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For the classical wave equation (REF ), this phenomenon has been observed by Harmse {{cite:b0e20fffa01b51ff1a8f79d99a8e1401d66357b8}} and Oberlin {{cite:86199e5bad4a4958cf5cb50bf25dfc043692ecd7}} for the diagonal case {{formula:945e7095-1e51-42f0-8d31-09c399fc23b8}} and {{formula:65a060ca-0156-4eaa-80c3-c239ddcd00ce}} . Later, Foschi {{cite:93f79853e387d0ef3a9b6c6252206659541fa78d}} followed the scheme of Keel–Tao {{cite:b366fc7a382374b957820fd7553622a7520c8488}} and obtained the inhomogeneous estimates for the currently known widest range with {{formula:cd47ba10-d644-4e68-b670-4fb047b96606}} and {{formula:3e2099e8-9fae-455e-b9ea-c61e78c4f7d9}} .For related results on the Schrödinger equation we refer to {{cite:f3a2ab9916cf7044e72d7089c5222b9506134ec1}}, {{cite:24cfbb1357d685c51f09928b543a1dfd09732ae4}}, {{cite:b109a9652b455a2d16cdf9f29b0ecdf8c9bd9795}}. Furthermore, Taggart {{cite:85b547996ba17f5891dd18a1ef45a1478bb99f72}} obtained more estimates involving the Besov spaces. More recently, Bez, Cunanan and the third author {{cite:1174d207e782cc9b86bf1a0d4fed23b4295554f3}} obtained certain weak type (in temporal variable) estimates in borderline cases.
All of these results are essentially based on the dispersive estimate
{{formula:a627a796-5c4c-4764-a7d5-542d15c6b8bd}}
| r | 2a19ddd66f01806284c77cab65102cdd |
The models are trained using the Adam optimiser {{cite:63c4d1f28d55931a3da43a7e403db11fa68e9bfe}} with a learning rate of 0.0001. To reduce overfit within the models, the feed forward layers in all the models as well as the convolutional layers in the CRNN model contain an L2 penalty. All models also use a batch size of 32, as this is the maximum size the available VRAM can handle. The embedding layer produces a 512 dimensional vector in all models and the input spectrograms are three seconds in length and consist of 128 mel frequency bins.
{{table:d11a8d22-3e49-425a-a081-66a646f5b0c2}} | r | 9dfbe8f7c0418fb6e3ca99d445abd48b |
where the modified Mathieu function on the left can be approximated by the series on the right; the notation therein is different from the notation in our paper, but the {{formula:b9351339-5006-4464-8e8b-9fee1c95c360}} s are Bessel functions and the {{formula:43239b16-7c44-4939-81bc-131fa145cade}} s are the Fourier coefficients for the ordinary even period-{{formula:b34e0398-7c1f-4a95-87d1-6b527e1b1ad3}} Mathieu functions. These are not the only series one might use. In {{cite:bd7a028d042bf58e03a931f45fa6bfac065a1e60}} (and in {{cite:7969b865daf9bd1bc4580e5909f8e89ed35c0532}} and the DLMF) we find the following expansions, which the authors claim are rapidly convergent:
{{formula:4ff722ce-a0dd-4cce-b1a9-a36f878ea431}} 2n(q,x) = (-1)nA02 k 0 (-1)k A2k Jk(s)Jk(t)
| m | 950b703fe689380320cefa09530cc9e2 |
The problem is further complicated when the scene is dynamic instead of static. The majority of existing approaches have been developed for static scenes only - i.e., the corresponding relationship between two images is characterized by a global transformation (e.g., affine transformation and perspective transformation, as shown in Fig. REF a). Such single-consistency feature matching is not appropriate for dynamic scenes in which there are multiple separated local transformations associated with several moving objects (e.g., Fig. REF b). Note that due to the existence of multiple consistency, conventional wisdom of improving the robustness of single-consistency matching such as RANSAC {{cite:0c20b29612914740de0d5d83e865066645904a2b}} and USAC (the modified version of RANSAC) {{cite:7b18adcbdeda9933223a9ba544a53873fd3fcc0c}} easily fails.
| i | fd3ef5977d05258da73c898d9d257e58 |
ATOC (Attentional communication model) {{cite:f9f0e80919c5383ac64249349c3a27f0b16e6749}} designs an attention unit to receive hidden states and action intention for each agent. An agent determines whether to communicate with other agents according to the attention unit. ATOC leverages a bidirectional LSTM unit as the communication channel.
| m | 970d335d64d05270a2f583083565c8a1 |
One of the most remarkable results established at the LHC is the smooth evolution of particle
chemistry from small to large systems as a function of charged particle multiplicity{{cite:b0adb8e054232288576473a65abf343b352fcc5b}}.
The particle yields normalized to charged-pion yield evolve monotonically and continuously as
a function of charged particle multiplicity independent of collision energy and system size,
as shown in Figure REF (right).
These data also demonstrate, for the first time, the presence of strangeness enhancement
in high multiplicity collisions of small systems, the effect being stronger for particles
with higher strangeness content. The original interpretation of this phenomenon, considered as a
signature of QGP formation in heavy-ion collisions, is not anymore straightforward.
In the strangeness canonical approach, the multiplicity dependence can be explained by requiring
local strangeness conservation while the bulk of the particles can still be described in the
grand-canonical ensemble.
Deviation from this description is present for the {{formula:c3482228-bbc3-47bc-8404-4a287f00275b}} ,
while a better description is obtained for {{formula:641b4177-37ee-4812-a9a0-c850d74bd6be}} and {{formula:3b3003d8-66ad-4d8a-a262-3f66a1516d93}}
applying core-corona corrections. An interesting deviation, is also present for the {{formula:bb0d3cd9-0431-491e-bfc0-14f2e322ad5a}} meson:
being a strangeness-neutral particle, a flat multiplicity dependence is predicted, but a trend
is observed.
| r | e06be410dcb27ee6f2426a3d594d9c82 |
We have considered the Fe/Si mole ratio as an observable of our MCMC Bayesian analysis in addition to the planetary masses and radii. Even though the Fe/Si derived from stellar abundances and that obtained from rocky planet densities could depart from a 1:1 relationship {{cite:e13f28d03867b18329996d2ae0e7e11d5b0e1537}}, {{cite:15350057b5c25b95c4d0b95b1ca22d880b655dc7}}, considering the Fe/Si mole ratio contributes to reducing the degeneracy between the rock+mantle layers and the volatile layer {{cite:14ae7bb6db3f8266e26b3ff481acded9e1277e1d}}, {{cite:0224adccb9601fdd75ad7ddec2cefab13d6ad542}}, {{cite:a3403457f82f283c3f26f79765add8af04152de0}}. Particularly, assuming that the planetary Fe/Si mole ratio is similar to the Fe/Si ratio of the host star improves the determination of the CMF, but does not necessarily contribute to the determination of the volatile mass fraction in volatile-rich planets {{cite:f2485e51fba4d5f7713d24646ebe2bfe99dff654}}. This is the case of the TRAPPIST-1 system, where the inclusion of the Fe/Si mole ratio as an observable in the MCMC Bayesian analysis refines the determination of the surface pressure for the inner planets of the system, but slightly reduces the uncertainties of the WMF estimates for the outer planets {{cite:c7cb93e3da8cb1e594cdc6acb179de2368eb14f1}}. Therefore, considering the Fe/Si mole ratio does not affect the volatile general trend of the planets within a multiplanetary system.
| d | 765978997e721ac28ea27f2b191ccb89 |
Our work: We propose MultiGuard, the first provably robust defense against adversarial examples for multi-label classification. MultiGuard leverages randomized smoothing {{cite:dad58a042a2f8ab02206843cba1d4ddcd8c5bb69}}, {{cite:df748d838c145396f16a28f3af82b712cff1da7f}}, {{cite:e6da638353a50e494628714bd9da8dc6eb63cb68}}, {{cite:f7b114ff08c04302be4a98a36843e3d0822437b4}}, {{cite:a66072f197214159c453d3b9dc94780b986b39f4}}, which is the state-of-the-art technique to build provably robust classifiers. In particular, compared to other provably robust techniques, randomized smoothing has two advantages: 1) scalable to large-scale neural networks, and 2) applicable to any classifiers.
Suppose we have an arbitrary multi-label classifier (we call it base multi-label classifier), which predicts {{formula:2293199b-5068-4d01-9d88-cd0a3f4e2582}} labels for an input. We build a smoothed multi-label classifier via randomizing an input. Specifically,
given an input, we first create a randomized input via adding random noise to it. We consider the random noise to be isotropic Gaussian in this work. Then, we use the base multi-label classifier to predict labels for the randomized input. Due to the randomness in the randomized input, the {{formula:c1d079a9-22bc-481f-9632-67418dca4a1d}} labels predicted by the base multi-label classifier are also random. We use {{formula:c89b66eb-09b3-48c0-add8-7e4411e6f07b}} to denote the probability that the label {{formula:a8143243-54aa-40d5-b631-5d31f1c8c726}} is among the set of {{formula:7b20e629-0131-4162-ab9d-7cbd05cf2edf}} labels predicted by the base multi-label classifier for the randomized input, where {{formula:01c306e6-f2b4-45ec-a925-40d313696d5c}} . We call {{formula:cd5de025-1a23-4afb-b3c2-4cfa2363deff}} label probability. Our smoothed multi-label classifier predicts the {{formula:66755927-0280-4bc1-81d4-5ae8624638b1}} labels with the largest label probabilities for the input. We note that {{formula:3ffbffa2-b66d-4d0a-a594-d4caf0b17634}} and {{formula:5c00aecc-9c36-4e46-9947-f09d88a117e3}} are two different parameters.
| i | 5ecd018cbc82fb13773bb1d57b71b982 |
Two-stage Methods Early methods in Novel Class Discovery {{cite:af97a7b20c1443aa741e799100eb676d5395db9f}}, {{cite:8fc29304f70c78c01fa60eb0aa2178581cf201c7}}, {{cite:01bd9e9f7f2334751d7f248c5f12af599f749c65}} operate in a phased setting. In the first phase, the model learns from the labeled data, and in the subsequent phase, it discover novel categories from the unlabeled pool. MCL {{cite:8fc29304f70c78c01fa60eb0aa2178581cf201c7}} and KCL {{cite:af97a7b20c1443aa741e799100eb676d5395db9f}} learn a binary similarity function using meta-learning in the first phase, and use this in the category discovery phase. DTC {{cite:01bd9e9f7f2334751d7f248c5f12af599f749c65}} first learns a feature extractor on the labeled data. In the next stage, these features are used to initialise a clustering algorithm {{cite:802d3413fe5dac355abd14a0b69115c7dd5024c4}}, which further fine-tunes these representations using the unlabeled data, thereby improving class discovery.
| m | 83e9de7316b407d1bf1c5d04d65fc272 |
Recently, numerous deep learning algorithms have been designed to classify EEG signals. A convolutional neural network (CNN) has been successfully applied to EEG-based BCIs for end-to-end feature extraction and classification{{cite:454e3bef3a9446ccdb8d5ab696645ff420232978}}, {{cite:381f0b3920a9e4faffd007d5e011e81b42d73f66}}, as well as computer vision and speech recognition. Schirrmeister et al.{{cite:ce0ab9478d80b28f14eb127bea5854032f3af6b5}} proposed CNN architectures to decode raw EEG signals with a range of different architectures. Although the features were not fixed priors, they achieved as good performance as filter bank common spatial pattern (FBCSP){{cite:2f5a34b8bb866009a4ecea41b6b201672bb5d604}}, which has been most popularly applied to feature extraction for MI classification using EEG. Lawhern et al.{{cite:1e8953cc1f79d4b5fdc4bd68c531eb4f7d1bbed9}} designed a single CNN architecture that is robust enough to classify EEG signals from different BCI paradigms (P300 visual-evoked potentials, movement-related cortical potentials, error-related negativity responses, and sensory-motor rhythms).
Some studies employed 3D convolution with 3D representation of EEG to preserve the EEG spatial representations{{cite:b53cded101a34bab84e0f6b68733a55eed1a237c}}, {{cite:2622373208aa773de23718dfa3c7ecc31446dc36}}. Still, most of these approaches result in sub-optimal spatial feature extraction due to null values around the corners of the channel montage.
| i | 82441adf60f2c2cafc2ea51ac76a70f7 |
1. {{formula:a844351f-d509-4df3-8cf1-45fa0ff662c2}} -completeness for estimating local quantities. The proofs of our first two {{formula:a68a2e21-6063-4be6-a1ae-07f33b4236d2}} -hardness results (Theorem REF and Theorem REF ) are similar, so we focus on APX-SIM here. Intuitively, our aim is simple: To design our local Hamiltonian {{formula:42534722-d250-464d-826a-51c64e3ca9cd}} so that its ground state encodes a so-called history state {{cite:5b08ddc73302628f147dc425e3da2f67946044cc}} {{formula:77cc4aa5-5224-4404-95fa-7000d1592bf8}} for a given {{formula:23748c39-3d52-4b86-9599-36aef065f5cc}} instance, such that measuring observable {{formula:d954d88e-ccc2-49d1-a9eb-e5fdcf439363}} on the designated “output qubit” of {{formula:a799d460-2a0c-49f3-bab5-c9041b6dcf8f}} reveals the answer of the computation. At a high level, this is achieved by combining a variant of Kitaev's circuit-to-Hamiltonian construction {{cite:5b08ddc73302628f147dc425e3da2f67946044cc}} (which forces the ground state to follow the P circuit) with Ambainis's “query Hamiltonian” {{cite:74a2c8d91ab1e7ede2142cd359541f65b24400e1}} (which forces the ground state to correspond to correctly answered queries to the QMA oracle). Making this rigorous, however, requires developing a few ideas, including: A careful analysis of Ambainis's query Hamiltonian's ground space when queries violating the promise gap of the oracle are allowed (Lemma REF ; more on this below), a simple but useful corollary (Cor. REF ) of Kempe, Kitaev, and Regev's Projection Lemma {{cite:ba02f43cc2786c0270ba1ff6d35223b7410c2759}} (Corollary REF , showing that any low energy state of {{formula:6d88fab7-cb80-4171-8dcd-91517305f702}} must be close to a valid history state), and application of Kitaev's unary encoding trickIn {{cite:5b08ddc73302628f147dc425e3da2f67946044cc}}, this trick was used to reduce the locality of the clock register. {{cite:5b08ddc73302628f147dc425e3da2f67946044cc}} to bring the locality of the Hamiltonian {{formula:641b6ba7-2010-49cb-b7d4-d0ed06674f66}} down to {{formula:589f55e4-b484-4f81-b874-476c5c7538d1}} (Lemma REF ).
| d | 9883c428c709b03871dc6a0b740d0760 |
COCO. We also evaluate the proposed DucTeacher in classical SSOD setting on COCO {{cite:00600840a24297114cd3c1e0014f974f8b05764c}} following Unbiased Teacher {{cite:6b9ddefab9eca083df7c49af06af319d12d7397e}}. Table REF shows that DucTeacher achieves state-of-the-art performance under different ratios of labeled data. Note that 1{{formula:4210db8b-31fc-4fff-82bd-b766a7c55def}} means that 1{{formula:b1115539-5bc8-4824-94d5-b72984d5b621}} of the total image are labeled, and the others are unlabeled. Although DucTeacher is focusing on tackling the noise prediction problem caused by multiple domains and class distribution shifts among this, DucTeacher can also improve detection in COCO.
{{figure:13ea690f-18e6-4aba-a212-bbdabe70b11d}} | r | 8b0fc1194f6781c66c138de63939a4bf |
where {{formula:ff25f367-9d22-4bce-ad3c-2b671a457aaf}} is the standard deviation of the pulse, which is related to the frequency at which the pulse has the highest magnitude, {{formula:e7f1afa0-19d9-4d22-95dd-566eea2fefea}} , and {{formula:66e911fe-489e-4d2d-a926-a930ae151788}} is the time at which the pulse peaks, which is set equal to {{formula:1a46225f-5f31-4a4d-8a7a-e59c24531ca6}} to start the pulse smoothly.
The pulse is applied uniformly on the {{formula:759a4cf8-94d6-4595-b5e9-0d74ff34dbd6}} edge-centered points of the Yee-grid {{cite:0afaab498adc2cc37f33ae07700679c9a7fff2d6}} located on the {{formula:9d471f0f-f23d-464b-ae24-938cdca52d63}} plane bounded by two metal conductors, as indicated by surface `e' in Fig. REF for the packaging and microstrip circuits.
A soft source is used to avoid undesirable retroreflections from internal parts of the circuit from disrupting the incident signal {{cite:ca321a78a0ce02e5d8a4725f24144250b062826f}}.
| m | c70253750af57459acde83bc86e75ebe |
(ii) In {{cite:adb55454ada55d865f35d0ab0b0ca0eda10b3f87}}, {{cite:074cbd2ee244c9c20a1fc92d42ad9f0238638cbc}}, the authors have studied the distinction between black holes and naked singularities using the images of their accretion disks. They have considered a simplified model of spherical accretion onto the central object and studied shadow and images of Joshi-Malafarina-Narayan (JMN) {{cite:72fa4ab37dc2178d269049b5fa40ce460c392066}}, {{cite:34cbc2ec3f9d365a1c5b9ab71dd826c6478cb92c}} for naked singularities.
| d | 4ba987a61b419d1c035b9b87d7c14368 |
OLSTar: the population ordinary least squares (OLS) estimator on the target data.
{{formula:ac4ac60d-aab4-4a5b-9ebe-63b7d5225d83}}
This is the oracle target population estimator when we restrict the function class to be linear. Hence the target risk of OLSTar defines the lowest target risk that any linear DA estimator can achieve.
Causal: the population causal estimator via the linear SCM
{{formula:05f7a718-ead6-4a25-99ea-f768675b5f31}}
where {{formula:9bc0e765-c05d-4a56-88ef-d5124ea32613}} appeared in the last row of the SCM matrix in Equation (REF ).
Note that this formulation of the causal estimator assumes that there is no intervention on {{formula:49f6bda4-3aaa-4ff0-bbfa-deda04e5e755}} and the intercept is also zero. The Causal estimator is closely related to distributional robust estimators. That is, the Causal estimator is the robust estimator which achieves the minimum worse-case risk when the perturbations on the covariates are allowed to be arbitrary {{cite:8492cac797c98e75fd7e4e57641ba8041f0df8f4}}. However, in our DA setting where target covariates are also observed, it is no longer clear whether Causal achieves a low target risk.
| m | f7516815a4d4f7ee232263a95ce7a5d9 |
On the other hand, when a mechanical constraint is put to graphene, however, it causes deformation, which changes its properties and improves its technology uses.
This unusual range of elastic response opens a new opportunity to explore the changes induced by the mechanical constraints on the electronic and magnetic properties of graphene.
It is found that the local field of a non uniform deformation can open an electronic gap {{cite:a1d796d99e45890eb350053a162270a661a0ac1b}}, {{cite:dd953028536e81391b2c1ff8e88bb93072fcfad2}} or create a pseudo-magnetic field larger than 300 T {{cite:33ed01e66b272016b63351205415bd439e83a5eb}}, {{cite:a31eae10ce82e2fe6959ea3678342bd8fe72fa58}}.
Furthermore, researchers are currently interested in electron processes associated with dressing fields, which are being investigated in a number of systems
{{cite:2b5c4ee0fc3319610c97b0ac0e7e10e40a3bd022}}, {{cite:8452c23ad55f5c4042fae463fd9a1f6b2588d545}}, {{cite:7a88c488c02ba93282006a9a1a3fc7920cff6955}}, {{cite:d3f066fca18216dbfb108f5cf7bb006ebb4a9734}}, {{cite:c96b383b8074230cf20cc0be681bfdd96db36d89}}, {{cite:16bba96cdd8fa98ea562c24ee13863d3b393aeed}}, {{cite:acaa832c7e0e328de92c527df727aacdaf620a05}}, {{cite:5767fb2ab479b2a62bc40ea6b6bfe7ead6686d6e}}.
Moreover, the production of dynamical gaps in the spectra of Dirac electrons {{cite:8c570d755c00cc0316bd2032a6c22fa313dd9c05}}, and the removal of the Klein tunneling effect by strong radiation {{cite:8b266f107bc283ce4bbdbad529d703514949e452}} are among the first noteworthy results obtained with graphene dressed by the monochromatic field.
Many theoretical investigations of electronic transport have demonstrated and shown that the behavior of the transmission probabilities is highly influenced by the amplitude and frequency of laser light {{cite:769f0d8217412d131a62edd51517d86e111dcc37}}, {{cite:27fd3f3906c5eeb73706e7b49e1ab62a0694dc08}}, {{cite:b265c084a2f2da0ffa32190141293053aa748a79}}, {{cite:aef0fa0e181559421838d8a8106543fbd6f7b2e9}}.
| i | 4ef03d926e9440023a1da07c55a5974d |
There is of course the possibility of using lasers to accelerate a sail to relativistic speeds in the space of a few
minutes, as proposed for Breakthrough Starshot. However, even for a mass of just 2.4 g and a theoretical
albedo of {{formula:5e2ba527-cd6f-48d7-8a07-9795cdc47cb4}} , which no metal has, even in the microwave band, this is fraught with many, perhaps insurmountable,
challenges {{cite:69dfca318830687b90440b298f801a33116f23cc}}. `Oumuamua has a much lower, and realistic, albedo and even if we assume the possibility that
the surface has been tarnished from {{formula:a3ec4552-64ec-4ceb-870e-12c674cd9e82}} by its journey, its mass implies a power requirement of {{formula:11aa2357-5a22-46d8-8da7-91100e18230f}} W,
which is {{formula:8cadcc62-65ca-425c-9c3a-9b0791699f3e}} times today's most powerful lasers.
Other fantastic power sources include massive stars, microquasars, supernovae, pulsars and active
galactic nuclei {{cite:d6ed205fce8f154f880fa7d9bd20bc50b9c23836}}. However, life cannot evolve in proximity to any of these objects and there is no
discussion of how the sail would be transported close enough in order
to take advantage of their immense power output. Thus, the Sun (or any parent star) remains the best option,
since it provides vast amounts of continuous power for free, the full utilisation of which would be an indicator of an
advanced civilisation {{cite:079e07047585898200d2e2fafa5a3dd4ff5f791c}}.
| d | 3119fd4fb53197f60a5d47393d872cd6 |
Finally, as alluded to above, there is a second motivation for believing in the existence of preclusion, one
completely unrelated to any role that may be claimed for preclusion
as a desideratum for addressing issues of probability in the Everett interpretation. It has been argued for decades, using a variety of approaches, that quantum mechanics and relativity taken together imply the existence of a minimum spatial length scale at or near the Planck length (for a review see {{cite:f5af1b92d9640aed85bf212734c2e2e45da57d7c}}). Buniy, Hsu and Zee {{cite:ef600849ef9b1c717f7fa2702d358238afccde03}} argue that the existence of a minimum spatial length leads in turn to the existence of a minimum length for state vectors in quantum-mechanical Hilbert spaceWe note that arguments that lead to this conclusion may imply a more complicated rule for preclusion than the one employed in this paper, with a fixed {{formula:d104f9ee-625a-4336-a815-b314a4d49e86}} in all situations. For example, a minimum length of the Planck length {{formula:ab8e4e4a-47c3-4684-bd1b-9e1438ed33a3}} suggests that a device of size {{formula:3474e412-b2fe-4889-9b68-8ffb9065799d}} can measure angles no smaller than {{formula:e6d63dcc-3589-4cd9-a5eb-3d1673f2b7e7}} . The change in the state vector of a qubit caused by a rotation, which change is itself a state vector, should be precluded if the magnitude of the rotation is smaller than {{formula:e3ae91db-f5f1-4b48-af7d-4c79d5107508}} . Performing a {{formula:c81d82cf-be87-4c90-9243-91867dcd5713}} rotation about the {{formula:158f8967-c72c-478e-a321-eb9ba7ae3f5d}} -axis of a state {{formula:8ce6833d-a720-4de0-bc7b-51c93e624f5a}} spin-up along the {{formula:1018da78-a4b5-4445-ae9b-54ba9d25ff4c}} -axis, and assuming {{formula:102a0396-b49d-4159-870d-946cfeb7e98d}}
so {{formula:f91be76d-3db7-4ddb-bcda-d1ccce7cc02a}} , the norm squared of the difference between the original and rotated states is approximately {{formula:a6323ca7-45c8-40d1-87a7-91e9676dc963}}—that is, to preclusion of states with norm below some minimum value.
| d | a84e0fcf9b278211309cc8098818b662 |
We are the first to explore the unsupervised domain adaptation problem between different devices w.r.t the super-resolution task.
We compare our method with existing Synthetic to Real UDA methods for SR,
including Cycle-in-Cycle Generative Adversarial Networks (CinCGAN) {{cite:45cbf01f06c89287b863e0d6f5fe1027df1f7fd8}}, Domain-distance Aware Super-Resolution (DASR) {{cite:c5bf3995ded0c1146032c4be7b268ef0a5ca31c3}} and Dual Regression Adaptation Network (DRN-Adapt) {{cite:fdb92105dc5421a17c25b275895b743de6188d78}}.
For fair experimental comparisons, we implement them under the Real to Real adaptation setting by replacing the bicubic images with real LR images in the source domain.
The super-resolution network of CinCGAN is also the CDC model {{cite:9df3f4a93f7f3df1d7ed8364e0333e57b0046cec}}.
Their comparison results are provided in Table REF . In this table, Source Only is the model trained with paired source data without model adaptation.
Target Only means the model trained with real paired data in the target domain.
{{table:d7a5130b-31f6-4589-aa76-db0c50973670}} | m | 3cb5581e6a015b08cd4b1fd45956e770 |
In summary, there are several resonances which affect the behaviour of the integral cross sections of the title reaction in the energy range {{formula:031d162c-3bcd-48f4-baae-f51c1827720b}} to {{formula:43fb2be1-f8c6-439b-9a1f-32c8ed33afc2}} {{formula:f9ae5214-25d9-4249-84ca-b5fd16a57e50}} {{cite:1f6e63bec729fee217430d3692de5ecdc69ddd68}}. Some have been identified earlier in {{cite:90b09f0bf46ca7413db9f44a3263612440fdecb8}} as one transition state resonance ({{formula:1bda4a51-23a7-45d1-aa61-d0faeddc7f2f}} ) and several Feshbach resonances arising from the capture in metastable states of the van der Waals well in the exit channel ({{formula:d21f7893-3161-4a7d-ab09-06aeeaa8452e}} ,{{formula:72f8ac0e-d2af-444e-b8b9-76fa6edbd69b}} and {{formula:4cd6042b-ec0d-412a-9ef3-df00cd6d6d46}} ).
In this work we present a quantitative CAM analysis of the effects produced on state-to-state ICS of the title reaction.
As the input, we use the scattering matrix elements evaluated with the FXZ potential energy surface (PES) {{cite:108b3871e7617aaf82ae60e869c21f0f58fe5445}}.
This recent ab initio PES is known to accurately reproduce many resonance features experimentally observed for the F+HD reaction {{cite:1f7c56f67c1aabb8dc2d1eb6471dc9f9320ee735}}, {{cite:a3991ffcf8499b31de58946ac97be6e2a67c0ac0}}, {{cite:158ac5a1b948b49658d9b69aa1127343bd168b5b}}, {{cite:71f71337e81fcc3d51b50c598a92a2205ab6617f}}.
| d | 392421aa98fadb5b024a7e5fb78625e4 |
It is always crucial to study the effects of experimental decoherences and noise sources in implementing protocols. We have not discussed them in this review, but one should keep in mind the limitations they pose and the rectifications thereof, for example see {{cite:bf7905ed0e198b2dde23205bb06aebf81d0693e9}}, {{cite:845e4bc26c354626da0b2f0a06ea738d7ebef0ba}}, {{cite:74c2296ab5910c805fe108ae3d874092c937dc9d}}, {{cite:c2e9bcc952c3bfe54bd311107af473814d624ba3}}, {{cite:7d129cc5354f5d049312103aea729490d08dcac0}} for possible error sources and corrections. We discussed here that the behavior of the teleportation fidelity with time is a strong signature of the nature of the dynamics, namely generic scramblers or the holographic scrambler. Even better, the teleportation fidelity identifies the real scrambling dynamics and decays due to decoherences {{cite:98e6f9a03e453578fd6f25a4c3a458efb5c94803}}. Furthermore, it would be interesting to find out the validity and corrections of the Hayden-Preskill protocol as well as the many-body teleportation protocol in presence of errors {{cite:fc6f3a86b1acdcfba93c5be2dabf94acfad3f7a4}}.
| d | 3d46f1fb7958ef3627044ce74d797726 |
Comparison methods.
Since this is the first work to explore UDA-GR from the indoor to outdoor scenes, there is no method directly developed for this problem.
We compare our method with the state-of-the-art gait recognition and UDA ReID methods.
For the gait recognition methods, we select GaitSet {{cite:ab512cc684525c144ee11035aad9da8546bdd367}}, GaitPart {{cite:e5ce6b5b0d9f0a4c2dce979c467980c64e8d759c}}, GaitGL {{cite:d48f1e2b0a42fd1d75b5cf2b9c5a5673b89af953}} for comparison. Different from using the same domain for training and test in the original setting, we train the networks with the source domain, i.e., the indoor datasets, and perform the evaluation on the target domain, i.e., the outdoor datasets in the proposed UDA-GR benchmark.
For the UDA ReID methods, we select UNRN {{cite:081926485a67a0a5a5608558c3699df2ef8d201e}}, IDM {{cite:0a297a3640c2fceffdb8158716c61e255126e45e}}, SECRET {{cite:45a3063e24ec19661dcac2147adc1fc900a6930c}} for comparison. Note that, these method all take a single image as input, therefore we compress the gait sequence into a single gait template GEI, and feed it to the networks for training and test.
| m | 7749224e6f2bba209f3a051b14df7409 |
denotes the Euler–Mascheroni constant (cf. {{cite:a77ba36e6648c0b632376c31953f493a8597d0b3}}). We also recall the asymptotic behavior
(cf. {{cite:a77ba36e6648c0b632376c31953f493a8597d0b3}}, {{cite:979367b89643aa263c22fee45530cd7e90d03fe2}})
{{formula:d5e97704-c3a0-4db7-a330-43d60e698830}}
| r | 99e917f81ceb58bc5a6566ae7248de72 |
In this section, we perform experiments on MS COCO 2017 {{cite:98eba85f0c89274cd24e0c6eac5a6780da5b6697}} using the baseline detector GFLV1 to validate our method. Then, we perform ablation studies to prove the effectiveness of each component. Finally, we discuss the application scenario of our method.
| d | d1b1a8c0e7fcad6141ab0c7d15563261 |
As shown in Fig REF , SimCLR is based on a Siamese-like network that learns to congregate different augmented versions of the same image, and separate dissimilar images (negative examples) to learn latent representations.
Given a batch of {{formula:c3c77511-010e-4492-883f-5946ae2b2ddb}} images, all images are randomly augmented twice to produce {{formula:f9d7572a-73b2-42d3-910b-9e04d90ff003}} augmented data points
{{cite:7e2757863efbce6d2efd95e5539ffa141bbc7d1e}}. Thus, for any image {{formula:60c5fe98-fd7a-4318-9eeb-5ff165aec7ce}} in the mini-batch, it has 1 positive example and {{formula:7603040b-26fc-40e8-a402-41b88fe20ef0}} negative examples inside a mini-batch. An encoder {{formula:c24885e8-88f4-45a2-bdae-4a84c90350fc}} together with a projector {{formula:4bbc8020-0593-4230-8af4-c723fccdf8e1}} are used to extract the latent vector that is fed into the loss function, where the encoder representation is {{formula:9c99ff2f-a926-40fd-ba8e-6561703ac9e2}} , and the projector representation is {{formula:ee0fa36b-0136-4e5e-a30a-07691b85316b}} .
Then the loss function for a positive pair of examples {{formula:b7ff2413-e806-4eab-b846-3a29e2bcbbe9}} is defined as:
{{formula:06dff07e-1298-491c-8b9e-b9d7e7fd7ccd}}
| m | eaa32a37b97bfaf676d2838e3d9ec620 |
We measured the magnetization using
the magnetic property measurement system (MPMS) of Quantum Design.
We carried out neutron-diffraction experiments
at the Swiss Spallation Neutron Source of
the Paul Scherrer Institut, where
we used the high-resolution powder diffractometer for thermal neutrons {{cite:0a9397ab44a7f38c3b599c8b596e4f99cf2e78c2}}.
The wavelength of the neutrons ({{formula:2147fef5-3051-4161-a3bc-d87819788993}} ) was 1.886 Å.
We carried out
group theory analyses of the magnetic structures
using the programs ISODISTORT {{cite:0a0134ce9a62e556543e13967873cbe41eaddf33}} and
BasIreps in the FullProf Suite program package {{cite:4b652ab5019a6b62ee63f3082d6d81b4fabe14e7}}.
We performed Rietveld refinements of
the crystal and magnetic structures
using the FullProf Suite program package {{cite:4b652ab5019a6b62ee63f3082d6d81b4fabe14e7}}
containing internal tables for
scattering lengths and magnetic form factors.
| m | 728895e79882b4b62855cb4e773b3b93 |
One of the earliest works to describe adversarial examples was that of {{cite:605906b02f6afb02ca42742c6a89560b02173798}}, motivated by the need for networks that not only generalize well but are also robust to small perturbations of its input. This was followed by a body of works that finds adversarial examples using various methods {{cite:b3bc1ce4c4df1980c27da3713dca2af3134cbc47}}, {{cite:58fa5febe155d9a2e0cfc6570aad5f195fa68a33}}, {{cite:c6dfefc62897313bb9d7d236714da15ca8ef548e}}, {{cite:5d7bf2bd4b487a243c26ed6939349834d0bdfe1d}}, {{cite:7d6fc7be1252154e09a83ba55e1e2af1ce887a06}}. Although lots of defense algorithms have been designed, most of them are quickly defeated by stronger attacks {{cite:5d7bf2bd4b487a243c26ed6939349834d0bdfe1d}}, {{cite:98e3c8fc5071a41381c02f73af3a864847f18740}}, {{cite:0a12bd2a3ff9baa6132839064dc2d54160f53ac4}}. Much of the prior work has focused on this empirical “arms race” between adversarial defenses and attacks; yet, a deep theoretical understanding of why adversarial examples exist has been somewhat limited.
| i | fc34bca7cce280e3f46fc1cc0c88c581 |
The Integrated Gradients (IntGrad) method represents the integral of the gradients along the straightline path from a base input {{formula:da4541ca-a2b4-440e-aa0f-1d5535e20171}} to the input {{formula:dc4659bb-7abd-4e1b-ad68-44ec7aae5fad}}{{cite:9622442ec90c61f5f89e4675405361645cdc9cd1}}. The base input can be a root point of the desired function, which, for instance, can be the black image for the networks.
{{formula:345d87af-b8a3-4af3-9eaf-e860581ade39}}
| m | 7d06442d77fc42690afb8502538c0cc4 |
GNN Models & Evaluation Measures.
We use three well-known GNNs as base models, including Graph Convolutional Network (GCN) {{cite:933c8dabefb839185f7b4f6abac83826b80b56b1}}, Simple Graph Convolution (SGC) {{cite:f7adfb04e5d779246d853e3e82c6322b58afbdbe}} and Graph Attention Network (GAT) {{cite:073b8532d64672d8287af4a7490e7ee9e4d472fe}} on the node classification on the aforementioned datasets.
Since SGC first aggregates the neighbor features and then applies a single projection on the aggregates, we cannot apply our KEdge-layerwise variant.
We report for each GNN model and sparsification method the test accuracy and the percentage of dropped edges.
The percentage of dropped edges is calculated based on the original graph's adjacency and the last sparsified adjacency matrix.
Hence, for KEdge, we compare {{formula:2c5e6fff-aa02-4711-9c3f-dbe9aef80dba}} and {{formula:c1182196-14d1-4661-9b4d-cb306f37f85f}} and for KEdge-layerwise for a 2-layer GNN, we compare {{formula:87c1924c-d3c8-4d2a-8069-97608ba52341}} and {{formula:286e0294-7f5c-4dd4-97d5-dd1ef8e169fd}} .
Only those edges with a mask value of 0 are counted as dropped edges for our soft-mask variant.
| m | 885f397593f947892746f161216e3724 |
Ultracold atoms in optical lattices have, in the last two decades, been fruitful systems to study the physics of periodic quantum many-body systems in clean and highly controllable settings {{cite:78aeb3251bd5341a3f4a8814d44ada3c14f72fb7}}, {{cite:fec38c6e11675bab7714bd0cd6a868897e255b6c}}. These range from the paradigmatic realisation of the bosonic {{cite:f6fdc3a982a4e0969f789c34629c462f6184fce1}} and fermionic {{cite:3e9d92bc9109ffafc1635c0df678b548df73ae48}}, {{cite:567a17cc9e5698636b152e2f5f11820bb71a1017}} Mott insulator transitions, to the creation of systems with topological quantum matter {{cite:e215f586cc849990fe59db26ff728f47beec3348}}. However, as optical lattices are static potentials, they do not allow for phonon modes and therefore any possible connection to condensed matter systems is incomplete. While Hubbard models with phonons have been suggested to be in principle realisable in systems made from self-assembled crystals of polar molecules {{cite:7ddb887d4ce73be0247a33f443cf20a1adb0c299}}, these have not been experimentally observed yet.
| i | 5c3e2b2ec9e6d5c1097ece21a0562eac |
In this paper we have shown that linearized Einstein's equations around the BTZ black brane can be obtained from the first law of entanglement thermodynamics, {{formula:062803ee-9d2e-4cd0-b49b-1afc6f58e662}} , where the reference state was taken to be a thermal state of the CFT which is dual to the black brane. It would be interesting to check if non-linear Einstein's equations can be obtained from some constraints on the entanglenemnt entropy of the thermal state of boundary CFT as well. In particular, in {{cite:407f58d3938b9747b1661ac9bc019ac7449747b4}} the vacuum state of the boundary CFT was perturbed by some scalar primary or stress tensor operators and it was shown that for such excited states, up to second order in the perturbation, the entanglement entropy of all ball-shaped regions can be obtained using the covariant prescription for holographic entanglement entropy from the corresponding dual geometries. It was shown that the corresponding dual spacetimes must satisfy Einstein's equations up to second order in the perturbation around AdS. It would be interesting to extend their work for the thermal state of holographic CFTs.
| d | a84a62c1201957e572a1c6209741e6f9 |
The availability of computation as a resource has been growing exponentially since at least the 1970s, and there is every indication that this resource will continue to become cheaper and more available well into the conceivable future. Researchers have been able to leverage the large amounts compute available to better control robotic systems, and advances in computational capacity and algorithmic development continue to open up new domains. One promising manifestation of this is model-free reinforcement learning, a branch of machine learning which allows an agent to interact with its environment and autonomously learn how to maximize some measure of reward. The promise here is to allow researchers to solve problems for systems that are hard to model, and/or that the user doesn't know how to solve themselves. Recent examples in the context of robotics include controlling a 47 DOF humanoid to navigate a variety of obstacles {{cite:7d0f97033ac39002713a662cf3981bb81a1abf0c}}, dexterously manipulating objects with a 24 DOF robotic hand {{cite:4f045c3ad2657a55094ae261bafda66ae3d9fc21}}, and allowing a physical quadruped robot to run {{cite:8389c73f9b254f067ebd3ce4ef415865259c473d}}, and recover from falls {{cite:63b1b36dc27907f92c715894bced5d63a7fbdcc5}}.
| i | 6b99a699b00f0a56608540cbcaf4755c |
Ever-increasing model complexity has greatly limited the real-world applications of deep neural networks (DNNs) on edge devices. Various methods have been proposed to mitigate this obstacle by the vision community. Generally, existing research can be divided into network pruning {{cite:12aa99ebb3bb0a91d80369190a4766fe1339667d}}, {{cite:8b60b1f67662d79833df4c50eb59eb695618ade4}}, parameter quantization {{cite:e5b7b270233eaafc325c833858971039ba197a03}}, {{cite:058b8429fd32a16faf806a41f8fdf37dfd1252c6}}, low-rank decomposition {{cite:f2d18d8f25577ebd85b4e24bd3bcd63a35c9c386}}, {{cite:6347b9bd98a14c3c4017d1c9a912d006025a04f9}} and knowledge distillation {{cite:aae118326e0bf7c0386400c0bf24e9ff4cd0f726}}, {{cite:8f88757d97acb54863d020ce8b096581bdf379c7}}. Among these techniques, network pruning has been known as one of the most leading approaches with notable reductions on the network complexity and acceptable performance degradation {{cite:b53b867bf2e76f82a6d13dff4e68a3f4ce0ad586}}, {{cite:adf8a686d737cddf2ea63f9bade3d7c906f9b42e}}, {{cite:ecf3a266dd88874c9900c89bc1f4ea9cb608c007}}.
| i | 4e3a560a9d2a3c5798ba6d291c66515f |
Let {{formula:16420a2a-0fe7-4aad-80a9-2d6e2e77d702}} be the set of all
admissible infinitesimal variations of {{formula:e13f34ae-f572-4cf9-a305-2a2d6c4214ab}} in {{formula:ac83cbf5-2613-4e4e-bda7-d00b28fbe0d4}} ,
defined as in (REF ).
Since {{formula:58651e92-5c4f-435d-8050-45f4a5e5a336}} is a global minimizer,
{{formula:ce2f0e21-8de0-445a-9ad3-e97dc219bea8}}
By Lemma REF ,
every function of class {{formula:9926a339-6264-4592-a7ec-edc96b26427b}}
with compact support in {{formula:a8949209-25c3-4593-8701-ec34e0be697b}}
belongs to {{formula:baf73ec5-da7a-4402-a479-bb3fd47d2afb}} .
As a consequence,
by a standard argument we obtain that
{{formula:2af6a934-20fd-4b4d-bfbf-d8d12892704a}}
and we can reduce our analysis on the interval {{formula:717e20c5-636b-4aca-b95b-730004eea42e}} .
Let us now consider a variation in {{formula:591cea51-e200-49c2-a322-19eca67cee10}}
with compact support in {{formula:b63ee914-dcc7-419a-bf0f-8f13d15eb3d7}} .
By Lemma REF ,
{{formula:e411f129-b24d-4b26-8fb2-4a67cc40b527}}
so we can integrate by parts (REF )
and obtain
{{formula:41a34546-3702-4081-bb19-167e0c0ec9c1}}
where {{formula:fcaffd14-a78a-45a9-88fb-d7cee52ac3cf}} if {{formula:1836c589-d7db-4622-9019-bec09a613d46}} .
Set
{{formula:598fec1c-d943-4e85-90c7-4963bb010d0f}}
Since {{formula:a12675ce-c7dc-4f3c-bec7-cbf517f31ade}} ,
using {{cite:008c5674dae14682a1043b5410d952e30daaa46e}} we obtain that
{{formula:474744cf-9bea-4308-822e-30a8c4d98efb}}
a.e. on {{formula:a8a47518-863d-4b17-89af-cad20a834516}} .
Recalling also (REF ),
we obtain
{{formula:8e5bedf4-f2ae-4dd9-9095-81cdae44f71d}}
As a consequence,
from (REF )
we deduce that {{formula:f092b8b4-a97b-4684-9fb4-af8978da9e29}} is a set of measure zero and (REF ) follows.
| r | 2a2132a7abe0edfc61cd5ec7ba601caa |
We used T1 weighted slices from the full 3D volumes of 780 subjects from the HCP dataset {{cite:dcbf8f6a94b9107aefadd80ae2a02d46d35e79f4}} for training of the VAE. There were in total 202800 slices of size 252x308, with an isotropic resolution of {{formula:d95585af-0197-42d8-8ade-38083cb20b5c}} . We ran the N4 bias field correction on the images and used the corrected images for training. The training ran for 2250000 iterations. We also trained another VAE after downsampling the images to 1mm isotropic resolution to work with lower resolution images for 1750000 iterations. For both, we augmented the images by translating them randomly (-4 to +4 pixels) in both directions and trained till convergence.
| m | e5525fe0288a4cba85fa40f9c1efebe1 |
Alongside direct measurement of two-point correlation functionsCorrelations along the {{formula:3a33cb0e-f112-4b05-8ad3-9939142d1c67}} and {{formula:b1cd74fc-8281-4536-8ac1-715f61962586}} spin axes can be measured directly via in-situ imaging {{cite:ef6c7f5e8a4af9418f3a28fa7278abb8dd5aef25}} whilst {{formula:96498155-5f86-48c9-ba72-a3ff4b26a0d7}} correlations could be measured by associating doublons to molecules and performing time-of-flight measurements {{cite:1188fd4992a4913a019c7a6ad26914b087cf1055}} which would verify the results presented here, measurements can be taken in this setup which cannot be done computationally. The optical conductivity spectrum provides information about the transport properties of a state and can be used to distinguish superconductors, conductors and insulators. This cannot be calculated computationally for the steady states in this paper as it requires access to the eigenspectrum of the Hubbard Hamiltonian on an unbalanced lattice for system sizes well beyond the reach of exact diagonalisation {{cite:119c92e374da0176a09a82ab25a264b0f35ce4ca}}. In optical lattices, however, this spectrum can be accessed via spectroscopic techniques {{cite:431fc4d47283cd66f51eaaa90b9b4b1233a0507f}}, {{cite:345c1e88b3a155a83d0961c3d6abf918f00f9c39}}, {{cite:fc2249e34adb469552d6fdc75155070b944d9890}}.
| d | 3aa7e88c2834fe93b57b661dc9ad5a8f |
which holds for {{formula:6f45c887-75d0-4c0b-9c1e-b0e86ea429bb}} and {{formula:554d8141-0c27-4a09-8cd9-1280d77e4762}} solving {{formula:6af34062-70e3-4635-952e-ba9e730c1ba4}} and {{formula:e680388c-049d-425f-bedb-7e05b2fa44ac}} respectively, wherever {{formula:13dd1411-68bf-44ae-97ab-0fd4a82d5620}} . They, then proceed by constructing of special solutions, called complex geometric optics
solutions (C.G.O- solutions), that are to be used with the integral identity (REF ). We mention that the method of C.G.O- solutions that is used
for proving uniqueness question for higher order elliptic operators
goes back to Sylvester and Uhlmann {{cite:22f5431a864aef963a44db03e131e04fe9bb6417}}. The complex geometric optics solutions to the polyharmonic equation take the special form
{{formula:12f6e6f7-9963-44ca-898f-f0513bfb4ae6}}
| r | 4d8961d13a4709844734cf459b50f657 |
The conjecture has had quite fascinating implications for single field inflation, particularly those regimes in a General Relativistic Cosmology. It was shown in {{cite:b13405cfdc10dcb76f3e103954f2ef4fb2435a01}} that the swampland conjectures Eq. (1-3) are not consistent with the cosmological data on single field inflation in a GR based cosmology and for them to be viable with this form of Inflation, the string theory- motivated definitions of the conjectures would have to change. A lot of work has since then been done to understand the issues of the distance and de sitter conjectures with single field Inflation {{cite:54dc5f30dabf3172cbf8d89d5337af5e325b7390}}, {{cite:ba70977ad00c1ba155fdf71eac3ff7965833334e}}, {{cite:4e36ccb1ec5983ca11e04a94608690dcc2d9ab91}}, {{cite:53f577cb8bd5992cb8d4af93424e38ccc8321bb6}}, {{cite:a1a1f10458e1e8974ec9689af72a345b1649bbcc}}.Besides these conjectures, another recently proposed swampland conjecture by the name of the " Trans Planckian Censorship Conjecture(TCC)" {{cite:dc2f202b0e73c5ef7fb6499fa6dc441358086f27}} , implies that single field Inflation in a GR Based Cosmology would have to be severely fine tuned in order for it to not lie in the swampland {{cite:ee2e607acc26d5afabd2ce768fb85dcf85cff492}} . If Inflation is plagued with severe fine tuning problems itself, which were the kind of issues in standard big bang cosmology which prompted work on Inflation in the fist case, then it is certainly a very dire situation for Inflationary Cosmology keeping in mind these conjectures. A lot of work has been done in order to understand the issues of single field GR based inflation and the TCC in more detail {{cite:626089305c22808de1719b432d6a8ebe04a852bd}}, {{cite:cb8f2e432f7b28b546958f197483b28a177f772a}}, {{cite:3b5bb85486b858011be5e231d08e95846cbebb42}}, {{cite:9074d804964054a8b77356918681e1dbf90b5932}}, {{cite:814fe57dfe31e17c8397604423374cf1a1d9a0f1}}, {{cite:da0cd78141e1c3fd522801831de07b32a295e833}}, {{cite:771b60950341da21ddd547a2a0a7566b974c3cf5}}, {{cite:d94b46328e539c477f8db7be1f9b5627c1049c7b}}, {{cite:7593190d715087603af39c9d815d10cba206ea15}}, {{cite:44413548ca9a1e25f1b3ef5262dff5dedcdfb46d}}. A particularly interesting observation was made in {{cite:e2543f4a17deae57254c75f07700ba004e5d0878}} , which showed that the TCC can be derived from the Distance conjecture (1) considering that criterion to be true. The swampland conjectures have also had some pretty interesting implications on the paradigm of eternal inflation {{cite:d724d4a5c8fee66c363abb649991296af3b467c6}}, {{cite:0ca8e0a1277a059faaa9817438504d870ad2048c}}, {{cite:c87b94bff87adb6b2e0fd2dabdac5b47a365e5fa}}, {{cite:8b095811a57c2edc9c7135707868c6ac39277d01}}, {{cite:c682d33900eb2859d0a2e9bb51ff8bb39fa4d927}}, {{cite:18503ffbba954cae16fe6ff22ab0637e42e48c6e}}.
| i | a70f28f743f3520c30248a47a87633cc |
Any enrichment in water-ice material would be only fractional, however, as
discussed in previous studies ({{cite:2ec18204e9d43f8bc2908896cda10e7a72327681}}, {{cite:f62b073d442531e5a048765e5bce054c5aa90bec}}, {{cite:d1f9f759d83a603fe49beb1e6d0d4077bed99ec1}}, {{cite:cf4633681f1921bf70f97b8a5cdbb920e8614967}} and {{cite:ed20fe7db8048f2f04199c0453f96881fa972687}}). In particular, the
analysis of surfaces observed by the VIRTIS infrared spectrometer, in which
bright surfaces were visible, led by {{cite:3ff986ee20bb6031b0378ea50b8d42077206db56}}, has indicated that
areas presenting a spectral slope lower than 10 %/100 nm in the 500-1000 nm
range at a phase angle of 95{{formula:99b32757-a0c2-4753-a1c2-1903ac48bd73}} could be composed of just over 1% of pure
water-ice in an areal mixing scenario and of well over 5% in an intimate
mixture scenario.
| d | d5e958a89263a3fd9e6bf57866e414d7 |
Knowledge of microscopic events which drive macroscopic properties is of a fundamental interests in the description of materials. The understanding of structural phenomena at the atomic scale is indeed of a crucial role in the potential conception of new materials, which can be part of the resolution of contemporary societal issues such as the reduction of energy consumption or even conception of new drugs {{cite:a273e5633a185e9636ba34fd5df0bd26ad1b7b90}}. However, lot of information at such low spatial scale of the order of the ångström is still out of reach experimentally.
| i | 3e0ffd3d92ceccdd78b91cb7d42d5bee |
From this perspective, a semantic similarity measure bears resemblance with a human expert being summoned to give her opinion on a complex semantic problem.
In domains such as medicine and economic policy, critical choices have be made in uncertain, complex scenarios.
However, disagreement among experts occurs very often, and equally credible and trustworthy experts can hold divergent opinions about a given problem {{cite:e649fc9871296c4948e3c6d173d6ea2516ea5649}}.
To overcome decisional deadlocks, an effective solution consists of combining diverse opinions into a representative average.
Instead of identifying a supposedly `best' expert in a domain, an opinion is gathered from a panel of experts, extracting a representative average from their diverging opinions {{cite:b8bf7158b7cc94b5dfb3418ff54b55e06a1440b6}}.
Similarly, complex computational problems in machine learning are often tackled with ensemble methods, which achieve higher accuracy by combining of heterogeneous models, regressors, or classifiers {{cite:36e539ab1412c91be3b56a456cefa8e3ff50b44e}}.
This idea was first explored in our previous work under the analogy of the similarity jury {{cite:e644e25cf97b3d7598ca422700ecefb2117e92e9}}.
| i | 08a066d9cdeef0fa48a9d54363138174 |
Traditional feature matching methods use Nearest Neighbor (NN) search
to find potential matches. Recently, many approaches {{cite:bc9065959392eea63d37c608d98fc8d3896a4040}}, {{cite:ea81b2c97b277a95c213238cfb61dbd00769dd07}}, {{cite:70df54e592798afc3a946e1d5891fca4eec97fb8}}, {{cite:adaae61256e2b9d91be01b335076fa8c6adab863}}, {{cite:45374ef9c43f2ac70a30653bec2e1587ed7d515a}}
filter outliers by heuristics or learned priors. SuperGlue {{cite:8caae7bb7a5e8c7b4be4c27c43edfa5d61ee9262}} uses
an attentional graph neural network and optimal transport method to obtain state-of-the-art performance on sparse matching tasks.
Unlike the method mentioned above, given some keypoints as queries,
COTR {{cite:e0ff9defa43cc6b0f9ad5d91411f13506e3ee922}} refines the matches in the other image recursively by correspondence neural network.
Following COTR, we design an end-to-end model to accelerate this
scheme.
| m | efbd91b235e381e15504e1e07ca95945 |
The ramification index {{cite:ce3f92f262123795eba574dcc85747325d0051cb}} and different exponent {{cite:ce3f92f262123795eba574dcc85747325d0051cb}}
are related by Dedekind's different theorem, e.g. cf. {{cite:15a000d2eed8ef086d2ef381780b128d38034f6b}} or {{cite:ce3f92f262123795eba574dcc85747325d0051cb}}:
| r | 302eb4ca2e34be681d99be2391bcaa61 |
The self-attention based methods (also called transformer) {{cite:2ef277a88db824d2aca604c1d90bf1047087649d}}, have demonstrated promising results in various natural language processing (NLP) tasks recently. The transformer model exploits the short/long range context by connecting arbitrary pairs of position in the input sequence directly. Further more, the model can be trained in a parallel way, which is much more efficient than conventional recurrent neural networks.
| i | c6f74085ff17ff706b0fb70aeec85cf7 |
We develop an alternating direction method of multipliers (ADMM) algorithm {{cite:c3fe4185fe33c9d6ce525b5aeee948533a41415f}}, specifically tailored to solving (REF ).
Our ADMM algorithm is based on solving this equivalent formulation of (REF ):
{{formula:b2a44c5d-dade-404b-93ae-a972a5e57778}}
| m | 0f66d03a97de724a8cea0ecca9fb0685 |
Phase field fracture method is powerful in fracture modelling {{cite:2fe5c1d938df71e48abfba34c23a88c3a54caef7}}.
The difference in tensile and compressive strengths of the material can be considered by dividing the strain energy density into a tensile part affected by the phase field and a compressive part, which is independent of the phase field,
{{formula:0837bb20-524c-491d-82ee-a38071dadf1c}}
| m | 187f13a69591e1c7c99ec5cb5f9661cc |
Our main argument is that text-to-image generative models are being trained on databases originally created to different purposes like image segmentation, hence limiting the way they interpret human language in the specific context of art generation.
SemArt {{cite:d895b1d46daa3082e872ec7be80f8e953640dbbc}} and Artemis {{cite:2439b488ac421cc29f5d4975cb5ccbaf78c90a09}} are examples of datasets specifically aimed at understanding the role played by language in the description of artworks, thus paramount instances of the idiosyncrasy of the language used in artistic contexts.
Similarly, incorporating to our study the descriptions of the challenges contained in the AVA dataset {{cite:5429bea87ffbc8cd92395998ad5750970955daf4}}, we gain insight into how people ask for new pieces of art (in this case, photography contests).
Opposed to them, MS-COCO {{cite:07e9a3a9ef4d834848ef464832a225268627f39d}}, Conceptual Captions {{cite:4ef7cfe59a235620a3f821fd0e8080024b280742}}, Captions12M {{cite:420f8dd78051885c91da5412f2908be184323dc5}} and Laion-Aesthetics {{cite:47929d3b31b6e8587c7374bb60fb9542bdf5f694}} are publicly available databases that constitute part of the training material used in text-to-image diffusion models whose language is essentially content-based and aimed to a neutral description of the scene.
We qualitatively describe the sentiment valence {{cite:d324071911a0ef4d4702b2e81bbd1e836b387772}}, subjectivity {{cite:9f06d305f8f85960b8e6bde86b3adbdf93fbe121}} and average term concreteness {{cite:346e320872bff130b12f2cd3ab3d25c5ac063018}} (the inverse of term abstraction) of image captions following the procedure introduced in {{cite:2439b488ac421cc29f5d4975cb5ccbaf78c90a09}}.
| r | cf78a5d04f2ddacb35d280bb07b1d236 |
Table REF displays the results of all tested methods.
Based on the table, we have the following observations:
(1) For SD data set, we observe a huge performance gap between validation set and test set.
A similar performance gap appears between I.I.D. split and ComDiv split on both Math23K and MAWPS.
This indicates that all families of methods are vulnerable to compositional challenges MWP solving.
Among these three datasets with compositional challenges, SD dataset causes the biggest loss.
This could be explained by the nature of big compound divergence of SD data.
(2) Comparing the first three sections, in terms of the most robust method to compositional challenges, there is no absolute agreement on all the data sets.
Nevertheless, GTS shows relatively good compositional generation as it has the lowest Rel.Gap on Math23K and MAWPS.
This may because the tree-structured neural module which outputs an expression tree is more powerful when generalizing to unseen compositions.
(3) Our data augmentation could provide positive effect to MathEN and GTS methods.
This indicates that data augmentation is effective in improving the compositional generalization capability of general MWP methods.
Meanwhile, data augmentation shows the significant contribution on SD dataset with {{formula:1170b56b-5a74-4059-833e-f2a43f2107f0}} and {{formula:aa05d9b6-8994-486a-9571-80378c32b542}} percentage points improvement to MathEN and GTS, respectively.
This implies it indeed plays a key role in bridging the gap of compositions.
It's worth noting that data augmentation provides the largest performance gain 15.6% to GTS model on SD test set.
It may because that data augmentation includes more lexical and structural variations for training and tree-structured neural network has a better inductive bias to capture them, which is also verified in prior work {{cite:462ac702bdbf45ed541bf9fed186deac96ed6506}}.
| r | 653947ef4012fa6a2342b580fba08f36 |
Random neural networks have been extensively studied in the literature {{cite:49c2c9705f1f78a42cd79541a40d184dd1cfda7b}}, {{cite:f756945446023228241e733dce0c9e042b6bfb25}}, {{cite:229900bf1c7999452f81cf54d9a8f954cc89484b}}, {{cite:eb524f08ef85e200102cf5e5407ad3f90940e016}}, {{cite:55e967cdeb1774d0c13b35a398b69b33a0672d3e}}, {{cite:e7b8462970672f51219428ece677c643e04538bc}}.
However, this literature does not reveal the power of depth since it relies on laboratory neural networks: {{cite:55e967cdeb1774d0c13b35a398b69b33a0672d3e}}, {{cite:e7b8462970672f51219428ece677c643e04538bc}} use linear activations, {{cite:49c2c9705f1f78a42cd79541a40d184dd1cfda7b}}, {{cite:f756945446023228241e733dce0c9e042b6bfb25}}, {{cite:229900bf1c7999452f81cf54d9a8f954cc89484b}} use networks with infinite width, and {{cite:eb524f08ef85e200102cf5e5407ad3f90940e016}} does not consider batch normalization. We investigate the role of depth for standard modern random neural networks with batch normalization, finite width, and non-linear activations.
| i | 17769e5ad2f0fce48ee548b5813ba55f |
Van der Waals heterostructures comprising a variety of 2D layered materials have emerged as potential building blocks for the future ultrafast and low-power electronic and spintronic devices {{cite:a3b9d978f6e3a1dce9179477a3321466d02c067d}}, {{cite:b6395106752a575cd54589d4756a3cbd1e881f1b}}, {{cite:ed6225aacbe922378a263a714ca3e4fd5c02b1fa}}. The atomically thin nature of 2D materials promotes the design of artificial materials by proximity effects that originate from short-range interactions. Such a designer approach is essential for making materials magnetic without hosting magnetic ions and is particularly compelling for spintronics, which typically harnesses functionalities from thin layers of magnetic and non-magnetic materials and the interfaces between them.
| i | 9101bbc63c3d15c8f17965d7dbd273b8 |
Points 1 to 5 of Theorem parallel exactly
those of Theorem , but of course the
definition of {{formula:ea70372a-cc8d-48d1-a935-76d0e609ab91}} is a different one. It is through this definition
that we capture the potential interaction between the ontology and the
structural measures. Note, for example, that the class of OMQs
{{formula:ffc17c04-55ea-415e-84f4-a5f590e92953}} , {{formula:50a297a6-62fb-4730-9635-8e77c4552eb5}} ,
from Example would be classified
as #A[2]-equivalent if {{formula:54fe5fe8-9392-4d5d-bc0a-f5672686800f}}
was replaced with {{formula:bba5c936-1bc0-44fc-8023-590d7d493a19}} in the definition of {{formula:0ec7a78d-7368-4b78-8534-963b7798eddd}} while
it is in fact in FPT.
Also note that the statement in Point 1 of
Theorem is absent in
Theorem . In fact, evaluating Boolean OMQs
from {{formula:3da180b8-613e-4af0-a567-c2781acfcd5e}} is -complete {{cite:1681b269d9e8c8bc5ea630c0d9edb6a5a6a07552}} and
since for Boolean OMQs evaluation coincides with answer counting, cannot be
attained.
| r | 37922e7dbaea9f6a1dd848192f693e39 |
PDFchem provides a fast calculation of key abundances and emission line ratios that are most commonly used, for large-scale (tens-to-hundreds of pc) inhomogeneous clouds characterized by an {{formula:27447721-fdeb-4e78-8d93-057a7931fb0b}} -PDF. As described earlier, while many such distributions have been obtained for regions in the Milky Way, the limited resolution for extragalactic systems does not allow to determine such PDFs at high-redshift e.g. in the crucial {{formula:fc6ce5c3-be86-4f98-b7b7-4a4f8c4c68a1}} range for the cosmic star-formation theory {{cite:4fd9cf0ab66d40b7fdff011dc52d69619e472a08}}. In terms of spatial resolution, the ISM at {{formula:99a680e0-87f6-4911-a47f-bfe65c574b3b}} is observed at a sub-kpc resolution {{cite:6d10d32d0af02122d6b03283ef6b3efff683e6ff}}, unless gravitational lensing effects occur which may reveal scales of {{formula:7da694c7-2ae9-4dbb-8e51-ae0afc637557}} {{cite:66f07b9d04dac46d200bb10a0a67dea0bc5f1a4f}}, {{cite:c6ef7f0ec472523f9de2624fb6f71d0e8ebf3eeb}}. It would be therefore interesting to use PDFchem and input educated guesses of {{formula:5d1db8a9-dafa-4007-a2a7-302b735e9ab1}} distributions to explore the trends we may expect when studying extragalactic objects, particularly high-redshift galaxies.
| d | 0b7f05008a546eac137e4843fdc15887 |
Due to its irregular format and permutation invariance problem, how to process unstructured representation is one of the greatest challenges to point cloud analysis. PointNet {{cite:e1a1b4efab88f2e6dcadab806da0a7d502e6b07a}} is the pioneering point-based method working on irregular and disordered points, via point-wise {{formula:7bb586e8-8852-400e-9e3d-aaf4b7a7516a}} Multi-Layer Perceptrons(MLPs) {{cite:28c8218ae4404c262ec771b6e1ed9676b99c1adc}} followed by a global max pooling layer to aggregate information.
| m | 47d541c0edd3a4834f1bf2ffd8e0488c |
which can be estimated via the popular Newton-Raphson algorithm. In this way, {{formula:d29a1edf-71f3-4caa-a730-8ac7f270af97}} being a convex combination between two distributions, {{formula:2b438112-7082-486d-b609-17a4de25574a}} and {{formula:ec3cb4bf-43e1-4948-a7f5-4d6c2e73bf43}} of equal H-value, and being H at the same time a convex functional, the monotonic decrease of the H is ensured.
Let us stress that, as it was shown in {{cite:1536c4b720607f196c524aab38953ad22a1d37f3}}, the ELBM equation cannot be considered macroscopically as an approximation to the weakly compressible NSE with the addiction of a sole eddy viscosity term of the form of Eq. (REF ). Indeed, this term appears in a macroscopic equation of motion that requires a Chapman-Enskog expansion of third order in the Knudsen number, while the NSE are recovered at the second order. As a consequence a number of extra third-order terms are part of the implicit ELBM SGS model. This makes the actual ELBM closure even more complex than a simple eddy viscosity, and in principle, able to outperform standard methods.
On top of this, as already discussed in the introduction, the macroscopic approximation of the ELBM eddy viscosity, Eq. (REF ), has itself a very interesting formulation, being similar to a Smagorinsky eddy viscosity {{cite:1173b276a4e8a26d174aa815fb8c064095b70340}}, but being not positive-definite and therefore allows events of energy backscatter, i.e. energy transfer from the unresolved to the resolved scales. Indeed, while energy in 3d turbulence is on average cascading from the large towards the small scales, in real flows there are local events of energy going backward with non-trivial implications on the statistical properties of the resolved scales.
| m | 137ea2161ffa27095704aa358e81b616 |
Here we present self-consistent
cosmological zoom-in simulations
run with our updated KETJU code
({{cite:6a29a4af8356483cdf87935d0eb0d1fb8c745d54}}, {{cite:7f6bca0a62e0ff3b940abf5aa9b1f2ce31067048}}, {{cite:0e1d55b2c9fe6c336b752d5162ae140a35845246}}), which is able to resolve the dynamics of merging SMBHs down to tens of Schwarzschild radii, while
simultaneously modelling astrophysical processes in the surrounding galaxies, such as gas cooling, star formation and stellar and AGN
feedback.
| i | 2bc841c8c05ed68ac031285b1e12bd33 |
Significant progress in deep neural network (DNN) for
vision {{cite:41a95e4d0c30b596eb3624b9039b71b41ac540d1}}, {{cite:f11722cc791646f9023c8a78f3e6c6e5cb4d84f8}}, {{cite:9285ffe0c873f9ee84f4fdbdfa830979791a634a}}, {{cite:0201dd8db7aaf6cf57cfcccb90a695a2ab2c46f6}}, {{cite:5928dda91bfa651220a07059c7f518c31982c4ae}}, {{cite:a2798df11e3937707b4c80e9babf9deec51ec733}}, {{cite:73f3e7915d8335e6f523a25ac13b2bb645e99f41}}
has recently been propagating to the field of super-resolution (SR) {{cite:7c082135ba4d4cf54335216777ca6779edbd750e}}, {{cite:e48d951c2f922604462b46e38d9584676e39e437}}, {{cite:3c31147f78217a0392806e5f9549ddecdd1301d8}}, {{cite:de5ad3e5d64a18970bb3047bb3dcf6b31c7923a7}}, {{cite:9edbd8ed7e8ee8bdb854794ef61e08e485bc6cd8}}, {{cite:779efccd59c30db058222933ac807e2b0d01cbb0}}, {{cite:9b4def7f50b6287b0b29aea6f59206e4b4690a84}}, {{cite:c2ffd1c6fcf9069ac896cb456e3059ecd3c390c6}}, {{cite:da5d990c634ad44f2042176c290ab3124f6f601c}}.
| i | 7fdbd35e3427a240c51ec4b85d8326f4 |
MS COCO. We also evaluate our method on the COCO dataset, a more challenging dataset, and the results are listed in Tab. REF . In the coco-35/80 setting, compared to the baseline method DD, our method achieves a 2.4% AP improvement, which is prominent for the COCO dataset. In the coco-115/120 setting, where a larger-scale dataset is adopted, we observe that previous methods obtain higher accuracy compared to that on PASCAL VOC, which indicates that more available data is beneficial to semi-supervised learning. And we notice that our approach also achieves better results. Even with a 1x schedule, our method still outperforms many current methods, which usually adopt a 3x schedule and more training time. We further adopt 3x schedule and the same data augmentation strategy as that in {{cite:81396f763af11ed2210cf758904a1de2bcd7163c}}, {{cite:632bc3af727b17087fb5bd06371535cfe3601283}}, {{cite:c61769549817b033f9bf1601a04dc0a813f9cc81}}. Our method achieves a better result, a 43.2% AP, 0.8% more than the state-of-the-art, which further indicates the superiority of our method.
| m | f6b43da20040ae9949b5501c57fccc93 |
While bridging the sim-to-real gap has traditionally been addressed via domain randomization {{cite:0bd92ca97947faae5b4fe8af2e112c4372ee5672}}, we take inspiration from the robust control literature, and tackle this challenge by developing an approach for adversarial learning of stability certificates for dynamical systems.
We show that under suitable conditions on the underlying system, requiring that a learned certificate is robust to adversarial perturbations that enter the dynamics carries little additional statistical overhead.
Taking inspiration from {{cite:40d75c4a1451cac687400da6ce8e486e9a37944f}}, we prove our results by converting the robust stability certification problem into an adversarial learning problem, and subsequently bounding the Rademacher complexity of the resulting adversarial loss class.
To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system.
Our results build upon and extend a line of work which shows that underlying system-theoretic properties translate into the difficulty (or ease) of learning over data generated by dynamical systems (see e.g., {{cite:31cd824e5cb3135ad24641d0a352546f28b345e4}}, {{cite:b076497676d78bd3341bb92a69856500c69c64ea}}, {{cite:ae42f47ac175316a1ac881b9b27b648475ed8f2c}}, {{cite:14c6fdd95024189967ea57d0ca60a39f9982d282}} and references therein).
We further provide a practical algorithm for approximating the adversarial training algorithm, and show that adversarially trained certificates are robust to various types of model mis-specification on a damped pendulum example.
Our results are presented in continuous time; however, they readily admit discrete time analogues, which are detailed in Appendix .
| i | ad1f7ee08d1cab491bc8c47699d4bdf8 |
One bottleneck of existing image-based 3D mesh reconstruction methods {{cite:8f850b692293f9ae4d7db02d040d8101fa65468b}}, {{cite:33d60104187659a784b5a17ce2e3645e1ba11176}} is that the predicted shapes are assumed to be symmetric.
This assumption does not hold for most non-rigid animals, e.g., birds tilting their heads, or walking horses, etc.
Our second innovation is to remove this assumption and to allow the reconstructed meshes to fit more complex, non-rigid poses via an as-rigid-as-possible (ARAP) constraint. As another constraint that does not require any labels, we enforce ARAP during test-time training as well, to substantially improve shape prediction.
We use two image-based 3D reconstruction models for training (i) a weakly supervised one (i.e., with object silhouettes and 2D keypoints provided), and (ii) a self-supervised one where only object silhouettes are available. The image-based models are then adapted to in-the-wild bird and zebra videos collected from the internet.
We show that for both models, our innovations lead to an effective and robust approach to deformable, dynamic 3D object reconstruction of non-rigid objects captured in the wild.
{{figure:33b5887f-1ad0-4f2a-8139-647d6bdc907b}} | i | 4496e06d3ed8977b9c901cc5a7a27890 |
In this task, our backbone model is a GRU (RNN) network with hidden size 128. We convert tweet sentences to sequences of 300-D GloVe {{cite:202c9899c3ac75bbdd12cef9621e90d92a646451}} word vectors as input to the GRU model. We add a binary classifier upon GRU hidden output to classify negative and positive sentiment.
We examine the performance of baselines and our models and observe that
| r | 39d69f23f34dab703b48bdca2c8736d6 |
Water molecules are modeled using either the TIP4P potential {{cite:8fca00236ae6da70bd022c1fdd95282332a19b58}} or the SPC/E potential {{cite:d047ceceeb1aaeceef8c8e3c3e7eebbca69ec5e2}} and maintained rigid with the SHAKE algorithm {{cite:0dafd9fdcf055e248e8c16cc964ebe45bf2f0b30}}. Lennard-Jones (LJ) parameters of all considered species are summarized in Table S1, with cross-parameters determined with the Lorentz-Berthelot mixing rules {{cite:2057f2e381213bfe2afaa54075f2240870440f21}}. Interactions are computed using a spherical {{formula:b832b970-22fd-4a3a-99b8-bf6a6fa6b397}} cut-off for LJ potentials, and long-range Coulomb interactions are treated with the particle-particle particle-mesh (PPPM) method {{cite:46fd665dbae6ff4718a6ea83e295a576415380fc}} and a slab correction to deal with the non-periodicity in the {{formula:ec433cb1-fb3e-445d-b7d9-47769f818973}} direction {{cite:ea8d0e0059894a9dd13478351ad67a8ce415d229}}. Finally, the integration time step is {{formula:8bc3ea53-ffce-4ecf-ac1e-c545c92e0f31}} and temperature is fixed to {{formula:7ea98c88-ddd9-4892-a3e9-c7d2e59e9322}} using the Nosé–Hoover thermostat {{cite:eaa1131735ce25c2e20e734141262febd3c9f815}} with a time constant of {{formula:442c0650-af62-455c-b15f-8e25fc273999}} . Simulations last {{formula:269f0c9f-ccea-4002-8760-7b499900d6b5}} time steps, corresponding to approximately {{formula:6ebe7660-9f08-4d99-a6fe-0c2a85d46064}} of physical time.
| m | 9231334da81a549c8b40309d06497231 |
In previous literature, both single-antenna and separate-antenna full-duplex models are investigated. However, using single-antenna as a function of SI cancellation is more attractive because of twofold reasons: first, using two antenna full-duplex system may not achieve any higher throughput than using two antenna in half-duplex MIMO system spatially multiplexing two independent packets at the same time {{cite:8716c147a4f8cc5a52bd6e718b5ce579f6ee71b9}}, {{cite:e781f67805f2e965d8e8b72a9d76fc72e21fe40e}}; second, using single-antenna transceiver system results in a compact design. Existing single-antenna full-duplex antenna and analog cancellation methods typically achieve 50-60 dB cancellation {{cite:5a0f2ddad9cec1d341fe245358bf8962bdb70189}}, {{cite:8fc60fb4380bc62c1f113d580a5be190a7529cb3}}, {{cite:e9154711f63438ed33131c9af73ee2ad3a0ec413}}, where separate-antenna system provides higher cancellation. For a practical receiver, this limited RF cancellation results in a higher effect of receiver RF and baseband (BB) nonlinearity on the SI signal.
{{figure:57dbddf5-9236-43c9-84e5-b7643c14cc06}} | i | f1092380f50833de120be503b1228ebb |
We have a lot of choices for the general framework of the style transfer model from some of the existing literature {{cite:c8607f5960d1b1527615f65d3b2e6ff91d1e635d}}, {{cite:b484489afc4b876c20ffe2b574cbd0208fa115e0}}. We use the model from Gatys et al. {{cite:c8607f5960d1b1527615f65d3b2e6ff91d1e635d}} as our baseline model that we will try and compare against for improvements. We also focused on the architecture design of the transfer model, and tried different feature extractors like CNN, ResNet {{cite:e38047a3434ea98051e5fad708b4893dae8c0c9b}} or ViT{{cite:17317e9db95e0c4448853aadec19fc3ea8ba842f}}. We can make different changes such as the number of layers, type of layers, kernel size, stride, number of filters, and more to see the impact on performance. Ultimately, the two best feature extractors were SqueezeNetv1.1 and ElasticNet_v2.
| m | 41734ac568bb47daea8f3074bbefee04 |
which is equal to the usual dual index (see for instance {{cite:f8c7152b0bea29680dad6f2eefdb4613ff7e6793}} for the precise definition)
of {{formula:5c423e00-c4d1-44aa-b1e8-c09c8bcc5902}} .
| r | c2e7f91996ef707d9eb1d1aaf026f310 |
Our work is not without limitations: DP-SGLD provides only point estimates of the network's parameters and thus sampling from the posterior when the privacy budget is exhausted is not possible. Furthermore, DP-SGLD converges onto a single mode in the posterior distribution, and is thus not capable of capturing multiple, diverse solutions (modes). Future work could explore other, more expressive probabilistic formulations of Bayesian neural networks such as DeepEnsembles {{cite:7c42dd26a26068bda84b9e409df4f0ce48f0dce1}} or SWAG {{cite:cdaf11f19a4288dc00b57cf986b98734c5be7613}} for differentially private training. Our method employs pre-noising and we conjecture that this improves ergodicity in the posterior space, but leave it to future work to explore the effect of pre-noising and/or the decaying learning rate schedule on model calibration.
| d | fefc5a21007e4d8a32fdbdf5338c3325 |
All experiments were carried out on a Nvidia GTX1070 across 100 epochs, with each epoch taking roughly 2 minutes. The Adam optimiser was used with learning rate of {{formula:8ec01696-47e8-4e86-9fb4-36f987904080}} for the SATNet layer, and {{formula:d116a00d-e516-4992-9b3e-aceccd898494}} for the digit classifier {{cite:4a3b70c885bf553a0eee0186f017732847b517e2}}. Standard deviations were calculated across 5 runs. We used the Sudoku Dataset made available under an MIT License from the original SATNet work {{cite:e17b748aa91136bb8072542e71fe63c6ac8fb57a}}.
{{table:cedbbe20-ca7e-4df3-8bea-70e5050149a6}}{{figure:7e0ce836-ddcf-4a1e-a5a6-6ffba4756db1}} | r | 1a1842988eae2da1814dbb93c6fae63a |
For comparison, we consider the following schemes. 1) Proposed AO with dynamic IRS: employ different IRS phase shifts in DL and UL with the proposed solutions;
2) GR with dynamic IRS: where Gaussian randomization is applied to recover the rank-one {{formula:5062eb4c-a5fb-4af5-9539-23e783a4abef}} and {{formula:8ad38e7d-cf08-4a53-9e5b-fd4b5807b2ab}} based on the SDR solution {{cite:be3c2e85d0621d983218ad5eb4ea4d65e50edb99}}; 3) ETA with dynamic IRS: i.e., {{formula:00ace464-c3cb-43ad-941d-5fb0ddd2885d}} based on the solution of the scheme in 1);
4) Proposed AO with static IRS: use the same IRS phase shifts in DL and UL, i.e., {{formula:209d098b-4d32-4e07-a111-3cc5bc5c8f06}} with the proposed solutions; 5) Fixed IRS phase shift: Only optimize resources allocation, i.e., {{formula:486816da-944f-4799-a706-28937a742252}} , with randomly initialized IRS phase shifts; 6) Without IRS.
{{figure:6b43e8b3-e322-4a79-9340-1292ba43aaad}} | r | 9951773281f480004d9443fe59e4c1ce |
Differential privacy {{cite:5af0b391ffdc529345f235bb49d49d800e199364}} {{cite:9f1935052ea3e401785eb518249bef0412f0fc57}} has been gaining momentum in recent years. It is very reliable in the sense that when applicable, it can provide mathematical insurances to preserve the plausible deniability up to desired thresholds by introducing noise to the process in a controlled and measured way. To achieve this mathematically safe-guarded security, the parameters of this added noise should be set carefully depending on factors such as the number of epochs, the number of independent data samples and so on. While new tools like tensor-flow privacy library help with the implementation of differential privacy, there are caveats for the practical implementation of the algorithm in cases where the size of available data is limited. The performance of the algorithms trained in this manner suffers {{cite:0cb5ec3eb9b6b09cf4ea0afc9e163c387f25a17f}} especially in cases with limited amount of data and complex models. Moreover, as the number of dependent inputs increases, the noise should increase, and so the performance gets even worse. Thus, while theoretically ideal, differential privacy may fall short of enabling protection of sensitive data by decreasing the accuracy of the model and so potentially increasing the probability of releasing sensitive data. Of course it would be interesting to see the above propositions investigated with actual implementation of differential privacy and its effects, but that is beyond the scope of this work.
| d | b5cde8e89d9af0a4be8b5ae0cb5d0c22 |
More recently, the Schrödinger-Newton system was generalized by considering the effects of dark energy in the form of a cosmological constant {{formula:fdb0624a-0fa5-4721-9169-b59b22d8569a}} {{cite:f1571d82c8db97cc22ee56b97c54cd68acced496}}.
This is consistent with the standard {{formula:af8b9e8c-073a-45f0-ac57-a4c6da44703b}} CDM model of cosmology, in which it is assumed that the late-time acceleration of the Universe is driven by a constant vacuum energy density,
{{formula:680a8a12-57da-4535-a213-c6a5d4975517}} {{cite:ccdb9ac8d698ea02ecc368e3056bfa330235f048}}.
(For alternative models of dark energy as modified gravity, see {{cite:4819bcaa8a10de894b72c0b1107e4bb26832d43f}} and references therein.)
The physically interesting regime in which dark energy dominates both gravitational self-attraction and canonical quantum diffusion was investigated numerically and using analytical estimates.
It turns out that this takes place for objects with arbitrary mass that are sufficiently delocalized.
An estimate of the minimum delocalization width required, of the order of 67 m, was determined, and this prediction was verified by the numerical results.
| i | 79426ca5e920d3daeacd9779b181e7c3 |
The present work provides the basis to derive characteristics of interacting RnT particles and those subject to external potentials on the basis of field theories. Using this framework provides a flexible, extensible, systmatic and perturbative approach to active matter. It comes equipped with the powerful tool of the renormalisation group and a diagrammatic that has an immediate physical interpretation, as we have attempted to illustrate above. We believe that field theory, which has been so overwhelmingly successful in the characterisation of collective phenomena {{cite:d4c3854f0f18bcd39217496443a6b0f6234a3f25}}, is ideally suited for the challenges that lie ahead in the research of active matter.
| d | 21b904385a2344980aaa7e835e27dcb7 |
Another approach that is commonly used to address the problem of separation is regularization. In this approach, instead of maximizing the log-likelihood function, a weighted average of the log-likelihood function and a penalty function, {{formula:b2560eda-f79b-4a36-b9cb-81c722f62354}} , is maximized. This penalty function is intended to prevent parameters from diverging by penalizing larger values of the parameters. Lasso and Ridge penalty functions are two of the most used {{cite:5241add8658720c3b023c1b7326bde99eee4821e}}. A penalty function that has been used specifically to deal with the problem of separation in logistic regression is Firth's penalty function {{cite:a19fcba370bc7b8aa662126066814ba72cb1f67c}}. In fitting a regularized GLM, the regularized log-likelihood function, the regularized score function and the regularized Fisher information are computed according to
{{formula:6c608b6a-b6c6-4d56-a0a5-ec4fe066081e}}
| m | c87c823216a2747c2130ec7fa23dd701 |
We consider four multi-label classification datasets, summarized in Table REF : Cora {{cite:0a9c91b6102a0c03f700ebba89ea32ede7e4cb73}}, a Machine Learning citation graph labeled by subfield; CiteSeer {{cite:0a9c91b6102a0c03f700ebba89ea32ede7e4cb73}}, a scientific citation graph labeled by research area; PubMed {{cite:0a9c91b6102a0c03f700ebba89ea32ede7e4cb73}}, a citation graph between papers on diabetes, classified into three topics; and DBLP {{cite:f6938f5ee0377e88037e02a15361f152bd86ebec}}, a Computer Science citation network, labeled by subfield. To assess classification performance on these datasets, we look at the macro {{formula:e4c0cea4-0fd4-4bc9-a585-e4b281967f24}} score on test-set labels; considering alternative metrics such as accuracy showed similar trends. Unless otherwise stated, we use the default train/validation/test split associated with each dataset for evaluating the macro {{formula:0eb76d96-a0ee-4be6-8473-b2d94d32e531}} score, and use the full graph topology when training.
| m | df0be6a6a944153c33a34a1e1528d00e |
Our model consists of a student and a teacher model {{cite:367d8d12d7e0905d58ef4bcb66ffd1c1e67fe24b}}, denoted by parameters {{formula:5382d44c-45a7-4f7d-b5b7-89cb496de123}} , respectively, which parameterize the classifier {{formula:6a2fed34-803c-42fc-abac-9627f42355ae}} .
This classifier can be decomposed as {{formula:c864dd06-3494-4717-8a63-eb7555de3e79}} , with {{formula:4f392253-9b30-4209-be10-b534fd50989a}} and {{formula:e34b468c-73bd-4cb9-9a98-1ed11037a9ff}} .
The first stage (top of Fig. REF ) of the training consists of a self-supervised learning that uses the images from {{formula:f83dd866-84bb-42f5-925e-f55d5cedbf83}} and {{formula:e4eece02-e657-466a-b61b-37364996908f}} , denoted by {{formula:6a34baae-8f95-41e7-aca7-dbd774be6b27}} , with {{formula:3a09836b-1fc0-489f-9cf9-cc5d5a280470}} representing the images from the set {{formula:865960d9-fbcc-4945-a7dc-b15b83ca7584}} , where our method minimises the joint contrastive learning loss {{cite:5f3a68763db9e47ee46edd594020f9aa5d878bd6}}, defined in (REF ). This means that during this first stage, we only learn the parameters for {{formula:af6f9518-98f9-4b3b-b546-b119cff382cb}} .
The second stage (bottom of Fig. REF ) fine-tunes this pre-trained student-teacher model using the semi supervised consistency loss defined in (REF ). Below we provide details on the losses and training.
| m | 05cdb7e9bfd6637c3a01fb33c2115c82 |
Computational cost, observation window, and latency Our model has around 17M parameters, which is less than some SOTA SR DNNs, such as EDSR {{cite:355b9c533761d95bb92959620058f00c4cd49935}}, RDN {{cite:509a80e8f60f73f309a85101e41ef62289f7ce4b}}, thus the training time is comparable with others. The inference time is around {{formula:3af28593-668e-418f-a6f5-4efd47c2b95a}} ms on average when using NVIDIA 1080 Ti GPU. In our experiments, {{formula:80ed2cbf-637d-43b6-a122-f728b1d6153b}} events are gathered in 5 ms time duration on average. Events can be stacked with the fixed observation window as SBT in {{cite:ef627184b30857a9991ea9774e4ce25349453276}}.
| d | 637fbcebf74f4ddd473a3334a7c0076b |
There is a number of open inferential extensions that remain interesting directions for future work under our distance-to-set regularization approach. For instance, loss functions do not always originate from likelihoods, so there is value in extending our framework to more general settings such as Gibbs posteriors {{cite:de95b1ef86509a0139d76c2a9e0fdbd9ad176e0c}}. While our distance-to-set framework assumes an {{formula:895f7454-b68b-4ee9-be22-ef9a1468177d}} metric, considering other measures and divergences may be of particular interest for various data settings. Indeed, this is related to the underexplored connection between constraint relaxation and information geometry that we begin to examine via connections to exponential tilting. We invite readers to consider future investigation of these promising research directions.
| d | 043c31ac4e939011a95d8203aec40a27 |
As discussed in the preliminaries section,
accurate models with small quantization errors can provide better training performance
along with more stable weight convergence.
In existing works of binarized CNNs ({{cite:a6bb17edb2458a7fdd54a04edeb4fe74e164f1a6}}, {{cite:a111a50007038cd50b338e3729c8b19d3d1f8773}}, {{cite:c0a21c432383dcde95eb3fc976fdf29d29735240}},
pretrained weights are used in the weights initialization of the binarized models,
which can transfer the training results of accurate models into low-bit quantized models.
Let {{formula:073c135b-db72-4001-ae7e-c2fc63e8ba65}} be the pretrained weights after training an {{formula:c26dfbc5-dbce-4df8-9c2b-1da3717807f9}} -bit quantized CNN model.
Let us assume that the pretrained weights are used in weight initialization for {{formula:12747409-1857-4cd5-aff5-67b5f018b95a}} -bit quantized model.
The weight updating in (REF ) can be rewritten by {{formula:0c871659-8a77-4ef5-a383-48b5aa859227}} as:
{{formula:9164b61b-8c41-48d3-977e-3f4956d6d9da}}
| m | 471a413cd2b0476d7f0affa32cb1a077 |
A different perspective has been advocated in {{cite:d68114fddbd8513f1d3632e58c3a2317eb104527}}
which argues for the importance of proper distance to arrive at the rigorous result.
Due to the singular nature of the metric (REF ),
the proper radial distance here is not {{formula:81870172-bf18-4fa2-a047-b310db977447}} , but
{{formula:8fe92877-aa14-4318-a9b7-d9377744ed46}}
| m | 6f464eeea34b1cb2cf6bd7cdfb7aa49f |
Dynamic Modality-Level Attention Fusion.
Since we utilize three encoders to separately deal with the relationship between each existing modality and the target modality, we aim at deeply fusing features extracted by those different encoders. Inspired by the SE module {{cite:5a3e4b8b1a1101205380a06f181313eae85c8135}}, we propose Modality-Level Attention Fusion to perform dynamic modality-weighted refining and multi-modal feature fusion.
The structure of our Modality-Level Attention Fusion block (MAF-Block) is also shown in Fig. REF .
| m | dc60a13b4cef60a907acd84121ecf5cc |
where the nuclear modification factor {{formula:e4689e38-ab94-494d-be4d-a7cc4bbbffa8}} accounts for the fact that the gluon distributionRecall that the value of {{formula:aff255b7-8bd1-4d9b-92f3-9ff17c7818e1}} is almost completely driven by the gluon distribution. in the lead ion may differ from the sum of the gluon distributions in free nucleons. The value of the nucleon modification factor {{formula:4d468079-296b-4132-b7a9-c2b662ea4419}} at the corresponding scale {{formula:200283c5-b4b8-4ccc-83d2-0e61e3061ea5}} is taken from the EPPS16 NLO analysis {{cite:597a2c5ee52f8467a535781cf9e9d1b2cc4adbc9}}.
It is convenient to introduce the so-called `effective fluxes',
{{formula:d33f37db-8f61-4e9c-84b4-3a2acb3dc5f1}} and {{formula:bad98449-d8b0-46ac-8570-0291faadfe9c}} , which include the original photon flux {{formula:d6c547ce-e5a7-4ee8-9450-072cb839a675}} times the survival and nuclear modification effectsIt is not completely correct to use the word `flux' for a quantity which includes these additional effects; however we use it since it enables us to shorten the description of the computations.. The effective flux radiated by the lead ion is
{{formula:926e25ab-d47f-472d-9b8d-b2408eb9e6b6}}
| r | b619231b031be7cb4ece3ac5ff35670b |
In Fig. 6 we show the corresponding decomposition of the data contours for the XCDM model as well. In the upper-left plot we display the two-dimensional contours at {{formula:1cb7344d-490f-4b1f-af5a-88bc0420840d}} and {{formula:95ae827a-7e2f-44c8-a3a2-e3c8bd3698df}} c.l. in the {{formula:ef5cab61-72bd-45b6-acd2-6dd642e48b10}} plane, found using only the LSS data set. The elliptical shapes are obtained upon applying the Fisher matrix formalism {{cite:8117bf895f6fc4b2e6a879b6033ec667ef84dce9}}, i.e. assuming that the two-dimensional distribution is normal (Gaussian) not only in the closer neighborhood of the best-fit values, but in all the parameter space. In order to obtain the dotted contours we have sampled the exact distribution making use of the Metropolis-Hastings Markov chain Monte Carlo algorithm {{cite:13ebae7227967207819ece5561e97e53bdadafdb}}, {{cite:0117014adbaca59ede83596664f9ece46c544760}}. We find a significant deviation from the ideal perfectly Gaussian case. In the upper-right plot we do the same for the combination BAO+LSS. The continuous and dotted contours are both elliptical, which remarkably demonstrates the Gaussian behaviour of the combined BAO+LSS distribution. Needless to say the correlations among BAO and LSS data (whose covariance matrices are known) are responsible for that, i.e. they explain why the product of the non-normal distribution obtained from the LSS data and the Gaussian BAO one produces perfectly elliptical dotted contours for the exact BAO+LSS combination. Similarly, in the lower-left plot we compare the exact (dotted) and Fisher's generated (continuous) lines for the CMB data. Again, it is apparent that the distribution inferred from the CMB data in the {{formula:1e28d100-95f8-4cf1-b692-823108c6d5ba}} plane is a multivariate normal. Finally, in the lower-right plot we produce the contours at {{formula:6d004ffd-e4bb-4182-a46c-b4f711b7732d}} and {{formula:f647eda8-7aa2-4e61-9f3a-9a0da1e7cf95}} c.l. for all the data sets in order to study the impact of each one of them. They have all been found using the Fisher approximation, just to sketch the basic properties of the various data sets, despite we know that the exact result deviates from this approximation and therefore their intersection is not the final answer. The final contours (up to {{formula:f72116a9-624c-4388-9e18-ae365066b251}} ) obtained from the exact distributions can be seen in the small colored area around the center of the lower-right plot. The reason to plot it small at that scale is to give sufficient perspective to appreciate the contour lines of all the participating data. The final plot coincides, of course, with the one in Fig.3, where it can be appraised in full detail.
| d | 96cb62e174b6b265817e8cfe47ed938b |
We evaluated three DRL algorithms, Rainbow DQN {{cite:9d2176d96d741c92bf2577db1c50eec97177c619}}, Discrete Soft Actor-Critic (SAC) {{cite:10f334be8123d7049cfe81f1fcc26b980482e675}}, and Advantage Actor-Critic (A2C) {{cite:064162253f1cefc8d73c8b49a2556359154998b7}}, and a random agent baseline.
All DRL algorithms used a fully connected neural network with two hidden layers trained using the Adam optimiser.
Each hidden layer contained 128 units and used ReLU activation between layers.
Policies used a reward discounting factor of {{formula:b24075df-39e5-4032-9b38-0839e60ec7de}} .
Our Rainbow DQN (Table REF ) implementation used distributional, dueling, double-Q and noisy networks with a prioritised replay buffer and single step returns.
The discrete action space variant of the SAC (Table REF ) was used.
A2C (Table REF ) is the synchronous version of A3C and used Generalised Advantage Estimator (GAE) {{cite:fa1f8fe4945d39e792e29e70861d0baaa655a703}} with {{formula:ffd21c5e-2a4a-4768-9a08-654657917eae}} .
{{table:9b1543bf-f0eb-4c38-9f49-e33aa49604cc}}{{table:3d86bb63-701a-41d3-9cf3-2c54c6b610af}}{{table:9479adb6-a1b2-4e82-a731-447d99f8dc1e}} | m | a82d445c44f7dbe44f092fd5f7945f2b |
We further evaluate our approaches on the PASCAL VOC 2012 test set. Following prior works {{cite:40e493227e14ede61f961e65cb42a9b956115f54}}, {{cite:3363189ebdc8e1b13100dfe4e6df407e9cab71d7}}, {{cite:4a1dd263462c14d3d4770b05f0eb1cd1348d88aa}}, before evaluating our method on the test set, we first train on the augmented training set followed by fine-tuning on the original trainval set. As shown in Table REF , DeepLabv3 with categorical clustering based feature binding network achieves 80.5% mIoU which outperforms the baseline. Additionally, co-occurrence based feature binding network achieves 81.1% mIoU which marginally outperforms the baselines and the categorical clustering based feature binding network.
{{table:1350cc45-1789-4a8b-a1db-c94a9a0f35c2}}{{table:577f53ca-8d8c-4899-8ef0-6af0e7a8e1a2}} | r | 3ab4e2f8f7e2c73203709299ed44ff44 |
Besides boosting relevant tasks using StaQC, future work includes:
(1) We currently only consider a code snippet to be a standalone solution or not. In many cases, code snippets in an answer post serve as multiple steps and should be merged to form a complete solution {{cite:e0d248b173ec38389eaf0bb9fc85944808af6ade}}. This is a more challenging task and we leave it to the future.
(2) In our experiments, we combined BiV-HNN and its two variants using a simple heuristic to achieve better performance. In the future, one can also use StaQC to retrain the three models, similar to self-training {{cite:0192f64472b5a82ed0f34fd0a5616961ce4fe122}}, or jointly train the three models in a tri-training framework {{cite:8334b99f3d2cbc3b8fbfb7f9c61d5be0cc30c28c}}.
(3) One may also employ Convolutional Neural Networks {{cite:8479b44ae5e47e59657c44acf3c6e728b8274181}}, {{cite:3a881f2182f00fa6df3071d3225b877713d3ade0}}, {{cite:e9b053478b4539f8254b0efa73052897b422c5e6}}, which have shown great power on representation learning, to encode text and code blocks. Moreover, we can consider encoders similar to {{cite:5b99bfaaf897b4e2b529f63ccd5af20dda7625ab}}, {{cite:61e5317c57c8260f0023b7199f49ceba8153f3f8}} for capturing the intrinsic structure of programming language.
| d | a9b58c9eab576205bf284d16738abcb0 |
All reactive molecular dynamics simulations has carry out performed by non-equilibrium molecular dynamics method {{cite:85b8b5dc24106974cbac7831c689bad0e9bd8664}}, {{cite:a9e7995ae0782bc7f52ded8e7527e4579874dbdc}}, {{cite:3d34a94cc42ebec941d438c3d6b01ca603390e74}}. The numerical atomic positions os carbon atoms are calculated by large-scale atomic/molecular massively parallel simulator (LAMMPS) code {{cite:4ab36088bace44d9517a11c397edc4ead4f8e81b}}. The interatomic potential used in all calculations are a modern reactive force field ReaxFF with set parameter described by references {{cite:4a74e587eb90ec98289ce7443384b210efd4c050}}, {{cite:487c8a6e5a2db051fbd202570832e91ab7fc5c9a}}. The reactive force field ReaxFF is parameterized using available experimental results and first-principles calculations {{cite:4a74e587eb90ec98289ce7443384b210efd4c050}}, {{cite:487c8a6e5a2db051fbd202570832e91ab7fc5c9a}}, {{cite:904ac204126814af802b02d9c1ab8482c27abc7c}}, {{cite:d2e362c319866f1d315d383d685159cd345f67a5}}, {{cite:4f1673d8b11a839b5a79adc299a258cd05a247a9}}, {{cite:5a338c0011bcfaca21a1a4d616cc2d92ce89a92b}}, {{cite:4294fa1012022f360b2b65d761dec6f33968671c}}. Approximately to empirical non reactive force fields, ReaxFF is divide by partial energy contributions, as in the follow equations {{cite:4a74e587eb90ec98289ce7443384b210efd4c050}}:
{{formula:df452d08-3757-4c4a-a1e2-f1efa2800b65}}
| m | e59148fcac3e61c9f1438cce5edb0b75 |
These approaches vary in defining typical motion characteristics for clustering. Yan et. al {{cite:1803feb4258bc129bf95c7792066d8c18f9869cd}} propose to cluster trajectories based on geometric constraints (trajectories of the same motion lie in a manifold) and locality. In {{cite:611a65943fa403877eec440cf342f8ece2e08f56}}, {{cite:a4bf32785a1c0cdbc36c2fffbac26078e93c6b00}} the segmentation problem is represented as a minimum cost multicut graph problem, where edge weights are computed from motion, position and color cues.
| m | ca872b9ad305e6948c22a81371d55601 |
The space {{formula:68d9f1fe-2c11-4ce0-9223-064f2f9d12b1}} is a complete metric space and so is the product {{formula:2ce073f8-6026-42a6-a79b-c370ab8b2175}} with {{formula:8cfd74e4-93e7-43d4-850e-809f39b770ea}} . In {{cite:08e8e7614fbca4788defa1320d8e7471ef535811}} the following was shown by extending techniques of {{cite:51b56afe6f70324df8383e54081222d31153c5f2}}: if for all {{formula:11222e21-41c4-49f3-b051-00920042e105}} it holds that {{formula:51bd33bf-1e08-4984-98c2-43287b6a9611}} , that is {{formula:6397e947-8756-4010-87b0-57a24d41a3d0}} , then the restriction of {{formula:0ff69adb-d354-443b-b23e-3b2c405518dc}} to {{formula:ef5971fc-a3c3-4bea-8459-a5c6c1de5743}} maps to {{formula:c5042dd0-e6a7-43e4-8ba2-600b540eea8f}} and is a {{formula:56411dd2-119e-4f70-958a-d7ceea96945f}} -contraction with respect to {{formula:7952fd1a-e938-4d5c-9cc8-7dc848ae9939}} . Banach fixed point theorem yields that the operator {{formula:8f51d142-7f55-425c-8149-2476979e2a80}} has a unique fixed point {{formula:a6c7b3a1-8baf-431b-b1ec-3040375f344e}} . The latter also follows from our results: if {{formula:1e1a851a-6041-4276-86f9-99b7fd389f23}} for all {{formula:e6b8c021-4899-4642-8b09-9bf5d7c42c77}} then {{formula:2cc05a65-97c0-414b-a847-ed5122eb26b1}} for all {{formula:84df2fe8-3a38-45d2-aa2f-b8994be4b123}} and by Theorem REF there exists a unique fixed point {{formula:f31d42f6-685a-4044-9bc5-17d4ee09a2f4}} . Now {{formula:fb52d263-4f0c-41a1-b04b-11ac8840d033}} for all {{formula:d2e57d61-b2da-41e5-adf8-e4e97c901c3b}} implies {{formula:6f8efe34-9b2e-4cee-8be5-6c9b20e8ca1a}} by Theorem REF .
| r | 854e7a3445d42a6792380675b6c1f4a8 |
On the other hand, to remove the need for differentiating through the LL optimization path, especially when the LL dynamic system iterates many times, a type of implicit gradient-based BLO methods (called I-GBLOs for simplicity) is employed in {{cite:0761a56506668e4c75ce2ddb6223745e73fa756e}}, {{cite:433a615078d7941bce9f6a75bc8ce4fb2de61a41}}, {{cite:d56b08e5f0f58c6032aa2a9302a47a6bd1ade1de}} for hyperparameter optimization and meta-learning. In fact, I-GBLOs first leverages the implicit differentiation to derive an analytical expression of hypergradient, and then solves inexactly the LL problem up to a tolerance and performs an approximate matrix inversion accurately. Hence, I-GBLOs requires executing a large quantity of iterations and computational burden is naturally caused.
| i | 779da6aa2d9990a080fe9d8567fe73a9 |
Novelty, anomaly, outlier, abnormality and out-of-distribution (OOD) detection are closely related topics {{cite:d6584d46cbbe7587c7064691ef10d58c9116b26a}}. The distinction between them is vague across variety of literature studies {{cite:1a09f993c24e941879672d9934dadeb6c6e68309}}, {{cite:4663c658d763b21be6c559e3c6b9a08252da985a}}, {{cite:344204a359400a1c9f0d42d2d3bd72eb6a2daac4}}, {{cite:aa834c983d1be8b73ec5a1bec9abdca7b07990e5}}, {{cite:0b2ad353a103984d45c9edb01527a0caf810eb16}}. For clarity purposes, we consider novelty detection to be the overarching paradigm, since it makes contextual sense to have novel abnormalities/anomalies/outliers but the converse does not apply.
| i | ed8d8ee700a1c9836265c32a932b620a |
From the considered spin correction in eq. (REF ), we have obtained the expected results for the spin vertices as in {{cite:e8cc7771cb861d60a4b51a95c3a7626b2d742ef7}}, with the difference that our spin supplementary condition and relativistic spin allow us to remove any acceleration dependent correction, to express them in terms of the spatial relativistic angular velocity. Such findings suggests that there should not be acceleration dependent terms in the action, and that the current higher order PN results using the theory {{cite:e8cc7771cb861d60a4b51a95c3a7626b2d742ef7}}, should be cross checked with our considered higher spin correction. Moreover, it is worth considering higher order corrections to the one considered in eq. (REF ), to find whether or not they contribute to the dynamics as well.
| d | 9e90d5e04f79986d4c669018f409547a |
Large-scale language modeling has demonstrated exciting performance gains in zero-shot classification when combined with explicit, prompted supervision.
Here, existing labeled datasets are transformed into prompted training examples, which redefine classification tasks as generative, text completion tasks {{cite:c033d2e5b119d2c8763a92a158b6623ed2a0daae}}.
T0 and FLAN have demonstrated improvements in zero-shot generalization using this training approach {{cite:260dfc8bf409e4b820da766f4e63f4f5b9c32b85}}, {{cite:51422645754fb8a3dce38543c07674b6647f2674}}.
Increasing the number of prompted training tasks can also lead to improved generalization even when the number of model parameters is fixed.
| i | cccb84c4209c154ab1667d74b6574ac4 |
The relative {{formula:a473e8fe-d834-4056-9d1e-db4916f8c54d}} yields as a function of the relative charged-particle multiplicity measured at mid- and forward rapidity in pp collisions at {{formula:c85664e9-0cd6-403c-a4dc-70cfd7ee4640}} , 7 and 13 TeV are shown in Fig. REF . The measurements differ for the physical event class they refer to: inelastic events (INEL) for the measurement at {{formula:c37a5e86-03c7-49f5-8395-61f443b1383d}} TeV, inelastic events with at least one charged particle in {{formula:51e15399-1d9f-474c-8987-1e43b25fa32b}} for the measurements at {{formula:3ab9c136-cc94-4527-bcaf-56b5e983f500}} and 13 TeV. The vertical bars and the boxes represent the statistical and the systematic uncertainties, respectively. A close-to-linear trend is observed for measurements at forward rapidity at various collision energies, suggesting that there is no energy dependence of the relative {{formula:3b2bb6d1-9cf5-42f9-8975-109a931e5bca}} production in the same relative final-state multiplicity domain {{cite:9d997552d77d9be3ab6e149e59669ee73158d87f}}. In addition, a comparison between the forward and midrapidity measurements at {{formula:cdf80a7b-3280-40b1-9763-ae8c45fcde75}} = 13 TeV is also reported. A faster-than-linear increase as a function of charged-particle multiplicity is observed in the midrapidity measurements. The results using midrapidity multiplicity selection based on the SPD detector and forward rapidity multiplicity selection based on the V0 detectors are also shown in Fig. REF and found to be compatible within uncertainties. This suggests that, for {{formula:3cc60f69-68d5-4575-922e-045cbec51589}} mesons, the difference in trends between the forward and midrapidity measurements is not due to possible auto-correlation bias that arises from the multiplicity selection {{cite:9d997552d77d9be3ab6e149e59669ee73158d87f}}.
| r | 61056c135adba0b4eeef96eb3bd30979 |
Nevertheless, the corona parameters ({{formula:ee50dcd3-a7a2-44fb-85ee-759121eac7de}} , {{formula:b9892b06-ffa5-44bc-9df3-97d18ab801b0}} and {{formula:97ce128f-f1d6-49a3-b43a-3019b6d32bfc}} ) change little during the soft-to-hard transition, although the inner part of the corona (from the NS surface to the corotation radius) has been expelled out the system.
This finding implies that the structure and property of the corona have little dependence on the radial distance, and
the whole distributing of the corona is stable in this region.
Since the disk viscous power is a strong function of the radial distance and decays rapidly outwards, this stable corona is against the origin that the corona's power comes from the thermal electrons from the disk's viscous power.
Thus, another origin of the corona–the magnetic field is favored, and it could be the reservoir depositing much more energy than the thermal energy content {{cite:e63abe51cc6961c6bcee6d125b87ebf3fbe996d9}}.
| d | 87885d42019aed0c99a695f04528b04f |
The three parameters of the adopted model as shown in Eq. REF are {{formula:b5dcf218-3154-4019-a6fc-9f0a939ac272}} , {{formula:fcf368c7-c71c-4d63-932e-d419daf6cd27}} , and {{formula:60aec7b0-6455-4a5b-89ad-4b6285e8d0de}} . A Markov Chain Monte Carlo (MCMC) {{cite:d8efc742b5dfbb942911f02bddd306822c01325c}} sampling method, constrained by the latest release of Planck CMB data, {{cite:6dcb2a2aee6c4a79ffed43cd07bdb759e0d5f970}} was implemented to compute the allowed ranges of the model parameters. A modified version of the HLattice code {{cite:64771f3f9572896708b71dd5331a4d96b4af3f92}} was then used to study the (p)reheating dynamics of the adopted model.
| r | 3d0fb84303feec52de6c424b4d38c4b6 |
We investigate which probabilistic deep learning model design could concurrently learn both to provide calibrated class probabilities in-domain and to accurately identify OOD samples after being trained only on data from the target domain towards a single objective. We take Evidential Deep Learning (EDL) {{cite:69dd7d8eb312e0a3bd57a628a42ccef2ad078a93}} as the starting point due to its reported empirical success in OOD detection {{cite:d03eb320b71ae8642c4fa298683cdca7da8f53ab}}, {{cite:45fdfe0264dbf4d00e6f5d12e6d53b5a78364bc6}}.
EDL characterizes the class probabilities of an input pattern as a Dirichlet distributed random variable with concentration parameters determined by a neural network. We build on the fact that the EDL training loss can be framed as the Evidence Lower Bound (ELBO) of amortized variational inference of a Latent Variable Model (LVM). Based on our empirical findings on the relationship between the training regularizer and in-domain calibration performance, we extend the prior distribution of the resulting LVM with an additional global latent variable whose sufficient statistics can be aggregated from an in-domain context set. Such a model amounts to a Neural Process (NP) {{cite:eda089d4ac98596a73e7e90a511f8ec9bd11193d}} employed on a conditional LVM derived from EDL. While the NP extension equips EDL with improved in-domain calibration performance, it necessitates an available context set also at test time. We lift this limitation and enrich the encoded context information by extending the aggregator variable of the NP to a Neural Turing Machine (NTM) {{cite:3277642058894d10a5784095c2d9620c21e76f47}} that can store multiple entries in an associate memory and retrieve them via an evidential adaptation of an attention mechanism. We name the resultant model as the Evidential Turing Process (ETP).
| i | b64791c7738363485a5846ae7a8b0ff5 |
The particle nature and properties of dark matter (DM)
can be probed by the direct detection experiments, typically utilizing nuclear or electron recoils {{cite:a4999c6ede86fc6064a4c08e1ca548053d8abbd9}}.
Recently, the XENON1T experiment found an excess in the electron recoil spectrum around {{formula:07cab9f3-c341-418f-a0de-30cc761d03eb}} keV {{cite:4916f48a3d79c62431926bb87eb9b06b67547ed8}} which was independently checked by the PandaX-II
experiment {{cite:3c9768d58a28052d5a62f2ca6000581ae14026cc}}. Although
solar neutrinos can also scatter with electron via the Standard Model (SM) weak interactions, this signal can contribute only {{formula:080e66f1-1bbc-4986-98b7-78addaae5eb9}} of the total events as background and more
importantly the electron recoil spectrum is quite flat in the observed keV range {{cite:89beab6ab38819aa95075b036664fa224a627859}}. The excess might indicate new physics beyond the SM (BSM) if not the tritium background {{cite:3b0d96fd2922bbf5ca1c4a2d3fc4a57d411d56ad}}. Possible explanations
include axion or axion-like particles
{{cite:69621cde664f31121e5f587bbaa4a57ec55824b3}}, {{cite:bf50e0718a950846ed0cbeca0b7d2dc321a3095f}}, {{cite:a3717d04080b30a19b4e7e73c7e62b686bead0ab}}, {{cite:86eb243ede876c4f7635664fd188fe6af95459db}}, {{cite:d4c1e05be0a0e5f99dbab0674a7013ab83a92ffb}}, {{cite:2d1a32d63d16dd7ee96518cfa917dd9863fd9338}}, {{cite:1a0179f09711470f8c444bcf49e8c72be8627b4c}}, {{cite:e6e82d285ea9afce0103c2e049a50c4c778e2a01}}, {{cite:5ebb4ffee32fab9e1acc6480e6a6bb6ff9bbae5c}},
elastic {{cite:3b03485ac592a253ed9ec5adc5f7056e4de2ff81}}, {{cite:ebbb454b757b52fecd2f084fc39b771b5b67abf4}}, {{cite:81b24d8595e5d8eb2b1755a0a24b051d3f5961b3}}, {{cite:79e6008421f47db3fd79df8abf23d45f29bd0fef}}, {{cite:458d664ba9b05be706013070187056f1fe72f314}}, {{cite:84524e265881f3514b110483ead5afc0e5e585c2}}, {{cite:c1d1a51af91d000593b3ca37ad6399f2e6444d8c}}, {{cite:51910912c5cef68027c3bfcac93a626a15a1d36f}}, {{cite:2ce44279c7ee0bbeeaad29963fee849f49ec7f7f}}, {{cite:f74044d5c6ab2eb90d672cbde840f8c46327e233}}, {{cite:8d9f76749258db459af729fd3c49a3821122b9eb}}
and inelastic {{cite:b5f331d0c78b87fabba8fde398a173834a51bb98}}, {{cite:076bd2cded9c07b55479ec5b1c44a5788f9a186a}}, {{cite:0f37c5dca19a92871d7a260b7f559aa707913503}}, {{cite:2b36aed7a3adfd79dc9b2916b80611967e732745}}, {{cite:b1df7f87fff956f9aac93e32175289857d9a205e}}, {{cite:9545dcdb39427eb19c099507d7a3daec3961c09e}}, {{cite:a558969045c4fd441ff755f1f9a3daea2fd2e3ac}}, {{cite:18a5102787188d3892412c34feba1f54e2312441}}, {{cite:23fcf4e0c23bce216e71b2dc5210c31ae60b0280}}, {{cite:adae07dc3991ecdbd6684f9f128eb8c5464e996d}}, {{cite:f057db8db11abdb7f5ff33d1f570e4b8e216ab8d}}, {{cite:5d1e973a91c93ecc6f5aa3ed5698fecdb71881f0}}
scattering between
DM and electron, the Migdal effect of DM scattering with
nuclei {{cite:99a9858a255512f48ba067086f4673d220790cf9}}, and DM decay
{{cite:b2f17287b86f1bf54ababc5d8f95b91e4cb245c7}}, {{cite:a0af648d089b325c272e974d8fea3781d62ed3c7}}, {{cite:aa625bd1ddfdcc45029529af43598724ff630d59}}, {{cite:aa625bd1ddfdcc45029529af43598724ff630d59}}, {{cite:72c7317c57a0c57ce41612f11e7c10e33221046c}}.
Another possibility is sterile neutrino as DM in our galaxy.
Either the sterile neutrino DM inelastically scatters with
electron into active neutrino and releases its mass as energy
in electron recoil {{cite:3b51f45ba9a9614508d4aae370fc2736e20fada3}}, {{cite:dc95e23f96e5d82d2debcce6ec1680b85c85f27f}} or sterile
neutrino decays inside the detector to produce a photon signal
{{cite:4acaad3ac81902f6ecb0cf377a6879017e45a8ed}}.
| i | fda282e5a37148aaa967f9ff0e38f678 |
The conductivity dependence on the temperature, determined by the response and transfer curves, which were acquired at different temperatures, reveals that the charge transport is dominated by a thermionic emission over an energy barrier. There are three main mechanisms of transport across an energy barrier: (1) thermionic emission from the high-end tail of Boltzmann distributed particles, (2) diffusion and (3) tunnelling (or field emission) through the barrier.{{cite:54a279526c8361131423633b6652c2e5bf4bf5fa}}, {{cite:e1aa17f00660b58c8310a5333777490a28fb0bbf}} For thermionic emission of charge carriers into a three-dimensional semiconductor, the current dependence with temperature ({{formula:1f7bbb99-6cc6-4ff1-b489-27c4bcae70bd}} ) is given by the Schottky diode equation {{formula:f89e3413-9cc8-4d41-a551-472ef9069a1e}} , where {{formula:9612af2a-42c6-41a9-b65a-42dd07ff27e5}} is the contact area, {{formula:e0df0120-bbb8-4c5f-ac40-d8353afb6e8c}} is the modified Richardson constant, {{formula:9e578652-fff2-49ed-bdfe-f9169d4b48e1}} is the activation energy required to overcome the barrier, {{formula:8fe377d6-43e5-460f-8849-aa63d07a17ea}} is the ideality factor, {{formula:bbf54432-8939-487f-bda0-7a1d0907dae7}} is the basic charge and {{formula:b5078560-c5c6-4ce2-89b7-eb3d897d0565}} is the Boltzmann constant. Other mechanisms of charge transport differ mainly in the exponent of {{formula:ae055546-3342-40fe-9a87-462278da8c73}} , which is 0 for diffusion and 1 for tunnelling. To determine the transport mechanism, the MoTe{{formula:2f7255b3-9bd0-4be7-8726-f30b6f644ba1}} FET current vs. temperature plot shown in figure REF a is fitted with I{{formula:79912fcb-12dc-412b-bba7-518339a5b83b}} T{{formula:1ebc34bf-30e4-4419-b7d3-df959f3ca040}} , where {{formula:357289bc-af2f-4975-a405-a239b4c28f91}} is the exponent of T used as a fitting parameter and {{formula:5d54c4dd-e12c-478e-a21f-e3146657a92a}} and {{formula:982961a4-8395-4dab-9df7-484bb712cc11}} are arbitrary constants. The use of the pre-exponential constant is justified by plotting the current at different temperatures with fixed V{{formula:619f9607-3212-4edb-b909-63e7acd83411}} and fixed V{{formula:169ec06b-135b-466c-a222-19974e88d31e}} . The extracted {{formula:dd83f211-566a-4049-a0e3-4595a4111eba}} is in good agreement with the temperature exponent for thermionic emission, suggesting that this is the dominant transport mechanism governing the transport in the device, while diffusion and tunnelling of charges play a negligible role in the temperature range between 40 K and 80 K. This is further supported by previous work that has shown the channel is depleted of its majority carriers,{{cite:9f59f0c4c3e2b3bce279aa37869197a6d19291fd}} leading to the formation of barriers as wide as 10 {{formula:903defdd-3342-48c8-b404-328fab6c2d07}} m in MoTe{{formula:5b6036a5-c38f-4d61-8b60-a77541e54134}} ,{{cite:863705ff733584dcadaa3849a1ae83a5fdfe6eba}} a fact which renders the efficiency of the tunnelling process insignificant. Further discussion on the additional transport mechanisms are included in supplementary information section III online.
{{figure:7bcd0e72-59ed-4b45-bcb0-b4b2e78f034b}} | r | 70c040023fce009411f47f07e28ea67d |
Set {{formula:845c9737-394a-4d97-a005-8b5d5a9250dc}} . Then, by the Independence Theorem {{cite:1c21c8350808468953cb750994abd9e887cbdce5}} and above remark, we have {{formula:ae5d6187-14bf-48f1-94f9-fd3dc5a078e2}} . Hence {{formula:c4499e43-8f25-4bd7-b3d1-0af5e9d8a36b}} is a right exact functor on the category of {{formula:a7928d9c-7d25-4921-9c90-70d02880db20}} -modules. Furthermore {{formula:5f1100fb-36e1-4510-b2a9-194b019f22c0}} is an additive functor that preserves direct sums. Therefore {{formula:2b2fc6e1-8746-4a11-8821-600bafc8a0e3}} is naturally isomorphic to {{formula:932d35ef-f575-4e01-885a-4aafc8f4902a}} on the category of {{formula:7fdc96d7-accb-4de7-be90-12dcf9f704ab}} -modules; see {{cite:ffff0b403530db268cad98fc3277c62faea9e0b2}}. Hence
{{formula:9e02386c-1f23-42ec-babe-6ff913102e15}}
| r | b116ef9e533307e1aa7fc32780307afa |
We compare the performance of PUCRL2 with three other algorithms: (i) UCRL2 {{cite:ae33230fc724f2da8354733dbee26d074f57b08e}} which provides optimal static regret in stationary MDP setting, (ii) UCRL3 {{cite:f3e645edbcd80d028f0ccd684b4d1044f629e717}} which is a recent improvement over UCRL2, and (iii) BORL {{cite:a2048de8a4cb466401148a18b6b49859a02a067b}} which is a parameter free algorithm for the non-stationary setting.
| r | 5a0ee25b359da7c78e39b81e6c05d658 |
One of the advantages in using the probabilistic framework is that it makes the analysis of statistical certainty more straightforward. A posterior distribution for the test statistic, Kendall's {{formula:f3b53c75-62c6-47e5-a4ec-380adb1c315a}} can directly be computed from the model parameter {{formula:b18f2a3b-b799-4f7f-8a44-8f8732301a03}} . In contrast, in the non-probabilistic setting one needs to resort to indirect and time-consuming surrogate data analysis methods to generate an approximate sampling distribution for the test statistic. This can be relatively simple when a data generating model is known as in our simulation experiments. However, the data generating processes are often unknown in practice and need to be approximated in order to generate surrogate models. In univariate setting, for instance, the ARMA(p, q) model has been used to identify the optimal ARMA model parameters, in order to generate surrogates from this model {{cite:6385bd5f6ab103afa290c09d7fac6c1bbebb8c71}}. In multivariate context the corresponding model is VARMA(p, q), but fitting this model is slow and potentially unreliable with higher dimension. Hence, the ability to directly estimate uncertainty in model parameters without such extra steps is beneficial. Another key advantage of the probabilistic framework is the ability to use prior distributions to regularize model fitting, and to incorporate available knowledge. This can be particularly useful when sample sizes are limited. By utilizing Gaussian process (GP) priors on {{formula:657f3a3b-a938-47e9-a220-633fa5f50683}} we could restrict its posterior to differentiable functions, and by GP hyperparameter selection we could emphasize longer term trends in the target variable which are of most interest in EWS context. On the other hand the Matérn-3/2 covariance structure remains sufficiently flexible to detect relatively sudden changes as well {{cite:3c4e4c3fe22ce20376f67405c1fc14193c66c502}}, {{cite:4ffb83702f9099ab6597636206ce9c07348b0657}}.
| d | c8b73660aebc440a81c8c5de4d118bba |
Another major development was then achieved with the generalization of the QSLs
to the evolution of open quantum systems {{cite:2f019db0098dcb2e4ddab27af48b60f4bc6bd372}}, {{cite:c2953aafd3eb9202561af046864bc264d63eddb6}}, {{cite:7e3e74bffd68a08d2b544f3747d973a4743a9e31}}, {{cite:889c5bfeef40fd31f15cda79d6fe50c134e45299}}, {{cite:3c0aa281ab22b959ba627fbeb53b778d9bbf6565}}, {{cite:563a037370d757ff73c756230cc2daf5eab8e83d}}, {{cite:82e51ff561f163613426b4f01e0c7f360cf48186}}.
For any open system initially prepared in a state {{formula:4ac356b7-2d12-454f-9ada-524f3f8c11a3}} , and then left to evolve
under Markovian or non-Markovian dynamics, the rate of change of a carefully chosen
measure of distinguishability between the initial state {{formula:d89b5d95-0b19-4a3d-873a-80098bc54b2d}} and the evolved one
{{formula:fe538f52-728b-44fd-bc77-b9d8ae283f3e}} could be used to define a QSL. According to this procedure,
Taddei et al {{cite:2f019db0098dcb2e4ddab27af48b60f4bc6bd372}} found an expression in terms of the quantum Fisher information,
while del Campo et al {{cite:c2953aafd3eb9202561af046864bc264d63eddb6}} established upper bounds to the rate of change
of the relative purity for both Markovian and non-Markovian systems. A treatment based
on purity was recently proposed in Ref.{{cite:3c0aa281ab22b959ba627fbeb53b778d9bbf6565}}. Furthermore, Deffner and Lutz {{cite:7e3e74bffd68a08d2b544f3747d973a4743a9e31}}
derived geometric generalizations to open quantum systems of both limit times known
for unitary evolutions, the Mandelstam-Tamm bound, as well as the Margolus-Levitin one.
Note that the geometric QSLs previously proposed in Refs. {{cite:f07ede0958105a070f58200f38db22803351b722}}, {{cite:15c13a1309e18ba0394c7e9ef39ad4b414202773}} are derived
as upper bounds on the rate of change of a distance-type measure of distinguishability.
General geometric QSLs are analyzed in Ref.{{cite:a9214304048b2b2ba9f03fe103f098237c86f15a}} using as measures of distinguishability
a family of Riemannian metrics that are contractive under stochastic maps. Among them,
geometric QSLs based on the quantum Fisher information metric (involving fidelity) {{cite:6af8d44a794c619b7c67631f63b78d11395b3376}}
and the Wigner-Yanase information metric (involving affinity) {{cite:04f027954da16c7a9f4e8791a9da63dc9c6ec41e}} were compared
in Ref. {{cite:a9214304048b2b2ba9f03fe103f098237c86f15a}} for unitary dynamics and several examples of open-system evolutions.
More recently, some other QSLs were introduced, although they are not proper distance-type
measures of quantum evolution. For instance, in Ref. {{cite:563a037370d757ff73c756230cc2daf5eab8e83d}} one finds a definition based
on a "quantumness" notion, while Ref.{{cite:d283d096faf10c81108247ecb1919629877f2a69}} shows that quantum coherence plays
an important role in setting the QSL.
| i | ff4fca586bd8fc6396cef39deffa0d71 |
Subsets and Splits
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