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In two and more dimensions, specifying the local dynamics of the domain is insufficient to prescribe the domain's evolution in time.
Here, we have posed irrotational growth and no tangential movement along the boundary, which may be interpreted as the flow being generated solely by point sources of density scaling with {{formula:0f7ef575-a4dc-42fe-a6c0-fa1f84a0b081}} and the impact of the boundary constraint {{cite:a5d05b97e239b40aef3c2360ed0ceb330901e890}}. We demonstrated that this leads to domains which reduce boundary curvature over time for constant uniform local growth rates in Fig. REF . In this 2D setting, we also demonstrated how even simple growth dynamics can give rise to nontrivial domain restructuring in Fig. REF , and that growth and contraction can lead to more exotic phenomena as in Fig. REF .
| d | d73febb306a91b7776e5075d72c033fe |
see {{cite:08787e906001948882d06cf621f9f954ee41b83f}}.
| r | fbed4da853549c30069c5c0539bd48ba |
Exploring the human body pose to improve re-ID performance has been a recent development. Many previous works have analysed the dependence of human pose in person re-ID {{cite:81f9d94eaf4f06a8da212ea87ec52d3620703faa}} {{cite:ee93202333c4d9a9e8e9255c5607b740525e0681}} {{cite:ab311a035c27874e7330c101b1cd7caf6eb6129a}} {{cite:72869297a79e64fa21a09017cc6d0a0ecd6b66cc}} In earlier works, the Symmetry-Driven Accumulation of Local Features (SDALF) method was proposed by Farenzena et al. {{cite:1092089b972b2c4476d4aa780ffd44aab8014060}} where handcrafted complementary features are extracted depending on localization of perceptually relevant human parts. They achieve pose invariance by combining these features through a weighting scheme based on human body (vertical) axis of symmetry. Weinrich et al. {{cite:37962609124aa43c2eced0e71b809455b666bd61}} detect the upper body pose for tracking the human subject in egocentric image frames. The local texture features of the upper body are learned and a generative 3D shape model is used for re-identification purpose. In another direction of research, there have been attempts to apply metric learning, based on a transformation function for different camera pairs, that can be used to model the pose change of the human and then compute feature distances to boost person re-ID. Following this philosophy, Bak et al. {{cite:72869297a79e64fa21a09017cc6d0a0ecd6b66cc}} try to learn a metric pool, i.e. a pose change metric based on Mahalanobis distance by classifying human pose into 3 groups: front, back and side. All the aforementioned methods use typical handcrafted features to achieve pose variation. However, in recent times there have been increasing application of deep learning based feature extractors and pose detectors for re-ID. Zheng et al. {{cite:72869297a79e64fa21a09017cc6d0a0ecd6b66cc}} addresses the pose misalignment problem by ‘PoseBox’, a pose based body part extraction and reconstruction algorithm for the pedestrian images. The original image and the PoseBox output both are trained in a CNN to extract pose invariant features for re-ID. Cho et al. {{cite:3745f9eb7ff4af8c278137c915b7539836176dd0}} proposes a multi-shot re-ID framework by learning the transformation matrix from one pose to another by utilizing external camera parameters to predict the next pose (target pose) of the pedestrian and then use the matching score for re-ID framework. Sarfraz et al. {{cite:ab311a035c27874e7330c101b1cd7caf6eb6129a}} uses the detected pose keypoints with the pedestrian image as the combined input to the CNN for learning pose sensitive embedding. The authors use a view predictor, i.e. pose classification branch in conjuncture with the CNN branch for robust embedding generation. However, the improvement of the framework is largely contributed to the new re-ranking methodology. Zhao et al. {{cite:dda5127115efa45cea7c46ca381b0833a344d821}} proposes the ‘SpindleNet’ architecture that uses a Region Proposal Network (RPN) utilizing the human body structure (pose), and then extract features from each body part using the ROI pooling. These part-based features are merged using a tree-like ‘competetive’ feature fusion network with the full-image feature. Following this idea, Jhonson et al. {{cite:81f9d94eaf4f06a8da212ea87ec52d3620703faa}} tackles the person detection error by a SpindleNet-like body part based deep feature learning methodology by using an ensemble of handcrafted features such as Hue-Saturation-Value (HSV), Scale Invariant Local Ternary Pattern (SILTP) with the deeply learned model to produce better results. The fusion of Deep learning based features with handcrafted features have also been observed in Lee et al.’s {{cite:32d6ce70e0d261b3d7133a14007cd496c0f039ab}} work, where the authors use an ensemble of invariant features for re-ID, by combining holistic (deep) features and regional (handcrafted) features. However, the authors do not provide specific justification on how these features are pose invariant.
| m | a7a00ae64927d357e4dcafa89f835f4d |
Our in-house arithmetic dataset comprises of numerals modeled after the numeral distributions in real-world datasets DROP {{cite:c5c689cc5089b9fc82ddd646b7a0b7e45829f404}} and EQAUTE {{cite:342dab5fac2b84291556f0c76fe4d19ebc375ac8}} (§Appendix 5.2) with 21,838 instances of arithmetic computations. All models are trained for 50 epochs where the datasets are processed through the standard sub-word tokenization scheme of BERT {{cite:4aa92f0d59462adf9047b4e1244eed257cca1833}}. These models are then fine-tuned and evaluated on the range of GLUE tasks {{cite:da623daa5e7da69ad31d839e06782ddf8bbd9de3}}:
| r | ea818c580c016b90910f3eaca1a4e257 |
Table REF is a comparative study of our approach against two different versions of RRT {{cite:9eac5f771c68018db192ec0f42353a5169ffac34}}. Due to the complexity of the problem, existing baselines like RRT do not work well when directly applied to the problem. Hence, appropriate modifications were made. The sampling for both the RRT baselines in Table REF is performed in the 3D workspace of the robot. The difference between the two variants is in the EXTEND routine of RRT which is responsible for extending the nearest neighbor in the tree towards a random sample.
| r | e9aa7b0846b528af30cd456c55edc5e3 |
In rotationally supported disk galaxies, the EFE causes the nearly-flat RC to decline at an acceleration typically much weaker than {{formula:7860cf64-b6d3-4960-9bce-8efd5c8e1c6f}} . Weakly declining RCs in the outskirts of disk galaxies have been reported {{cite:ee5d49ea13d216c0cf5c7f63b83d24231db95d0a}}, {{cite:ba67e6a5a4cf2cf1c044c20a8fe7d445f4c107a7}}, {{cite:f060fbedb888f7879defcb612e834decbbde9060}}, {{cite:065d9fbc98fd31ae7dd0591a04da58ed40878cbf}}. The works of {{cite:f060fbedb888f7879defcb612e834decbbde9060}}, {{cite:065d9fbc98fd31ae7dd0591a04da58ed40878cbf}}, hereafter Paper I & II, have demonstrated that an unbiased sample of {{formula:c9ef3536-5d8c-4c8d-94b4-8a919c367ae6}} RCs exhibit a decline in an average sense and that RCs in higher density environments are more likely to decline than those in voids, consistent with the generic MOND prediction for the EFE. These works used a toy model for the EFE based on a one-dimensional approximation {{cite:9302895cd9b84e0aa8311cfa196078ab67edbda7}} because numerical solutions were not available at that time.
| i | f2d94cf6d5710756583a5cde32b02938 |
Spiking neural network (SNN) {{cite:f4375b92f2dba80c2a37fb2927639a862b2a7787}} is a machine learning technique designed using spike-based computation and bio-inspired learning algorithms {{cite:055f9523f30873111f8be6942d44f34558486607}}. Neuromorphic hardware such as DYNAP-SE {{cite:57356ae5dcd5f56f01c6cbd0ff0bf51e6a3ffab1}}, TrueNorth {{cite:a63989bc06f5b8b0889d9d2eb91541e8c65cc686}}, and Loihi {{cite:0eac6386cc58aef1d14bc52a4d1d72b944cebae6}} can execute SNN-based machine learning tasks in an energy-efficient manner,
thanks to low-power neuron circuits {{cite:7ba0f107015b8e521742145a244a6f3da591f911}}, distributed implementation of computing and storage as crossbars {{cite:fad60ec22cb00a4b80ead67d67edbb4053682719}},
and the integration of non-volatile memory (NVM) for synaptic storage {{cite:1be04927a8288a47d9df2c04e94c07051e5b917f}}, {{cite:8230e3926bfd75381ff49fb2b2dc9cf66c1e27dd}}.
Several techniques are recently proposed to map and execute SNNs on to neuromorphic hardware {{cite:7b18d7c3a6f0c560cc1c26bdc82a7a959f2019b7}}, {{cite:c63861a83a78861a5d96a688c05b40d23a02e4bc}}, {{cite:3679dbdbb53763e0e82a3b1eb2ea19ab70920ef0}}, {{cite:18f2dfa82a8b991225b9f9cc0ba894b6f976bc7d}}, {{cite:4c7c3d6f3ecdd8cc6bda43ff4492b5959981bcea}}, {{cite:cddfaede979c3383597c066ea4ef1c0e3f9436c1}}. These techniques mostly target performance (e.g., accuracy) and energy of neuromorphic computing. Unfortunately, neuromorphic hardware are prone to reliability issues such as limited programming endurance, read disturbance of NVM cells, and aging of CMOS-based neuron circuits {{cite:30ae58b0d7a6c91fbd2cb6e207c898f08fe05abc}}, {{cite:a08e2e93e493211fd742b1ad1ab84ef959f66c12}}, {{cite:8fda6b3470ab193aa77b829133e626aeb1ae3fd0}}. In this work, we focus on the circuit aging due to negative bias temperature instability (NBTI) and time-dependent dielectric breakdown (TDDB) failure mechanisms {{cite:4eef4a10b790a036bded5b8d34e70ae54eb1713b}}, {{cite:8298a1121e755ea9fe2b597d2596e044a409e921}}, {{cite:60272f256ccd6d49445cd1e03008b30f51a4e99b}}.
| i | cebd8c57e510074ab00ce5219b4c86f4 |
Deep neural networks have shown great success for numerous tasks from computer vision, natural language processing, to audio analysis, in which the underlining data is usually in a regular structure such as grids (e.g., images) or sequences (e.g., sentences, audios) {{cite:ce641d86918411c930772ddbb99165b3bb53f45a}}, {{cite:e8352f6e1537ca6a2462f1c8a7a1ae425d033df6}}. These successes can be largely attributed to the fact that such regular data structures are natively supported by the neural networks {{cite:ce641d86918411c930772ddbb99165b3bb53f45a}}.
For example, convolutional neural networks (CNN) are naturally suitable for image and video analysis. Recurrent neural networks (RNN) are suitable for data with sequence structures such as sentences and time series.
However, it is hard to apply similar models on data with more complex structures.
Recent years have witnessed increasing interests in geometric deep learning {{cite:ce641d86918411c930772ddbb99165b3bb53f45a}}, {{cite:71e88c5aa60667b8e3637b7408d14c056c339233}}, which focuses on developing deep models for non-Euclidean geometric data such as graphs {{cite:6198010cd2c04a5b98f0dc4c89304acebbd7cd25}}, {{cite:780344ca06f6cdfa207de62391a84ef017a5b142}}, {{cite:57f61661c07ce0aa1f722e2d7147b25495815f68}}, {{cite:23f2256e2a5597b190a0fb340ee941f8e00f48ef}}, {{cite:ab15fee7f8238a0ffd528837053c41833c97cf78}}, {{cite:e817e65a3656bb4dc113a71d99c67b62c18b3210}}, points {{cite:711b9a698cdd32fb4e75146e8f1e5c96d9485529}}, {{cite:5816675947f5675b390463200285a890737e664a}}, {{cite:d4f49893aa5ef6c5d93028b426e9aced0e3fce93}}, {{cite:1f9732f307a169ab41e0d2a53f7ef29793731dec}}, and manifolds {{cite:f80b0fc4e36a099c9f3a57124627fec9b7dda1b0}}, {{cite:71e88c5aa60667b8e3637b7408d14c056c339233}} that have rather irregular structures. In fact, deep learning models on irregularly structured data or non-Euclidean geometric data have various applications in different domains such as computational social science (e.g., social network {{cite:91c0632692942ef6dab486ced30b6453ec1f34c5}}, {{cite:d2eb8294b6deb774ab3706077367223aef028d65}}), chemistry (e.g., organic molecules {{cite:1a9e4269953bc8b04eeadd2517ea1282f62602fa}}), bioinformatics (e.g., gene regulatory network {{cite:3c15fbc3692749a2a41d873899575bb322d676cf}}), and geoscience (e.g., traffic network {{cite:f1df88167b56dc246162c35a7c73ada25e05985d}}, {{cite:40807dec7bd5dc3cfd8a6491b9bad178355bd7e2}}, air quality sensor network {{cite:ceede25bc826f07bd22f09b25980d55d2bd8bf48}}, weather sensor networks {{cite:2d18bcf2cfd092fbcb495faf813ab6272d477331}}, and species occurrences {{cite:d4f49893aa5ef6c5d93028b426e9aced0e3fce93}}, {{cite:1f9732f307a169ab41e0d2a53f7ef29793731dec}}).
This trend indicates that
representing various types of spatial data in an embedding space for downstream neural network models is an important task for geographic artificial intelligence (GeoAI) research {{cite:e8352f6e1537ca6a2462f1c8a7a1ae425d033df6}}.
| i | 43e9b6533da1a0513f7df002d7a6d4cf |
Conventional background subtraction methods use the average {{cite:e7a125d92db767976d537915faa1da390c3908b5}}, or the median {{cite:22c156a787b75067883a25439ca5dda801a540ef}}, or the histogram over time {{cite:f066535af0291379971054462be96fde285717ef}} to represent the video background. These methods can be easily implemented. However, modeling background with a single image requires a fixed background without noise and artifacts, which makes the performance of these methods not robust to real applications.
Statistical background subtraction methods basicaly model the background pixels by using a probability density function (PDF) and learn the PDF from the video frames. The single-Gaussian method {{cite:e60d0b2869e6cd891ae69118ce09bf71d13f9b00}} assumes that the intensity values of a pixel over time can be modeled by a single Gaussian distribution. To handle dynamic backgrounds, a mixture-of-Gaussian method {{cite:80ed600024f1f205555ffd51a4e1e6be27eaa22c}} is proposed. However, a fast varying background cannot be modeled accurately by a few Gaussians. To solve this problem, the kernel density estimation (KDE) method {{cite:18baec215369c8739975c8decc85a69cfaec4482}} was proposed. The KDE method is time-consuming which limits its application. Recently, principal component analysis based subspace learning {{cite:df57f89f06b1c849093ab5c2a245ac9be117ede9}}, {{cite:69df130f7ac8f7f962d5586cfd626af4159a8f4d}} are widely used to construct a background model and RPCA based methods {{cite:1f057fb9f7ba7ed7209cc1a341f2fd0b531ebecb}}, {{cite:8cd7c8034609ddfe9f388e48bcdef5a7817677fc}}, {{cite:5f0568558732a62b92a30adc30ce4abf70d0b5b0}}, {{cite:69df130f7ac8f7f962d5586cfd626af4159a8f4d}} provide a robust model for video background and foreground seperation. Other methods such as support vector based methods, and subspace learning methods also fall into this category.
Fuzzy background subtraction methods use fuzzy running average {{cite:e7db2f121ee84c406436481b63a66a7d3d36ff7d}} or type-2 fuzzy mixture of Gaussian {{cite:2f21c3cf5afd5939ebd2e71c011ee2955f29ee5b}} to model the video background. The forground is detcted using the Sugeno integral {{cite:065cc31ef0f1f54b8f7218c574c7d4cd57eb6fbc}} or Choquet integral {{cite:4a1b665cebf09781fe6958fc79abe22fa4523335}}.
Neural network background subtraction methods model the background as the weights of a neural network which can be trained by using training video frames. The network is trained to classify each pixel of the input frame as background or foreground {{cite:53068cdadc9fbf12a9c13781afb3fce24758edce}}. In {{cite:e83230d0594fd028c05a1c3a2ae8d4033bd023a9}}, a neural network which forms an unsupervised Bayesian classifier for background modeling and foreground detection is proposed. In {{cite:355da7c2c39def21b133066108527fc0fcbfaba5}}, a multivalued discrete neural network is used to detect and correct the deficiencies and errors of the Mixture of Gaussian algorithm. In {{cite:ebe2e6fae6a791baf492d13e41564a9dc2ad6bfa}}, an unsupervised competitive neural network to represent the background is constructed based on adaptive neighborhoods.
Clustering based background subtraction methods suppose that pixels in the input frame can be represented by clusters. The K-means based method {{cite:d4b109486c164694ce41d9f89d018e4fd9c6fd36}}, the codebook based method {{cite:9dddcc16db6dcb023483455d82b8df58ad8bc7fe}} and the sequential clustering method {{cite:43cd5403b3549fd287684eac5655607dd4b6f7b4}} belongs to this category.
| m | e450ffe0e6659c106f4639f327325afb |
Although U-Net {{cite:bf6b58407f2e45ba535032e30bbd065a20f2e216}} and its variants have already achieved some great successes, their segmentation accuracies for small objects in medical images are still unsatisfaction.
Specifically, in the context of medical images, the objects of interest are often relatively small, e.g., early tumor lesion {{cite:216de719c70250acc765960632dde9e411472eb2}}.
Moreover, in the down-sampling of U-Net, more and more abstract or coarse feature maps will be generated layer by layer {{cite:9543c1043d4ac8aea062662363c1e961c64c7bfa}}.
Therefore, in the deepest feature maps, the features of these important small objects may become invisible or even be lost {{cite:304a2b05ae9abac38a48f3a00a647b00ce3957bf}}, which thus results in inaccurate segmentation for small objects.
| i | 83b878b60bf83a79ce8045171b7f4817 |
For classic fixed masks, we consider four categories that are widely used in the literature: Cartesian {{cite:c51f8b916aff8f046af9c6396974ea337c57ff8a}} with skipped lines (dubbed VD-1D), pseudo Radial {{cite:9218f3b3524dc07957d3ae5d691f273bc2faa21e}}, Random Uniform {{cite:7b20b884507f5738df272ff9575f2a567f51b57b}} and Variable Density under 2D (dubbed VD-2D) {{cite:67a71824b3a7e1f1905d6351cd489893ca981193}} masks, where the first category is 1D sub-sampling mask and the last three are 2D masks. Note that a fixed calibration region of size {{formula:021ba63b-5a29-49c4-8597-89b20e91e2d0}} is adopted in the center of the {{formula:6768cfd6-f795-49fb-8e7b-c5ee0cbcff73}} -space for Uniform and VD-2D masks in order to yield better recovery performance.
{{table:9358f4e0-665d-4c1e-86e3-1baa7dea38a1}}{{figure:c2fa4a87-2705-4169-9b9b-cab3e8cf6617}}
For reconstruction methods, we consider two traditional model-based methods, i.e., PANO {{cite:ae5eab878f3ed87853df6aba5a31475dff52c2fc}} and BM3D-MRI {{cite:8714ccbc77ff97bab9b6014ee805276a49a90ec2}}, and one widely used deep learning model called U-Net {{cite:738e5a31aa92114319206669f25b577dc640cecf}}. Our reconstruction subnet (RecNet) is also extracted as a recovery model for fair comparisons.
{{figure:d94748c9-42c0-40fb-b093-c6e6c21e55e4}} | m | b65a19683856c9c386cdda46396fc72b |
tealThe ubiquitous synchronous training. One way to handle such issues is by utilizing asynchrony instead of synchrony in the learning process.
To explain the main differences, let us first set up the background.
In a synchronous distributed algorithm, a global model is usually stored at a central server and is broadcast periodically to all the participating devices.
Then, each device performs local training steps on its own model copy, before the device sends the updated model to the central server.
Finally, the central server updates the global model by aggregating the received model copies.
This protocol is followed in most FL algorithms, including the well-established FedAvg {{cite:e5dcf624bd1d324b9b07bf8751b88bfe2322d74f}}, FedProx {{cite:09f4b6b64fb38ad0a50cf6d470ab0f8684212b82}}, FedNova {{cite:ca812d04d4fc7b40ae854cb5138867f05b7d061b}} and SCAFFOLD {{cite:a1d308cc2f7f7053cb822ff6b84995b2191e5af9}}.
The main criticism against synchronous learning could be that it often results in heavy communication/computation overheads and long idle/waiting times for workers.
| i | 0782e8db63d85bed4ddca9b40502c90a |
We choose several representative models as baselines, including PBMT-R {{cite:40673a356706479b6a174f35f9903b3a7c378093}}, Hybrid {{cite:2df9c76116fa00650fe84dec6e6d2caf2c15a36d}}, DRESS {{cite:b9080c22ea258b87fcea19f47f91d31717c7622c}}, DRESS-LS {{cite:b9080c22ea258b87fcea19f47f91d31717c7622c}}, EditNTS {{cite:0907e621d389390db9654913df8ec9b565a72aa1}} and Transformer(BERT) {{cite:c19ea82a5a04ecf90a342a21cb13c098dd31e229}}. The Transformer(BERT) model has a standard encoder-decoder framework. The encoder uses BERT for parameters initialization, and parameters of the decoder are initialized randomly. We have implemented the Transformer(BERT) model and only use SimpleBERT to replace BERT in the encoder.
{{table:50ba7f18-678b-4e79-bd6c-7ac70a33f233}} | r | 6e02b81cb4aeb784b81dc90210a71069 |
To compare with the methods using multi-crop augmentations {{cite:9ecad5435323d6441bb1a523dbc3798b2bd5243f}}, we have conducted the experiments following the same protocol used in SwAV {{cite:9ecad5435323d6441bb1a523dbc3798b2bd5243f}}. The results are shown in Table. REF . We outperformed the other methods in this setting even with a smaller batch size of {{formula:713ccdbe-7a67-432f-8782-a0098377de3b}} based on the same number of four 8-Nvidia Tesla V100 GPU servers.
We believe the performance {{formula:f3a23894-e8f3-43ee-9a4a-8782a2578929}} can be further boosted if we can increase the batch size to {{formula:cd828c25-bd47-49e7-86ad-9cc033a8892e}} as used in other methods. However, this requires doubling computing resources, which makes it unaffordable for many research groups.
| r | ec4132c10a0b285f2f7e3800bc0c057e |
The curve considered in Corollary REF was originally considered by Gauß in his last diary entry. See Chapter for more details. The following consequence given a precise characterization of the Mazur conjecture for anomalous primes (see {{cite:c78aa9f5376e4dd6c77a5ece32adc45d955ae1f5}}), and we assume {{formula:d9b2d423-dbd3-4b24-9400-ba0cefce71d1}} is squarefree for simplicity. As one may see from below, the constant in the “asymptotic formula" can be zero in some cases, which yields there are at most finitely many anomalous primes. We will come back to this issue in Section for any {{formula:a72eb4af-a7a7-4e0e-bdf2-e7f92089c48b}}
| r | d842fceebd5213805817a063e95441ab |
Clearly if {{formula:4a772c45-a340-48a5-9b14-0d47be1f5f32}} , then {{formula:7a97d69c-ef5e-44a9-9652-29784d9cf175}} .
On the other hand, if {{formula:5d19ea2c-ce20-4c16-843b-b148478f805e}} , then by {{cite:0ad2985a53abd04328bb9ee6044f39c74d8da4fc}}, {{formula:19db8855-10b2-4200-803d-f1a0fd58c2e0}} . Hence by {{cite:0ad2985a53abd04328bb9ee6044f39c74d8da4fc}}, {{formula:211774cc-65f2-4016-9dca-bcd2ee31f277}} for some {{formula:ea22839b-92b1-4178-af99-56f621f988e9}} , {{formula:ce18f84d-58e5-4092-9eb0-9d4e85a516cb}} , {{formula:dcd13358-f651-4e46-bd3f-7fbc34b1e02d}} with {{formula:753fb11c-1998-416f-b61f-a3e211b94eef}} and {{formula:573e2dd4-b939-4fcb-8d8a-a8759ccfaa1e}} . By Proposition REF , we get {{formula:c41bc41f-2d01-474d-932c-13d48383e073}} or {{formula:26d97871-8964-42f9-ad06-615cb85f5c74}} . So by {{cite:75e029f9b41fccb2aa287bdddc50d5f87d948cf8}}, {{formula:be69e2f0-756a-4c90-9a89-b201c48fcb7b}} , which implies {{formula:7ae6c65d-62d2-4f91-b573-7b995ed689b2}} . Hence {{formula:d1696645-95f6-4f2c-b54c-7de226832ffe}} which in turn results in {{formula:700e5d65-0f43-4853-bfcf-d8e9af2b7410}} .
| r | c2f5515800c1d0eae362aafbb57056cc |
With respect to the difference between Theorems REF and REF ,
we first observe that {{formula:6456fe47-98b7-4035-a230-0265a557448b}} is recursively enumerable but not recursive while the
{{formula:a4fd6e63-97ac-4b0a-bdbf-f870e24d66df}} language is not recursively enumerable
(see, e.g., {{cite:1e7e1f52daf3d8d830879f3aa7a12feb47daad89}}). Although they are, both, not recursive (i.e. not decidable),
their “undecidabilities” are of different levels, with the {{formula:09eea237-38be-4869-93c1-934c256397b8}}
language considered “more difficult” than {{formula:5312958b-2e22-45ca-bcfc-d8ff1612a165}} in restricted types of Turing machines (Panopticons).
For example, the {{formula:bd54c1e0-1182-4b74-bb8f-fb1f6f0b330b}} language is decidable for
Context-free Grammars (i.e. for Turing machines modeling
Context-free Grammars) while the {{formula:2fbbcb40-139d-4e20-b2b0-d4ac47a0eeb1}}
language is still undecidable. Also, for regular expressions,
the problem of deciding {{formula:d5278b92-e821-439b-9c65-8a8d48c49909}} is solvable efficiently (i.e. by polynomial time
algorithms) while the {{formula:a2b4efcc-6bf5-4f50-b730-b531362f8f48}} language has been shown,
almost certainly, to require exponential time (in the length of the given regular
expression) to solve (see, e.g., {{cite:1e7e1f52daf3d8d830879f3aa7a12feb47daad89}}).
Therefore, a similar decidability complexity
status is expected from {{formula:c0362855-17e7-4264-85b9-2825239a4872}} (deductive Panopticons without external advice)
and {{formula:2f437271-3d7e-431c-a49b-4103fe00780f}} (deductive Panopticons with external advice in the form of an oracle)
since they are equivalent to the languages {{formula:8b9c0033-a4d6-4c71-8287-e5bf786a84cf}} and {{formula:a7f917a3-3d29-487a-9975-c7fca9558f8c}}
respectively. That is, when we consider more restricted definitions of Panopticons
that render the detection problem decidable, then deciding which Panopticons
belong in {{formula:68b53fd0-a06e-42f3-9f78-f7175a67c469}} is expected to be easier than deciding which Panopticons belong in {{formula:0f959c15-5c45-45d9-aae7-9c2a1af12417}} .
| d | 2316523059aa00fed6881613b1433fa1 |
In section REF , we will perform comprehensive fits to relevant data available in the vicinity of {{formula:fa05511b-0ed5-4335-bfb2-a17971e038d3}} , which include the {{formula:f44316f7-983f-4f00-a892-8d59b8e5458b}} {{cite:825e83adb73025c10456b9ec3fffa26a49538f45}}, {{cite:d6b8840089cca0edbcfac217cb072dc1751e03fb}}, {{cite:7068deb2987ee8b3220e2066a1cc1d1334383437}}, {{formula:0343f2c7-15f5-4b67-9bf8-22795079ad81}} {{cite:5e18da18fba5654af3bd044194b0e8ad4c6e97d3}}, {{formula:a844c8b6-852e-4bf0-bc20-7ef4cc35c250}} {{cite:b194b78371e2c021b710971430a6f2b10409fa06}}, {{formula:788945e1-07ac-467f-a165-40680d4785fd}} {{cite:6c0f933eabb1d628764a85f9900ff07f005aec5b}}, {{cite:a90b8f7cc3751cd120e9ec03854942adc5a508c8}}, {{cite:2a1f353be9d52b279c0c29f19b0c70c1366be5fa}}, {{formula:e5a4fcad-dc6d-4de3-81da-d8040bff053d}} {{cite:a00488c6833ffad2fad7066a04ec7cdd1d97e4f4}}, {{cite:5e231512c54e4b938fb853fed26eb1edbf18c647}}, {{formula:9d8733a5-d9be-4fae-a111-613065bfe505}} {{cite:12da7ad3bf8ba6f97470e0a0a66be3fc29b325c4}}, {{cite:8bd1d659608ae89791aa3567e47da8d029a9c75b}}, {{formula:2f466eef-3b2e-4065-98eb-b7b04b7d3b1a}} {{cite:5e724528cc3ffd8aea0fd34627c14f12b414cc2d}}, together with the previous {{formula:cdf9f565-8d13-4e91-8fa5-62e285de53b5}} and {{formula:07e23973-8dda-49b9-b0dd-971bfc02fb24}} data in Ref. {{cite:79199ff0a9619962d302516419b5e271d93a3106}}.
To be cautious, for the reason as already mentioned previously, the fit without {{formula:7e335fea-cb8d-48dd-b12b-34338b2538fb}} cross section data is also performed in section REF . Different results are carefully compared and discussed, and we believe that a clearer understanding on the nature of {{formula:b8b86640-7d6b-43e3-b087-2333eb062e89}} emerges.
| d | 9c84abf6664f0b1d6274d502ab126689 |
In nature, the Unruh effect is established for quantum fields. The action that the Fulling-Unruh radiation superimposes on the quantum fields behaves like a noise, which leads to the irreversibly loss of quantum information encoding in the quantum fields {{cite:0cc8cb524a3bd1371105f030e8de3da7f683b659}}, {{cite:1a2e5d8d8067bb0cc7a7f694519d7cf66ed8d941}}, {{cite:c5aee222986d93522bb1aa44a7b876294daf7fff}}.
However, the problem we here consider is the entanglement between detectors (two-level atoms) moving weakly (i.e. perturbatively) toward equilibrium with the fields rather than between quantum fields themselves. Now the Unruh and anti-Unruh effects are defined through the detector's excitation ({{formula:96ff3358-7f74-4df7-88e4-7b51a9f1075f}} ) and de-excitation ({{formula:28e40cf5-002e-45b7-a41a-5e7a25fd0cad}} ). The measure of entanglement is independent of the nature of
{{formula:6de5e91c-b7d4-47fd-b042-a98a823975c2}} and {{formula:8d3ab419-a680-4ea3-8b00-e54567c006e9}} . For any two-qubit entangled state, after the exchange of ground state {{formula:237ba4a8-d874-47d2-9d9f-0568be0bbad8}} and excited state {{formula:6b12ae5c-9b74-435f-9f8e-59797f4516e7}} , the entanglement remains unchanged. Consider a two-detector system, in which one detector is stationary and the other accelerates uniformly in a vacuum cavity. Let {{formula:59ffe019-37e3-42f7-b400-7d9b2238e514}} and {{formula:f63fa6a2-1984-4ae6-8845-a0750ec01945}} denote the two entangled states of the two-detector system with accelerations {{formula:9196ad6f-7082-4109-bb6b-ea646d956361}} and {{formula:ff9abf64-f905-4325-bdc5-801755e70fc0}} (assume {{formula:2813bd45-e3df-4744-a5f9-17d591cf0f3c}} ), and assume that the entanglement of {{formula:cf2a0468-5a52-4a94-a646-7d6cb4889464}} is less than the entanglement of {{formula:ce7af0dd-1521-4f78-955b-5b7b783507df}} . If the detector is excited more stronger in acceleration {{formula:4460f0ed-5d2d-450e-9132-b306cf4ff74e}} than in acceleration {{formula:3fefeacf-935e-48ab-b30f-3b7a9076766e}} , then we say that Unruh effect reduces entanglement between the detectors, and the process is described as {{formula:85e51633-8ba5-4aff-8c9e-f96d38ac276d}} . Now by exchanging basis {{formula:95359390-0511-458e-bd9b-682e773a2127}} , we obtain states {{formula:ab40c5b0-2c6c-4f3b-9d85-2bee371dc5a1}} and {{formula:94df9501-359f-4adb-92a3-c0f356602847}} . As basis exchange does not alter entanglement of quantum states, thus the process from {{formula:8a5d6922-c5f9-4919-be4c-dc06c08c43c3}} to {{formula:7ad8ad31-9ae6-4375-8f70-ad836ddb9fc7}} also leads to reduction of entanglement. But in this time, the detector is de-excited, i.e., it is an anti-Unruh process. Thus we get {{formula:d313cc88-64b4-4c5a-a1bf-332c37c08f86}} , where the entanglement reduces. In this way, from the hypothesis that Unruh effect reduces entanglement, we deduce the result that anti-Unruh effect also reduces entanglement. Similarly, we can also from the hypothesis that anti-Unruh effect enhances entanglement deduce the result that Unruh effect enhances entanglement. This demonstrates our result that the increase and decrease in entanglement have no definite correspondence with the Unruh and anti-Unruh effects. This explanation though is very simple, but has not been obvious to previous authors on this topic.
We believe our result is a valuable correction to the impression given in some earlier work in this field which suggested otherwise. Of course, further research is required to demonstrate the validity of this inference.
| d | 0c628f68465ea64f33bce0f171be07c9 |
which exhibits different decaying behaviors on different sides of the localization
center.
When {{formula:b3984d1f-eceb-4865-908a-b3bce3f5f67e}} , delocalization occurs
on one side {{cite:f7f66497f2c5a623cd63f4e9f00006e2d70c9e97}}, and thus the transition point from the localized state to skin state is given by
{{formula:f5ae3587-e6f4-4239-a02b-34c447330a12}}
| r | 6998cb6d31f289ac8e78bf75de169c6d |
Let {{formula:b2e8d19b-309f-4b95-9ee7-42e08207e299}} be a {{formula:38449de4-ac3c-4d08-b135-9616a8c14440}} Haar distributed random unitary
matrix. It was shown by Voiculescu that {{formula:5381e690-eb4f-4563-92b3-4a6be2bb014d}} is
asymptotically {{formula:fbbd4f16-85b9-44b0-8a10-a0170c386b3a}} -free from constant matrices (see
{{cite:461bb67a5c3a263a52190b6da8044f7f40dae888}} for a proof using the Weingarten
calculus). Suppose that {{formula:ef102eca-177a-4f09-9683-a5ffc0223319}} , then we can see {{formula:b8286ba0-7c17-4925-abbd-445ea8b266b7}}
as a {{formula:c392397a-2569-4e36-9ab6-0e1beed19f4d}} block matrix with block entries {{formula:bf44dfc6-1e2a-486c-8391-9e9a458c4d84}} for {{formula:d93b253d-06c5-478f-b81a-90b46cdb423c}} . Then, for fixed {{formula:67eea772-dd7d-43cf-8c81-7f9af062488c}} , the
joint distribution of the block matrices {{formula:c2987361-6df6-478f-adad-8fd25d2adf89}} converges (as {{formula:6ec10e87-3df0-475c-8da5-a8528b1cdc33}} ) to the
joint distribution of {{formula:42211f19-ecf6-466f-899e-88b80bb9b568}} which is
given by (REF ) and (). This was already
observed by Cébron and Ulrich in {{cite:b61a5501779c07f4392d18b6a7a2c6095595a92d}}.
| r | f54f47f0fafa3744ac650ec72ddae864 |
An attendant problem is how to identify reliable discriminative features with attributes which might be inaccurate and noisy {{cite:5ac0922ac0307e22ad37c50558a759d5b81a2cdc}}.
To alleviate this, we further propose a novel loss function (named center-characteristic loss) which encourages the selected features to capture the central characteristics of seen concepts.
Theoretically, this loss function is a variant of the center loss {{cite:68d331c14b83538a692764f34492dfa44bd42f31}} which has shown its effectiveness to learn discriminative and generalized features for categorizing unseen objects.
| i | 1e9072c514b39b7cc632ddccf4a4d428 |
The combination of deep learning and SLAM, also known as Deep SLAM, is yet to become the default SLAM strategy but has received considerable attention in recent years, especially for vision SLAM (SLAM for vision sensors). The idea is often to maintain a traditional SLAM pipeline but to replace manually designed models and loss functions, which may not be optimal, with optimized neural networks. For instance, {{cite:3b8563f3471dc1a3b9fe37edf55821fd4f36a330}}, {{cite:3c44fde111feb493fe2be9714d437c0598548015}} describe methods to use deep learning for key-point detection, and {{cite:c3e1e387f228066756ce32cf7969aa78f6d935cb}} presents a technique to robustly estimate the fundamental matrix using deep learning. There are also promising attempts at replacing a larger part of the pipeline with deep learning. For instance, {{cite:cd074fbfa61bd5cb63e13be2c7fb2a7e5c21fa2b}}, {{cite:fce1a4c23fea8650ef579bba241bca3eb83a9bef}} use deep learning to jointly estimate a depth map and a pose for each image, by pairwise comparison of images, and avoid some of the machinery which is common to most vision SLAM solutions.
Deep learning for mmWave SLAM remains virtually unexplored. However, in spite of the differences between mmWave and vision data, it is still possible that ideas from deep vision SLAM are applicable to mmWave SLAM. As an example, vision SLAM often involves a feature matching problem, where keypoints from different images are associated to each other, which resembles the DA problem that we face in mmWave SLAM. SuperGLUE {{cite:8379d0a6210db1afd1749485b07346f2a24e8a50}} demonstrated excellent performance for the feature matching problem using transformer-like architectures {{cite:7445a380f34e70d658a18c13545a85dbb56f82a8}}, and related architectures have also been used to handle DA in settings that are more closely related to mmWave data {{cite:049bf816cbedc6a59f30d9c9ea5ec8c6de553ef5}}.
| m | 6df9fef0c57b377cece9fccc19c58d33 |
We first study a naive lightweight network
by simply combining the shuffle block in ShuffleNet
and the high-resolution design pattern in HRNet {{cite:93e8e013ac8c1f7ac9d0c5ed8ee58430585373c0}}.
HRNet has shown a stronger capability
among large models in position-sensitive problems,
e.g., semantic segmentation, human pose estimation, and object detection.
It remains unclear whether high resolution helps for small models.
We empirically show that the direct combination
outperforms ShuffleNet, MobileNet, and Small HRNetSmall HRNet is available at https://github.com/HRNet/HRNet-Semantic-Segmentation.
It simply reduces the depth and the width
of the original HRNet..
| i | a922bf9d26bbc6ffce324b8fecfbf724 |
The accuracy of supervised image localization methods has improved dramatically in the last decade {{cite:efe4b4a82e3945236dc3dac0ad43373f51bd0487}}, {{cite:dc0b52ab81a154ce3af1b43a21f7b28032bc5339}}, {{cite:aa039cca9efc627d04d35b591dc66af2c8b627b9}}. However, these methods rely on bounding-box supervision, which is not always available. Weakly supervised methods have emerged as an alternative that relies only on image-level labeling to one of the multiple classes.
| i | 546aff1dc724c53da5be323859d4a46a |
It is well-known that Walsh-Paley system forms not basis in the space {{formula:b305721d-2b02-47fb-a519-1059f2ad3a11}} Moreover, there is a function in the dyadic Hardy
space {{formula:c44b3720-e199-4810-b2b1-323c20d947fa}} such that the partial sums of {{formula:10c99383-e596-4ae2-9b17-9b984713b473}} are not
bounded in {{formula:faaba988-d16c-41b6-ab32-1ddd864ea7ba}} -norm. However, in Simon {{cite:96b3acbbd2c028f3809df0101648bf6611f1a824}} the following
estimation was obtained for all {{formula:2bd1312b-5a01-4548-b1a5-3106dc335586}}
{{formula:ba992003-be5f-4125-9501-8bfa36845429}}
| i | a7b666a150a5c58c591373b7728f7bf8 |
As a probability distance metric, the Wasserstein distance has been widely used as a measure of the deviation between estimate and true distribution in the distributionally robust optimization literature (e.g. {{cite:70a49a59a9d312283569e1c689732ee5c51cbb7e}}) to represent confidence set and it has demonstrated good performance both theoretically and empirically. To the best of our knowledge, we are the first to use the Wasserstein distance in an online optimization/learning context. From a modeling perspective, the two proposed measures WBDB and WBNB contribute to the study of non-stationary environment for online optimization/learning problem. Specifically, the data-driven setting relaxes the common assumption adopted in the NRM literature that the true distributions are known to the decision maker by allowing the prior estimates to deviate from the true distributions. This deviation can be interpreted as an estimation or model misspecification error, and WBDB establishes a connection between the deviation and algorithmic performance. The uninformative setting generalizes a stream of online learning literature (e.g. {{cite:4f54f49a25ff54ab66b0dae30b7dd9b1fc5b5778}}), which mainly concerned with the unconstrained settings and includes bandits problem {{cite:b6c1e5796780ac9c70f44b51f0f5d379fb7e6c2a}}, {{cite:f9d177aaf0958bc9ff2f6457bdcaa459b6899acf}} and reinforcement learning problem {{cite:c46406534574254fedffcff0993f807ec0d0d99b}}, {{cite:52d568dc38305fefe512825c28e2220445004ade}} as special cases. WBDB adds to the current dictionary of non-stationarity definitions and it specializes for a characterization of the constrained setting.
| r | 448a9e02a63340e87323efe96c6c8911 |
Therefore the first statement holds. The last one is consequence of (REF ), Theorems 2.5.2 and 2.7.1 in {{cite:d6347f0b58f602dc8ca07edb317ab0d1721bea31}}
| r | 01c5627f2aa0057810f39847251f9bf2 |
{{formula:1731941a-d034-418d-96d2-c8ffabef56f0}} uses BERT {{cite:cb74a0406b09b65d826e21f0da7cc69a37de7380}} as the encoder. Specifically, we follow the way described in {{cite:7271118a2727f75be664c2c69f7b3e1de0475787}}, {{cite:31985714c0bd43b93fce5bbd0e79567cf9cee2f6}}: entity mentions in sentences are highlighted with special markers before and after mentions. Then the concatenation of head and tail entity representations are used as the representation {{formula:aceb41fa-42cc-4428-8b4c-94eb7b65d60f}} . Since {{formula:b4fb3246-6b99-4333-aa0f-35c3c3896f1e}} does not have attention mechanism, it breaks the bags and compute loss on each sentence:
{{formula:0f9ddc8c-2c9b-40d8-ab8c-05f6a59940d1}}
{{formula:6fff6316-06c6-495a-86c7-e04c96e3eede}}
| m | 98411428abbb253a340f9f0a9f5d7708 |
{{formula:130bbbb3-1471-4f57-8e0e-895013fe1297}}
{{formula:8b58e681-82e4-4d50-9abf-709831e5d3f4}} , where {{formula:a2ad15f3-a439-4cfd-bdb4-5a2fa05081fc}} is the Cheeger constant of the graph {{formula:785a2867-57d6-41be-ae2a-697223111f01}} . {{formula:fbaf501d-89d1-4e43-a755-e4b480589f08}} is defined accounting for the subgraph {{formula:060001d2-7248-4c6e-81e6-64b15ab4d14d}} of {{formula:20f2c673-d959-4b0d-983a-44d3fd096aa4}} and its complement {{formula:48b4be19-cf8c-4354-a67c-4fed5a4cdfd2}} , through the cardinality of their cut set {{formula:08950738-836d-4126-850c-ae095b0af391}} and their volume {{cite:1d158e8197f5b0cacd50ec3dcb53761c2c889402}};
{{formula:95d316ff-728a-4a9d-88bc-a243755d095d}}
{{formula:743fcc5a-a1ed-48bd-a6a2-d9d570e3c8bc}} , where {{formula:2a181b6f-14dd-446b-ad3a-a9d76d636f33}} with {{formula:b13a43f6-decb-4c8c-acb9-93f5d840946e}} {{cite:3a845177cb6e2e5de703487fe243becdaafb556a}}.
| d | d2b90950f0df14fae1def1a97558a820 |
and centered forms are already
mentioned in Moore's book {{cite:3f9d7519f2f960e77d0b002d870f9c396e29bd29}}. They
have been discussed in detail in the interval
arithmetic literature {{cite:908141d5db41aa423cf3239464520fd454f56715}}, {{cite:4d92149cb8d66e25496e69226b64085eb2648e10}}
and have generalizations called Taylor forms
or Taylor models {{cite:54e789353661060cba6ff9fe95be9e56ace58637}}. Our algorithm
uses only the plain centered form {{formula:0676743d-9ee7-4d91-8270-ae94ad8ee85f}} ,
and in situations in which practical implementations
of such generalizations are available we would
use them only as a tool to obtain more accurate
centered forms.
| i | afa955890e5e4221fb979ab7ddfc2dc9 |
The first step in our analysis is to determine the values of {{formula:27862f58-1899-49ca-8be8-26c75d98d2b7}} and {{formula:baa08aed-b97b-45d5-9ff6-552252505fe7}} that are consistent with CMB data, without reference to {{formula:507f503e-e2ca-4ed1-bb22-036150e971b6}} . To do this, we carry out a series of Markov Chain Monte Carlo (MCMC) runs within the Cobaya sampling framework {{cite:4e57e85bf457d7cbafe0cf9b5eacccf946f1002f}}, {{cite:6f2e442829c7dc42cba0fba8c2023d5aecc429c8}}, individually and jointly applied to ACT, SPT, and Planck data. We utilize mcmc sampler, and employ the convergence criterion {{formula:eda8689a-f75a-4a81-84a3-c4bf2b8b7e21}} , where R is the Gelman–Rubin threshold {{cite:074a3dcc185c753c1bf356b3aa1216206e8af048}}.
In each MCMC run, we sample the posterior distributions of the six standard cosmological parameters (baryon density {{formula:c0f13011-50fd-4cd5-82fc-f8d9e4dd7dce}} , DM density {{formula:591f7a55-53b1-4c9c-a87a-3d6c49fb9af2}} , acoustic scale {{formula:4e77247d-0465-4923-9cc5-503790da3439}} , reionization optical depth {{formula:317c78a0-6054-4d03-a399-9bafc4987116}} , scalar spectral index {{formula:676cc194-a33f-4212-909f-532081ba1a79}} , and amplitude of the scalar perturbations {{formula:7fbbf788-b44f-4a58-9de0-6a985e4731d5}} ), with the addition of {{formula:ef4f0681-4834-4d68-8589-fbf72182e64c}} and {{formula:eeb40e0f-4fe1-410a-b915-b722a5dd6b73}} . For each parameter, we employ broad priors listed in Table REF . Importantly, we allow {{formula:fd472d11-ca5e-42a1-b629-d9f47eb51879}} to vary in an unconstrained way, in order to determine values that are consistent with CMB observations, regardless of BBN predictions. Results of the MCMC runs are shown as 68% and 95% CL contours in Fig. REF , and are consistent with previous analyses {{cite:94de8979a303d8e54e7f7f0a6626c88ebb4f1269}}, {{cite:3a246844ef42306b39a7d50faf3a026a6f23171a}}, {{cite:02e6caf658d1fb128aec1e3fe45065e402d93f17}}.
{{table:f7448245-c300-4b91-b0da-4ab6a554bab1}} | m | 0663704da8b092329006fe695b066252 |
It is important to choose the bias term in the FP8 format properly. We see in fig. REF (right) that the standard fixed format of setting the bias to {{formula:1c1d31f9-4f98-40bc-8a26-3a21294dedfc}} can fail. This happens when values are either clipped too much, or not enough grid-points are used as the representable range is too big. We also see that having an integer bias performs worse than having a floating-point bias. This is similar to what happens in INT8 quantization, where setting the scale parameter correctly can have a large impact on the network's performance {{cite:76d331408d2df1dec0c1c72676154c36d9c20f23}}. As the bias shifts the dynamic range, this effect is less strong for the FP8 formats with a high amount of exponent bits that have a high dynamic range. For lower exponent-bits, one would preferably use a per-channel bias/scale parameter, similar to what is done in per-channel quantization {{cite:fd9a9619855081bcb1bfa3085a96653e2ef18655}}. Further justification for this can be found in section REF .
| d | eecd15581d329ffd7e0e85a06b65af45 |
To find the best hyperparameters set for GBM, we used the Bayesian hyperparameters optimization package hyperopt {{cite:f85ae49ace9afdb85dae61352319d385cf25ddf0}} with 500 trials. Each trial maximized the AP on cross-validation. In the case of CNN, we also used cross-validation and built 5 models. We used the snapshot of the model’s weights that yielded the maximum AP value on the validation set in each cross-validation split. The hyperparameters for CNN were found empirically.
| m | 83ac193c73f84d2cf030aedcde8ea129 |
Field dependent isothermal magnetization, {{formula:4bd7e941-8996-47b4-be2b-4f44d3b3015d}} , measurements are carried out at different temperatures to further access the magnetic state of our polycrystalline Mn{{formula:96060fcc-75ae-4396-aef8-b9a2162f9bc5}} Ga{{formula:4ad9bf9f-7482-4ecd-b1e1-2b1e659ded96}} Sn sample [Figure REF (f)]. A large saturation magnetization of about 8.58 {{formula:cbb14894-77d3-47cb-afa3-802efe59cb2f}} /f.u. is found at 10 K. A close look at the low field regime of the {{formula:ef75f4db-74da-4e56-b627-c77e88ec0562}} curves measured at {{formula:b542eacf-15dc-4c31-811c-38e5f7b04fcb}} {{formula:650cc6c9-fb7e-4904-affd-981be197bdf3}} reveals the presence of kink kind of features that signify the existence of field induced magnetic phase transition in the system. This transition like characteristic can be clearly seen from the first-derivative of the {{formula:06dcc87e-0ccb-4a59-8f8a-7bdeb67a480e}} curves plotted in the inset of Figure REF (f). A similar type of transition anomaly has also been found in many skyrmion hosting materials due to the first-order phase transition from the helical to skyrmion phase {{cite:20a64c0ee557e05f51676229f55b0135ca9fa7b4}}, {{cite:97f7313888c7654810807807a9d844e28658b771}}, {{cite:5cef727cfff0df3a2e9913142a1304720a08014f}}. For further verification of the observed transitions in the {{formula:cc5c918a-68fe-4485-969c-3383679f6828}} measurements, we have carried out magnetic field dependent ac susceptibility measurements {{formula:17a84615-5739-4308-9b17-9a7d2ad88a79}} at various temperatures from {{formula:1889fd17-154e-4582-918c-aa76d4c64b80}} = 10 K to {{formula:0edb4742-6564-4bc7-a7ac-0efe197470ca}} = 300 K as depicted in Figure REF (g). The {{formula:7614e9c8-a7d8-4354-8f21-f5f0f840bb6d}} data taken at 10 K exhibit a typical ferromagnetic like feature, whereas the measurement at 100 K shows an additional hump like anomaly that persists for the {{formula:3c0fb5ed-cbdb-427f-9371-ad2f67bd9d92}} data measured at 200 K and 300 K. It is important to mention here that the presence of transition like anomaly in the {{formula:2df27f05-7ab2-43da-ab99-3b897af00573}} data has been extensively used as a tool to indirectly probe the skyrmion phase in several skyrmion hosting materials {{cite:f1bdc323748e030b5e2027f87544119a23dfbb2f}}, {{cite:74bf116decd6456c20824d190979ce8e0ae26ab8}}, {{cite:fa6344565b6ccafefeb25c6692786caa1dac9ab6}}, {{cite:252cb1a721c17a63cf7edd2743c40a26fb5ca1e7}}, {{cite:7d52112f1c156c997a80a3ebfe71a60455dfbfd7}}, {{cite:8b834b709ca0b188e12a6c3e067ef1079d648fdf}}. Hence, the magnetic phase transitions found in the isothermal magnetization as well as in the ac susceptibility measurements suggest the existence of a possible skyrmion phase above {{formula:e5fe9ff8-3fff-411b-8bdb-ce4333258c7a}} in the present system.
{{figure:603f88eb-e2a7-467b-9635-ca5909681dac}} | r | 5eaff2a39fe5c77725b5d042ce312777 |
Treatments of QED radiation based on collinear approximations are included in all of the standard general-purpose event-generator programs {{cite:1c69b1e1513c8b5b5a0bc957ab500896b8033e97}}, {{cite:386732ec81bb90ed2939e9aca3f37fb55cad7ecb}}, {{cite:53227a321c09c9a5046a22985b7e13276bcec6a3}}. Modulo corrections from fixed-order process-specific QED matrix elements,
these approaches neglect the eikonal interference structure.
On the other hand, YFS exponentiation {{cite:66b0d3cb5c96c8e18334554d1877c7a628ba18f6}} is used in some cases {{cite:de7993b765b84b0e28eca0713aefd569bb672519}}, {{cite:b0da6c0634f687c3be9eebd453da83dc192f8075}} as a means of including the soft interference structure in a universal process-independent way, but the QCD and QED showers are then not interleaved. In an interleaved evolution {{cite:8643840f42428f80eae98fe91652e882f9ccc287}}, different branching types (here, QED and QCD ones) are allowed to compete with each other for phase space during the shower evolution. This produces
an arguably more physical relative ordering of evolution scales in the resulting joint resummation, compared to the non-interleaved case.
In {{cite:c3ef76a37736981084212dafbce1aed739a7f40a}}, the first algorithm allowing QCD showers to be interleaved with a fully coherent (multipole) treatment of final-state QED
radiation off fermions was set out, in the Vincia {{cite:7514cee9e0ec0cde6c4efa48c7b131bf15b2018f}}, {{cite:8cc08a4480a84ad9da9d01a8c341cbab36629801}}, {{cite:c812fdbabd7f3739c2e35cc8f4ae5d170120a28b}} antenna-based parton-shower formalism.
This letter describes the extension of that algorithm to initial-state radiation and photon radiation off {{formula:4a3825ba-3f8f-453b-a375-25275ce77d5c}} bosons,
and the implementation in the Vincia parton shower.
| i | 798a8101cfb1a673bce100451889f562 |
We compared the proposed method with both traditional and deep learning based methods, including K-means{{cite:f6ceb4ef860f9137501429d864a62d01f9509dba}}, PICA{{cite:a69b20ead3e1ebc7011691a4833befd68863f992}}, GCC{{cite:68350d74ef544088a878e66d0552012968d9f655}}, CC{{cite:8f796d61ec8db2975b1739d3f51d3a241a0a125b}}, IDFD{{cite:3be7c7ef60c5513c7e46364f753c3d221d11534d}}. We set the target number of clusters to the number of target clusters for all methods and run them in a unified environment.
Moreover, two known active query strategies are compared with our adopted strategy in our designed deep framework.
| m | e8ee88003bbcb5adc95d4b070b63a05f |
By equipping a large number of antennas at the base station (BS), massive multiple-input multiple-output (MIMO) has been widely regarded as the key enabler for the creation of the fifth generation (5G) wireless networks {{cite:b096aeab0a717548bdbb79fad26c53443b13ea24}}. By exploiting excessive number of spatial degrees of freedom, massive MIMO is capable of supporting multiple devices simultaneously without additional time or frequency resources. In addition, due to the channel hardening effect, massive MIMO is more immune to the fast fading and can provide deterministic communications required by the industrial applications. Due to these attractive advantages, massive MIMO is ideal for supporting industrial applications with stringent quality of services (QoS) requirements. However, most of the existing literature adopted Shannon capacity as the performance metric to optimize the resource allocation {{cite:9241ce78b5eb681adfc568f149f3dd3cc9f54834}}, {{cite:b17737ff7e31478aa283f13ff5a0a1deda7adad3}}, {{cite:78925e6bf7f82f1858c0c6c480447c78df7d1de3}}, which implicitly assumes the infinite channel blocklength. Therefore, conventional resource allocation solution based on Shannon capacity is not optimal for industrial applications with short channel blocklength. To the best of our knowledge, we are the first to study the resource allocation for massive MIMO providing ultra-reliability and low-latency communications (URLLC) for any number of devices. Specifically, our contributions are summarized as follows:
| i | 439652ef08f26ad526c2734595465bcb |
Since the projected gradient update (REF ) has the following descent property {{cite:c9f1c07600d91c542065afcbe541c5446587aef9}}:
{{formula:c31d28f9-d465-47eb-a284-d2d999758fe8}}
| d | 61bedb0f9531e27e45595ae84990e4f2 |
We have executed a systematic study to explore the optical, electronic and excitonic properties using Density Functional Theory (DFT) {{cite:f3148a500b96397a0db581dfc9a4abf4218c0341}}, {{cite:3aa9c555e7e1b5505c4892804ef07dab416bf1ca}} and beyond approaches under the framework of Many Body Perturbation Theory {{cite:ab2865ce7dc37665ddcf2d610ba0e5cfb5dcf093}}, {{cite:c2ab3e73f58f903a355d4d3a11b74a06eb1b1795}}, {{cite:f9215126eceb9e5e04a0f018f2af933e06a68c48}}. All calculations are performed with Projected Augmented Wave (PAW) potentials as implemented in Vienna {{formula:798d4bc5-199f-4856-b2d6-61d2e9a87df8}} Simulation Package (VASP) {{cite:dde1bd8ad8087da3823170b6d69eaffe1305acbe}}, {{cite:4b3886053956a909753a885a44654752414bf07d}}. The PAW potential of elements viz., Ba, Zr and S contain ten, twelve and six valence electrons, respectively. Ba{{formula:544ad94e-788d-41c0-badf-d824c592f9f8}} Zr{{formula:76b614e1-d5ff-4de1-8823-7f36be6f706f}} S{{formula:d99f19c3-7f70-4914-85cb-7cb52a1bbd3c}} (n=[1-3]) RP phases are tetragonal structure having space group I4/mmm [139]. All the structures are optimized using Generalized Gradient Approximation (GGA) as implemented in PBE {{cite:e9dba5c99c2b5f8dfd9d94e197db500002afb869}} exchange-correlation ({{formula:0f2f7eab-ee14-4f20-a6a2-8d8cba618900}} ) functional until the forces are smaller than 0.001 eV/Å. The {{formula:b4391b79-0a27-4411-a522-80bec1812fad}} -centered 2{{formula:d6acfd69-bb14-4827-9e7e-1a201c0b81ef}} 2{{formula:5fb5cc96-348c-4d6a-a44e-6bd158472d29}} 2 k-mesh sampling is employed for optimization calculations (optimized structures are shown in Fig. REF ). The electronic self-consistency loop convergence is set to 0.01 meV, and the kinetic energy cutoff is set to 600 eV for plane wave basis set expansion. To explore the optical properties and excitonic effects, Bethe-Salpeter Equation (BSE) is solved. Initially, we have used light 4{{formula:1c4fbb69-ff3b-4cfa-8d3a-68ce5fe2376c}} 4{{formula:f7a57669-6329-4d88-b393-b4a2c5c87f51}} 1 k-mesh for energy calculation (see Fig. S1). The convergence criteria for the number of occupied and unoccupied bands in BSE calculations is given in SI (see Fig. S2). In order to have improved spectral features with denser k-mesh, we have employed the model-BSE (mBSE) {{cite:ee26975c5390f437cea22d411bd172d761befaa0}} approach. Following this, we have performed Density Functional Perturbation Theory (DFPT) {{cite:30aff2b426f187a44312100fb74281e38c90d3bd}} with k-mesh 12{{formula:1742bf48-123c-4e18-8c0d-7cb4c86991e9}} 12{{formula:1beea6e3-96c9-42e1-9f47-a26da67d65c2}} 1, to discern the role of ionic contribution to dielectric function along with electronic contribution. Note that for GW and BSE calculations, we have used converged NBANDS i.e., 800. Lastly, by employing Frohlich model approach {{cite:7dccd6ab2b948417b4fc8b5ee2467a486dee473f}}, we have studied polaron effect in our systems
DG acknowledges UGC, India, for the senior research fellowship [grant no. [1268/(CSIR-UGC NET JUNE 2018)]]. AS acknowledges IIT Delhi for the financial support. MJ acknowledges CSIR, India, for the senior research fellowship [grant no. [09/086(1344)/2018-EMR-I]]. SB acknowledges the financial support from SERB under core research grant (grant no. CRG/2019/000647). We acknowledge the High Performance Computing (HPC) facility at IIT Delhi for computational resources.
K-mesh convergence for PBE functional; Number of occupied (NO) and unoccupied (NV) bands convergence in BSE calculation; Band structure plot with PBE and PBE+SOC; BSE@G{{formula:93ecc954-e520-484c-9907-0af9e9fa1cd8}} W{{formula:135bae6e-34c2-429f-a5fc-982d8989bd05}} @HSE06 for Ba{{formula:0ec7e38a-ca42-42c5-a356-977ef875a543}} ZrS{{formula:f546ac3e-4344-481f-87f6-0953750b2e93}} ; model-BSE (mBSE) approach; Projected density of states (PDOS); Effective mass of electron (e) and hole (h); Calculation of deformation potential energy and elastic modulus; Strength of electron-phonon coupling.
| m | 47e9ee8d1214936eacbcf99f290c7c67 |
Backdoor-based Watermarks {{cite:1b8910fe0d7c86c5094de495acd76449a23352f7}}, {{cite:b2b0a42738a214636a7c0eaebabad4760361820d}}, {{cite:3da8d9249ce3889995739b40f4f11281d07ed02f}}, {{cite:0a14f6135d7cefe51ab0f4eb5e412b0679bf4c95}}. Backdoor-based watermarks utilize backdoor attack {{cite:409e9f60e32fa496697ab21ecf9b441bf99ba160}}, {{cite:d317facb7388e6dc71e6decb619d7e2546d14ccb}} to insert specific trigger set {{formula:aad7e727-bc69-4d96-9dea-a07a3b1005d9}} into the DNN model. The backdoor attack leads to misclassification when encountering samples in the trigger set. The trigger set is unique to the backdoored model, thus the owner can verify its ownership by triggering the misclassification.
| m | 6602e0b864f7ab31e936f38816468901 |
Here we discuss hetero-crystals beyond 1144-phases. The so-called 12442-phase (e.g., K(Cs)Ca{{formula:42982f75-46f2-4344-9747-56c60e986f9a}} Fe{{formula:f6fa9f24-1f9f-4fbd-8544-2e03ec0f3ae5}} As{{formula:988c68f2-2d8f-4640-9bdc-fa40a1d4eac3}} F{{formula:e960623a-e2f1-44f2-a542-bdbbd2d38e73}} , {{cite:c56d09961afa3169daf00005fd5e2cfb52ee907a}}, {{cite:a9baa375acd849a86b6c64cfffc55730805d7a44}} Pr{{formula:b915a938-6b20-490f-a216-37ade549c302}} Fe{{formula:90cc0240-6b01-4879-9f41-95eea5256a5e}} As{{formula:31331ec7-c07d-4682-af8d-1ef00a92d41e}} TeO{{formula:6ce8802e-1e39-4023-9657-eaf629a43081}} {{cite:b17359d8df810de02777021b4baf07a3b792797c}}) is obtained by stacking two 1111-phases on either side of one 122-phase (Fig. REF (a)). Since Ln-O or Ca-F layers effectively serve as 1+ cations, it can be considered as alternative stacking of elemental cations Ca{{formula:72e29d35-71f2-4e20-b274-14644d4fdb96}} and composite cations (Ln-O){{formula:b174944c-62c8-4d01-a8d8-014ff8856fcd}} or (Ca-F){{formula:2d7bd3df-717b-4888-b787-b226fcf1f27d}} ; the TM-layer is (Fe-As){{formula:419e590f-1116-4873-8334-3b8b009c643c}} . Notice that the 12442-phase has a second stacking type (Fig. REF (b)), with Fe-As and La-O interchanging their roles. We may still think of it as 1111+122, but an alternative viewpoint is the Fe-As layer being sandwiched by two dislocated layers of 122-phases. The latter viewpoint is more insightful because the Fe-As layer is the playground for SC and magnetism, while Ca or La-O altogether merely serve as electron donators. A particular stacking of the two could be achieved by selecting proper precursors {{cite:c56d09961afa3169daf00005fd5e2cfb52ee907a}}, {{cite:b17359d8df810de02777021b4baf07a3b792797c}}. The 12442-phase implies that the cation could be a composite one, like (Ln-O){{formula:d0aabf34-3c3b-4bb9-958e-2f74f3d4a789}} , expanding the pool for cations, as well as allowing extra tuning parameters: the stacking type (distinction of Fig. REF (a) and (b)). Other examples include the 22241-phase (Fig. REF (c)) {{cite:1c1dd136a238e28af3d2556ce1913515fd7894ad}}, which contains alternative stacking of 1221-phases and 122-phases. Interestingly, it builds in oxide motifs, which are another big familiy of parent compounds. Recently, 112-phase nickelate SC attracted much attention {{cite:975263e949e5ef7f065e537a3aa25711b26888a5}}, {{cite:f859cfd4ac08f46f95aeabed5c47d71ddb7d79f0}}, which belong to the same structure family of cuprate SC {{cite:74124aa53ab4c4cff1c8a80f030f57421ddac203}} and is a limiting case {{formula:718f5c91-a950-4a36-a825-26b082668f55}} for the series of compounds La{{formula:bc74381b-9aa4-42cc-a3d7-9abdc0035f0b}} Ni{{formula:680424ae-1a63-4466-afaa-30dc21d14304}} O{{formula:6d38ba0d-b627-42c2-931f-b7e2ba1cd5da}} {{cite:5c52842b68fc99678df3f08d389ba648e72a0fd4}}. In 112-phases, cations RE or IIA atoms are sandwiched by NiO{{formula:e29ef591-9b8c-4423-9448-503d55ce879f}} layers. We have seen many hetero-crystals in Fe-SC and it is interesting to examine Ni- or Cu-based SC.
{{figure:bef6013e-1ec8-4eea-a393-59138b3def05}} | d | 11e1d608f82ce0f4f8a515803e009928 |
For instance, two dimensional conformal quantum field theories are well
understood in terms of their operator content characterized by
infinite-dimensional algebras of local conformal transformations {{cite:37163a9770a923429179a462cd90ab5e8626ef81}}. A large class of such theories, minimal models {{cite:be658b331005f79b72ca851b1e1f058fccc2a2f2}},
are known to possess a finite operator content and the treatment of unitary
and non-unitary theories is formally identical. The simplest massive
non-unitary field theory consisting of only one real scalar field describing
in its ultraviolet limit the critical point of the Ising model in a purely
imaginary magnetic field, the Yang-Lee edge singularity {{cite:09da47eadf25f220003f589dd259bb1a6249cbc9}}, {{cite:f1f9ef553b2df658f3793a718fa3626057ee47fb}}, is
known for a long time to correspond to the non-Hermitian Lagrangian {{cite:a22f03a7c215912a4ec0bb73bd0b38f05c251d73}}, {{cite:7360fea64ec19dc08c0b5fff4e0b25a576b51e24}}
{{formula:e5174623-1b84-40a9-b3ee-c821ac590f7b}}
| i | 923781b88e86debb3df0241fd9d1c098 |
Linearity A network, which is a linear combination of other networks, should have explanations which are the same linear combination of the original networks explanations {{cite:7608ea6c27dc03482315dc4457fe03996ac20a71}}.
This axiom states that an explanation method should be a linear function of neural networks given the input.
| m | 380a5bfab730df50d18c9185db209f1b |
The core of our deformable registration model (Fig. REF ) is based on VoxelMorph {{cite:4ee5b5db7c07e13ef9bc03dc15b7fa0b6476b014}} with the following modifications: (1) increased feature channels for each layer and (2) deformation field downsampling by a factor of 2.
The input is a randomly selected pair of patches from the moving and fixed images. The output is the predicted x, y, and z displacements at half the resolution of the input.
{{figure:439a1bbc-e1c7-4dc0-8a66-a4eed8b840b8}} | m | 32beb4027cb0077fa56aea5774e8fb81 |
The main idea of DLDL {{cite:3de66e6430e7fe1cefa55f4072fa70bbacc4dfdf}} is to reformulate a regression problem by discretizing the value range of the regression target and then learning the model parameters such that the probability mass function (pmf) over the predicted discrete class is close to a desired probability density of the true regression target.
| m | 90da28552be166d437a19d2ef49f4720 |
As we have mentioned, even in the classical field description, there are many freedoms to
define macroscopic distributions. For example, one could adopt the Israel-Stewart approach and
define a frame vector from the full current {{formula:03bacfe5-bf9b-4d1f-a494-6b9ed26dd46c}} , with {{formula:5ee80da7-646b-4eaa-b0a5-adc961db2077}} .
Concerning the multipole moment expansion, as we mentioned, hadrons are distorted in phase space due to Lorentz contraction. This effect is dynamical.
It is customary to introduce a rotationless Lorentz boost {{formula:44520c8b-1ef4-4cd3-893e-66956248f061}} with {{formula:d1741ac7-dfa3-4576-a24e-a05515f57f78}} to
define “intrinsic" multipole densities {{formula:c2e22ca2-eb2d-44b5-ac03-c43e59f09707}} in a momentary rest frame. As such, the kinematical part of the Lorentz contraction may be removed. However, the choice of {{formula:691cf539-4329-4d48-8e1a-05332280775a}} is not unique {{cite:aa2d9d88c019b94a8fbc36fb17d61abe16422462}}, leading to different intrinsic moments. One can show that with the canonical boost, only the monopole density, i.e. the Sachs charge distribution, survives in Eq. (REF ). N.B. both the spin and the current components will change under the Lorentz boost. Indeed, Rinehimer and Miller showed that boosting
the current to the infinite momentum frame converts the Sachs form factor {{formula:a4224822-6ff8-4cba-a01a-44c2c566a822}} to the Pauli form factor {{formula:ac774564-e5b0-43fb-8d1d-675d2b512810}} {{cite:b6dc9d75439c3513fa342599cad1606ab9cd7a5a}}.
Finally, the inverse problem of Eq. (REF ), known as deconvolution in signal processing, is not trivial even for a given Gaussian wavepacket {{cite:ebd9bee8932f21a9e08bcffa2ca6c95e98b4d485}}.
| d | 6b5f6439f0cf60dbe890879221971632 |
Past work {{cite:6abd219c76131ffccf10b5f22dd4bfa7573e9ffd}}, {{cite:96cb0e5814116a62e274691b6d4733560e040313}} has analyzed the MSE score for rejection sampling.
Papers introducing more sophisticated algorithms, however, have often used heuristics like the acceptance rate or effective sample size for evaluation {{cite:ef5fb37d32d8dd111d935b82f24c768756bacfce}}, {{cite:4e6271709a9690967a1f213a4eb8ef8e35b1deb0}}, {{cite:d2f98b637964f0bed9f33ee82dac315b164ecd2a}}, {{cite:bfc791d1d2b9b35d682378236b6160de203771d8}}, {{cite:56b4983e308c33d9650bcc2ba785a1144168c898}}, {{cite:374f859dadd8081410114ba3c8391ce9c9ad8fb4}}, {{cite:3da2c045623a836477878b46ca0f22c696162837}}.
We are not aware, for example, of a treatment of the variance of ABC-SMC estimators comparable to Barber et al's analysis of ABC rejection {{cite:6abd219c76131ffccf10b5f22dd4bfa7573e9ffd}}.
This paper begins to bridge that gap by optimizing the distribution of simulation parameters directly for the MSE score.
| d | 7b6c9f561324edb662b29066dab48c80 |
We set {{formula:7fe07d52-ff2f-4e6f-a689-a2b5207151ad}} and run the ranking procedure
on several networks derived from our data set.
The choice {{formula:35ae1323-acd7-4a29-8475-b3a47201b334}} is mainly due to
tradition. This is the value originally used
in the PageRank algorithm {{cite:d3450bd242004db3f00c7cedf52c7ce146beecef}} and then
adopted in the majority of papers about this type of
ranking procedures {{cite:1c42003909d53d4d07bef0917afeed3cdc88275d}}, {{cite:af1a4f989df8347ec228934c72cacd0ce0fbb090}}, {{cite:5371eac22642e6bdb012ba9daadf5517be3f8eb2}}, {{cite:08739292ee00ecddbad0165c6680875d40511306}}.
It should be stressed that {{formula:415f7bee-d974-48ef-b45e-033d3bbc10be}} is also a reasonable
value because it ensures a high relative
score for the winner of the tournament as stated
in Eqs. (REF ).
| r | b1d79490da2ee4d6a3318be8ee51dbc4 |
Since VML-AHTE and VML-MOC datasets are recently published datasets we run two other supervised methods. First method is a holistic method that can extract text lines in one phase and is based on instance segmentation using MRCNN {{cite:69962f6d27b942bd5eb1390bf04870509776c81d}}. Second method is based on running the EM framework using the blob line labels from the ground truth and we refer to it Human+EM. On VML-AHTE dataset, FCN+EM outperforms all the other methods in terms of all the metrics except Line IU. It can successfully split the touching text lines and assign the disjoint strokes to the correct text lines.
{{table:d7e223cc-bc6e-40af-95c4-c3f43d853ddc}}{{figure:79609c77-7a5c-4464-b9a8-46f3ab6cf979}} | r | 357698751bdb7849e7f9cc29f06d7491 |
In this work, several molecules are detected towards SMM1-a and analysed. Most notable are the detection of the C{{formula:08c484b4-231d-4600-8f78-4f533da8de55}} H{{formula:3d69c559-412e-4520-8d74-6f7c8bbe4dc7}} NO isomers CH{{formula:b097434b-4b18-4b38-8dfb-0c1eb69c0417}} NCO (methyl isocyanate) and HOCH{{formula:62ba2785-0823-47d2-a93b-c4b3d4c4b228}} CN (glycolonitrile). For HOCH{{formula:130e4065-ed85-41da-a93b-538e49e0f868}} CN, this is only its second interstellar detection. CH{{formula:33feb6a5-e497-4daa-b0cc-b330da0ddb11}} NCO has been detected in multiple interstellar sources, but this is the first detection towards SMM1 and therefore also the first detection towards an intermediate-mass source. These new detections serve as additional evidence for a large and diverse reservoir of prebiotic molecules in star- and planet-forming regions, which can contribute to the emergence of biomolecules on planetary bodies. Of the C{{formula:2a56bff2-b5ac-4b21-bbcb-5022bc64c702}} H{{formula:a9d0e2ff-cee6-4c3c-80ea-f69e52af749a}} NO isomers, CH{{formula:027718ec-e23a-498f-ac6b-347332966ec4}} NCO is energetically the most favorable, followed by HOCH{{formula:f1f85d6a-4941-4ec1-b8c2-3fed2b508555}} CN, which has a higher relative energy of 12.1 – 18.6 kcal mol{{formula:73d12ccf-a186-4184-8174-5f1cf86ce60f}} (0.5 – 0.8 eV molecule{{formula:5fb594a8-45e9-4101-a7ce-e9232ceb25aa}} or 5800 – 9300 K molecule{{formula:94c81651-0689-4274-82fa-aaafbbd83928}} ), depending on the level of theory used {{cite:8ee010de33085d54366a93fc51ce92fb3345e6a9}}. In a thermodynamic equilibrium, lower energy or more stable products are favored and in such a scenario, CH{{formula:72b67d11-035c-4892-bb7a-6ac4847d01b2}} NCO is expected to be more abundant than HOCH{{formula:2290cade-c40e-4833-b852-57365fc6cca1}} CN by a factor of at least 1{{formula:f3f055be-24d0-4111-affb-09875bb6bf5e}} 10{{formula:c631e2d3-2d6b-4339-aa79-17c81622f011}} (assuming a temperature of 300 K). The fact that CH{{formula:3d40a83e-d588-403d-adb6-b8c6498e9afb}} NCO and HOCH{{formula:f23c71a7-a34e-4cb5-91c6-fc1ed7303924}} CN are found to be equally abundant is, therefore, evidence that the formation of these molecules is rather driven by kinetics.
| d | c91ccf400869684569ecedb929cc7b53 |
The multi-particle cumulant method {{cite:ec0da2e1bdb2916c737584f08843cc35d81c24ce}} has the advantage of directly reducing non-flow correlations from jets and dijets. The mathematical framework for the standard cumulant is based on the Q-cumulants discussed in Refs. {{cite:c52bd2447e37529329d31a1d6424e88238804247}}, {{cite:88faa3f735ab1e0a368e6be82886b8968ebe6ab6}}, {{cite:05503dace5724519be5af10f0a7e1bb88be912c0}}. It was extended recently to the case of subevent cumulants in Refs. {{cite:26f11bea240702f358078d1d73cf591b7d98c81b}}, {{cite:0b25359f7f786a6fdcf78df96a1bb39da493de1f}}. These methods are briefly summarised below.
| m | 362d37095bcb4306f476db68af6d6bad |
Datasets. We evaluate the effectiveness of our proposed approach on two SSDA image classification benchmarks, i.e., DomainNet {{cite:3e4def6c666e43686b8d9d90d5e1f36496e5f02b}} and Office-Home.
DomainNet is initially a multi-source domain adaptation benchmark. Similar to MME {{cite:1cf5efdcf5d1d5c6f4b21837359bbea491a2b5b7}}, we only select 4 domains Real, Clipart, Painting, and Sketch (abbr. R, C, P, and S), each of which contains images of 126 categories. Office-Home is a widely used UDA benchmark and consists of Real, Clipart, Art, and Product (abbr. R, C, A, and P) domains with 65 classes. For fair comparison, the settings of our benchmark datasets refer to the existing SSDA approaches {{cite:1cf5efdcf5d1d5c6f4b21837359bbea491a2b5b7}}, {{cite:e4519a93ebbad66952988de576f1f736b7233465}}, {{cite:e2ab5d7a9113d7410625ecb4db0a2ebffc3d35b6}},
including adaptation scenarios of each dataset, the number of labeled target data (typically 1-shot or 3-shot per class),
sample selection strategies, etc.
In particular, we choose MME {{cite:1cf5efdcf5d1d5c6f4b21837359bbea491a2b5b7}} as our baseline and report the results on both ResNet34 {{cite:f6adec61c609096f8325e849c58b3b25a6bdb49f}} and AlexNet {{cite:5a0425480b2e75a3a15ce2240dacee7e020c9d79}}.
| r | 982fc266967d008c2580e4e06155d0b8 |
The conventional approach to MRI image recovery {{cite:07ea40883ef16f6ea3460c729038d0a90f029439}}, {{cite:59d78b71d3bb8fd0e7bc428acc11c3b2107f6bcf}} is to pose and solve an optimization problem of the form
{{formula:87028491-b894-432d-a00a-1a451dbef64c}}
| m | 622ff581efc1ba2377dc33289c9f6c8c |
There are a number of limitations in Dream Fields.
Generation requires iterative optimization, which can be expensive. 2K-20K iterations are sufficient for most objects, but more detail emerges when optimizing longer. Meta-learning {{cite:a23079ce913f19c926ab72cb5e0f15cda42fc379}} or amortization {{cite:806f9f3b507a7677d8011189e566e8cf3b6b0c76}} could speed up synthesis.
| d | 65415618d87f41586d503d33d8f35141 |
As mentioned in the section FWI as a constrained optimization problem: full space versus reduced space methods, ES-FWI can be implemented with penalty method or augmented Lagrangian method. It is well acknowledged that one issue of penalty methods is related to the adaptive tuning of the penalty parameter such that a sufficient constraint relaxation is generated during the early iterations while the constraint is satisfied at the convergence point {{cite:4e9da57121bd8054572166524072e7dad4f2dd17}}. Augmented Lagrangian method allows for a constant penalty parameter to be used because the Lagrange multipliers will record the history of the constraint errors in iterations to progressively remove their footprint in iterations following an iterative refinement procedure (i.e., the iterative solution of an ill-posed linear problem) {{cite:422db9a30c0761af148cf942e02feb83bc95f177}}. As an illustration of this recording, one can readily check from equation REF that the Lagrange multipliers {{formula:61745d2d-96a9-47b9-a75a-89d901e0fd47}} , also referred to as the dual variables, reduce to the running sum of the constraint violations in iterations, when [i] the primal variables, namely {{formula:4c055f8e-24bc-4db5-8a77-f389e2fb8e73}} and {{formula:ff30a0dd-7e29-4803-949e-edc0a0770503}} , and the dual variables {{formula:a159f7e3-47c8-4725-b89a-bb1f6d5695b2}} are updated in alternating mode, and [ii] {{formula:a6059978-bb42-40a9-bc6a-e76b256ab0f0}} are updated with basic gradient ascent steps. The reader is referred to {{cite:c846957dd9ad016ca2fe61bd972add3f79bd5b6c}} for a comparative analysis of penalty methods and augmented Lagrangian methods from a mathematical perspective, and {{cite:422db9a30c0761af148cf942e02feb83bc95f177}} for their assessment in the context of ES-FWI.
| m | 62b5c558107b95b9775aab9bce717347 |
Evolutionary or genetic algorithms are used for various applications mostly for inverse design problems {{cite:9eef4f2bd646499a33b54ff5e975e013e224e999}}, {{cite:2e165d8491129b88726e5966eaa78bfd67055bc9}} and have also been applied in the field of modern optics {{cite:fe9f5db534b3851c38752b87ec1479cb82d7cfbd}}, {{cite:f61ad0924ff03a87a06153e3b5473e79098838aa}}, {{cite:d473a2419781256a6c5bc6a86ebd2b83d5bad35e}}. In forward design of optical cavities, for given geometry and boundary conditions the corresponding cavity optical field can be calculated by highly developed and well known numerical, semi-analytical or analytical methods. However, it is not often possible to find parameters to create a target optical field distribution using forward design methods. Here we demonstrate a method which is based on consecutive “mutations” of an initial spherical mirror shape while calculating the mode spectrum and conducting gradient descent to optimize the mutations. The method allows us to find mirror profiles which provide significant enhancement of a target parameter, such as the cavity cooperativity.
| i | 5b8820b34b76cf24750329847cc4a231 |
We perform further analysis of gsf in this section. The t-SNE plot of features obtained from the output of the layer preceding the final fc layer of BNInception backbone is plotted in Fig. REF . We visualize the 10 action groups defined in {{cite:b6933c6eb71fccbf91d56f3d95d68720b140bb47}} in the plot. From the figure, one can see better separation of the features when gsf is plugged into the backbone cnn. This allows the model to correctly recognize the action present in the video and results in improved recognition performance compared to the baseline tsn.
| d | 7e8e606667323cf160666abf2a3510d6 |
It is believed that a black hole is formed by
the collapse of matter and it radiates the thermal radiation whose
temperature is proportional to the surface gravity {{cite:a88bc61ef7017f555f643cc2e5fa2e7322131e1b}}, {{cite:e861b8260b0786f047adc7f22c211cd5e4948797}}, {{cite:17276d52fa9f45473bf104be8e30977b620906e2}}, {{cite:d6d5b45d580026568599ab0236847e73d47509a5}}, {{cite:6a6797e03a7684a24d0c3a952cee8064576713b0}}, {{cite:23acb7511b7ea2a6ae7c6bad56e07208e241a4c5}}, {{cite:d48e7b1f559fbc3d0fb7b3380018012022fc45ea}}, {{cite:593b37be0fa62913373a475770678d3f6cef2e4c}}, {{cite:0797acaacd24cb29ac9398cddd3ff98525db8001}}, {{cite:949fcb16304ac43c873786da4e185ebe5373cc5a}}. In {{cite:a88bc61ef7017f555f643cc2e5fa2e7322131e1b}}, it is assumed that the spacetime is to be static or stationary for calculating Hawking Radiation. This assumption will be valid only when the radiated energy is so small compared to the mass energy of the black hole. When the radiation becomes sufficiently large, it can be modified via Einstein equation. In this context, Vaidya {{cite:b8d86f9fbaad45dedf78325f8c84d99bd2abca8f}}, {{cite:4ef5b1af42458358b8dcf611431edb919355af2d}} has solved nonstatic solution of the Einstein's field equations for spheres of fluids radiating energy. The nonstatic analogs of Schwarzschild's interior solution in General Relativity (GR) has been established in {{cite:7404ec5256c0ff683941b3769de30e9e66fa011c}}, {{cite:8bdbf52d0d2f3b8ccb17e85b709dc61529d71325}} and the problem of gravitational collapse with radiation has been solved in {{cite:c4c80ebea02da5e88217dd204877e95cbc33445e}}. The solution has satisfied the
physical feature of allowing a positive definite value of the density of collapsing matter,
and it gives the total luminosity of the object as observed by a stationary observer at
infinity to be zero when the collapsing object approaches to the Schwarzschild’s singularity. So, we can say that the Vaidya spacetime {{cite:b8d86f9fbaad45dedf78325f8c84d99bd2abca8f}}, {{cite:4ef5b1af42458358b8dcf611431edb919355af2d}}, {{cite:7404ec5256c0ff683941b3769de30e9e66fa011c}}, {{cite:8bdbf52d0d2f3b8ccb17e85b709dc61529d71325}}, {{cite:c4c80ebea02da5e88217dd204877e95cbc33445e}} is a non-stationary Schwarzschild spacetime.
Husain {{cite:deca65c06fed0bb2f1502b557830abcdc0b37661}} and Wang et. al. {{cite:16384996e316deda5ed37ae56e807d167ff6dc92}} have developed the generalizations of Vaidya spacetime corresponding to the gravitational collapse of a null fluid. Recently, Manna et. al. {{cite:74dd5a4ac31a6bcb5a58e26639d624d02dbc1069}}, {{cite:72cf25974232b88e5df0ebdc408c19825ffcebc2}} have established the K-essence generalizations of Vaidya spacetime where time dependence of the metric comes from the kinetic energy ({{formula:0eb2cf51-6236-46e0-9715-93d432696d61}} ) of the K-essence scalar field ({{formula:acba3cd5-1761-4e8e-bf99-b8bed5e0e2c5}} ).
The Hawking radiation {{cite:a88bc61ef7017f555f643cc2e5fa2e7322131e1b}}, {{cite:e861b8260b0786f047adc7f22c211cd5e4948797}}, {{cite:17276d52fa9f45473bf104be8e30977b620906e2}}, {{cite:d6d5b45d580026568599ab0236847e73d47509a5}}, {{cite:6a6797e03a7684a24d0c3a952cee8064576713b0}}, {{cite:23acb7511b7ea2a6ae7c6bad56e07208e241a4c5}}, {{cite:d48e7b1f559fbc3d0fb7b3380018012022fc45ea}}, {{cite:593b37be0fa62913373a475770678d3f6cef2e4c}}, {{cite:0797acaacd24cb29ac9398cddd3ff98525db8001}}, {{cite:949fcb16304ac43c873786da4e185ebe5373cc5a}} has been discussed in {{cite:12bbe5760b5525a037f784b8195d8fff4d6f2c51}}, {{cite:653cd657f65327a89c86bed21cc5d282d3aec8e0}}, {{cite:1dfae89628828a5c957a497ca81440bdd32f6af8}}, {{cite:fdd63a2493c603a5af17c2c92664d2c55728aa32}}, {{cite:d7504a6032986ffc410870ed3f94b109bb57c2cd}} using tunneling mechanism. Also, it was developed by the method of complex path analysis which is used to describe tunnelling
processes in semiclassical quantum mechanics in {{cite:b935a13a7da1674f44bbf034c298a725392f2c6e}}, {{cite:a99cea93c1776647ee1b3e7ddd8a0def8a53a8bd}}. Kerner and Mann {{cite:6ca444ffa7c4bd365ea0167e4361c815f3c3aed4}} have established, in general, that the Hawking temperature is independent of the angular part of the spacetime. In {{cite:46d434b9b2139ccc1ff0305a2c222a99a345a350}}, {{cite:a0f6c9db2f4a155fc83e009304d8f54d02d05256}}, {{cite:c221aa9fdcee259be19d7a2d4921f96450b1755b}}, {{cite:3ff853fc5abe546bf5d94e724a371d7ecaeb2702}}, they have discussed the Hawking radiation of Vaidya or Vaidya-Bonner spacetime.
| i | d0b3dedbe0cb48997df7dec1deda57d7 |
In the present contribution, we investigate configurations associated with axisymmetric potentials for general {{formula:f1f3b2df-aa26-4c15-b6da-df31cdefce0f}} spacetimes with star orbits present only in the visible {{formula:fc1f3c21-3507-4d81-95cc-4ec86ed0794e}} space, focusing our calculations in the stability of perturbed stellar orbits. The motivation behind the {{formula:da320bde-2608-4fb7-8509-44c873a06f65}} consideration resides in the general introduction of spacetime extradimensions in theories like superstrings {{cite:015b5fb3560edb6522355274e7c806b24557ed64}}, braneworld gravity {{cite:714713cb9c08ecff10b2e0ce9c2edeabe2e536a0}}, {{cite:4b93f216088530af57d6159881aa8e14d8e10a6c}}, {{cite:a2daab307aeec818b70f83476dcbe664e165ed13}}, {{cite:8c666c390ec29d286c79cf1e207dbdf3b03b98f6}}, {{cite:f73bfaa2ac2c81c351c3ad0ba0b7306709708eaa}} and models of galaxies within a multidimensional universe {{cite:3a9d2449d92cb2111d6d1ddfafc4d07f89ee888a}}, {{cite:cb6e693d298c6e51ac2e96970a5617d2c146d170}}, {{cite:13755fdf1bca42d90890618a9a9d815bedf95eca}}. In other words, we want to answer the question “could extradimensions affect the stability of the {{formula:b1781f17-a252-477b-8529-9df077430eb6}} orbits in the equatorial plane of a axisymmetric configuration?”. In this aspect, compactified or warped extradimensions should represent perturbations that possibly could break the stability of the system. The possible presence of extra dimensions in the universe is one of the most astounding features of string theory. Despite the strong theory formalism, extra dimensions still remain unaccessible and obliterated to experiments. Since the presence of ten or more spacetime dimensions is one of the central conditions of string theory and M theory, it is not unrealistic to say that experimental observation or constraints on the extra dimensions properties would be a major advance in science. In other hand, the lack of experimental evidences is usually explained by compactification which is the main geometric feature to explain why photons do not escape to the extra dimensions. Nevertheless, an alternative approach involves an extra dimension which is not compactified, as pointed by Randall-Sundrum (RS) {{cite:714713cb9c08ecff10b2e0ce9c2edeabe2e536a0}}, {{cite:4b93f216088530af57d6159881aa8e14d8e10a6c}}, {{cite:a2daab307aeec818b70f83476dcbe664e165ed13}}, {{cite:8c666c390ec29d286c79cf1e207dbdf3b03b98f6}}, {{cite:f73bfaa2ac2c81c351c3ad0ba0b7306709708eaa}}. This extra dimension implies deviations on Newton's law of gravity at submillimetric scales, where objects may be indeed gravitating in more dimensions. The electromagnetic, weak and strong forces, as well as all the matter in the universe, would be trapped on a brane with three spatial dimensions. Only gravitons would be allowed to leave the surface and move into the full bulk, constituted by an anti-de Sitter - AdS{{formula:c9cb13ad-1130-40d2-8114-5092bade0575}} spacetime, as prescribed by RS models {{cite:714713cb9c08ecff10b2e0ce9c2edeabe2e536a0}}, {{cite:4b93f216088530af57d6159881aa8e14d8e10a6c}}. Here are the main motivations concerning the choice of RS as the metric to be tested in the present paper.
| i | 47c742d76e56e5f965fc2b739eaf58ba |
The notion of stable envelopes is introduced by Maulik–Okounkov in {{cite:620b27c7f90f3f3a61481e6f0535f4eace2389f0}} to study the quantum cohomology of Nakajima quiver varieties. Stable envelopes depend on a choice of a cocharacter of the torus {{formula:27f87096-db8b-4641-b9f1-bc45599a7888}} . The Lie algebra of the torus admits a wall-and-chamber structure, such that the transition matrices between stable envelopes for different chambers turn out to be certain {{formula:f3d3dde2-1b49-46b2-9bdc-b0402ea50bc9}} -matrices satisfying the Yang–Baxter equations, and hence they define quantum group structures. In {{cite:3ef28a329c8e1e111d9b44b46a13483f8ea6f8ab}}, {{cite:410537a6958126a86013ef6b7a90b7cfc0548f22}}, the construction is generalized to K-theory, realizing the representations of quantum affine algebras. What appears new in K-theoretic stable envelopes is the piecewise linear dependence on a choice of slope, which lives in the space of Kähler parameters.
| r | 74c54415a429a07980df1e2a18947566 |
Recently, science problem solving benchmarks {{cite:182b2d8beb93358f467b8606af802036711a7c9e}} have been used to diagnose the multi-hop reasoning ability and interpretability of AI systems. To answer science questions, a model needs to not only understand multimodal contents but also extract external knowledge to arrive at the correct answer. Since these tasks require domain-specific knowledge and explicit multi-hop reasoning, a model would be not interpretable if it fails to provide explanations to reveal the reasoning process. However, current science question datasets {{cite:182b2d8beb93358f467b8606af802036711a7c9e}}, {{cite:db56c1f911cff76065436ad915354f40e14a3f66}}, {{cite:f20b48f3edf8790e75a836c34f76b74024d6de95}} mostly lack annotated explanations for the answers. To address this issue, other science datasets annotate the explanations, but they are restricted to the textual only modality and limited to small data scales {{cite:37cb5a9bdcf5a788edaae687d33526e9456cc5f8}}, {{cite:ba665c483c2af18da803ee452c26c682fbee88f3}}, {{cite:5b9c80bd285f4483f60a2b6a7a15cf1f73db883e}} or a small set of topics {{cite:e119701109fab7cf818ce8453547571468bd9ac5}}, {{cite:f5f0383caa57e3a2fe048d7bf51921acf234cf12}}. Therefore, we collect Science Question Answering (ScienceQA ), a large-scale multi-choice dataset that contains multimodal science questions with explanations and features rich domain diversity.
| i | 20eb3e1c57e58635a401837b4b96482a |
To analytically analyze what is reflected by the ratio in Fig. REF , we start from the definition of high-{{formula:51f26f70-93c6-4c28-a3f3-c7d15c896a21}} particle suppression, assuming only collisional interactions within the QGP. To obtain the final particle spectrum ({{formula:493cf3c4-06a2-49ca-af9f-06b0cd7ade1c}} ) at midrapidity, the standard procedure {{cite:d957d01e4ded0d3de92efd5f915fd926296c0274}} is a convolution of the initial parton momentum distribution ({{formula:980a986e-9aa5-4d4f-a446-f77fe00f260b}} ) with the energy loss probability ({{formula:c58957de-cc78-4ce1-8544-38e2cab1d36e}} ) in the final stage {{cite:d5d797bad71c848489bbb1bbe9da5330216a4d9f}}. The assumption that energy loss of a high-{{formula:970e9820-5a02-4ee8-935e-17d37c2654ae}} heavy flavor is small (i.e., {{formula:9e63a01c-9763-4fef-a0a7-daa37e10986f}} ) allows Taylor expansion in:
{{formula:6991539a-2bed-480a-be5a-a4237219e194}}
| r | e4d8520b223793e94be998ee65c748ac |
We have considered various macroscopic models for systems of active Brownian particles, which describe a class of self-propelled particles whereby the swimming orientation {{formula:c9597afe-c3a1-4873-939a-69fff6dea521}} is governed by a Brownian motion. Despite being arguably the simplest model for active particles, the addition of purely repulsive interactions between particles can lead to striking phase separation, known as motility-induced phase separation (MIPS) {{cite:445eb158bf7f5e390cdb8603bec58997deee0cad}}. MIPS is caused by the interplay between repulsive interactions (which are used to model size exclusion) and the active self-propulsion speed, leading to segregation into a dilute phase (where particles can swim almost freely at their desired speed) and a dense phase (where the effective speed is greatly reduced due to crowding). To investigate the nature and the strength of the interactions required to lead to MIPS, in this paper we obtained four different macroscopic models for the density {{formula:5fe82b8d-f6ae-4132-bbae-fd1c2eb12f52}} depending only on two non-dimensional parameters {{formula:2451d794-3b91-4a27-923f-0499c5bede2a}} (the occupied volume fraction) and {{formula:e49af2d3-a562-4652-9e74-5661ff0d1ff5}} (the Péclet number). These differ from slight variations of the underlying microscopic particle-based model and different coarse-graining procedures:
| d | e26f502d34154301404de7af60e3cc75 |
Remark 5.1
Instead of using the augmentation with the square of {{formula:561b930c-a07a-4b07-ba58-4e55ecedc46a}} -norm {{formula:4b1ce3c4-23c1-46fe-a347-b3cb19a34606}} according to the definition of augmented problem in {{cite:bb5b899669de93c6aa45256b249895d8fcda8285}} we use the additional penalty term with {{formula:041e93fa-0793-4b23-8106-e25b19d60fd8}} -norm to the {{formula:6b248088-2584-4895-91d4-2abec2ee36bc}} th power {{formula:2534b1d5-bf10-4022-8087-2ba6713c7860}} in problem (REF ).
This strategy has been discussed in {{cite:60faa695b924a62ab2d7c80c2ad488270f923e28}} for the case of {{formula:de70f1be-13df-420e-824d-f5800a0463ce}} .
| m | 8b463f39901dc3d4611ddf25c3a84518 |
The problem in propagating this measured modification to the dielectron spectra is that the modifications from CNM and energy loss effects affect the dielectron spectra in different ways. While the energy loss affects each of the quarks, and thus the electrons, independently, the CNM effects affect the pair. To accommodate for this an approach was chosen that is able to include both effects with the expected impact on the pair.
As a starting point the measured {{formula:7ff4aa39-4925-4232-b115-bfb1c29b5dca}} of {{formula:8cafcf52-75f4-4280-be8e-29f3a76df0f9}} was parameterised. To disentangle CNM and energy loss (EL) effects a calculation based on the EPS09 nPDF {{cite:0c8262eeef1d8b32980652c9ec1a0287c7fa43c6}} set was used. By dividing the data parameterisation by the nPDF expectation, one can construct the expectation for the {{formula:d24dd1e7-ed70-49ca-8b05-466bd1473870}} that originates only from the energy loss of the heavy quark.
In a next step two different {{formula:39a83841-796c-4b10-8ea2-b0689cd26025}} for the dielectrons, one for energy loss and one for CNM effects, can be calculated in a Monte-Carlo approach. Here the single electron {{formula:2d116f9b-7b81-40db-9021-00031e71b313}} are used as weights. In the energy loss case factorisation is assumed and the weight for the pair is calculated as the product of the electron weights {{formula:3e8366df-62c2-4c98-b474-cf86875e5af2}} . In the case of CNM effects no factorisation is expected and the weight for the pair is the average of the electron weights {{formula:8e9c27fe-ac89-4a2c-9bbf-6375ba268611}} .
The heavy-flavour dielectron nuclear modification factor can then be calculated as {{formula:0f5fdd7f-158c-4c89-b755-1387e9026101}} . This factor is then used to modify the cocktail based on {{formula:3da87b68-ac28-4c05-bd0e-8dddf5834603}} -scaling. The effect can be seen when comparing the dashed lines in the upper left panel of fig. REF with the solid lines.
The middle and bottom panels show the ratio of the measurement to the cocktail expectation for the case of {{formula:dd107408-fe5a-45a7-8b55-f421c0cd3085}} scaling and including the {{formula:48471239-2cf3-42af-a132-db749901af02}} , respectively. In the mass region between the {{formula:778b7463-7619-42dd-9084-e5fa6e81ded3}} and the {{formula:f057ba4c-3855-448e-aecc-542743a62baa}} we can see that the data is below the expectation from {{formula:66fbdb9b-681d-491e-bc3c-c874b9f71fb5}} -scaling (middle panel) which is expected, since there is an overall suppression seen in the {{formula:0c754ae6-ca19-4a13-bc1f-4c43b4cbdd0a}} . Including the {{formula:7423a17b-873e-45bf-9ddc-84dc17e00421}} estimate slightly brings down the cocktail which leads to the cocktail being closer to the measurement (bottom panel). However, as discussed before, the uncertainties are large, and no conclusion is possible. Calculations for a dielectron contribution from a hadronic and a partonic phase {{cite:269f7bd8bf207af6d683599c8ee9f47e364b1840}}, {{cite:7e35f1ef14c3af379b67248081bfd0ef6250757d}} are shown in both ratios to indicate the size of the expected signal.
| r | 89c585cc2d56799f43a159b5f93b4f15 |
We setup NNs based on TensorFlow {{cite:39b106fce5d3f899a736d6bb0ba3799f21ee7e18}} using the hyperbolic tangent as the activation function. Problem specific parameters such as network size are mentioned in the relevant subsections. A set of common parameters and settings is listed here: We train using the L-BFGS optimizer {{cite:4eab9899b3b4efc377c8a4564fb088bdbd341fc7}} with learning rate {{formula:9a4454e7-3bb3-4fbb-8c31-c3ea7314790a}} unless stated otherwise. The NNs rely on the hyperbolic tangent as activation function and the data-driven and physics-informed contributions are equally weighted with {{formula:28b66bf3-c629-4765-9857-29635ef2407a}} unless explicitly mentioned.
| r | b65b4e063fafca2a706f4479aa49e20f |
We study Lattice QED in external electromagnetic fields using methods
developed for Lattice QCD. Since QED in background electric fields has a
complex action, because the vacuum is unstable against decays into electron-positron pairs – the Sauter-Schwinger effect, {{cite:37e0a8074d70a8df22e9940311da0a09a265856b}}, {{cite:275a0ca115acfdcb7cde763fdbcbefb2c5f16150}}
– standard simulation methods which rely on importance sampling cannot be
used. Because of this we start by considering Lattice QED in background
magnetic fields where the action is real and bounded below. This enables us to
perform simulations using standard methods. We use the Rational Hybrid
Monte-Carlo (RHMC) method of Clark and Kennedy {{cite:c029551e686b290c6184fe0ba8a9ea54f4cbbde3}} whose
implementation we describe in the appendix.
| i | b24e1fde637ac07ef3d87d913403fab2 |
Weight Consolidation and Elastic Weight Consolidation regularize the fine-tuning process by encouraging fine-tuned weights to be close to pre-trained weights {{cite:ff39bb2c34d7b057adeb086957318be6836c2dc4}}, {{cite:e6b5ca7c55d467f2266afa4326730cd7f60ce7cc}}. Mixout is a variant of Dropout regularization that replaces dropped neurons with the pre-trained model neurons, thereby mixing pre-trained and fine-tuned parameters {{cite:88fa6b0fcec185754aed751c4e38a35b0e56d9f6}}.
| m | 9d0d7f4a2a0186f5a98a484955614a42 |
Recent work {{cite:9293dbdfcb641dd9144a9889d6c797dc208f6f9e}}, {{cite:2ab9525ca2b8234fbb9f59c90335abadb41a9da8}} proposed diverse data augmentations to improve robustness and uncertainty calibration against common corruptions. However, robustness to noise corruptions remains a challenge. Digital noise corruptions occur often in real world scenarios due to imaging sensors and/or other devices hardware imperfections, and environmental conditions {{cite:e9f678886101d5510cb62a7d355f5e1f3486b057}}, {{cite:633e7af48bfe59d33e314cdfed722ac2b4fd7958}}. The gaps between clean accuracy/uncertainty and accuracy/uncertainty under noise domain shifts are still large; it remains an open question how to close these gaps.
| i | 05218002082799332d0e15170d15700a |
Recall that two orthonormal bases in {{formula:50d849b0-7080-4df6-abe4-ec9f3cdbdfde}} , {{formula:e29440e7-9efd-451b-b450-19c744f8b7d5}} and {{formula:45becc3c-6b19-431b-a18e-30feefaa1fd4}} are called unbiased if for every {{formula:5dbf01c1-ab77-409c-b713-c2f2fddf835a}} , {{formula:7b21a1d5-5643-4f7a-92d8-2ad8a8158c29}} . A collection {{formula:37ff5b18-f8f3-4b0b-8747-eb1a587f6f94}} of orthonormal bases is said to be (pairwise) mutually unbiased if any two of them are unbiased. If the dimension {{formula:48280797-56b3-4d17-86ca-ac75a2e3f1b1}} is a prime-power, then the maximal number of MUBs is well-known to be {{formula:c054126b-7e4c-4f1c-b5df-f986c326b1d7}} (see e.g. {{cite:f7b034b75c75ad501e5a7b3271b0987a0fe24046}}, {{cite:d5905203e158f7b7e18607f9a5b9ae15fb22d8d2}}, {{cite:febf02f947835cdc0d4a69ce96e5615ba756f05a}}, {{cite:a4151e5c7d5f70ecb4cde9a02f2a6c865cb08173}}). It is also well-known that in any dimension {{formula:ce6752d0-6f05-4780-b0c2-1ec6ac55d795}} the maximal number of MUBs is at most {{formula:86ae2e80-a547-4396-b577-62704625f3f9}} (see e.g. {{cite:d5905203e158f7b7e18607f9a5b9ae15fb22d8d2}}, {{cite:4dad97e1dab7d7d5347f95614b25fe3be7901166}}, {{cite:f265cf331e714de899b6a3ff3fb4deaa94f7e13f}}, {{cite:16312d23a921c077ebb3fe9758afe85590470e80}}). For this reason, a set of {{formula:d7406da7-a3a4-4a96-8a45-302a6db1a69b}} mutually unbiased bases is commonly called a complete system of MUBs. However, for any {{formula:bb507485-1143-4f19-ac3d-997421b5f6db}} which is not a prime-power, it is not known whether a complete system of MUBs exists (even for {{formula:b6cedff2-7a64-4942-a9f5-0249261bfce9}} , despite considerable efforts {{cite:f87a0b2a27ce42eb701ae9633bad8f97826410fc}}, {{cite:80bf4053a105acb0ea70f3536fd760c2484191c7}}, {{cite:c08fe1bfb8b2220c65241da23089af7ae892c2dd}}, {{cite:3a93a00ae32aba8a8577aef50f25150a543fda33}}).
| i | e0d98e0e7831841ac6c2621aa37f22d1 |
As an example how this result is used let us consider the spectrum in the graviton sectorAs in {{cite:befbc927b29b7d0c0738c7b3d439c467a6d26179}} we will use the notation of {{cite:ea981913792eb3d18c9a2d15570be5e79369457e}} which includes the parity of the field, as in, e.g., {{formula:51966e55-c8a3-4d2d-bcb7-68332226c62b}} .: In units of {{formula:9dee53f2-f263-4371-808f-23404e0bb6e2}} the {{formula:b27f196c-2155-48ec-b043-7517d32a0750}} irrep defining energy {{formula:5826ca8a-08aa-470a-aac1-c416de2c6edc}} is {{cite:62537fb531d779f468f133046ce6e396915b8c56}}, {{cite:625b0e1dd15b23678cc7dd07e263455a8f5c9499}}, {{cite:6e78fc03cbd79e6ad378c56037a1ca13abd7fdfe}}
{{formula:4402ebb6-537c-4b82-8574-57ceb498399e}}
| m | 650678b29e937ffa44f6edc3a5611d63 |
For all encoders ({{formula:f933e822-f0b8-4034-8588-fcdfbe997d51}} and {{formula:cafa777e-ddfa-4361-b8f6-6bdcac3be85c}} ), we stacked two GNN or linear layers with the ReLU {{cite:f0125b389384a7de7c896d419f05d9a1a6335006}} activation functionExcept the SGC model, which increases the power iteration times of the normalized adjacency matrix to replace stacking GNN layers..
All the hyper-parameters are tuned on the validation set.
The tuning range of dataset-specific hyperparameters is as follows:
| m | c087aa7ec7ae4b22fc6fd57cd68259e3 |
We choose the same {{formula:6728b1e2-d148-4c58-9679-c4ab925f7ff8}} as {{cite:c23069ab57eed7de459fcd7bea005459f24c26ee}}, which is {{formula:75c0d810-f4fe-44f4-98f7-968d858c9977}} -norm between activations of the last layer of VGG16.
Given unlabelled data of size {{formula:070e47a4-4865-4c95-82c6-6e2605e60f54}} , labelled data of size {{formula:78f4e66b-0c41-40b2-9e4a-f4633ee017a4}} , feature size {{formula:aced9db9-c147-426e-a325-de7d2e5081ed}} , batch size {{formula:37c6ac14-d1d0-44e6-bbc3-b2c6cbb513e5}} and labelling budget {{formula:3a403413-3da9-4fcc-9639-21c2ece97083}} , Algorithm costs {{formula:4855c022-b36a-48dc-89eb-cded70f38aa5}} steps and {{formula:7581c9dc-2527-41f8-a37e-7a4e2b8801f2}} memory with the bottleneck on line 5.
Excluding line 2, Algorithm costs {{formula:036edc45-4ac1-4d71-bda3-14259e3367d1}} in both computation and memory with the bottleneck on line 11.
Since both the original core-set algorithm and our modification requires fine-tuning VGG16 per addition to the training set, and computing the class probabilities requires only a single linear transformation, the final computational complexity is the same as the original core-set search. For core-set sizes 5k to 15k, compute time scales linearly from 25 s to 50 s on a NVIDIA Titan GPU.
| m | 2cfded936bc1c8d1576d64087f86815d |
Previous STR works are focused on regular text and irregular text {{cite:107947f15cc1d65e0eac4203c135212a637c4edb}}, {{cite:44920eb426595d82a99ca6263153bc7b8fa290dc}}, {{cite:a77a385f6944c851895d4bd5566e12f445cb89bd}}, {{cite:eafe768a93de633ddbd0eca8fcee720e447fa785}}, {{cite:f252bd2b3ab81ea9d88134401f4c184d221258ba}}, {{cite:95380b34efd32ea610a5e35190973147f14ea4d6}}, {{cite:c1506f8184ca9e0b5d7eb9ba7905617204a0360a}}.
While high performance has been achieved on these tasks, past approaches struggle with imperfect and noisy input images (hard text). In this work we look at common failure cases in STR models and how models can be designed to be more robust to them.
Conventional approaches to STR {{cite:a77a385f6944c851895d4bd5566e12f445cb89bd}}, {{cite:c4b0dbca44dfab81af0e5b6e3013aa261e08786c}}, {{cite:73a1035de31c614ff2909d83ec6ba5dd4032d93f}}, {{cite:902932549653666f277dd4edaa5855e3b40d4321}} only consider the cropped text image when making predictions and discard the larger but useful scene, which implicitly provides information that can aid STR, particularly on hard text samples.
| i | 3fcb681f0ad8974fe467b0979a7380a7 |
A closely related topic concerns the physical connection between AGNs of different types. While the orientation-based unified model {{cite:ea83d435326945eecd330a7b7bcdef79026ff5dc}}, {{cite:c67e6406a9a4bdcbbe2448450e8a5ff052c1a264}} has enjoyed much success in explaining the relationship between broad-line (type 1) and narrow-line (type 2) AGNs, there has been mounting observational evidence that the two AGN types must possess true intrinsic differences, which are in part or in whole mediated by evolution (e.g., {{cite:7075249f19bf6119e5eecd02d2f71c1bbabc0c69}}). An incomplete list includes differences in host galaxy morphology, star formation rate (SFR), velocity field, and environment {{cite:b2fb6a4b9f710349391c264101f8aecc53e8d0c8}}, {{cite:84d3b6837f09904962f79f2c6d146f87410004c0}}, {{cite:760a31fe06c57935aecabbda413ea76df432921b}}, {{cite:040a29e31a62fb91b736d9937d0e5d88e98361e6}}, {{cite:ffe33b7c5542481f19e7b8f8feeb7df4883b4ca9}}, {{cite:4cce629b23b8d32f2141abffc025ab4b07a2fe54}}, {{cite:7bf995eef188e58356e3d66d061b0e110aa6b52f}}, {{cite:1266437aa59e771804751f4f35aecfe8edc7b992}}.
| i | c94996d9214a5512af6f38f838010c94 |
In this section, we present the main results of this paper, where we derive the convergence rates of GDAD under different conditions on the objective function {{formula:d29af338-0b21-4419-8078-f3e78ea9d43b}} . Our results are summarized in Table REF . First, our approach improves the analysis in {{cite:a9c16de166972f5b3a3b0274073c08036ceae285}}, where we show in Section REF that for two-sided PŁ functions the convergence of GDAD only scales with {{formula:af830e15-12ce-4af1-9c8d-ebf446d2ed4e}} instead of {{formula:3fffbf31-198a-4e64-bc70-99240c2a67ba}} studied in {{cite:a9c16de166972f5b3a3b0274073c08036ceae285}}. Our result addresses the conjecture raised in {{cite:a9c16de166972f5b3a3b0274073c08036ceae285}}, where the authors state that such an improvement may not be possible. Second, our analysis achieves a better result than the one in {{cite:2be9fe603ce3c03bb858ddc4169474884626715a}} for the case of one-sided PL function by a factor of {{formula:00eb957d-ddc2-4076-b237-107e3eccc7cd}} . We note that a nested-loop is studied in {{cite:2be9fe603ce3c03bb858ddc4169474884626715a}} while GDAD is a single-loop method. Finally, our result is the same as the one in {{cite:2a5c74dd0c3d9438e9e74f0ef56429fdd37a6e03}} when {{formula:0830b3f6-60d6-4f21-94b9-0498bbaa0a0d}} is either strongly concave in {{formula:60dfc0bc-2fa9-4aae-88f1-5135df10a747}} for fixed {{formula:d79c1c77-f2e6-478c-bc84-352b3e8cba58}} . In Section REF , we will show that this observation also holds when {{formula:07362073-070c-4fdb-a114-2f6f4ab7c2dc}} is either strongly convex in {{formula:8752cefd-2924-4156-a613-8ca6323dc3b2}} and nonconcave in {{formula:f8232ea3-2a6b-4921-960e-32f3a68fcd03}} . Note that as compared to the analysis in {{cite:2a5c74dd0c3d9438e9e74f0ef56429fdd37a6e03}}, we use a simpler analysis and simpler choice of step sizes to achieve these results.
| r | 2b07166c4a0cf5fee69dff16d0cc4ae8 |
SPGAN {{cite:9cb2a447c16fc6cda3a463012fb7347e1d4b0839}} considers the style change among different datasets and trains a style conversion model to bridge the style discrepancy between the source domain data and the target domain.
However, due to the huge gap between the vehicle datasets in the real scene, e.g., the diverse viewpoints, resolution and illumination, it is challenging to obtain the desired translated image, which is crucial in SPGAN {{cite:9cb2a447c16fc6cda3a463012fb7347e1d4b0839}}, and thus results in poor performance for vehicle Re-ID.
ECN {{cite:32ab59bee75279fbb9595388ae80270e08716d93}} joins the source domain for model constraints while using the {{formula:d6285876-e60a-4ff6-b8b2-ad15d0ab4497}} -nearest neighbor algorithm to mine the same identity in the target domain.
The setting of the {{formula:87614da3-1e18-4ca7-a26b-e20d37b49dcf}} value not only has a greater impact on the experimental results, but the most similar top {{formula:821b7aac-0d44-43c8-b7b3-c939001a931b}} samples are always at the same viewpoint.
UDAP {{cite:362bd40b765a33e58526e12b96f5224398e290c0}} uses source domain data to initialize the model and theoretically analyzes the rules that the model needs to follow when adapting to the target domain from the source domain.
It achieves satisfactory results on vehicle Re-ID due to the strengthening of the constraints on the target domain training. The target domain feature extractor has stronger learnability while obtaining the source domain knowledge.
However, it relies on global comparison, which may cause more clustering errors, especially on VeRi-Wild {{cite:06a7a2a893a54af59b3bee18e7d70de759c7567d}} dataset presents a much smaller inter-class differences than VeRi-776 {{cite:19526c7c7c962fbb7207e6fa3ece3fc57940468f}}.
{{table:8e46882f-1af4-4bb7-94aa-c4ef182becff}}{{figure:0f371086-eab3-442b-851b-e1b48970ef0e}} | m | f5823cbcbc9b93898cec7717064a82d2 |
We propose a Bayesian non-central {{formula:082b112f-de37-45b0-a70b-1f39d9437795}} regression model for neuroimaging
with the Rician model as a prominent special case. The model is applied
to real diffusion data from the Human Connectome Project {{cite:1136da5de19fec4c34148b1f128428d68fc2d6e0}}
and to simulated fMRI data with different SNRs. We show that the results
from the theoretically correct Rician DTI model can differ substantially
from the approximate Gaussian model typically used for diffusion tensor
estimation. The Gaussian model greatly underestimates the mean diffusivity
(MD) and substantially underestimates the FA of the single-diffusion
tensors, which is consistent with previous results {{cite:8bce721d72a0c02873f0c55f5c8fe17e9f4eccf7}}.
We also show that the differences between the Rician and Gaussian
models increase with the b-value, which is natural since the SNR decreases
with a higher b-value. Our results for real fMRI datasets are consistent
with previous work {{cite:df3231933b39add89dead1378c56472151392222}}, {{cite:0ae1e7194236e6904cd520b88ae0aa2b06365090}},
which also come to the conclusion that there are negligible differences
between the Rician and Gaussian noise models. We demonstrate, however,
that the Rician model is remarkably adept at recovering the activations
for simulated fMRI datasets at very low SNRs, which are more common
in high-resolution images; we also show that the Gaussian model fails
to detect activity for low SNRs.
| d | 970091e6157d1a0598390aecfe19e7dc |
In this work, we argue that language descriptions and program abstractions can act as repositories for human inductive biases that may be distilled into artificial neural networks. To test this idea, we considered a tile-revealing task with 2D grids that were directly sampled from human priors.
We found that grounding on human-generated language and programs in library learning not only improves machine performance on tasks that people perform well, but also impairs performance on tasks that people perform more poorly.
Although the idea of co-training artificial agents on language to shape their representations has been explored before, most works utilize synthetically generated language descriptions {{cite:67c5d8e2a9d11d8222727a41c3461f76f62d0d63}}, {{cite:4b06976a1d6bf6e3bcd67f285153b59a81f8b1e9}}, {{cite:4bbfe4ed143aa55a950b4474f205cdb5d9e04994}}. Our work suggests that not all language is created equal: human-generated language leads to more human-like performance than synthetic language descriptions. Human-generated descriptions contain information about abstract concepts (e.g. lines, shapes, letters, etc) that compress description length and are reflected in tasks directly sampled from human priors and therefore better capture human inductive biases.
| d | 571c3600a0125e0a527691febe110e57 |
In the case of bounded uncertainty, the recursive feasiblility and stability have been established in several SMPC methods. For instance, in {{cite:0e779eff177dc07a94a3638d05fc9baecfef2480}} the authors propose an SMPC scheme of time-varying constraint tightening along the prediction horizon based on the tubes of fix-shaped cross section and variable scaling which is computed offline according to chance violation. The tubes in {{cite:a6e5a249ab524290698036be9804888a56c6f553}} are constructed directly by making explicit use of the distribution of the additive disturbance. A recursively feasible SMPC scheme is proposed in {{cite:07ec6a641c0df4037961283f89a6f850db51e184}} by exerting additional constrains on the first predicted step. The work {{cite:2bc9027c803cf8c28a9651acdd4bdc2f440665cf}} guarantees recursive feasibility and asymptotic stability by computing the constraint tightening based on confidence region of uncertainty propagation and adopting the flexible initialization methods. When considering the unbounded stochastic uncertainty, it is typically impossible to guarantee recursive feasibility, since the uncertainty is indeed possibly (even with small probability) large enough to make the future optimization problem infeasible {{cite:864b9feecd24680d2f53f0088604bee56d188c5d}}. One straightforward approach for guaranteeing recursive feasibility of the SMPC problems with possibly unbounded uncertainties is to set the initial nominal state as the predicted value of the previous time instant. However, it disregards the most recent state measurement, without allowing for the feedback, which may degrade the closed-loop performance {{cite:7889331164f7641bda93efbe37beed2f041b8659}}. To cope with this issue, an improved method of choosing the initialization between a closed-loop strategy and an open-loop one online is proposed {{cite:8291ab4201e63069c1ac6311ce9af05deff7dd1f}}, {{cite:82a787ce86899f056a2305b895e2f9c1dcdbca40}}. The key idea in this approach is to choose the closed-loop strategy using the measurement when the problem is feasible, and to choose the open-loop strategy when infeasible. Although this approach guarantees recursive feasibility, it requires to solve two optimisation problems at any time instant to decide the choice between the two initializing strategies. Another recent work {{cite:b5f5af01625c1538244b38b06a04bacb25dd0961}} sets the initial nominal state equal to the predicted value of the first time instant, and introduces the indirect feedback via the cost function, which facilitates the recursive feasibility analysis. A special approach guarantees recursive feasibility for the system with unbounded disturbances in the case of that the chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon {{cite:f8cf84bebc97c171e6f2b45f33b4abe3afd17547}}.
| i | acbd65a8fbe742b45a55c76e60ae0dd4 |
In this section, we provide some initial theoretical results for COLA's uniqueness and convergence behavior, using the Tandem game {{cite:0b76287f86127e795221e9a2fed6e259a156fd83}} and the Hamiltonian game {{cite:7cb7eabcdec91c800d0c2aaa1207b95db6088da1}} as examples. These are simple polynomial games, with losses given in Section . Proofs for the following propositions can be found in Appendices , and , respectively.
| r | 3dd4da984aa8bf1d32eedf2374a17d54 |
3D Model (Fig. REF , {{formula:2c8ae8b1-6783-4df5-9c43-bd595486046c}}{{formula:377483f2-625e-496f-a227-664d35c2fc0f}} ).
Mix3D is independent of the underlying 3D deep learning model.
In experiments, we use MinkowskiNet {{cite:faa152dffdc38458ed5f75f044c5bf1751a1b66a}} and KPConv {{cite:8d5de90b7dc5c62a4e47ae62f9718cacf767886c}}
as state-of-the-art representatives of both voxel-based and point-based models.
The exact experimental setup is described in more detail in Sec. and the supplementary.
| m | 14e2e3708395aa28a75ec20668a229d4 |
We found five sets of observations containing the position of MAXI J1409{{formula:d75b3365-f3ec-439a-8850-fa697a59a291}} 619 in our
BeppoSAX/PDS archive, performed in 1997, 2000, and 2001, and one in the ASCA archive (March 1998). In all our observations the source was in a low
state, with 15–100 keV fluxes in the range {{formula:adde53ac-0aba-4db3-a2b3-51a538d28742}} 2–8 mCrab, and no
spectral variability during the observations. For comparison, an integrated
exposure (over 5 years) of 2.4 Ms by INTEGRAL/IBIS provides
2{{formula:f4ec5649-8704-4d20-a079-0173efb1f7ab}} upper limits on the persistent quiescent emission of 0.2 and
0.4 mCrab in the 20–40 and 40–100 keV energy bands, respectively
{{cite:cf9472091c1de700be589db049df2ebd2455d453}}. When assuming the source fluxes in outburst as measured by
Swift {{cite:758aa4109a34e1bc2f09f8d61719e83b5dd2d907}}, {{cite:69fa2916207c84876e7f88232e7e16fab03d4867}} and RXTE {{cite:e989d6984530d49acef13ee7cfeada32440c876d}}, from
our low state measurement we can infer a dynamic range of 400 in 15–50 keV,
and of 300 in 2–10 keV.
| d | e1fe34f53719c50a313c2aa205c99777 |
Now, since in Palatini {{formula:1f4eb52e-9487-4397-83aa-4aa07f72365b}} models torsion naturally emerges, in {{cite:38f68fd7fb4ef6f1be256ae92f9df1a240c7275b}} we proposed the idea that for formulating {{formula:801c77c8-1052-4bca-8360-184d3bbf46d1}} gravity in the connection language we have to include torsional contribution already into the Lagragian. In particular, also in relation with features of Loop Quantum Gravity (LQG) formalism
{{cite:25c15afa2f1b597187b755a1bf7547948d61b142}}, {{cite:c31bcf55aad6829a4bc32c01a6c3d76233f7f0a1}}, {{cite:8d05f42bac251a338d5deb9a356893fb773efc77}}, {{cite:50ab2f1105ddd42d267d295097908af4dfc43c19}}, {{cite:568ac523d50bf26a00fb520dab61c01a057ce6fa}}, {{cite:b14f519f1c624a04b63dca2780a4ee0f73e24004}}, we considered in the Lagrangian
density a Nieh Yan term {{cite:0aa5c7c3142a713e6364167afd3e00445ca5b4b9}}, {{cite:16e0455640f33af8801425dd5673b22a8ad1c051}}, {{cite:1d1b48098e8cdc8f6b03ed5e646326fbe9107306}} with the Immirzi parameter promoted to be a field {{cite:8f508348cab0ea5e1564a249454b28d534eedac4}}, {{cite:e3bf0701d05b864c9c0ae2783b45e114e19c2ccb}}, {{cite:d86869118c26b7675e15f65ec193fe0237d00238}}, {{cite:04db869e09b3ecd0c44914a6f66667906870b9d3}}, {{cite:ffc091ffa0b9b6284034ce51cfdc02a71feb1e45}}.
| i | 472e3a00e2dc329b3990d1079ebb8bd0 |
Toy model: We consider various configurations of point defects (vacancies and interstitials) in a two dimensional triangular lattice. As the reference model we will use an embedded atom model (EAM) {{cite:e8daceb4c8f90c49b408c331502045b125c63b5b}} instead of an electronic structure model. This highly simplified scenario, and the fact that elastic fields decay more slowly in two dimensions, allows us to more easily perform large-scale simulation in which we can most clearly observe the expected convergence results.
Tight-Binding model: We will also perform tests on configurations of multiple vacancies in three dimensional Silicon (Si). For these tests we employ the NRL tight binding model {{cite:78cbc65da06efd0b1277e13716fb7c3c5af01112}}, {{cite:8ee7df63c7c2e3eba6cf6a847014a62a98260891}}, {{cite:d2df66cc56ab3bef9518e498c331605e32f16eb4}} as the reference model; see Appendix for a brief review.
| r | 8cfd347cb27ea14176b31b9c17926679 |
TFN: Tensor Fusion Network (TFN) {{cite:eae7c33e670b8d9dda1aab8cc16a6de9f340df51}} combines individual modal's embeddings via calculating three different outer-product sub-tensors: unimodal, bimodal, and trimodal. All tensors will then be flattened and used as a multi-modal embedding vector.
LMF: Low-Rank Multimodal Fusion (LMF) {{cite:8a613cda57ace06c71dd70a00b08b02d6b4a58b0}} learns the multimodal embedding based the similar tensor processing of TFN, but with an additional low-rank factor for reducing computation memory.
MFM: Multimodal Factorization Model (MFM) {{cite:9a032bbdd127c9cfdf2b8473241c9ed80dc291dd}} is consists of a discriminative model for prediction and a generative model for reconstructing input data. A comprehensive multimodal embedding is learned via optimizing the generative-discriminative objective simultaneously.
{{table:ff48f572-d36d-48da-86d4-63345ca5dfab}} | m | 830cd9120c19443b64f64dcb3cf0795d |
The Standard Model (SM) of particle physics is now well established after the discovery of scalar Higgs boson {{cite:9e7906b95ab53ed78d9d18a5aa2128a09b8b23f1}}, {{cite:b8004d173fdfde7b6fdb07b3ecdcc1dd8e623357}} at the Large Hadron Collider (LHC). The properties of the Higgs boson is being tested at a very high accuracy in the hope of new physics beyond the SM (BSM). A large class of the BSM scenarios are motivated by the large hierarchy between the electroweak symmetry breaking scale and the Planck scale, known as the gauge hierarchy problem. A wide class of theories have been proposed to address this problem through the introduction of large extra dimensions in the TeV scale brane world scenarios. In particular the models with warped extra dimension as proposed by Randall and Sundrum (RS) {{cite:6f5df68c4de401fda6090c28ac8bffd5efaf26f0}} are attractive candidates to solve this gauge hierarchy problem. In its simplest version, it predicts spin-2 Kaluza-Klein (KK) excitations in the TeV mass range which could be accessible at current hadron collider LHC or in any future hadron colliders or electron-positron colliders.
| i | f51104643e87e270074ab239bab43fcb |
In the past few years, convolutional neural networks (CNNs) {{cite:dfc0cd7896968023411fd3ed7e39bdd911dfce04}}, {{cite:5e02733de677a5fa25aee4b2ef84b1451bb64cec}}, {{cite:2147f215e818f928ecfcdf7d23cede10b7238adc}}, {{cite:bf2ef45216b0a1ba6eb4a3859c13cb6571afda25}} have achieved remarkable success in general image classification tasks. However, recognizing fine-grained object categories (e.g., bird species {{cite:ea8114aef6f118de9d84db11464b066d62ebce25}}, car {{cite:b6966ca8486de8fc81e26e6ca6dea1ba71144dc9}} and aircraft {{cite:dbfb7b395e120f10758d4a4244e515c4f5cff350}} models) is still a challenging task due to high intra-class variances and low inter-class variances, which attracts extensive research attentions.
| i | 1667832e652f5883608f60a9190fab6a |
We also list results for the {{formula:351e8d80-a5b1-495f-9240-d1ce5e3181e7}} and {{formula:49fdb78f-6761-43aa-8d7a-d73f19e94190}} states, since these classical Lamb shift levels were involved in the
muonic hydrogen laser spectroscopic experiments determining the radius of the proton {{cite:755a3277aaa8d79d0339aa71460eb897d5753012}}, {{cite:9772e0b245d249a50b46566ad3d3187642825cad}}. The uncertainty of
the experimental muonic Lamb shift, {{formula:dc48e82d-c656-43c6-b9bd-ad0729e8d7b3}} GHz {{cite:755a3277aaa8d79d0339aa71460eb897d5753012}} (or, more recently, {{formula:69664733-8b8d-49b8-8afe-c08ed153dd0c}} GHz {{cite:9772e0b245d249a50b46566ad3d3187642825cad}}) translates
to {{formula:f7e3a385-fc6e-4f3b-a0ca-d78981b4e77d}} meV, which would be in principle sufficient to resolve the hadronic VP contribution, motivating an accurate evaluation of the latter.
However, currently the experimental value of the muonic hydrogen Lamb shift is limited by the uncertainty of the proton radius {{cite:755a3277aaa8d79d0339aa71460eb897d5753012}}, {{cite:9772e0b245d249a50b46566ad3d3187642825cad}}.
| r | 335bc6a97cae52876a373b60799c02e7 |
The most important difference between entropic herding and other methods is that it does not require specific data points and only uses the aggregated moment information of the features. The use of aggregated information has recently attracted increasing attention {{cite:6afca4f64bf72c53392e9b00f79407502097881c}}, {{cite:c0fcb92a1737ea7840df82b83a9ae1c5aefc9db3}}, {{cite:431ac241cb8291d37a0a4611c5da2df97a8c4ace}}, {{cite:4fc219d70a7a86c3a8d11275d029c102239888e4}}, {{cite:e0c8da606f9c54eb85e5171b8e3f5676a8cd8664}}. Sometimes, we can only use the aggregated information for privacy reasons. For example, statistics, such as population density or traffic volumes, are often aggregated to mean values by spatial regions, which often have various granularities {{cite:c0fcb92a1737ea7840df82b83a9ae1c5aefc9db3}}, {{cite:431ac241cb8291d37a0a4611c5da2df97a8c4ace}}, {{cite:4fc219d70a7a86c3a8d11275d029c102239888e4}}. In addition to data availability, features can be selected to avoid irrelevant information depending on the focus of the study and data quality. These advantages are common to entropic and point herding methods, but nonetheless distinctive when compared with other probabilistic modeling methods. Notably, kernel herding {{cite:2d977c09c465854f914bbe1ccbb49413be6fba28}} is a prominent variant of herding that has a convergence guarantee, but it does not share the aforementioned advantages because it requires individual data points to use the features defined in the reproducing kernel Hilbert space.
| d | c284d35431d621f7951ff014b0c3a268 |
There have been a great number of policy gradient methods since the development of A3C. For instance, UNsupervised REinforcement and Auxiliary Learning (UNREAL) {{cite:743f6e50dbbca8f4f0adb7ee75d3c942e228d1c6}} uses multiple unsupervised pseudo-reward signals at the same time to improve the learning efficiency in complicated environments. Rather than estimating a stochastic policy, Deterministic Policy Gradient {{cite:231f36d32ee62d0539257b081135516c05ab2af0}} (DPG) finds a deterministic policy, which significantly reduces data sampling. Moreover, Deep Deterministic Policy Gradient {{cite:11f7979af2435b3679fa493e07299d680f4e282d}} (DDPG) combines DPG with DQN to enable the learning of a deterministic policy in a continuous action space using the actor-critic architecture. The authors in {{cite:66ed6c6ed531952d04ad7b065379a954af192ea3}} even propose Multi-agent DDPG (MADDPG), which employs DDPG in multi-agent environments. To further stabilize the training process, the authors in {{cite:f48807b40c88b4e92828892cdbbddeebee324995}} introduce the Trust Region Policy Optimization (TRPO) method, which integrates the Kullback–Leibler divergence {{cite:c8ba36c4e8d126cd400dba5a3f0c4f5b3857ffdf}} into the training procedure. However, the implementation of the method is complicated. In 2017, Wu et al. {{cite:5270e72d7188c871772b14697fde037610f24402}} proposed Actor-Critic using Kronecker-Factored Trust Region (ACKTR), which applies Kronecker-factored approximation curvature into gradient update steps. Additionally, the authors in {{cite:5cd0dc964a1aa699425293a52aec241217c945dc}} introduced an efficient off-policy sampling method based on A3C and an experience replay, namely Actor-Critic with Experience Replay (ACER). To simplify the implementation of TRPO, ACKTR, and ACER, Proximal Policy Optimization (PPO) {{cite:606d2508ffff984fc5b6820b5d079bf4adca9b77}} is introduced by using a clipped “surrogate" objective function together with stochastic gradient ascent. Finally, some studies combine a policy-based and value-based method such as {{cite:6b9b945012948824cc43c40b350a98b3d57c4519}}, {{cite:9f88e005940ebe7d7eccfaecb592b8e3690b674a}}, {{cite:d2c2eb11aab13f418eb7adfd1ddc6be85ca1cdeb}} or an on-policy and off-policy method such as {{cite:32cfe329d7b0e456a022902077c1ea104b875db4}}, {{cite:f552ac114dd17218d2e25b10777d2eb9275d25b6}}. Table REF summarizes key deep RL methods and their reliable implementation repositories. Based on specific application domains, software managers can select a suitable deep RL method to act as a baseline for the target system.
| m | e3a8413a024c903aa47dd944f27f65d3 |
The Madelung equations {{cite:4d1f9b90c6aa5fa258b1183be03feff16635e22d}}, {{cite:b09c4a21f8068f60e473286bbee5fb36de312af6}} are two equations that are equivalent to
the one-body time-dependent Schrödinger equation, where the working equations are the same as
the ones for Bohmian mechanics for one-body systems, and the velocity field for
the electron trajectory becomes a fluid velocity field.
The Madelung equations provide a fluid interpretation of the one-body systems of quantum
mechanics, including a conservation of mass equation, except that the Madelung equations do not
contain a pressure, and this is an essential element of fluid mechanics.
The possibility of a quantum-mechanical foundation based on the Madelung equations is
investigated by Wilhelm {{cite:0689c2e218e6ef55b3addd21a57707711c97b437}} and Sonego {{cite:ee32ddf48d2a62bb1fdd12b72ddbe62eed7380d1}}.
Heifetz and coworkers {{cite:b5009280fafb8db4f9bdd552a76a6a6f4a95ac34}}, {{cite:62186fd73fd888ca56d651d7222cb6a47691a728}} explores the thermodynamics of Madelung fluids.
There are many generalizations of the Madelung equations {{cite:fd0223ac5585132b668b5f6a8fa3f41b1f8bb76d}}, {{cite:f6fe0763464b85c978765221f19d475c5610ac97}}, {{cite:9ad21a40bf79fe9c7da32ccc41b22cd26dda54d2}}, {{cite:6554a46a55d969035f34a0655d421572382e5780}}, {{cite:8c5bc00c36664881d467df2c5acf720050d2fac3}}.
The generalization by Broadbridge {{cite:f6fe0763464b85c978765221f19d475c5610ac97}} and Jamali {{cite:8c5bc00c36664881d467df2c5acf720050d2fac3}} use a complex velocity.
Tsekov {{cite:113aebb681a7e5002b99c96b5332269ebcbf33fa}} also uses a complex velocity to derives a complex Navier–Stokes equation.
Vadasz {{cite:db083b3cf2cdd441d42f9745ea5f95a7dc4e8542}} derived an extension of the Schrödinger equation from the Navier–Stokes
equation. Because of the velocity definition, the Madelung equations do not provide a
reasonable model for quantum mechanical stationary states with real valued wavefunctions
{{cite:95782cc84166fc7621d4ba1f9593f5b9963f07f4}}.
Such quantum states provide a static Madelung fluid, and this is not in agreement with states that have
a non-zero kinetic-energy expectation value, suggesting that a satisfactory model should have
some motion.
This problem of a static-electron fluid can be treated by either introducing the same velocity
field mentioned above for Bohmian mechanics, or, for the case of real valued eigenfunctions,
by the method discussed next.
| i | dd51a84accd21ceaec0e3085caa55834 |
Along such lines, it has been observed that well-understood analytic properties of scattering amplitudes have a novel realization in celestial correlation functions, yielding surprising features from the viewpoint of standard CFTs {{cite:bccbe3e61a50213d2dd89d80325601d00bc09c8f}}, {{cite:2043e30985542e4ed4c1d8b0f9d79e9b3fdc4ff2}}, {{cite:d9364ccd5035b638981ad521420e2094eb4ff4c0}}, {{cite:1b29daaacb1b87d223b810d90a0eef1dc73332da}}, {{cite:02a130d69b1e6fe50c05fcfef9ed059076c51bfd}}, {{cite:c04fe18326a0b5fb2cf330e812d34c968f524247}}, {{cite:9d4cfeac802eac86fbd7f1f7e45a369f8cae8f6d}}, {{cite:97bb9d9c43b9747f25f084f3b59b90ec5263c953}}. In particular, references {{cite:c13b85c1f283da031708f9487e096859c5f277ec}}, {{cite:128278b229c9c40f5fe2f4f4f309af231b59e5f9}}, {{cite:4339d81ac269c74506b1e64988cefa1e45295468}}, {{cite:b0e803d4dd8960623271a892074c4519834a890c}}, {{cite:bd8df3808336237b0da689b872a3558d3f99ed2c}}, {{cite:dce063cb4943190b6f30bb46dfa4845efcaf7c16}}, {{cite:1013c12d0ba5ed3ebe20786774867a86cebb9976}} have considered the celestial realization of the tree-level S-matrix with massive particle exchange at both three and four points. It was observed that the three-point correlation functions are regular and non-distributional (as opposed to the all-massless ones) and the four-point function has a simple structure closely related to a Generalized Free Field Theory (GFFT) (see also {{cite:1013c12d0ba5ed3ebe20786774867a86cebb9976}}). Indeed, using a scalar theory as an example, {{cite:c13b85c1f283da031708f9487e096859c5f277ec}} pointed out that such four-point correlation functions in CCFT satisfy a novel realization of the optical theorem. More precisely, the four-point function has an imaginary piece controlled by three-point correlation functions through a conformal partial-wave expansion {{cite:c13b85c1f283da031708f9487e096859c5f277ec}}, {{cite:128278b229c9c40f5fe2f4f4f309af231b59e5f9}}, {{cite:b0e803d4dd8960623271a892074c4519834a890c}}, {{cite:dce063cb4943190b6f30bb46dfa4845efcaf7c16}}. This follows directly from the analytic factorization of the S-matrix and provides a first approach to the underlying unitarity of CCFTs.
| i | d11d07f562a0397c5d2188d50df65467 |
In this study, we have used distributions of injection electrons with a broken power-law form, which has been commonly adopted in studies of blazars observed by Fermi LAT (e.g., {{cite:000459e3488f26b16b5b6841cd567bedf625086d}}). The break energy {{formula:b9528345-e7f0-45b9-a8b7-97df907c159d}} used in this work corresponds to the anticipated threshold of a diffusive shock acceleration (e.g., {{cite:fc17bb13ebee373f6c6f21ad54f03b200f2aacd0}}). On the other hard, the high accretion rates are adopted in order to fit the RXTE/PCA data, which exactly corresponds to a standard thin accretion disk mode.
| d | 236b99326fe185d9781f53066b3e4d0a |
This work is the first attempt to design neural memory networks for traffic forecasting.
Although effective as shown in the evaluation results, there are limitations we spot in the approach.
First, we extract traffic patterns to memorize in advance, but it is possible that the extracted patterns are redundant even after strict filtering or may not be used.
As such there is a need for finding important patterns and optimizing the number of memory slots.
For example, a future study may investigate how to learn and extend the key space during the training phase {{cite:b58a9066e66f7798510da505a5207492ee27fee4}}.
Second, the learning of PM-MemNet only proceeds in referred patterns. Because there are no further losses to optimize memory itself, patterns not referred are not trained. This training imbalance among memories is of interest, as a model could not generate meaningful representations from rare patterns. A future study may research not only how such representation imbalance affects the performance, but also design a loss function to reduce the representation gap between rare and frequent events.
Third, we use cosine similarity in this work, but it may not be an optimal solution since it causes mismatching with noisy traffic data. Also, the optimal window size for the pattern matching is one of the remaining questions.
A future study may focus on approaches to effectively compute the similarity of traffic patterns.
Designing a learnable function for the computation is one possible direction.
Lastly, we show that a model effectively forecasts traffic data with a small group of patterns.
It implies a new research direction of comparing results and learning methods that work with sparse data, such as meta learning and few or zero shot learning {{cite:b58a9066e66f7798510da505a5207492ee27fee4}}.
| d | 66bd69905ce8764bf1c1a1c711bec34e |
LoRRA {{cite:07f7c36473320a17e1f929fd8f0901a472570ce8}} was proposed as the baseline for the 2019 TextVQA challenge and is composed of three major components - one to combine image and question features, another to combine OCR and question features and the third one to generate the answer. M4C improves the fusion of the input modalities through the use of Multimodal Transformers which allows both inter-modal and intra-modal interactions. The multimodal Transformer uses features from all three modalities and uses a pointer-augmented multi-step decoder to generate the answer one word at a time unlike the LoRRA model that uses a fixed answer vocabulary.
| m | 65acd92237de9db634948bdbdaa7990e |
Nevertheless, all of the aforementioned approaches share the same limitation: they require representative pairs of decimated and fully sampled data, which is usually not available in most seismic processing projects. Whilst relying on synthetic data or field data with similar characteristics (e.g., from nearby survey) may alleviate the arising of generalization issues, the trained network is usually expected to perform sub-optimally at test time when applied to a different dataset. We refer to {{cite:383612db32b1c3e08c4fd6d47a86fd23ef49fe96}} for an in-depth analysis of the generalization issues of supervised learning approaches in the context of seismic data reconstruction. So-called domain adaptation techniques (e.g., {{cite:e5be5ba0c8dd3fcbf4a9a1f9ef53d4f67fe28e7c}}, {{cite:796778d7bfafafb031dd9f72522215ee0ed35b2c}}) may provide a remedy to this problem; however, such generalization issues have also motivated the development of a second wave of deep learning based algorithms that use neural networks in combination with the known physics of the problem to drive the solution of the inverse problem towards physically plausible solutions. Along these lines, {{cite:1bc92602192adda0f6e84bb255c250ca3dba10c1}} propose to solve the seismic reconstruction problem in an unsupervised manner using an untrained network as a deep prior preconditioner following the Deep Image Prior concept introduced in {{cite:a7d0acee74d3a15b67130f116fe580d3734bf0fe}}. Whilst this approach circumvents the need for any training data, it is currently hindered by very slow convergence and it is shown to be incapable of recovering strongly aliased events. Anti-aliasing, slope-based regularization {{cite:c0c530406427e03ed9e32b4b459543791b55ae05}} or a POCS-inspired regularization {{cite:f3b65332d363ec9e0f4bc24d815e36dbe9f9c3c1}} have been further proposed to increase the interpolation capabilities of such deep prior networks.
| i | f8bc6de1d9ec35fc2389ef5339e97a72 |
To demonstrate the effectiveness of the proposed CMVAE, we draw comparisons with several state-of-the-art cross-modal matching baselines. For background music recommendation in this article, each video has exactly one background music as the ground truth, so the co-occurrence information necessary for collaborative filtering methods does not exist. Therefore, collaborative-based methods (e.g. NCF {{cite:4aa7214aa7afc6ffdce6054d0dec0d0c5e74f0b0}}) are not applicable in our paper. For methods where the original task is to match two sources with a single modality, we concatenate the visual and textual features as the “single modality" representations of the micro-videos. The baselines are listed as follows:
| m | fecb5961e442454e5b834f0602cb27c1 |
In addition, studying planetary populations for orbital periods of less than 2 days is essential for understanding planetary systems and their evolution. Indeed, such orbital periods seem to highlight the presence of strong planetary magnetic fields (cf. §5.3). They may also highlight the presence of some star–planet interactions not taken into account in this work (see §REF ). Uncertainties remain regarding the value of the planetary magnetic field {{formula:112709bd-6317-4e7b-86de-fea50a511316}} . Indeed, this latter could reach values much higher than those assumed in this work {{cite:42b322c7403cab7ad35178d21b897065b1d491ab}}, {{cite:613cd00720c469074e6c5193e973023a061dc663}}. In particular, from dynamo considerations, magnetic fields as high as 4000 G are expected in hot Jupiters during the PMS {{cite:e90373d5ba935dc4814283a1e779de1e29bcf250}}. This would significantly affect the planetary distributions by enhancing the depopulation of star–planet systems at short orbital periods, whether in the case of super-Earths or even giant planets. Finally, although star–planet interactions may be necessary to account for planetary populations, they only concern planets close to their host star, which are thus located below the habitable zone {{cite:7e4a01da789771ba5c105c009386b7173cf127c6}}.
| d | f55931ce3da7737eeb267cda0ac91f24 |
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