国家和地区的4000余支队伍报名参赛。实验室将依托人工智能大赛平台，以赛引才、以赛促研、以赛兴业，引领人工智能发展潮流，打造浙江人工智能科技创新高地。
+2018年10月17日，之江实验室理事会正式聘任浙江大学信息学部主任鲍虎军、阿里巴巴集团搜索事业部郑宇化博士为之江实验室专职副主任，浙江省副省长、之江实验室理事会副理事长王文序为两位副主任颁发聘书。浙大、阿里骨干力量的加入，将有效推动之江实验室“一体两核”深度融合。
+2018年11月5日-10日，之江实验室携最新科研成果“以网络空间拟态防御技术理论为基础的成套设备和系统”亮相世界互联网大会，面向全世界展示了实验室成立一年多以来的建设进展与成果。实验室与阿里云、浙江中控共建的supET工业互联网平台项目入选大会15项全球领先科技成果。
+2018年12月28日，之江实验室园区一期工程奠基动工。省委书记车俊、省长袁家军出席奠基活动。占地1358亩的实验室园区将在未来科技城南湖拔地而起，按照“智能、生态”的理念，打造世界一流的基础研究中心和“未来城市样本”。
+2018年，之江实验室在工业互联网、人工智能芯片等领域布局启动了9大自主科研项目。这批重大项目的实施，标志着之江实验室在科研发展上迈出了关键的一步。经过科研人员的不懈努力，部分项目的科研成果已初步显现。
+2018年，之江实验室共举办11期“之江讲坛”，中国工程院院士潘云鹤、方滨兴、杨小牛、吾守尔·斯拉木、图灵奖得主等顶级学术大咖分享最新研究成果，推动实验室形成浓郁的学习型文化氛围。
+2019年11月2日，之江实验室牵头，联合浙江大学、阿里巴巴等多单位共同研发打造的“天枢”人工智能开源开放平台在浙江杭州正式发布。 [5]
+2020年7月，之江实验室获批牵头建设智能科学与技术浙江省实验室 [21] 。
+2020年12月19日，从之江实验室获悉，之江实验室·AI莫干山基地正式开工建设。该基地位于湖州德清莫干山，是之江实验室的首个科研“飞地” [1] 。
+2021年6月，之江实验室纳入国家实验室体系 [21] 。
+2022年11月6日，之江实验室发起并正式启动生物计算国际合作科学计划，携手伦敦大学、华盛顿大学、以色列理工学院等国际顶尖科研力量，共同开展生物计算创新探索研究，赋能生命健康、新材料、环境等多领域发展。 [10]
+2022年11月11日，启动“杭州市新型研发机构联盟”建设。 [12]
+2022年，之江实验室推出了“之江瑶光”智能计算操作系统。
+2023年以来，之江实验室算力利用率增长了近50%。截至4月，在之江实验室，每天要完成超过200余项计算研发任务。 [14]
+体系架构编辑 播报
+之江实验室体系架构：
+科研条件编辑 播报
+实验室选址杭州市余杭区南湖区块，位处杭州城西科创大走廊的核心区域 [6] ，总规划用地约1358亩，秉持“人本化、生态化、数字化”建设理念，致力于打造布局合理、条件过硬、环境一流的未来社区模板和科学研究综合试验场。
+一期建设用地约613亩，分为科研办公区和生活配套区，主要包括主楼、计算与数据中心、大科学装置、实验平台、各研究院（研究中心）用楼、行政会议中心、文化设施（展厅）、食堂、体育设施、学术交流中心以及人才公寓等。一期已于2021年3月正式启用。
+二期建设规划总用地约745亩，其中科研区规划用地约577亩，主要建设内容包括数字反应堆功能区、融合创新区、未来大厦、之江讲堂、综合服务区等 [20] 。
+科研成就编辑 播报
+学术期刊
+2021年11月16日，在之江实验室、美国科学促进会旗下期刊Science和Science Robotics共同主办的2021世界青年科学家峰会系列活动之“智能计算创新论坛”现场，之江实验室与美国科学促进会（AAAS）在中国杭州、美国华盛顿两地，以视频方式在线签署联合办刊协议，双方将共同创办科学伙伴期刊Intelligent Computing（《智能计算》）。之江实验室主任朱世强与《科学》系列期刊出版人比尔·莫兰代表双方签约。
+该期刊计划于2021年底前开发建设完成投审稿系统，在Science网站上搭建完成伙伴期刊网页。2022年1月开放投审稿系统，正式接收投稿。 [7]
+荣誉表彰
+2022年5月，之江实验室智能计算研究院智能超算研究中心被授予第26届“中国青年五四奖章”。 [8]
+2022年5月，入选浙江省科学家精神教育基地名单。 [9]
+2022年11月9日，在2022年世界互联网领先科技成果发布活动上，之江实验室的“基于高性能人工智能训练芯片的智算集群”科技成果，入选2022年世界互联网领先科技成果提名项目名单。 [11]
+2023年3月，之江实验室深度参与的“FAST精细刻画活跃重复快速射电暴”入选“2022年度中国科学十大进展”，并位列第2位。 [14]
+机构领导编辑 播报
+管理团队
+党委书记：佟桂莉 [17]
+主任：王坚 [1] [16]
+党委委员、副主任：袁继新
+副主任：鲍虎军、郑宇化
+党委副书记：赵新龙
+纪委书记：韩常灿
+党委委员、主任助理：李碧清、陈伟
+党委委员、总工程师：赵志峰 [15]
+学术咨询委员会
+学术咨询委员会是之江实验室最高学术咨询机构，主要作用是为实验室出谋划策，指导和把握实验室科研方向，进行学术工作评估。第一届学术咨询委员会委员共33人，由国内外知名院士、科学家、特级专家组成。
+主任：路甬祥
+副主任：潘云鹤、邬贺铨、邬江兴、吴曼青、徐惠彬
+词条图册
+更多图册 
+参考资料
+1  之江实验室首个科研“飞地” AI莫干山基地开工建设-中新网   ．中新网[引用日期2020-12-20]
+2  之江实验室首批5大项目启动，将建先进人工智能算法平台   ．澎湃[引用日期2018-09-27]
+3  浙江成立之江实验室：混合所有制，将争创网络信息国家实验室   ．澎湃新闻网[引用日期2017-08-31]
+4  之江实验室挂牌成立   ．浙江在线[引用日期2017-09-14]
+5  “天枢”人工智能开源开放平台在杭州发布   ．新华社[引用日期2019-11-02]
+6  最新！余杭南湖畔 之江实验室园区打下第一桩   ．新蓝网．2019-05-10[引用日期2019-06-03]
+7  《智能计算》创刊—新闻—科学网   ．科学网．2021-11-20[引用日期2021-11-20]
+8  第26届“中国青年五四奖章”评选揭晓   ．中国政府网．2022-05-03[引用日期2022-05-05]
+9  23家入选！浙江首批科学家精神教育基地名单公布   ．微信[引用日期2022-05-28]
+10  之江实验室携手全球研究团队开展生物计算国际科学合作   ．中国新闻网[引用日期2022-11-07]
+展开全部 
+学术论文内容来自 
+ None.    欢迎与之江实验室共成长． 《 信息技术与标准化 》 ， 2020  郑小洁.    实现国家科技发展的共建共享——"一体双核多点"之江实验室． 《 vip 》 ， 2018  朱世强.    之江实验室:志在高端突破． 《 cnki 》 ， 2018  刘娟.    之江实验室VS国家实验室、美国能源部下属国家实验室——探索新型研发机构模式． 《 cnki 》 ， 2017  刘娟.    之江实验室VS国家实验室,美国能源部下属国家实验室——探索新型研发机构模式． 《 cnki 》 ， 2017
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diff --git a/zjlab/content/zjlab-fake.txt b/zjlab/content/zjlab-fake.txt
new file mode 100644
index 0000000000000000000000000000000000000000..50a4bbe2c656c195012b9fe72ed9ef8b13b46f68
--- /dev/null
+++ b/zjlab/content/zjlab-fake.txt
@@ -0,0 +1,4 @@
+之江实验室成立于2018年5月。
+2018年5月6日上午，开放协同、混合所有制的新型科研机构——之江实验室在杭州未来科技城“人工智能小镇”正式挂牌成立.
+
+2018年4月，为认真贯彻落实习近平总书记科技创新思想，深入实施创新驱动发展战略，以科技创新为核心带动全面创新，加快推进网络信息国家实验室创建工作，积极探索一条从人才强、科技强到产业强、经济强、国家强的发展新路径，浙江省人民政府决定成立之江实验室 [18] 。 之江实验室是开放协同、混合所有制的新型科研机构，按“一体、双核、多点”的架构组建，即建立以省政府、浙江大学、阿里巴巴集团共同出资成立的之江实验室为一体，以浙江大学、阿里巴巴集团为双核，以国内外高校院所、央企民企优质创新资源为多点的组织架构。
diff --git a/zjlab/content/zjlab-zhejiang-Uni.txt b/zjlab/content/zjlab-zhejiang-Uni.txt
new file mode 100644
index 0000000000000000000000000000000000000000..99b5ea65648a8b6f37f5e71c72d63cc4a01da27f
--- /dev/null
+++ b/zjlab/content/zjlab-zhejiang-Uni.txt
@@ -0,0 +1,49 @@
+之江实验室
+编辑 ：创高发布时间 ：2020-08-25浏览次数 ：3870
+实验室简介
+
+之江实验室是浙江省委、省政府贯彻落实习近平总书记科技创新思想，深入实施创新驱动发展战略的重大科技创新平台，肩负了建设创新型国家、世界科技强国进程中的浙江责任与担当。实验室由浙江省人民政府、浙江大学、阿里巴巴集团共同举办，以国家目标和战略需求为导向，以重大科技任务攻关和大型科技基础设施建设为主线，以打造国家未来战略科技力量为目标，形成一批原创性、突破性、引领性、支撑性的重大科技成果，汇聚和培养一批具有全球影响力的高层次人才，建设世界一流新型研发机构。
+
+实验室按照“一体、两核、多点”架构组建，“一体”即具有独立法人资格、实体化运行的混合所有制单位；“两核”即依托浙江大学、阿里巴巴集团，聚焦人工智能和网络信息领域，开展重大前沿基础研究和关键技术攻关；“多点”即吸纳国内外在人工智能和网络信息领域具有优势的科研力量，集聚创新资源。
+
+总体目标 
+
+01整合协同一批重大科学基础设施
+
+02汇聚一批全球顶尖的研发团队
+
+03打造一个国际一流的基础研究基地
+
+04取得一批具有影响力的重大共性技术成果
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+05支撑引领具有世界竞争力的创新型产业集群发展
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+06建成国家实验室
+
+主攻方向
+
+聚焦人工智能和网络信息两大领域，重点在智能感知、智能计算、智能网络和智能系统四大方向开展基础性、前沿性技术研究，以全球视野谋划和推动创新。
+
+主要任务
+
+重大前沿基础研究与技术攻关
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+大科学装置和科研平台建设
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+国内外科研合作与交流
+
+高层次科研人才培养
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+承担国家战略性人工智能创新项目
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+科研成果转移转化及其产业化
+
+联系我们
+
+杭州市余杭区文一西路1818号中国人工智能小镇10号楼
+
+电话：0571-56390515
+
+传真：0571-56390666
+
+网址：http://www.zhejianglab.com
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+实验室简介 / Overview
+之江实验室成立于2017年9月，坐落于杭州城西科创大走廊核心地带，是由浙江省人民政府主导举办、浙江大学等院校支撑、企业参与的事业单位性质的新型研发机构，是浙江深入实施创新驱动发展战略、探索新型举国体制浙江路径的重大科技创新平台。实验室以“打造国家战略科技力量”为使命，主攻智能感知、人工智能、智能计算、智能网络和智能系统五大科研方向，重点开展前沿基础研究、关键技术攻关和重大装备系统研发，致力于建设国际一流的智能感知研究与实验中心、国际一流的人工智能创新中心、国际一流的智能科学与技术研究中心和全球领先的智能计算基础研究与创新高地。
+
+科研概况
+/ Scientific Research Overview
+之江实验室以国家战略需求为导向，坚持“四个面向”，探索形成了以智能计算为核心，智能感知、人工智能、智能网络、智能计算和智能系统五大科研领域协同发展的科研布局，开展理论体系、技术体系、标准体系、软硬件平台、装备应用等全链路科学研究，集聚国内外顶尖科研团队和资源，建设大型科技基础设施和重大科研平台，建设开放协同的合作生态，为科学研究、数字经济、社会治理等领域提供新方法、新工具和新手段，抢占支撑未来智慧社会发展的战略高点。
+
+
+科研方向
+/ Main Research Areas
+智能计算：瞄准世界科技前沿和国家重大战略需求，研究存算一体、类脑计算、光计算、图计算、生物计算等新型计算模型和器件，研制系列智能计算机，研发智能计算操作系统、广域协同平台、图计算平台等软件系统和平台，构建智能计算数字反应堆，探索“计算+”赋能科学研究应用领域，推动科研范式变革，为数字中国的科技创新体系和产业发展体系提供先进的计算芯片、强大的计算能力、高效智能的计算平台，实现智能计算的“中国定义”。
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+人工智能：围绕创建类人智能理论体系，建立通用智能数学模型与算法理论、主动感知及计算理论、以知识理解为核心的认知计算理论、多模态智能融合计算理论及统一表征理论和模型，研究人机协同计算方法及新型混合计算架构等新型人工智能方法，突破人机增强智能、跨媒体智能、群体智能和大数据智能等方向的关键核心技术，构建类人智能知识库系统，开发人工智能算法与平台，探索建立数据和知识双轮驱动的人工智能理论和方法体系，构筑人工智能创新与应用生态，推动新一代人工智能的发展。
+
+智能感知：围绕多维感知融合、类人感知、极限感知的需求，全面研究智能感知的机理和方法，突破高性能高分辨传感器件和芯片、极限精密测量、类人智能感知、泛在智能健康感知、超高灵敏环境感知、多维数据智能融合处理等关键技术，建设感知领域跨学科、软硬协同、标测结合的多维智能感知中枢重大科技基础设施，打造世界领先的智能感知理论、技术和生态体系，引领全球智能感知创新研究和核心技术研发。
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+智能网络：围绕新型网络、宽带通信、工业互联网安全、网络器件与晶上系统等研究方向，研究并攻克智能网络基础理论、新型网络体系架构等关键科学与技术问题，重点突破全维可定义智信网络、多模态寻址路由、网络智慧共管、高速光电太赫兹通信、硅光高速互联、晶上系统集成等关键技术，建设新一代工业互联网信息安全大型科学装置，输出一批业界领先的核心技术、关键产品与解决方案，打造功能、拓扑、标识、安全等全维可定义的新型网络体系结构与平台。
+
+智能系统：面向数字经济、社会治理等经济社会发展需求，全面攻克自主无人系统、健康医疗、智能社会治理、智慧教育、金融科技、科艺融合等各类典型智能系统的关键技术和工程实现方法，研发智能系统共性关键技术与应用平台，打造广域协同、普惠泛在、随需接入的高效能智能系统，支撑智慧时代新型数字基础设施建设和战略新兴产业发展。
+
+
+人才概览
+/ Overview
+之江实验室始终坚持“人才至上”，全力构建开放创新的人才生态。截至2023年5月，人才队伍总体规模已突破4000人，其中全职员工达2200人，科研带头人260余位，研究序列人员中博士学历占比超90%，一支“领域专精、层次高端、梯队有序”的人才队伍基本形成。实验室秉持“分层分类、实战育才”的人才培养理念，依托“之江书院”统筹建设人才培育体系，重点打造“领航计划”等培养项目。实验室坚持以创新质量和实际贡献为人才评价核心导向，贯通人才发展各项通道，全方位激发人才创造活力。
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