text stringlengths 54 548k | label stringclasses 4
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where {{formula:848f99aa-f99d-4aa6-81a8-ef8b3f91e658}} is independent of {{formula:be8d26e5-e18d-4470-87b1-8b6d3a4e5306}} . The proof is complete.
The following lemma shows that the the coupled term {{formula:3e3ac0d0-0823-4361-9436-1c33e441308d}} has BL-splitting property, which is an another version of Brézis-Lieb lemma {{cite:9accc46b3e83c0ca4029030c049469ab49917120}}.
| r | 01baaf901be852d6012af3a9df4b36ed |
We begin by using the MPLC to ceritify high-dimensional entanglement{{cite:60f8eaf57d59899cf1dcd48c7b4cc4539764b732}}, {{cite:c6def48859d6b0b4249297feeaca8d1103999ab6}}. To certify entanglement in two or more dimensions, one must measure the quantum correlations between the photons in at least two MUBs{{cite:60f8eaf57d59899cf1dcd48c7b4cc4539764b732}}, {{cite:3e3f4da7a6ed5f08f0a9b3a9afdc8e0e3477066e}}. In our case, we utilize the reconfigurability of the MPLC to switch between measurements in the 'standard' {{formula:0a0fa623-aeca-408e-844c-d805b094baee}} pixel basis, and in the discrete Fourier transform (DFT) MUB defined by {{formula:e00a1391-ba05-4130-9631-3613b2b639dc}} , where {{formula:1f64d50d-4558-4ce0-9c7a-a98b248d89b8}} is the dimension of the Hilbert space of each photon and {{formula:c0cb0a83-7975-4910-88c8-f40c740dfe52}} . It was recently proved that this set of measurements is sufficient for obtaining a lower bound on the fidelity {{formula:ce596df8-bafa-48f9-a46f-69321e477a66}} between the inspected quantum state and a maximally entangled target state{{cite:60f8eaf57d59899cf1dcd48c7b4cc4539764b732}}. Using this bound, m-dimensional entanglement within an N-dimensional state is certified for {{formula:78322b5c-0a5a-42ca-ad3c-ce4de919c122}}{{cite:60f8eaf57d59899cf1dcd48c7b4cc4539764b732}}.
| r | e71364b6c0a353bd389113412b7c9ac1 |
Supervised Descent Methods {{cite:b20be5cf32742761f96e6d42b20aec03f55e255b}} {{cite:1679546efffe33d98dcf2c49db5d93188e16ccf7}} draw
strongly from non-linear optimization methods, which have been
classically applied to the face alignment problem. Supervised Descent Methods are
closely related to Gradient Descent Methods, in that they
employ a linearized estimate of the parameters and refine this
estimate iteratively until some convergence criteria is reached.
| m | 5a74e87b2fdc5ac4878d139ad2ab3b56 |
This section shows that hammer also works in a multi-agent task with continuous control and individual rewards. Figure REF shows that hammer performs substantially better than unaided independent local agents. Like in the cooperative navigation task, results here are averaged over five independent trials, with an additional 500-episode moving window to increase readability. Additional results in Figure REF confirm that hammer outperforms independent learning in the case of 5 walkers. In the case of N=3 walkers, we used a message length of 8 for the central agent, whereas an increased length of 10 showed a better performance for the N=5 walkers scenario. We did not include this result as Gupta et al. {{cite:686fe7c38b77a258bcb04747d17ea82962a7fc6d}} already show that independent learners outperform a centralized policy in the multi-agent walker domain.
{{figure:ecf8e4b2-c9e1-48d5-b54e-e7067472e6e8}}{{figure:46d7375e-e399-4b07-a23b-3fdb6ae5f81b}} | r | 58a5c77a496f1c53ac75deccb931dbe8 |
The successful implementation of representation learning in natural language processing domains (e.g., word2vec {{cite:a05e58518cf3d332e66ba9badda2cc97d2a07303}}, {{cite:f0cdfbeff253afc66b376fd7dd5a6d5b4c1ea80b}}) paved the way for new directions in network representation learning by optimizing the neighborhood preserving likelihood concept. A document is a collection of words. In word2vec the features of the words are extracted from the relative occurrence with the related, or in other words, nearby words (being in the same window size). A text document consists of already existing sentences. The sentences are the natural constructs representing the relations among the words. There are no such sequences or grouping for the nodes of the networks. The difficulty of using representation learning techniques on the graphs appears to be constructing sentence-like structures. To obtain such structured constructions which introduce an order for nodes and reveals hidden features, random walks are the best candidates and often employed.
{{figure:22da9409-a87f-42b9-beb1-a4a620bf2892}} | m | 3333eb2925e09b536f0b4c5664e16313 |
The fact that on-shell the trace {{formula:5398f161-8268-4ffa-8525-5a5729e3810e}} of the total energy-momentum
tensor of the system vanishes {{cite:9898728e9d5daa30812574e7ceafd3922291da05}} has implications only for anomaly of
global conformal symmetry. By adding a spin-2 field (understood as
matter not as a dynamical spin-2 geometrical current), coupled to
external geometry represented here by the tensor of rank-2 namely
the metric of the spacetime, one can cancel the global anomaly ('t
Hooft anomaly) of the conformal invariance. This is evident from the
fact that on-shell the energy-momentum tensor of the total system
(gravity+matter) vanishes {{formula:48b46585-da8b-41c9-a027-111b3d6267ff}} {{cite:71d8ea2476889146dbfc55c41d5769588c59b423}}. For the cancellation of
the global anomaly this condition is exactly necessary and sufficient
and should hold on-shell. Similarly, a gauge current conservation
in some globally gauge anomalous theories (because of the presence
of chiral fermions) is due to on-shell condition and after all (after
adding some new matter fields) the total current is conserved, so
there is not a global anomaly anymore. For the 't Hooft global anomaly
(and current conservation or the issue of the trace of the EMT) the
off-shell situation does not matter at all.
| r | ed4d388f58013b68729d384217be56f7 |
Gradient-based approaches such as back-propagation are widely used for MLNN training, but have drawbacks such as being sensitive to the initial weights and a tendency to get stuck in local optima. Population-based metaheuristic (PBMH) algorithms such as particle swarm optimisation (PSO) {{cite:d330638fe9b79199061e56676af06c7373a0c2e5}}, differential evolution {{cite:5288bbf498d312289d0f2ac8cfb7c5b301e79906}}, and human mental search (HMS) {{cite:17f7877f429626486d3b0c59f2c9513a79d0b8ac}}, {{cite:bdb8c5e1049723fb31af7b17f9e59da4b849d088}} are capable of overcoming these problems. PBMHs are problem-independent optimisation algorithms that find an optimal solution using a population of candidate solutions and some specific operators. Nowadays, these algorithms are extensively employed for MLNN training due to their simplicity, flexibility, and ability to escape local optima. PBMH-based training algorithms have been introduced using particle swarm optimisation (PSO) {{cite:0979074eaeb9c4581cad02eb38c5f5e574eb2a1e}}, {{cite:1faa3545dd354d6252cd8b1aee9662e807ef20ea}}, {{cite:feaa2458c9d5ae1f64d9de57540a12b7f2d7619c}}, artificial bee colony (ABC) {{cite:bcf1f932d4958806e8266e153381d76c19f2dd8f}}, imperialist competitive algorithm (ICA) {{cite:9f5aa5f5637002774226b0644ef1aa74483ad9a8}}, {{cite:d2609918c2685b08eed41054fe4c53e3455b82d0}}, {{cite:ab379b0326fc480a7f64d1e169c86cf392ae93dc}}, firefly algorithm (FA) {{cite:96329fe5e0270a3c30aaaf02fa9b4dc3feccdaf7}}, grey wolf optimiser (GWO) {{cite:076f3d2c2d1258eb9b64741b35548313da7152f2}}, {{cite:7fade94157a41a28087314513a48471201208e8d}}, ant lion optimiser {{cite:7dca46ef7bd4c821b9df051284d568b87620849a}}, dragonfly algorithm (DA) {{cite:3a64bd0019e152787fd4a00bdf0051f57b8d0ca0}}, sine cosine algorithm {{cite:f38fc8fdf8842ffed8b8f9a82b1c8a05e348c2a3}}, whale optimisation algorithm (WOA) {{cite:ed8e1932834f6a07431ab47bedd744d256df8d60}}, grasshopper optimisation algorithm {{cite:82f389fc5408607d0f8e3833b707adf2f548aa25}}, and salp swarm algorithm (SSA) {{cite:f8d9e81c8fc9ad0b72fa3663d9a80b5954d428eb}}, among others.
| i | a3121cdd9d345a5f9b893d705e63a5f3 |
More recently, {{cite:0a5fe10fd279be0af60aa458da2a95b586786f81}} fitted the density and gradient profiles with
both the DK14 model and the GPR method. They found that both methods produce
reliable results, and that the D14 method performed better for
gradient profiles. We performed tests using both methods to fit the two types
of profiles, and found that the uncertainties in the DK14 model are larger because
of the complexity of the profiles. In contrast, all the profiles can be well
fitted by the GPR method, with locations of all significant extrema identified
reliably (see below). More importantly, we found that some small
local minima and peak features, which are of interest to us, cannot be
identified by DK14 model. Because of these, we decided to adopt the GPR method.
| m | 45b0fcd93244357232048baea98620f4 |
Adversarial examples are an “intriguing property of neural networks” {{cite:f9c7bc2264fb923d377915a68fca98409f90b4b5}} by which the network is easily fooled into misclassifying an input which has been altered in an almost imperceptible way by the attacker. This property is usually undesirable in applications: it was proven, for example, that an adversarial attack may pose a threat to self-driving cars, by making them misclassify a stop sign as a speed limit sign; and that this attack can be implemented in the real world through stickers physically placed on the road sign {{cite:de188113e7e9f409e8931b0e4e8003fb85502eb9}}. Because of their relevance to real-world applications, a large amount of work has been published on this subject, typically following a pattern where new attacks are discovered, followed by new defense strategies, in turn followed by proof of other strategies that can still break through them (see {{cite:d925dfd72dcf2e52ecd1183187ac3e487bb112f2}} for a review).
| i | 5709f9bd74ca347fe837f7e7f2320dc6 |
The flowchart of the first model is as shown in Fig.REF (fig:dwcc). The positive and negative (i.e., COVID-19 and non-COVID-19) CT scan slices to different distribution by Swin-Transformer {{cite:260524b603ba19bf059f61251712c02b41ac48f2}}, and determine the percentage in the middle of CT scan that has significant symptoms. Next, we apply outlier removal, and Wilcoxon signed-rank test {{cite:aaf5358c6c5c8db1fe9b9a4deb1c596f27e73910}} for these generated samples. Wilcoxon signed-rank test can give meaning and explainable to the predicted results by statistical inference.
| m | fc1f3fdfb8838ad1c17dbffc19b3963f |
Figure REF shows example tracking results of CenterTrack {{cite:32eb54441e03191dbc991a5b3e986ad8d0f68f5f}}, SiamMOT {{cite:cf20f4e1716691a609cb8ea13b654ed0107b6290}} and EnsembleMOT (CenterTrack + SiamMOT).
Just bboxes of two objects (a woman and a man) are visualized for clarity.
For CenterTrack, the woman (in green bbox) is well tracked, but the man has an ID switch.
However, for SiamMOT, the man (in rufous bbox) is well tracked, but not for the woman.
The third row presents the ensemble results of CenterTrack and SiamMOT, in which both the man and the woman are well tracked.
In other words, the EnsembleMOT algorithm can obtain the best results of both trackers and produce more complete trajectories.
| d | 2ee054db74df8dffcfcbe9ba4c794143 |
Such dust layers partially obscuring the BLR could be located between the BLR probed by the Balmer and the MgII lines, as the latter is only slightly redshifted ({{formula:6ed489b5-15fc-4c2a-bbb3-f884826f4169}} =480{{formula:7209e25e-15e3-45f0-9df9-48bb6aed8500}} 100 km/s). To examine how our target relates to the bulk of the SDSS AGN population, we compared the measured H{{formula:f8284143-0173-48b5-a646-6d716e9c207f}} /MgII and H{{formula:8dee89c7-8c5a-4a67-9c91-bb628dfd5174}} /MgII line ratios of our target with those from the catalogue of {{cite:9c6cf71e3ad926e580244e2d2eb5ca92c4136064}}, finding no difference with the majority of SDSS AGN, while the H{{formula:042496a2-c622-4094-ba90-4e42a5bc2bf8}} /H{{formula:26c8c2a8-e1c0-4a27-8cf1-df87d6012516}} ratio falls in the tail of the SDSS H{{formula:a617a90a-d904-4a1f-ad90-df29f4144fa0}} /H{{formula:e8a8d445-656c-4f55-a707-368fb0a13f70}} ratio distribution. No peculiar properties are found when considering the relation between X-ray luminosity and Balmer lines, as shown in Fig. REF . Here the Balmer decrement is shown as a function of the L{{formula:70b35a28-eabe-4bee-90f4-ae64f482de79}} /L{{formula:83b3876c-f366-48db-af19-dc03973ec68a}} ratio for a large sample of Seyfert 1 galaxies from {{cite:6b3a38dabff074c335581d4df2ce2ccb3cd4aeb1}}, who found that the differences in the Balmer decrements are due to reddening rather than to an intrinsic property of the BLR. RBS1055 appears to be consistent with the trend reported in Fig. REF , which supports the hypothesis of nuclear reddening.
{{figure:c3a6ad6a-5385-4f35-ab7b-48f3c7e5b9f9}} | d | f73591ffefd1655629e112e26cdd2732 |
In this work, we did not include the general relativity effect on BH orbits during the simulation, but considered it in the post-process analysis to detect the BBH mergers.
We therefore cannot detect hierarchical mergers, which can be the sources for massive BHs detected by LIGO/VIRGO {{cite:681034906e2b426db9ac30564ce6d00e37eb0b2a}}, {{cite:aea27f266213d626efbb8e035914a9e79f75c4a8}}.
With the same reason, in our simulations, we also did not find intermediate-mass black holes (IMBHs), which are discussed in {{cite:1ee0ea399cdaf1a73f66d7b50ee95198080df9ee}}, {{cite:f55eb9e18510c55cd7c4d0a2aa02a3f79816bf8e}}, {{cite:282f70402bdc60f3f8ba4625414dd67ac033a0d5}}.
| d | 909364ff9daefe5f1fc5b154dc2e1e61 |
Since linear equations lead to only exponential or periodic motions, analyzing systems characterized by irregular motions calls for nonlinear autoregression models which advantageously employ neural networks. Retaining the basic form of Eq. (), neural autoregression models can be expressed as
u(k+1) = N[u(k), u(k-1), ..., u(k-(m-1)); ] + e(k),
where the model parameters {{formula:8ecc144c-3c46-426c-8161-a6b8864f8869}} of the neural network, denoted by {{formula:71ed9536-1fc1-45c0-90e5-965860305f57}} , are determined by minimizing the deviation {{formula:f5b3a8d8-41f6-4dfe-b775-8520ddc1b3e4}} . Since the first application of neural networks to reconstruct the governing equations underlying a chaotic time series by {{cite:a3f99b62ee515eeea84ea31719c23c96dd67fecf}}, various network architectures including multilayer perceptrons {{cite:c61f2858dfff6252b813e13248abfaa09d85a650}}, {{cite:594aba1c4fb42bf765f7e5da6ef4f05dedb824ea}}, time delayed neural networks {{cite:95177dc9e65c6241c7ad45db1a46b84bf83a684f}}, {{cite:87a96816a0489c0272b6d33ad066151f6ef3746d}}, convolution neural networks {{cite:2a75284d18c78c97ea48ab682971fc26c0566226}}, recurrent neural networks {{cite:9aacffd7f588d059c421eed95314df9f70f3ebf6}}, {{cite:702420ae92c555c8f359c5a9ffd69ca34d619a0c}}, {{cite:bde082fc85991fd16e23906e38520fef0bf48039}}, and more recently transformers {{cite:c4ad79c9436da4a98fd23b065d836a61a3e71709}}, {{cite:9fd1ce05e402205f3e1878066cf7ae3090d84d25}}, have been explored to model time series arising from physics, engineering, biological science, finance,...
| i | 2fb4ceb2b2c26fab79523ff8994e0d4b |
In order to compare our results with data, we will make use of the connection
established in {{cite:aed84bb6e7375e075c478c34f2a9c9c6220159a0}} between {{formula:dcdd47e9-c1a1-4545-a1e4-59819f41cc7d}} and {{formula:2d5a5c63-46dd-4559-afe4-cb7fa3058a3e}} . Although the
power law fit (REF ) is very useful because it leads immediately to
(REF ), a somewhat better fit of the points shown in {{cite:aed84bb6e7375e075c478c34f2a9c9c6220159a0}} can
be obtained with the form:
{{formula:a48bd704-e637-49db-b22b-ed7b41df23fe}}
| r | 9980e3894744264947f19d3a8c5e28d8 |
High-resolution VLBI observations are ideal for probing the compact structure near the central engine.
Previous VLBI observations of OJ 287 have provided key information on the parsec-scale structure and dynamics of the jet {{cite:9fcd333286ce447382afabb1e8c23fbfced2fdef}}, {{cite:35726b3783b0068c717badd44da5c5e24dfd732d}}, {{cite:a4fdcc39ac12e20b94112364f3c7afa6d7a8e493}}.
In particular, {{cite:76550864a6a942ff31a6e1f8c316607027e980f8}} recently presented 22 GHz images of OJ 287 with unprecedented angular resolution for the source obtained with the RadioAstron space-ground VLBI observations.
The images revealed a progressive bending of the inner jet with increasing angular resolution by comparison with multi-band ground-based VLBI images.
The inner jet components show high brightness temperatures that exceed the inverse Compton limit, indicating strong Doppler boosting in the jet. The polarized images show electric vector position angles (EVPAs) aligned with the jet axis, which indicates the jet has a predominantly toroidal magnetic field. Multi-frequency analysis shows hints for a rotation measure gradient across the jet, which suggests the VLBI core is threaded by a helical magnetic field.
| i | 1ea7557ebe03928757cc56294fb08ab0 |
Our strategy for obtaining confidence regions is based on the observation that the problem of estimating the location of a peak of a random field is mathematically very similar to that of finding the location of the maximum of the likelihood function. Standard asymptotic theory for the latter gives a central limit theorem (CLT) for the distribution of the observed maximum about the true maximum. {{cite:6ec85de4d1d2f800b95fccf59908788869ac7e44}} extended these results to the more general framework of extremum estimators, see also {{cite:10dc830693dda10e883d522eb0fd55d43401bf35}}. We will take advantage of {{cite:6ec85de4d1d2f800b95fccf59908788869ac7e44}}'s framework to derive CLTs for the local maxima of mean and {{formula:147d473d-25da-4e9b-98ac-178d4fea8f90}} -statistic fields. To do so we derive the asymptotic distribution of the derivative for mean and {{formula:b5fb1195-af1f-4367-a925-a82d23a76afd}} -statistic fields (giving an exact form when the underlying fields are Gaussian) and show that the scaled second derivative converges almost surely. Combining these results yields asymptotic confidence regions for the true peak locations of the underlying mean and Cohen's {{formula:55fb9177-fd42-4e38-83df-b28148d5a079}} .
| i | 8e703e19789cfa31d0455c89333a59f8 |
In online learning problems such as the multi-armed bandits (MAB), the decision maker chooses from a set of actions/arms with unknown reward.
The goal is to learn the expected rewards of the arms and choose the optimal one as much as possible within a finite horizon.
The framework and its many variants have been successfully applied to a wide range of practical problems, including news recommendation {{cite:4c25b671494c508d981421e225a3216daec36498}}, dynamic pricing {{cite:e8fffc00ca8700c2f79426a104c86f57f47361c9}} and medical decision-making {{cite:389b73af9a9e339d83d188ce96a9e134fba44e0a}}.
| i | c8a4af2b8206987c92a10efe7d1f6afe |
We emphasize that bulk reconstructions that are causal in this sense cannot work for the interior of the Python's lunch because no causal horizon can intersect the lunch. The CFT encoding of the Python's lunch appears to involve highly non-local quantum gravity effects. An example of such non-local dynamics is the ER=EPR conjecture {{cite:8d3a0214c916aeed8af0a177d74534385273ed6f}}, {{cite:9796112760c23f9573399c4ee34bdc05a5b4d395}} which asserts that the entanglement between an evaporating black hole and its Hawking radiation after the Page time must allow complicated operations on the distant radiation to change the state behind the lunch, drastically violating the naive causal structure dictated by the background metric. It has been speculated that wormhole-like “corrections” to the background geometry connecting the radiation to the black hole interior could explain the “true” causal structure not captured by the background metric. It is natural to speculate that similar dynamics are at play in the Python's lunch encoding into the boundary.
| d | bc54012822f76cce668b5bcd317c2f5a |
Transformer models have been used successfully for various NLP tasks {{cite:108596957049a599e2f50e1cce24719539b3e474}}. Most of the tasks were focused on English language due to the fact the most of the pre-trained transformer models were trained on English data. Even though, there were several multilingual models like BERT-m {{cite:108596957049a599e2f50e1cce24719539b3e474}} there was much speculations about its ability to represent all the languages {{cite:6b1f5c7e0511792f3ea0c8eb272b491ecc39e3fe}} and although BERT-m model showed some cross-lingual characteristics it has not been trained on crosslingual data {{cite:6a8b22910c1eda860a5ce4ae938779bed9542b2b}}. The motivation behind this methodology was the recently released cross-lingual transformer models - XLM-R {{cite:b940acc3247a50bbabde45bf0149ef7ffd272412}} which has been trained on 104 languages. The interesting fact about XLM-R is that it is very compatible in monolingual benchmarks while achieving the best results in cross-lingual benchmarks at the same time {{cite:b940acc3247a50bbabde45bf0149ef7ffd272412}}. The main idea of the methodology is that we train a classification model on a resource rich, typically English, using a cross-lingual transformer model, save the weights of the model and when we initialise the training process for a lower resource language, start with the saved weights from English. This process is also known as transfer learning and is illustrated in Figure REF .
{{figure:5289eef0-65aa-4e29-9dc2-3d322f07694a}} | m | 6d8d56b92d354ea26dc3ef45a22625c0 |
The expressions we obtained for the Maxwell and Weyl spinors exhibit a Weyl-type classical double copy in on-shell momentum space, which follows directly from the double copy of the three-point scattering amplitudes. We then showed that this leads to the previously known Weyl double copy in position space, which applies to certain algebraically special classes of solutions {{cite:3911527dee8ff52614de89071c25fda9224eb4c8}}, {{cite:f26dc26858692d96df39bc0b56d7d5a280f869b9}}, here in the simplest case of the Coulomb and Schwarzschild solutions. We emphasise, however, that we expect the structure of the double copy in on-shell momentum space to be much more general. We see it as being formally equivalent to the convolutional double copy {{cite:2ac6255872c99066ff144b7426663548875b7756}}, {{cite:40b44c67c3571ef53704d40c9cd419b337b1ebd7}}, {{cite:d70d14e3f32cd1b8b7bc6b9653112bb2c4d24b0e}}, but with the advantage, from our perspective, of being supported on on-shell momentum space, with a direct connection to scattering amplitudes.
| d | 749e4d3b7a09ec98f1b92e31795dfa1a |
A fundamental constraint for any visual KWS system
is detecting words which sound different but involve the same lip
movements (they have the same `visemes' – visemes are the visual equivalent of phonemes; phonemes are the smallest unit of sound in speech).
For instance,
the words `may', `pay' and `bay' cannot be distinguished without audio as the visemes for `m', `p' and `b' look the same.
Other difficulties include intra-class differences (such
as accents, speed of speech and mumbling which modify lip movements)
and variable imaging conditions (such as lighting, motion,
resolution) {{cite:3c1f0407e5e22b033660f4cd6ba0edba428458df}}. Spotting words from continuous
speech is also challenging as there may be co-articulation of the lips.
| i | be996238b8886f06ff63abcfb3777cb6 |
As a data-driven supervised learning approach, DNN-based speech enhancement can be mainly categorized into time-frequency domain {{cite:4af434d5e6eddf83cfbef247c5658f8c2f347e21}}, {{cite:3227f700ad35d4101f82e559d03c40bb99c78c0f}}, {{cite:7ea6943bbb514172d25e3943c7c34994d7f6d14a}} and time domain {{cite:d607416db47303bee82cc9046d74b4a6bba902d1}}, {{cite:ecee3b9eae30a6ce91a0ca3dd249b871db10b6b6}}, {{cite:f6910dcefb3beb35be08600fd2227b12365a342c}} methods. The time-frequency (T-F) domain methods aim to extract the acoustic features (e.g., complex spectrum or logarithmic power spectrum) of clean speech from the features of noisy speech. Common training targets include ideal ratio mask (IRM) {{cite:66289bc3d1947e9c5fe536d25376403057f6baff}} and target magnitude spectrum (TMS) {{cite:3227f700ad35d4101f82e559d03c40bb99c78c0f}}, etc. The phase spectrum is also considered to benefit the speech quality {{cite:67bbf58546b9bc75f05ce7fe93f5be541e70af59}}. However, it is difficult to estimate phase spectrum directly because of its unstructured characteristic. Phase-sensitive mask (PSM) {{cite:7ea6943bbb514172d25e3943c7c34994d7f6d14a}} was proposed to exploit phase information for speech enhancement. More recent methods, such as PHASEN {{cite:dee771fa7dd08d4f00c6a25daff89d015fa3970d}}, make use of the inter-connection between the magnitude and phase spectrum for better phase estimation. Some other methods retrieve phase implicitly by optimizing the real and imaginary parts of the complex spectrum {{cite:f93b0b27ad633729c4c445a6e75dc47894232c51}} or estimating complex ratio mask (CRM) {{cite:e35cd83223a30d6b6a55d3e6bb1f5807f24459ab}}. Since complex-valued weights are suitable for modeling the inherent information of the spectrum, complex-valued neural networks {{cite:fd9cf3ca0b3a7d63aa34ddee189c01b36758d059}} have also been used for speech enhancement.
| i | 771994f27afd9d28e7c95420281153f4 |
Towards this end, we utilize the k-nn non-parametric density estimation technique {{cite:53bcb6e1de3d87de5a2dd1ec07ded2e5236c485a}} for estimating the unknown probability distributions of the data samples in the feature space of the output layer. In this way, we are able to directly estimate the posterior class probabilities of the data samples, and use them as soft labels. The estimated soft labels explicitly encode information on the similarity of each training sample with the classes, while it is expected that as the training progresses we learn more and more reliable and meaningful soft labels, since they are driven by the supervised loss. This argument is also experimentally validated. Furthermore, it should be emphasized that as opposed to a general classification task where when estimating the posterior class probabilities some errors lead to the accumulation of errors, and the goal is to minimize them, in our case, propose to estimate the posterior class probabilities utilizing the k-nn density estimation technique, so as to use them as soft labels, that is as an auxiliary task to the conventional supervised loss. Thus, our goal is not to directly minimize the estimation error for them, but rather to continuously estimating and considering them through the training process, so as to assist the main classification objective.
| i | ad31ec56996eb027a8efc6358bd60dd3 |
The single network-based algorithm is tested with the stacked LSTM architecture with 3 hidden layers (all {{formula:06a34931-d6e9-46c0-b991-ed9b8ba63619}} dimensions). We choose the hyperbolic tangent function as the activation function and use the Adam optimizer {{cite:43d020906ebb22e9ced9c8684c3f28cf2f35c4db}} for the SGD process. We implement our algorithm on the defaultable option with {{formula:2f735a14-eaf0-4e4e-96df-c3d13dce3faf}} (number of time steps), {{formula:6a75ee9a-0824-4660-91ff-baa6ed46c730}} (number of paths for the Monte Carlo loop). All tests in this section are run on a PC with a 2.80GHz Intel Core i5-8400 CPU and an NVIDIA GeForce RTX 2060 GPU using Google TensorFlow in Python.
| r | 9090061735d140b2d07fcf0c3c52dd1d |
To prove th1.1, we need the following two lemmas. The first lemma (see {{cite:85d8a4d3b19649975855a56ac840a294507d8ef4}} and {{cite:66dc2c2eff5d9914fdac44b5d992bb853003f5e6}}) deals with extension from a bounded domain to the whole space. This allows us to use the Gagliardo-Nirenberg inequality in the whole space.
| r | 26a2af6d9290ff14bd403743a518e69a |
Most of the aforementioned approaches against label noise require complex networks (often more than one) or extra data resources.
Given the early stage of this field in sound event classification, we are interested in exploring simple and efficient approaches, agnostic to network architecture, that can mitigate the effect of label noise.
Specifically, we seek approaches that can be plugged into existing learning settings composed by a noisy dataset and a deep network, without need for network modifications or extra resources.
Our contribution is to provide insight on the model-agnostic approaches that can be incorporated to deep learning pipelines for sound event classification in presence of noisy labels, as well as the performance boost that can be expected.
In particular, we consider regularization techniques external to the model, as well as noise-robust loss functions (Fig. REF ).
Regularization aims to prevent overfitting and improve generalization, which can also be beneficial against label noise.
Common regularization strategies include weight decay and dropout {{cite:73c94f56dd7babf12fb8345797701adda511856f}}, which act on the weights or hidden units of the network; dropout has been shown useful in reducing label noise memorization {{cite:72cd0199d4d489be95850ae62b91d5249a11e06c}}.
In our attempt to regularize the model from the outside, we consider label smoothing regularization (LSR) and mixup.
The former operates on the ground truth labels, while the latter operates on both ground truth labels and input data (Fig. REF ).
In addition, we explore two strategies to ignore potentially noisy instances in the learning process through noise-robust loss functions.
Section describes the methods considered.
Section introduces the experimental setup.
Section describes the experiments carried out and the results.
Section provides final remarks.
{{figure:c0609d7e-5d67-4349-ad22-8c66da1184e9}} | i | 33065a1ebfaf4216cd78284260d7f0fa |
Our approach uses contextual word embeddings and permutation-based statistical testing to detect semantic shifts in scenarios where data is limited.
While our approach can be applied to any method based on contextual embeddings, we used the method proposed by {{cite:b3341a000ff1d05c42320d37e7a75aea76f1ab57}} because of its conceptual simplicity and faster run-time compared to other methods. We generated all contextual word embeddings with BERT {{cite:125d3c3aa1e9d8704c991c2e3d63cf85160ffb6c}}, using the implementation from HuggingFace's Transformers library {{cite:b50fb8fcc7baafc84e1e251b775f8f2e6c666152}}. In all experiments, we used a base version of BERT (the exact pre-trained models used are specified in later sections) with 12 attention layers and a hidden layer size of 768. All parameters were set to the default values used in the Transformers library unless stated otherwise.
| m | 9d8868566ee8970f10308c64ae17ef6d |
We aim to replicate previously demonstrated racial disparities in end-of-life care using MIMIC-III {{cite:1060bb7a0242716e660cc47786cc8c9585e68bda}}. We take as reference a set of three recent papers which examined the racial disparities in end-of-life care for nonwhite or minority populations {{cite:6525fef058d9af786f0d8def35ada6b51d3efc50}}, {{cite:09eca23d14ed1c80ed5b9ea281d47d9bb674975d}}, {{cite:55f8b64e17b305fad2790532abe0aa41a77f6bab}}. We compared the differences of patient outcomes between white and black populations using Mann-Whitney analysis for non-normally distributed variables (treatment durations, mistrust metric scores). In accordance with prior work, we consider p-values {{formula:894c1c04-cd78-4846-9fa6-517236ba6473}} to be statistically significant.
| m | 03fa7940eb9673e25b58ff143d6458ac |
Concerning the error analysis, starting from the fundamental estimate {{cite:4a56669c32687bf10343f2e593d7ccabd8fe645a}}, {{cite:86c0b4b379afbc98c8c88eefb2c0c469ee192d22}}
{{formula:7c679962-a401-43fd-85b1-5a35f157caa2}}
| m | e6808f8571c0bb933ef139360142919e |
The orders of the parameters are constrained theoretically and experimentally as follows {{cite:12aa46068f40440ed3146b1350605ea90da2f653}}, {{cite:6e4c585d54ce0923c7f73016af2d945e68e65027}}, {{cite:ae65da112cf2e03101f20d9e5c3b3af396133fab}}, {{cite:5c9d9c3ddf0d2a45a06fba47353a158e9cbcbbee}}, {{cite:0a2b145d3a05ed86d18a5090e6b37336911d1756}}: {{formula:66df27e7-6130-4f3b-ad75-44bd1b689bf8}} , {{formula:a8f3c234-a25b-47ab-b841-ceea3272b4f9}} , {{formula:8af9ba0d-07d0-4780-b26c-a44b8d32998a}} , and the current cosmic density {{formula:83a41fbe-ce1a-447d-963d-9d57457dd75b}} with {{formula:4bc98590-5003-469b-ae38-16eb6b10f5f2}} . Therefore, the maximum of {{formula:9de03253-e106-4d73-ba1f-8712fd9e043e}} is greatly larger than {{formula:3f672080-5fb0-4d97-ab17-d800ff373e42}} , i.e., {{formula:94bee696-be3f-4149-a640-5529955d9b60}} , where {{formula:c78ef137-a724-4a98-9d8a-e523accd8b1f}} is the reduced Planck energy. At the maximum of {{formula:6059f4ca-a103-4d11-ab0f-2553e287ded2}} , the interaction range is estimated from Eq. () to be {{formula:4eac59f1-e0c0-4eaf-aeee-8fe6cc924c5c}} with {{formula:dd30ca7c-bebc-4b8e-bded-3d44c7036a48}} . Due to {{formula:7aef800e-9d7b-4f73-8358-71d2076b0c52}} , one has the interaction range {{formula:f0c67cb1-1844-4fc0-8666-12ed59b3e493}} in the case of {{formula:f353c44a-1b98-4655-ba81-3e0e37281cc2}} . Thus, it is impossible to observe the sub-gravitational force in a very dense ambient density due to the very short interaction range.
| d | 135d59ae05fb675bfec0081096b748e9 |
While our proposed method yielded a competitive performance, there are potential areas for improvement.
First, we are aware that the performance improvement brought by the proposed method is not uniform across participating clients. Since the proposed RL agent jointly optimizes the whole system, minimizing an aggregate loss can lead to potentially advantage or disadvantage a particular client's performance. We can also observe that all FL methods exhibit a relatively small improvement on the client with the largest amount of data. This is a common phenomenon of FL methods since the client itself already provides diverse and rich
training and testing data. Future research could include additional fairness constraints {{cite:cf3bf1fc188739f89e47dd913a1a9a40a1a09dec}}, {{cite:ed03b6ac0446ff90cd58e70821462ca6990561a8}}, {{cite:ce58c896a19bbbfa5c1df0fc83cc840376b5bbcf}}, {{cite:8cb44f0bdd63d09c38ed02d3ce02ebdee7d2f810}}, {{cite:5df3de1e8d33fd8a82efc7c95d6de80f1b144614}} to achieve a more uniform performance distribution across clients and reduce potential biases.
Second, the NN-based RL agent could be benefiting from transfer learning. The effectiveness of RL transfer learning has been demonstrated in the literature for related tasks {{cite:af9d25825fa33f4b5160d071915a66a96bf4bb13}}. Pre-training the NN-based agent on large-scale FL datasets and then finetuning on target tasks may further boost the performance of our approach.
| d | 64a5f71396bcffe03572c31d6ab1edae |
The macroscopic large {{formula:ca2ea8c5-0f96-44f2-b613-8d2685e4a51e}} behavior of the eigenvalues is described by the limit of the mean eigenvalue distribution as {{formula:ab487104-2b44-4fbb-984f-3cf75e39f996}} , which we denote by {{formula:02a90cff-9b8b-424b-af42-fc43e3d9b297}} , and which is independent of {{formula:aeb16462-602a-411a-a783-d50c4d1e0fda}} and {{formula:a082c9d4-5d65-44eb-9b55-c95abc0694b3}} , for {{formula:af154236-0149-4731-9c22-db42fcefe0db}} , {{formula:3ce3808d-9e99-40fe-8399-48e30db34c11}} bounded.
It is characterized {{cite:9241649a0c9e9a17dc158e923b870212813c3d62}}, {{cite:59ef4a1997f776ea53885d9324cee7160cc0ec08}} as the unique equilibrium measure {{formula:ebc9ebea-14a7-49be-92e4-2a9c242fd634}} which minimizes
{{formula:f5b8a200-293c-48d7-836e-2d034ba40748}}
| r | a53591f204904c50f531dcde7fdceaa4 |
The production mechanisms and properties of winds from hot accretion flows have been intensively investigated (e.g., {{cite:90bb3f1822abce416c306184fe200e13d3e08f11}}, {{cite:1caf546c40f2ac29dce1b7959c4271350fb2f872}}; {{cite:0881c789306b35ef804f78c23ead4d74476df75d}}; {{cite:6a0fc57db7ceabd718886cd669db53e99955a064}}). It is found that winds are launched and accelerated by the combination of gas pressure gradient, magnetic pressure gradient and centrifugal forces.
| i | da60dcaaf15033b169d4bf061fe73736 |
For fMRI images, most of the publicly available datasets contain data in NIfTI format. We used two different data formats to train the models: one using the raw NIfTI version and the other using pre-processed normalized version as shown in figure REF . For self-supervised pre-training, we only used NIfTI data for all four subjects in the BOLD5000 dataset. As shown in figure REF , the encoder was trained using MoCo {{cite:e845184e994cdebcb8978d2cddb8f35a9b13ff63}} algorithm and Adam optimizer. The pre-training was carried out for a total of 200 epochs. The starting learning rate was set to {{formula:816fa992-f099-44cc-93df-2f2c69678dfa}} with a weight decay factor of {{formula:b14e3c34-e0ac-4626-9e77-b0b91912481b}} and momentum parameter as 0.9. The learning rate was decayed by a factor of 10 at 120 and 160 epochs, respectively.
| d | 7a1b5d9eae24b2fd4a31656ab05b0ebb |
We present the quantitative results in Table REF and Table REF . TransResU-Net has achieved a dice coefficient of 0.8884, mIoU of 0.8214, recall of 0.9106, precision of 0.9022, accuracy of 0.9651, F2 of 0.8971 and speed of 48.61 FPS on the Kvasir-SEG. The most competitive network to TransResU-Net was DeepLabv3+ {{cite:4233284c03f9f249329d9da78e769a166ee2124b}} to which our architecture outperformed by 0.47% in DSC and 0.41% in mIoU. On the BKAI-IGH {{cite:57399ff68ce4327ac225582ac31a491c7a31862c}}, TransRes-UNet achieved a high DSC of 0.9154 and mIoU of 0.8568 and outperformed DeepLabv3+ by 2.17% in DSC and 2.54% in mIoU.
| r | 62bedb14a6ebda8efe42ba40d534d2df |
Just after the second data release of Gaia {{cite:de6e87764b0f2d3b0f5c449cd88a26e648504863}}, various researchers deduced numerous values of zero-point offsets for trigonometric parallaxes {{cite:6b790fb44215b1d173c8609f36baa8f873830ba8}}, {{cite:b195e94b5c7bc70b3c4c0011690a14e58d33f1dc}}, {{cite:5eedf7f0e6c6ba4145c7a8d85ca05b1087fe3624}}. {{cite:5eedf7f0e6c6ba4145c7a8d85ca05b1087fe3624}} estimated several zero-point offsets using parallaxes of different objects (dwarf galaxies, classical variable stars, open and globular clusters). They concluded that zero-point offset values are within the {{formula:83af90ad-9ef1-4982-8a84-298df3b13d73}} to {{formula:b252598f-975e-49f5-a17f-c82148495e12}} mas depending on the type of object and also are a function of systematic errors, positions on the sky, and magnitude/colour of the objects. In addition to this, there are many zero-point offsets whose values are among the {{formula:4953833a-202b-4717-86bc-412ed8bba16c}} mas {{cite:6b790fb44215b1d173c8609f36baa8f873830ba8}} and {{formula:e33124b5-9f8a-4d7b-91ef-b2e6f9c73109}} mas {{cite:3e121defb5285b77317d9b1648f39773a6fea0c6}}. These were calculated by taking into account trigonometric parallaxes of quasars, classical cepheids, eclipsing binaries samples, RR Lyrae stars, Kepler red giant branch and red clump stars {{cite:6b790fb44215b1d173c8609f36baa8f873830ba8}}, {{cite:3e121defb5285b77317d9b1648f39773a6fea0c6}}, {{cite:b195e94b5c7bc70b3c4c0011690a14e58d33f1dc}}, {{cite:152acf4ad9847b9bf544cbf5441055eef1e89a2f}}, {{cite:29647d524ec8cbb6fbc18b9356b84143a90097fa}}. Moreover, some researchers reported that the offset correction of parallaxes in Gaia DR2 may increase for distances in excess of 1 kpc {{cite:3e121defb5285b77317d9b1648f39773a6fea0c6}}, {{cite:b501f31e0722bb283678afeb88d8a850bf3766ee}}. The commonly accepted value for the zero-point offset correction was {{formula:83bf2abf-20c8-415a-9b69-a83caa2bdf59}} mas in Gaia DR2 which was determined from the quasars {{cite:6b790fb44215b1d173c8609f36baa8f873830ba8}}. Recently, some research groups investigated parallax zero-point values from Gaia EDR3 data taking into account parallaxes of classical cepheids, blue RR Lyrae stars and eclipsing binaries, quasars and red clump stars {{cite:f57a5be180ef0ecfcc7e8a11f801ac170980031f}}, {{cite:59dc37aff27f9abb5b3f0d0c757b8fe09e304a55}}, {{cite:33e73a1ac22b76e974b8bc768deb705711d2d3f1}}, {{cite:d716b4dd3fe248cd1fea6e007b7ba22f954c73ab}}, {{cite:0542482d9857e2e981909fbe50e86a2476bd0bcf}}. According to these studies, the zero-point offset values range from {{formula:f951d768-f063-4026-9ce1-3644ee5c82bc}} mas {{cite:d716b4dd3fe248cd1fea6e007b7ba22f954c73ab}} to {{formula:18da4fe6-e692-4ad8-824d-c1110d300a47}} mas {{cite:0542482d9857e2e981909fbe50e86a2476bd0bcf}}. As mentioned in previous studies involving Gaia DR2 parallaxes corrections, the zero-point offset values are functions of factors such as colour index, magnitude, and position on the sky {{cite:6b790fb44215b1d173c8609f36baa8f873830ba8}}. In this study, we transformed the distances estimated via fitting PARSEC isochrones and used the Gaia EDR3 data to parallaxes linear expression, comparing the values with each other to understand how these change. For Czernik 2 the isochrone distance ({{formula:ab9e57ac-2a87-4012-8fc2-0b536636191a}} ) and Gaia EDR3 distance ({{formula:23b565b5-6592-4026-b7ed-66c3e91cac2d}} ) parallaxes are subtending to {{formula:4bab89ff-9d56-4c1b-96db-caa7de717fbe}} and {{formula:2c30d6a4-f699-4663-a612-0ba8a3024975}} mas, respectively. The difference between two trigonometric parallax values is {{formula:cd8db8b8-e87c-47d7-9581-134f7de28725}} mas. For NGC 7654 the distances correspond to {{formula:25773614-0e09-4a94-b11b-e84b8161ff9a}} and {{formula:79db1027-a1c7-4c24-b77e-6c31a34c349f}} mas from which the difference is {{formula:900d809c-4029-4cea-a4e5-0acd26c9149f}} mas.
{{table:5fc8c5db-e9b8-4fba-b28c-fbf51f12d4fa}}{{table:efc382e0-8930-48c6-9167-eaa00c56b02a}} | r | 560cefd3b8bc00fd6f42a40a50e1ac42 |
Model architecture
DME is composed of two multimodal encoders based on the transformer network {{cite:ed4e6204fb0324857107e098c3daf289f8baf4f0}}. In AQVSR, both user question and a context video segment are multimodal, i.e. both of them are composed of vision input and language input, requiring a model for learning joint contextualized representations. Inspired by the recent success of the vision and language model {{cite:9a119f268ede3f9bbfdb857ce6347e3a727e0c73}}, {{cite:a352f66bacf163d034a14928ed5e5ad42c1443ab}}, {{cite:6ba64081a4c27b07e1848b212a9e51ab1208183b}}, we follow {{cite:6ba64081a4c27b07e1848b212a9e51ab1208183b}} to use the self-attention mechanism within the Transformer to implicitly align elements of the input text and regions in the question and model the contextual information of the input video segment.
| m | 3ffb1b161dd82fba385c02660920010f |
The detection of BH–NS mergers is of great interest as they are expected to emit across a broad electromagnetic spectrum
and have been suggested to produce radio flares {{cite:7b6f87d6b1a49283a02853b0932a5d4086d8899e}}, {{cite:8f7baa43b9b864c49039a8e3fa363d2f47299ac0}}, kilonovae {{cite:8429a8bd4a9998ff21566b24bc4a891cc8d05cb9}}, {{cite:405f17d96beba4b58ccd88ee2c8499b4f7a5c685}}, short
gamma-ray bursts {{cite:a7a5d3f76b2888fb44e9a0eb6720e6cb9b1f0476}}, {{cite:62be1aed4ae286ef041601e7fbed896c0627a7b2}}, and so on. A recent quite comprehensive study of BH–NS mergers can be found in {{cite:542612790042b7c2cbab6951e5cb58d25eebf3ca}}.
Before merger, Galactic BH–NS binaries are possibly observed as binary
radio pulsars {{cite:d3ef0000d83678b899dce9d19107e1fa16b0bb08}}. Close BH–NS systems in the Milky Way may emit GW signals
with frequencies in the LISA band {{cite:f28fb0e0a6f7f6f059a5041c050de18288ad4696}}.
| i | 6dd0b2924a0d62f3f4a479946265849c |
where {{formula:6abcb148-8c43-4b1c-806a-c10e4ea43cae}} . The random feature approach can be employed in an online manner where the nodes estimate the missing values online. In this approach, in each iteration of the successive approach denoted by {{formula:7cd93983-bc3b-4d83-b17a-0a47bba717d1}} , each node solves
optimization problem (REF ) via online gradient descent {{cite:a528546252914c501990a07555ba9ec85e32ab4b}} to update its parameters which is expressed as follows:
{{formula:a374af66-9620-4ff4-848d-00bcbc3f4852}}
| m | f4cad96bdab029997e7d067d67e34f9e |
Systems with very low mass companions could either be (i) polars in a prolonged low-state of accretion, like EF Eri, or (ii) detached binaries that will eventually undergo Roche lobe overflow, or (iii) old polars that have reached the orbital period minimum {{formula:0d5c0443-39fc-4cd9-bf0c-36ca8f6ef8ce}} for CVs and are evolving towards longer periods (period bouncers). Genuine PREPs, however, are expected to exhibit longer orbital periods {{cite:119d210146b6dd97e33a98838a35d13396263308}} and this seems to be the case for most systems currently classified as PREPs, except for IL Leo (=SDSS J1031{{formula:f65aa5a8-aa14-4246-9833-2818fa0c0de1}} 2028). IL Leo has {{formula:24c2d05c-a373-400a-b5ee-c0c9d89725e8}} min, a white dwarf with a field of 42 MG and a companion of spectral type later than M6 and likely to under fill its Roche lobe {{cite:c1538fb12f754c570f279b8843dae43a5effc1ec}}.
| d | 6c8d94467eba42f9045b998d5f40d1d4 |
When it comes to offline settings, {{cite:db69fea8902ea197176cc3320891f0ee63a131a8}} presented a off-policy policy gradient theorem and proposed the first off-policy actor-critic algorithm, with critic updated via Gradient Temporal Difference(GTD) method{{cite:fe6077ae85db5d930a54f2c89ea75c4869a843d0}} and actor updated incrementally with eligibility trace. Though converging in the tabular case, it can result in asymptotically non-vanishing bias in more subtle settings. Theoretically, {{cite:60fd81359ed4b3869fafce8f9b934c2ccc68af8a}} invented a doubly robust actor-critic algorithm and established the first sample complexity analysis for off-policy AC algorithm. Its sample complexity to achieve {{formula:ba7400c8-3be9-4ed4-9fdd-50a77a300931}} -optimal policy is {{formula:52db371a-926f-49b8-a6a9-f12c248c0324}} Another off-policy Natural AC algorithm proposed in {{cite:cf4c98c2c44e58d01b7da3ebad30caf1023b6f7f}} improved this bound to {{formula:a16f5ef0-85c8-4bf9-a17b-51724517106f}} which beats a lot of on-policy AC algorithm. Recently, {{cite:492ff3d087c7e891f8ea40033606dc4354dfa81c}} design a pessimistic actor-critic algorithm that iteratively optimizes the lower bound of the optimal policy value using linear function approximation. The critic pessimistically provides an estimate of policy value by a suitably perturbed the result of least square Temporal Difference method, while the actor updates parameters by mirror descent algorithm. It is theoretically proven that regardless of the mis-specification error, the remaining part of error is less than {{formula:3c6cc72b-f0bd-4700-b3c9-049e8680e081}} with a {{formula:9ca4dd5f-5b62-4bf3-84b0-656a2b06484a}} sample size and {{formula:d4fb477f-0c19-41de-acc5-44a6ed19f8fb}} iterations. For other finite sample analysis of PG method with actor-critic scheme, we refer to readers {{cite:e28cb7dcf1e45b0a7108b8a91f9df699e913cab7}}, {{cite:85184ca5ef21620bbc18a7b273437e974977b62d}}, {{cite:cd7491a7658ef48f0aa8f2dd9e7ef1eab879de03}}, {{cite:cf4c98c2c44e58d01b7da3ebad30caf1023b6f7f}}, {{cite:17bdfbc379e9f5587d871f2b53ce7245dea2c623}}, {{cite:36e4fb420e4f290f7d638a2ad1950a4f6564e440}}. For a more comprehensive summation of sample complexity of (N)PG-AC algorithm and their variants, we refer to readers {{cite:8487b511fa8e089b38c7e0c19cc85e8748cffd4f}}, {{cite:312e5aaa18bfa3e8ae7e676f03c612859164001b}}.
| m | 76d92a381cb7bdf0b87a635a156cc8f7 |
Similar to the findings in § REF , JARN advances the adversarial robustness of the classifier from the standard baseline against all four types of attacks. Interestingly, uniform noise image augmentation increases adversarial robustness from the baseline in the SVHN experiments, concurring with previous work that shows noise augmentation improves robustness {{cite:ecfe4bf83824586ee85b77363d6449683777e9a5}}.
{{table:0a7603bc-0795-48e4-8d49-1f56e4dbaac7}} | r | 742f63827ddabd92e202ce0438eb9a39 |
We compare the pronunciation accuracy of our Dict-TTS with other systems, including 1) character-based systems, where we directly feed character into the linguistic encoder; 2) Phoneme-based systems, where we convert the text sequence to the phoneme sequence {{cite:ab30c3f68c5f0d79beaf568b07c428ba2c98f0d4}}, {{cite:43eaaefa505a20496a304f8bb8cfa5b88f551be8}}, {{cite:33ef809dc56933120f7fa0fe9be3b2b18ac70b49}} with most popular open-source grapheme-to-phoneme toolsWe use pypinyin in the Biaobei dataset, pyopenjtalk in the JSUT dataset and pycantonese in the Common Voice (HK) dataset. More detailed information can be found in Appendix REF. We measure objective phoneme error rate (PER-O), subjective phoneme error rate (PER-S), and subjective sentence error rate (SER-S) in the evaluations. The phoneme labels in the objective PER evaluation are from the corresponding dataset (since the Common Voice (HK) dataset does not have phoneme labels, we only evaluate the subjective metrics). In the subjective evaluations, each audio in the test set is listened by at least 4 language experts. We ask them to write down the mispronounced phonemes and discuss them with each other until a conclusion is reached. Note that for SER-S, the error rate is calculated in sentence level (e.g., a sentence with multiple errors will be counted only once). More details about these evaluations can be found in Appendix REF . The results are shown in Table REF . It can be seen that Dict-TTS greatly surpasses the character-based baseline in three languages. Moreover, Dict-TTS achieves the comparable objective and subjective PER with the most popular grapheme-to-phoneme tools on two relatively larger datasets (Biaobei and Common Voice (HK)) and maintain a good pronunciation accuracy on a relatively small dataset (JSUT), which demonstrates the superiority of the explicit semantics matching in our S2PA module.
| r | 825b726b8f866e990482f482d6e9b990 |
One common strategy which is shared across multiple methods for local policy search involves leveraging weighted probability averaging to perform parameter updates as opposed to using estimations of the gradient of the performance metric, which can be noisy {{cite:dbd1834428a3b2b98bdee0e96db6b8a1df76cbb5}}. The structure of these algorithms is as follows: 1) Sample {{formula:64851187-e047-4f63-8d45-00abc807b09e}} parameters from a distribution; 2) Sort the samples with respect to their performance given by {{formula:e0512b2a-a91b-42a9-8a87-13fee5bfa887}} ; 3) Recalculate the distribution parameters based on the top {{formula:39b92139-0203-4f80-8b49-d3d9a36a0da5}} `elite' samples in the sorted list; 4) Repeat this process with the newly calculated distribution until convergence or after a number of iterations. Algorithms within this class differ significantly in their implementation of these steps. For example, Cross Entropy Methods (CEM) {{cite:8b45f2a112618e024111f46e3bfb3a286fbf29b9}} recalculate the mean and covariance of the sampling distribution after each step, while Policy Improvement with Path Integrals (PI{{formula:7dc95c42-bd97-482c-a5fe-182e4975b234}} ) {{cite:dbd1834428a3b2b98bdee0e96db6b8a1df76cbb5}} only updates the mean. In their design of PI{{formula:ce1724b9-ad25-4e1b-b380-09a7640f1f5a}} -CMA, {{cite:5d8a0e6931a5100ba1ba5ea34cca18b1539c006a}} integrate a CEM-like probability-weighted averaging to update the covariance of the sampling distribution into the base PI{{formula:9ec9c0ce-05c2-4a00-b0ba-af2f15342255}} algorithm, enabling it to autonomously adapt its exploration.See {{cite:5d8a0e6931a5100ba1ba5ea34cca18b1539c006a}} for a more thorough analysis of this class of direct policy improvement algorithms.
| m | a3427b78cb5be0fb002bc1e515f6be7b |
Novelty search is helpful in this case {{cite:1e42ee14f2b3529525058437ccb435ea6d2155fa}}, where rewards are replaced by the novelty of the policy behavior, which encourages exploration. However, this method requires a behavior characteristic, which is domain-specific.
In addition, Deep GA with novelty search essentially sweeps over the entire policy space, thus preventing exploitation or focusing search efforts on more promising regions.
| r | 9dcbc905167d651e437fb423bc01fb64 |
low 8 [9.0, 9.7) 10{{formula:a7336f34-1614-451b-ae07-1f2a048d2022}} {{formula:3c1d6b62-f99c-4b3a-913e-383bd6e50a26}} {{formula:3e67974e-f788-4402-9359-5412b3cd0b70}} {{formula:2c5dc2fb-a66c-44ce-96d0-d74232813b6b}} {{formula:13f34168-ea26-4ee2-a245-2ddf03dc61e0}} {{formula:1ad5cf81-0950-408a-b4ae-56dac1431c84}} {{formula:12113734-18dd-4ae2-adcf-06f4439470b4}} {{formula:cbf369d8-3ca2-4031-a352-c32a9ee8ef88}} {{formula:986cf9fa-5c9c-4373-ae54-4d976e589649}} {{formula:17b44e32-82c2-4b19-b703-b53e4781340c}}
The multiple emission line flux ratios are measured from the stacked spectra shown in Fig. REF . The {{formula:29e9a032-e69f-47a0-8d3a-c16aebb8574d}} and SFR results refer to the median value of galaxies within each mass bin, with 1-{{formula:43d5084c-ea88-40da-be9b-32544eeb4a47}} uncertainty represented by the standard deviation.
aThe median stellar mass of galaxies within each mass bin.
bThe metallicity inference derived from the measured line flux ratios in the stacked spectra presented in each corresponding row, using the method described in Sect. REF .
Here we use the strong line calibrations prescribed by {{cite:50d7682ee5feaa5cee6297d3d2ae0c9905e0ce54}} as our default results. See Table for the relevant coefficients.
cThe difference in metallicity between our galaxies in overdense environment and the field measurements inferred from the fundamental metallicity relation prescribed by {{cite:6bbd2e718950fc824dfad9a7d55386d844931027}}.
The intrinsic scatter of 0.06 dex has been combined in quadrature into the measurement uncertainties.
dThe metallicity inference derived using the strong line calibrations given by {{cite:9d6812a6cb23b57f5a8b627aa1c8e4c6cfd86ac6}}. All other assumptions and data are the same as our default results using the B18 calibrations.
| d | 3974dfeecee0667fb896333ff725d54e |
In this section, we introduce our hands-on experience of deploying TWINS in the live broadcast recommender system in Alibaba.
As industrial recommender or ranker systems are required to response to massive traffic requests in a short time interval (e.g., one second {{cite:0dbb020e232d0198ad9a5225b1781503aa004a64}}), then the storage and latency constraints would become the main bottleneck for deploying existing search-based model {{cite:0dbb020e232d0198ad9a5225b1781503aa004a64}} and sequential model {{cite:9f79e0fb94c74897841b139c039d76fa848f877d}} to the online system.
We here develop two kinds of techniques to light the current TWINS model and develop an effective data structure, and introduce a new online live broadcast recommender system in Figure REF .
We further show the details as follows.
| d | 92047bbb777a67d576fd14050aea33cb |
In this section, a detailed derivation of the MCTDHB [or MCTDHB({{formula:97060383-a0d5-468b-86d4-02ff09dccbc6}} )] theory which has been originally introduced in Refs. {{cite:bd85e4dced1fbaec432525e4e9837464be01f0e3}}, {{cite:7e4c54530917e513c48343485d4972e8f32b5478}}, is presented. It originates from the closely related MCTDH method {{cite:84b97b38df8fe4373e3d1a81f8113b68e8e70ddf}}, {{cite:9dab8f6e2014cb677a10f7118e8313a7f16f7b80}}, {{cite:130788247fa5ad1924ffa10d4a320b28ccc0c109}} which is a widely used technique to compute the dynamics and excited states of nuclei in molecules. Further extensions of MCTDHB to the case of type conversion of particles, to mixtures of bosons and fermions, to Hubbard-type Hamiltonians of BECs on lattices, as well as to BECs with internal degrees of freedom can be found in Refs. {{cite:08d1d94f684a666e6277ac9531e2ce1280b77b9c}}, {{cite:808855804029b39643ec4a5500edacb6121abbe3}}, {{cite:9fc15a55cec033d3cdbcd99d0b3d693523e0f435}}, {{cite:1f0748d8e632b12b5cccbd29e04ee1ae2a803698}}. Other many-body theories for the ground state and excitations of BECs were utilized as well. One example is the density matrix renormalization group (DMRG) theory {{cite:87cbfa30365182846c0cf727a9232f9460a398f4}}. It is particularly designed for applications in the field of one-dimensional condensed matter physics, but was extended beyond this to quantum chemistry and quantum information. An early review can be found in {{cite:cff4277a484d05f53136a3d5260b70f32b7b744e}}. Furthermore, DMRG has been extended and applied to two-dimensional systems as well {{cite:45eac10f0f24001c9a29de9c3fb3cf546d7c552f}}. However, this review deals with MCTDHB and its LR theory.
| m | 4b16ea74632968bd53b04d8c4532b25b |
Ablation Study. We conduct ablation studies to evaluate the effectiveness of our HSVA in terms of the structure adaptation constraints (denoted as {{formula:e70ede7b-8818-4758-a7af-4eb507fb77c5}} ), distribution adaptation constraints (i.e., {{formula:d15ea573-6bea-468a-9771-d9f2a0b38a81}} ), and only inverse CORAL {{formula:28dfad41-c249-4a02-9a66-6d4166a2c24d}} . Our results are shown in Table REF . HSVA performs poorer than its full model when no constraints are used during structure adaptation, i.e., the harmonic mean drops by 4.5% on AWA1 and 2.1% on CUB. If constraints are not used during distribution adaptation, HSVA achieves very poor results compared to its full model, i.e., the harmonic mean drops by more than 23.4% on coarse-grained datasets and 4.7% on fine-grained datasets. These results show that distribution alignment is essential for common space learning, while structure adaptation is necessary for semantic-visual adaptation. This is typically neglected by distribution alignment methods with one-step adaptation {{cite:259b30e0d7c9fddf266148784de619978bcd9f1e}}, {{cite:cd6b83907f01256227970e415636edb4404cd8d6}}, {{cite:183c9b0b4dff5aee9ecf92dca58b95761f22ffc4}}, {{cite:fa68ac29e17eebd55d7e3e318642ddfe52411f3f}}, {{cite:81785d03c28f2bd94ad8b03139659110e7a6a2d4}}, {{cite:9b8e4fc45f7a5f06d9a975c42f8a36c72e369e26}}. Moreover, {{formula:ccaa4b71-b93c-4cc0-8789-9667a145b0ed}} pushes unseen classes away from seen classes, which explicitly tackles the seen-unseen bias problem. HSVA cooperates with iCORAL to improve the accuracy of classification using softmax, achieving harmonic mean improvement of 4.4%, 3.0%, 1.4%, and 1.5% on AWA1, AWA2, CUB, and SUN, respectively.
| r | 3076ede66260c655cb397e55b0b34763 |
See {{cite:106f480343e153af6d60d7b1d5984336b81ec974}} for more details on this definition. Then it follows from the regularity result in {{cite:106f480343e153af6d60d7b1d5984336b81ec974}} that {{formula:9fac8c52-de02-474d-83ff-8104e55d1f42}} is locally Hölder continuous in {{formula:5e6c887b-2517-404a-b22e-3bcf343f28a7}} . We say that the origin 0 is a removable singularity of solution {{formula:f4e7f38e-a734-41a2-bd3b-105e84fdcbe5}} of (REF ) if {{formula:bf1db157-29d5-4ee7-92c9-bc91aa792e7d}} can be extended as a continuous function near the origin, otherwise we say that the origin 0 is a non-removable singularity. Our main result is the following
| i | 056bb99cf5ab23ed6f361bd386a169f3 |
Another issue associated with the MCMC is the proposal generator. The earliest methods developed by Metropolis {{cite:0d02350d3ad3a46e87b6950510f7ff3a51c634d0}} use the random walk to generate the proposal. Many other methods {{cite:1f6901dbe1c5e65823a122add6d338a7a8539d5a}}, {{cite:250267b6afe5b75084bb18b7ba303b756e855dbf}}, {{cite:bda4ad29f19b60efc1c93e6a78ba8d731f75097f}}, {{cite:301d2b7bedf6fcf52e8856815129970d9e84441c}}, {{cite:a13f0cb73e05b4f1bde79a619ac2b2e6b7be8664}}, {{cite:dd7f17d373d238449a2ca570b08c029a459e9b9c}}, {{cite:a9f025d9456de0336566547b2878617dc44904ad}}, {{cite:7b76d51efde8b2c8e61cad9f6700e55a3fb7fd93}}, {{cite:ac6227717a72ea39dd2cbe9dcb73a571c0302ec1}}, {{cite:0bbc19447ec4828a6b2d935c4123eb1cf09e1771}}, {{cite:6bd0ff2e05c778f837c52575585072bea0e5e30f}}, {{cite:0b3ad5903cc95a8eb97fb6e58487d1981f380017}}, {{cite:68ede91f273d080b45edc7ae4a8c3024003df3a8}} including using kernel adaptation, Hamiltonian dynamics, Langevin dynamics, parallel marginalization, kernel coupling and multiple chain simulation, parallelization have been proposed to improve the efficiency of
MCMC methods.
Deep learning method has been widely applied to solve the problem with multiscale features {{cite:b13efd46fa2c99ed1a0904dd12e77993230bb2c3}}, {{cite:5f52f09e4796a895a58692c1ef4ab5e7525f0666}}, {{cite:f8f314454d599ba797a733b03c9385d5fa4d7df6}}.
In this work, we will recourse to the reinforcement learning approach and propose to use the reinforcement learning to accelerate the MCMC sampling.
| i | 2b2a33c8e12d544aba9e9ba0bd710d1e |
In this method the interacting Hamiltonian {{formula:7be67c9a-3519-4fb5-9c3a-b3d31ae38a31}} is decoupled into
two non-interacting parts {{cite:2471feff8c1e36e2eaf3c16aa983094c05d0fb98}}, {{cite:2fede3b06702d8504d0c8c69e99930882fc08074}}, say, {{formula:edeae952-968c-486f-832f-e5f7df7ee381}}
and {{formula:32c8eeda-e729-4c47-8b41-13f3f0c8343e}} , associated with up and down spin electrons.
Diagonalizing these non-interacting Hamiltonians ({{formula:9858b321-d888-4695-b05a-eaf32f34b23b}}
and {{formula:72f6ec80-0ef4-4b2d-b32a-73f6b944c8df}} ), we find energy eigenvalues, and eventually,
calculate the ground state energy at absolute zero temperature for a
system containing {{formula:137e2b25-d291-48e0-95fa-28ee62ca6131}} and {{formula:b34c7ae4-9b6a-4263-a1cb-4a561af855c9}} spin electrons from the relation
{{formula:717bfa38-9265-4fe2-af3f-f821d575a657}}
| m | dbac5667335f3339816238f40c3d91c2 |
{{cite:3a9100505128384bd6c1c05815d7cd8c5c7a135a}} Nallapati2016AbstractiveTS first proposed to use an RNN (i.e. encoder) to encode the source document into a sequence of word vectors, and use another RNN (i.e. decoder) to generate a sequence of words as the generated summary based on the word vectors from encoder.
The encoder and decoder could also be implemented by CNN {{cite:a77893c2ef6c95299a9c3da3095bc8c29d0dbbf0}} and Transformer {{cite:e813cb23cfa1ecf866ef889d4d919fb6ebcbe0e4}}.
The decoder of those sequence-to-sequence based neural text generation is a conditional language model, which makes generating readable and fluent text possible {{cite:e5043e71f3a1ba529ffb1a9c2ac27f4eaa010dd9}}.
However, most summarization systems are trained to maximize the log-likelihood of the reference summary at the word-level, which does not necessarily reward models for being faithful {{cite:ac803dc6809926d3649a0573cadcd01224dc5ace}}.
| m | 83b4f100396603429ee4bad7be46c6c2 |
Normalization in Transformer. Previous works have demonstrated the importance of normalizations in transformers {{cite:e91294a5ff6d0dadadcfb4045269adb9a095fdbf}}, {{cite:a9aca359173aab57cf00b569e23cca84376c8fb6}}, where Layer Normalization {{cite:afa3110ec5ac93851e5e04d76d8571172d50357c}} plays a key role in their success. With further developments in normalization such as PowerNorm {{cite:4f8c5e455e478b92c464387e203417365b0a637d}}, transformers on language modeling have received a performance boost. As the paradigm shift becomes success in computer vision, analysis and attempts on normalizations in vision transformers have been made in {{cite:a4970442d26a5df95c1f4f826f1f56d4690c056c}}, {{cite:5264b7b82167e365eef6192e6f607aacbfadffa2}}.
| d | 599c829c38be878e9030c9723b1fe948 |
In this work, we follow the standard mechanism for privacy protection by adding randomness at certain locations in the machine learning model.
Another way of improving privacy could be to exploit the intrinsic randomness of ensembling algorithms such as subsample-and-aggregate {{cite:07a34d0df27980d7b1e2347af1c40224afd33c7c}}, {{cite:e27214a9430b6af67dff5d97707f90bc7935e127}} or bagging {{cite:28ae61fd48b711755f4d894306c607e033189974}}.
An interesting direction for future research is an investigation of data augmentation techniques for privacy protection {{cite:ccd43d236ceccbe54764f6322cc16e296cea2fd5}}, {{cite:08c48802214ca974f5f846c3e08b19ea7afb07c8}}.
In these approaches, data are randomly cut and recombined to generate artificial training data that have the potential to protect the privacy of the original data.
| d | 456aaf6e8d003e68f5395d45dbdeceae |
A better global view: Based on transformer {{cite:f1723ac4085decf7e168abf0a67f148bd34ac064}}, a self-attention layer connects all positions with a constant number of sequentially executed operations, whereas a ConvNet layer requires {{formula:53efc25d-f224-4de7-868f-e819ea08a85c}} operations, where {{formula:846097c3-15a3-4779-9ada-f2878ddb57ee}} is the kernel size and {{formula:a738f1b7-330c-40f5-9d38-da2d5815634f}} is the sequence length (in vision, it is related to image width/height). Swin-T{{cite:7ed88d6969ec0b8c8b0c534f994045b14dd469a9}} applies transformer in each small window, which has {{formula:843b697a-8cc7-4c52-8a83-497fd4f10d76}} image patches. The {{formula:fd3b8ded-f273-46f6-a04e-b53285a83e7e}} is typical set as 7. It means that the receptive field for Swin-T is in a {{formula:184a43d2-c6de-4f38-b88e-9514e703c5ab}} scale. Meanwhile, at the first input layer, the image are organized by each patch, each patch contain {{formula:7e0ca8e4-09fd-43ae-81f0-95e5d9099631}} raw pixels images, so the effective field of the first layer is {{formula:5e96ef1e-70e7-441f-b562-b411ac6fa9a9}} , which is pretty large compared with ConvNet kernel which has a typical size of {{formula:dd82c0f6-7ee0-4fee-a7f8-d69d977e7985}} . What's more, the shifted windowing introduced in Swin Transformer {{cite:7ed88d6969ec0b8c8b0c534f994045b14dd469a9}} further increase the receptive field. The shifted windowing was proved effective in object detection in the Swin Transformer work. Increasing the kernel size of ConvNet can solve the problem, however, the increased kernel size will greatly increase the FLOPs as it is increasing quadratically with the kernel size (see equation 1 from {{cite:f21678da5013baf1e017117600edc0d8f292689a}}). A detailed comparison of the receptive field of ResNet-50 and Swin-T based on the SUN RGB-D dataset we used is shown in Table REF .
Swin-T has more powerful feature extraction unit: As shown in Table REF , when comparing the number of channel/dimensions used for ResNet-50 and Swin-T, we firstly see that ResNet-50 has more number of channels. However, when taking the number of multi-head attention head number into consideration, the Swin-T has more basic computation units.
| d | da6749e73ee308c4360f8380b52d45d3 |
In numerical simulations of {{formula:4c1be6db-3c0a-4643-aa68-93fce84daa3a}} dimensional, incompressible, flow, a turbulent steady state is generated by adding large scale friction which removes excess energy from low momentum modes. More precisely, energy is pumped into the system at the driving scale, {{formula:432d95e2-10ff-4aa8-919f-075f226a2258}} , and gets dissipated at large scales (by, say, friction with the boundary). Once a steady state is reached a condensate will form. While it would be appealing to generate such a condensate in a setup of the type discussed in this work, it is difficult to envision how large scale friction may be incorporated in a natural way within the framework of holography. One possibility is to induce appropriate boundary conditions on the boundary manifold possibly following the line of reasoning in {{cite:9fa1748b233d774cd2f6dad574b97d1dc8c22489}}.
| d | 87bd2adb6625615b86b949a122d58c38 |
The numerical simulations presented in this work reveal very rich collective pattern formation phenomena.
For rigid active particles, the symmetry of individuals determines the symmetry of the interaction potential and, thereby, constrain the symmetries of emergent patterns: self-propelled discs may undergo dynamic clustering or motility-induced phase separation {{cite:bcdac955202698087ae1c9a1433516f5ea88dc38}}, {{cite:5ec302b3c1100a5e52d00809c1cf942ffddacf3d}}; in the classical Vicsek model with polar alignment interaction, polarly ordered structures are observed at the macroscale {{cite:5dcc96ea662b096ad92429c70b10835cc9bf49ba}}, {{cite:f820cc67b16499a92ccd809ab6cd49d303430e41}}; elliptical self-propelled rods, in contrast, may form polar or nematic patterns, which may even dynamically coexist, depending on the strength of self-propulsion {{cite:4b91fcab54fa1ebc7cadc2f9b5a64a5ecd83e93c}}, {{cite:c39451200882fef11c33f9db469cc144bff88a15}}. Collective dynamics of cells is strongly determined by the interactions among them. While we consider here only repulsion, there are other phenomena involved in cell-to-cell communication {{cite:dbe5e5fe9f31589c4afe9b4d43470a2279929eb5}} and in particular cell-to-cell contact-inhibition {{cite:b3432a8fbd176bf28ae7be45342319b6068c813b}}. Such interactions can be easily included in our model. There are already some attempts to include deformation in collective cell dynamics. A protrusion region has been added to rigid spheres to simulate the deformation of the cells {{cite:4d5efe20ae68c2ecc3522f45a38a2c84edfadbc5}} and some phase field models have been already implemented to describe oscillations in epithelial cells {{cite:b5508c7eec239cb43ab8039bb99a538348277b01}}.
Deformable cells, however, do not fall in any of these categories as the particle shape and, thus, the symmetry of the interactions, is a dynamic feature which is determined by intracellular biochemical processes as well as the complex, nonlinear interactions with other cells due to collisions that, in turn, induce additional cell shape changes.
Accordingly, we found different interaction scenarios that may lead to alignment, anti-alignment and stuck/push configurations, whose relevance depends on the relative position and orientation of two cells before the collision event, the stiffness of particles as well as the global cell density.
| d | 844b4b3f6823db0c3a003818057c6a1a |
Ablation Study.
We conducted the ablation study on the val sets of PC, MC and CS datasets, and reported the results in Table REF . “MEA” denotes using the MEA loss consisting of {{formula:bb29c5b7-2878-43c7-989b-b00c503e6417}} and {{formula:bd246611-ed37-4609-babc-87719325116c}} .
We used the SOTA WSSS method, namely CONTA {{cite:1e17f1adb018746a6632ef90d2c52a3aed5be117}}+SPGNet {{cite:55c2191fcf7a2814b4d03deb1fc80668e845f018}}, as the baseline here and show its results in row 1.
Comparing row 5 to row 1, we can see the proposed SR loss brought clear performance gains, , {{formula:3847ac54-b2e7-48b3-aee0-b73e65b1d591}} on PC dataset.
Intriguingly, comparing row 5 to row 2 (and row 1), we find that distillation-based loss terms ({{formula:615e873d-a18c-4981-bdcc-c1368e8a0ef8}} and {{formula:0a8d3321-11e4-48be-a9ea-114edcb8634f}} ) brought higher improvement margins than using only MEA loss.
As we mentioned under Eq. REF , this is because our SR-L and SR-F terms encourage each individual layer to learn the “soft knowledge” (from a superior layer) which is richer than the “hard knowledge” in one-hot labels (used for computing the MEA loss).
This phenomenon is consistent across all datasets.
| r | 671f4e9ab657399fb5facaeeb96c224a |
Our DGMN2 is related to DAT {{cite:6f8e8886c0cd1c9743cf9d5efec2bc995ccfb415}} and Deformable DETR {{cite:0c2790da98e6aeb69537ff60ef2864b0b3a271e0}}, but has key differences:
| d | 0796fe3af0bbe07b6169220284eca528 |
The reported results in Tables REF ,REF ,REF show that Vision Transformers have great potential on FGVC. Moreover, our experiments show that attention-driven augmentations and important regions detection help to improve their performance on fine-grained classification, achieving state-of-the-art performance in Stanford Dogs {{cite:ab3aba6b094a2734846180121be08e61c0f24b55}} and CUB-200-2011 {{cite:f319b26ff36e0cbe18a85ef6ea6e4516a80dfc44}}.
However, we must expose the limitations of the proposed multi-branch multi-scale architecture: (i) the selection of the region of interest (ROI) based on the attention map is not fully differentiable, and thus, the model is not complete end-to-end trainable, it requires to train it in a sequential (multi-stage) way. (ii) ViT-based models require important computational power.
{{figure:462bc40a-af94-47a5-b3db-3f821b33977e}}{{figure:a6e5732d-c049-46a8-a76d-41c1143f17a4}} | r | 947b6f5d8ce99f7cd71528c1e43bd5fd |
Early analyses considered collective disorder to be a return to a “natural condition”, whereby crowds temporarily forgot civilized behavior and instead regressed to more primitive ways. This phenomenon was referred to as the “madness of the crowds” {{cite:80e390093e8b6fe904467890d56bfb78f29bdd3c}} and “mass enthusiasm” {{cite:2778135ffd24c17475f29c196f58289cf0c6d1b0}}. The alternative suggestion that conscious and rational decisions were involved in the participation in riots and public disorder began with the pioneering work of Granovetter {{cite:48b545df2dcaa2a075621f609e6513849304aa69}}, {{cite:61a1d7d7cdd1be705a355e11a61b1d15b72cb182}}. In the models presented, potential rioters evaluate the benefits and costs of joining public disorder, taking into account the social influence of other individuals. Later developments, such as Epstein's formulation for social conflict {{cite:5d395348e70427bdccb5c19a858213245ad83730}} using Agent–Based Models (ABM), successfully described more detailed classical patterns in public disorder, such as the long calm periods interrupted by intermittent bursts of collective violence. Further approaches to this problem were made by using partial differential equations, capturing important features like the contagious nature of rioting behavior and reflecting the observed patterns from the French riots of 2005 {{cite:527251ef35f59c1edb42565fb102574af7952ceb}}, {{cite:5ee408ef14f24b353111fe0ebfd73b960afeba3c}}. Also using differential equations, Davies et al. {{cite:0380e3887e7c6ef4d42c0e124ddbe907f027be4b}} successfully captured the quantitative dynamics of the London riots of 2011. This model was based on empirical evidence from London that rioters chose target locations on the basis of their characteristics {{cite:d4da7b8394ba81346eb53a42eb7ce9a35026d9cc}}; such behaviour is consistent with the `rational choice' perspective on criminal decision-making {{cite:cc4fe456ff77b480aed6ba4820dd988d4ea2dfc9}}, in which offenders are assumed to select potential targets from a range of alternatives in such a way that they maximise reward and minimise risk {{cite:64234fb23343b33c94f7165c036eb55ac76821d9}}, {{cite:004bcda970bd0a0d9dcc02f58f14fdd0d4b42ca0}}. In the Davies et al. model, the participation of rioters was influenced by the volume of retail activity (i.e. potential for looting) in possible target locations, as well as the number of other participants already present (as a measure of `safety in numbers').
| i | bda41539b3a172fa43bece1e51c9b075 |
Polar Kerr angle measurements under magnetic field.
We first present the polar Kerr angle {{formula:711e5454-9cc6-4dfd-b735-b9d0477ad21b}} under magnetic field. Because of the Faraday effect of the lens, there is a background signal contributing to the measured {{formula:a7b87f95-35e1-49f9-85e0-8812f43cdbf6}} . In order to examine the signal from the sample across {{formula:d49ce62a-817c-4280-941e-0e5adffccb8a}} , we use the measured {{formula:71f88d25-3f8d-43e6-b4aa-0224883af3ea}} of a Nb metal sheet to subtract the background signal {{formula:fcc95f0c-86db-4264-aa6e-4a2ae75f9db7}} (see Supplementary Fig. S2). Figure REF a shows extracted sample signal {{formula:0b7847db-8fc3-4c9f-8b40-29fdfff8192b}} divided by magnetic field. At {{formula:5ab83af9-feac-4033-bdcb-c4a6ce5603ea}} , {{formula:37d905cd-099b-4470-b8ea-1db1f67bc812}} jumps and gradually increases with decreasing temperature, consistent with a first-order transition as previously reported {{cite:0e89b1f21796f823d9bc7e227895e14737ae16cb}}. Moreover, with opposite magnetic field, {{formula:ced9869f-ea3c-4a0d-a940-14700c731862}} changes its sign to negative.
The fact that {{formula:aff8b705-7be2-4ddf-b023-4ea632343056}} rises concurrently with the CDW transition, and reverses its sign with opposite magnetic field direction is in agreement with the intensity-modulation reversal observed in STM spectroscopy {{cite:bf3428780f96f7ba43809b9f88b0985c46dd9ba2}} and the AHE {{cite:11512d90457a434ae562e6fb9dfa679d1d1d57e5}}, which are interpreted in terms of TRSB and large Berry phase in the CDW state of CsV{{formula:9a22f340-df58-47cf-855a-80160af8b555}} Sb{{formula:3fa94b44-ed90-4e37-b0f8-5ad3d12c9c4f}} .
| r | e18a79caf58e2f4fc03f9922acc582de |
More extreme nonlinear dissipation, enabling one- and few-photon Fock states, could be achieved by combining these resonators with matter systems supporting single-photon-scale nonlinearities (e.g., cavity QED systems with photon blockade {{cite:4f4e5ff7f54f4d1d74c0dd97e130f18b6f5b73da}} or Rydberg atoms {{cite:dce31a0aadcf429b15206e88471ef8a72c9f38c6}} with BICs).
| d | 0e47edcdbde90e7dbb568efa0e058b3a |
Asymptotic root distributions for sequences of univariate polynomials has been a topic of study in analysis for many decades {{cite:33ec249eba5ca67f8f08f6b6b0579c97f7ab0b6c}}. In particular, sequences of polynomials with all real zeros are important in many branches of mathematics. Such polynomials possess several nice properties. For example, if a polynomial {{formula:75f269b2-2ff8-403a-913c-0abb1142aedb}} is real-rooted and has nonnegative coefficients, then the sequence {{formula:c7e76d9b-1fc9-43e8-a581-b7d187457658}} is log-concave, i.e {{formula:7a7c0e28-2277-426d-aba1-e50e9a07b987}} for all {{formula:0c7f9555-b79a-4c4c-86a0-4f247461c6de}} {{cite:1927010da0db29376c4ed834d0de8ac46d6fa56e}}. This log-concavity implies that {{formula:38e38047-8ffe-42a3-af3c-2e90f7f687e2}} is unimodal, whereby the sequence increases to a greatest value (or possibly two consecutive equal values) and then decreases {{cite:1927010da0db29376c4ed834d0de8ac46d6fa56e}}. In addition, polynomials with real zeros are closed with respect to differentiation and the zeros of derivative interlace with the zeros of the polynomial. A good source of information about real-rooted polynomials is a book V.P. Kostov, “Topics on hyperbolic polynomials in one variable" {{cite:fa0ef642c996696b8251a99312f1d730e147dc7b}}.
| i | 0518b099cf3a11c617b3892094cc75e6 |
We have run a series of Monte Carlo models to predict the diffuse background in both the FUV and the NUV bands for different combinations of a and g. We used a baseline of 100 million ({{formula:16d7c3b1-7801-4975-85ab-31ad5501c7b1}} ) photons for the entire grid but used simulations with 1 billion ({{formula:65553782-da72-4f16-8875-e4a613bf4c0a}} ) photons for values of {{formula:fa43caa5-df5f-4301-9aed-2d043fd4a0f8}} and {{formula:1eae78b4-bbdb-49d3-8999-e94e98fd245f}} near the best fit values. We cannot compare the models directly to the GALEX data on a pixel by pixel basis because of the noise intrinsic to the Monte Carlo procedure and therefore used the root-mean-square (R.M.S) deviation of the flux as a function of Galactic longitude as a metric of the goodness of fit of the model (Fig. REF ). We have plotted the R.M.S. deviations for both the FUV and the NUV as a function of {{formula:a7903ca1-4861-4ac6-a9f4-bc9eb7f66aac}} and {{formula:e5c34c0c-fff6-403e-8bea-f124c63ca6d5}} in Fig. REF finding that the best fit occurs for an albedo of about 0.3 in both bands. Although this is in agreement with {{cite:14cb4cc48b4e5ab013c3b9f1c7570e3a493cb354}} and {{cite:602457fc14ec964e6624bd5a1bbf35cda06588e8}} in the same region, it is lower than the albedo found in other parts of the Galaxy (compiled in Table 4 of {{cite:37dcd31cada7abfe695a1a06d8af234f71cda945}}). {{cite:4cd59b9ce7c2b8a68b8780d3126cc037896358ab}} showed that a clumpy medium, as in the TMC {{cite:43da23f20b3e08889528cb74fc894041367baa42}}, gives rise to a lower effective albedo and it is likely that the “true” albedo is greater than our derived value.
| r | 6fee42189fa51c6e8bfd3aaa4528d05a |
Furthermore, as mentioned above, any point on {{formula:3db9c932-bc0c-4f1d-8e55-1f69cb7fce27}} can be treated as an interior point of the domain. Then it follows form Theorem 6.17 in {{cite:1c8e1509c34b5b7cf80cbf119459b077ed5b3419}} that {{formula:cd5bb790-58c4-46db-9460-1bbfd32d35cd}} is bounded in {{formula:d0469be3-09f1-4dc3-b1af-9d28c1ae3dd3}} , which indicates that {{formula:13730c1f-3055-45ba-86a2-7bfa3e4f73bf}} is closed, as shown in sec:3.2.5.
| d | 9745524abfb844a1952b58a767ff204d |
For {{formula:b2ff8ec5-f719-4941-afcf-26f76baa750a}} trace theorem {{cite:ade678b7de5d19e29ea577c5ec7debd6060f4e6f}} shows the existence of a {{formula:0dc5598e-d908-495d-8dca-f2bd066fcec1}} such that {{formula:f4536363-66e4-43f0-a652-2a6391a6c547}} on {{formula:9458b542-31bb-49fd-9d3e-19fb06503da1}} and
{{formula:74cada59-c4d2-4ac3-b45f-41567ff057e0}}
| r | 162f82f08a2582a8d507dbe9426e797f |
One typical low-rank matrix estimation method is the low-rank matrix factorization (LRMF) {{cite:fd40f18ccecf4ccf8af1f7a0fabea8570e08f4ca}}, {{cite:716bf40295a4a0d55155ac639488a0433342fc63}}, {{cite:c2a4584951dc11e7cfdc8662d92b811f1ef36057}}, {{cite:0bca87dad70fb88bd7a4a0f2ad5472caa2272d92}}, {{cite:a7ee3226a5f2476bc78ee1f60835eaea3a1b5796}}, {{cite:efbea72f685fbdfd3b842f156ad1f0e515698ade}}, which factorizes an observed matrix {{formula:e0b17bfe-fc09-4472-945e-44bb40ff6e6e}} into a product of two matrices that can be used to reconstruct the desired matrix with certain fidelity terms. A series of LRMF methods have been developed, such as the classical singular value decomposition (SVD) under {{formula:bf1fbb30-f2dc-451d-9ec2-2c03ea3a897e}} -norm {{cite:716bf40295a4a0d55155ac639488a0433342fc63}}, robust LRMF methods under {{formula:6550926f-4bd0-448a-a021-be7e2c147f08}} -norm {{cite:c2a4584951dc11e7cfdc8662d92b811f1ef36057}}, {{cite:0bca87dad70fb88bd7a4a0f2ad5472caa2272d92}} and other probabilistic methods {{cite:a7ee3226a5f2476bc78ee1f60835eaea3a1b5796}}, {{cite:efbea72f685fbdfd3b842f156ad1f0e515698ade}}.
| i | 5bacf3c8acb03722040721535c7d6e55 |
Formation of photonic band gaps (PBGs) in photonic crystals (PhCs) has been explored in the past three decades after the discovery made by Yablonovitch and John {{cite:1b155dba64bd84c6e7a8771651d9d881e059ea79}}, {{cite:cb092dbb96f2d4eeff01ca6a226aa1eec4a2aea8}}. Although wave propagation in periodic structures has almost been a century-long study {{cite:236e7be6b2b33e765bd1f7a5551055feb7276da6}}, PhCs have gained attention due to their robust light confinement capability, scalability, and small footprint {{cite:d228a84d5bf17300793c4b93364b55f7b2f04e56}}, {{cite:8c73b8cde8fabb45e55796ee47947ff0923b99f1}}. Combination of different scatterers with unique lattice geometries {{cite:a8b01c81aa237d4ffba55fa187a1c9e66d841d77}}, {{cite:3491953bac93caa8a086895a7cce319acd6f40d6}}, {{cite:d652d8d3c96aeea25c34e86f27999853aa602b92}}, {{cite:2da32aed14bf542bd72da4d512e3ebf70ac38f15}}, {{cite:34d854b977f44a888086f0990fc792cf114a266a}}, {{cite:3f60a074021f13a9913f8ee47cd7ebcd250e041f}}, {{cite:425b0c2ac7df0afd9220792a37db4e5e255f4fd7}}, {{cite:64f94472c9f077eff1dbdb6b8149ea9b383adf6b}}, {{cite:5f7513696a0ee52c614cafb6bf486eeb83debcce}}, {{cite:547c211f79142256b8e95a64b6f0aae11084491c}}, {{cite:4c2064b612094e28700663df106defb55258e780}} has led to wider PBGs by reducing the structure symmetry and found applications in polarization beam splitters {{cite:4760ca6260661c7990de588a45a8fbee5550cc60}}, {{cite:9a911f4eda1dd94ebb7c85afed39a490c23e5063}}, optical logic gates {{cite:04a0ed6acbe0573e8fdfde78631ab30e821ef519}}, {{cite:e54585699b4966064330356adb512d9baa53ab93}}, mirrors {{cite:59ab57806fca9d7aae88d7727bd440de66073fbc}}, {{cite:295e40e7e0e9013dbf9637b4015b6f34d6c4077a}}, sensors {{cite:82d24a2544207242332c5737386f42f793920536}}, {{cite:b0b635ff7ab0c130e1e2c5fd8f685ca31a828d92}}, lasers {{cite:a6ae838e774f8f0e18a45bb53c6744f929fce7c6}}, {{cite:407be1da76ab0074397ecb8dafe90b2066a359d6}}, solar cells {{cite:72632b3efb0b096f70d5afba1f5ac417a3ef4239}}, {{cite:613123ab3e4f44596b9b4ae7078315e9a3c72f06}}, and more. Nevertheless, most of these studies have been conducted on either slab, rectangular, or cylindrical geometry.
| i | 2a805a8541161ceea17969b0c3ef906a |
We also note that, our method could be improved for task-specific applications through hyperparameter optimization and using different neural network architectures. Our aim was to emphasize on the method and the associated geometric intuitions, and thus we did not focus on finding the optimal hyper-parameters. Similarly, we note that the performance could be improved by using recent advances in contrastive learning such as what is introduced in {{cite:dd8659b8ad8db3fbfa6814da8a0edc0b4e38accf}}, {{cite:5c6cb1901e5d01a7c36c716c79487a685f64afa8}}.
| d | dc4d217e58679966a863a86a9ae67ffe |
Inverse probability of treatment weighting of marginal structural models ({{cite:4c348f2ec1f2ef93feeefb1206d3bc16630e5f54}} {{cite:4c348f2ec1f2ef93feeefb1206d3bc16630e5f54}}, {{cite:97cfe6d4069b784fb020d0a307a778d09a4fe0e1}} {{cite:97cfe6d4069b784fb020d0a307a778d09a4fe0e1}}) can only be used to estimate how a treatment effect depends on baseline covariates. It would be interesting to know whether coarse SNMMs provide more precise estimators than marginal structural models when interest lies in this scenario.
Efficiency gains of coarse SNMMs could be expected, because SNMMs use all observed data, whereas if a saturated outcome model is used, marginal structural
models use only the data that is consistent with the specific treatment regime. Our investigation
is the first step in the comparison between coarse SNMMs and marginal structural models: we optimized of the performance of coarse SNMMs.
| d | 1ac7d9136e174c0a2437d69b5e35b46e |
While we compare our architecture to an LSTM, it is possible that transformer networks {{cite:12bee0a3bc332ea7090f848cdd5233e4bb3569c4}} would perform better in this setting. They currently represent the state of the art in many sequence based tasks, including visual tasks {{cite:9a45b40777a681865f5064dbebd816e26237b894}}, and explicitly encode positional information. It is worth noting however that, while not explored here, grid cells can in principle encode 3D structure {{cite:2e25353c1d892cc14f56e704ffaf7b2da653f597}}. Transformer networks already suffer from efficiency issues with long sequences, for which the introduction of a third dimension in the input representation would be problematic. The performance of transformer networks on our task and the generalization of GridCellNet to 3D objects will therefore be topics for future investigations.
| d | a60dbb76a03ec2be29dc40b5f135d6d4 |
Our lower bound is proved via the non-deterministic variant of the polynomial method {{cite:fc1f20cbd38a0e3ab1b15e29d84dc5c312399a14}}. Since it exceeds {{formula:a3f43546-555a-484c-b6f4-5c3d4c161502}} whenever {{formula:ee592ff3-00d1-47f2-9eaf-e1888504f357}} , we cannot obtain this tight result from the standard polynomial method {{cite:a1c92ddfddd73e653d7e2fb7656e9f339073b379}} (which yields lower bounds that are at most {{formula:f83e8e15-c85e-4575-a31d-85131ce1f449}} ).
| r | 89072b5b856a12f2303863b2bcf9aedf |
We evaluate the performance of APM-LR against baseline example selection methods for logistic regression on a variety of datasets from different tasks, as measured by holdout test accuracy and selection compute time.Code at https://github.com/siplab-gt/APM-LR For each method, we follow {{cite:5457bcd241a1df114e107fbcbf589d072296718f}} and set the regularization parameter in (REF ) to {{formula:cba1d080-f690-449c-b842-6f9b25c91f41}} , which we solve with the LIBLINEAR solver {{cite:77ba027ddc4e41dd933862882a2bae5e413f725d}}. After each example is labeled, we approximate {{formula:6e83e337-6b34-4494-a262-bc31dbc5e335}} with a normal distribution by applying the variational approximation described in {{cite:04c5e1e37920b817a77e8575ec0c1502ff678fb1}}, which is solved in only a few iterations of an expectation-maximization procedure (referred to here as “VariationalEM”). The final component needed to apply APM-LR is the selection of power constraint {{formula:448aa727-5a31-4ab7-bd9a-8bd41bcc43b7}} in (REF ).
| r | 1144cac6c020090e3df04645b991055d |
Maximizing the modularity function as in (REF ) is not limited to the
Louvain-type method considered in DHNet.
Other modularity maximization techniques developed for a homogeneous network may be applied
to (REF ) with some modifications, such as the spectral method based on the eigen
decomposition of the modularity matrix or the stochastic optimization method in {{cite:515213bc237eac8f610533e768224d94557eeb3e}}. As noted in modularity maximization for other types of networks {{cite:7b519226cac9bbda005054194371de1cb0f9da4a}}, {{cite:986f3d742ae550b2a81d96b8dcce1ff1d34d308b}}, we find that the Louvain-type method is computationally much more efficient and yields a good performance in our setting.
| d | 315599f6c3112f5a97f7018f5ec10366 |
In the A-type systems ({{formula:cc270c46-4e67-4cd8-ad3e-2d1e64c1b6b4}} ), localization-delocalization transition (LDT)
appeared with increasing the perturbation strength {{formula:65fba574-3f25-4380-8e49-cf3e9be5d2ea}} .
The critical value {{formula:1e61fe20-9b48-4390-b188-be0a038cb0c4}} which appear the LDT is {{formula:34ff6dbf-8834-49f9-9952-43e73051b47f}} for KHM and
{{formula:ca8d3713-588f-4f85-b43e-765a4944b1d2}} for Harper model in a sense that
at {{formula:612a0807-3443-4f2c-a3a3-e65063484975}} , the LDT is not caught and shows localization.
The property for the number of the color {{formula:454a439a-0c5d-4504-aedf-8a1f790136db}} is summarized
in table REF .
The table also describes the localized and delocalized transitions
in the multidimensional Anderson model that corresponds to
the 1D Anderson map and Anderson model with the quasiperiodic perturbation.
In the case of KHM, if {{formula:70e80a13-14c9-4620-a1fd-8a352337699c}} can be identified with the spatial dimension {{formula:99ff49a2-6356-4232-924f-c28790e3b5c3}} , the
existence of the LDT is a qualitatively consistent result with those of
the LDT in {{formula:61fbeaed-1592-4bbc-8a69-8f221d88f387}} dimensional Anderson model.
{{cite:514e3d4e7d4474d0597b6786c8ae875bac717d67}}, {{cite:07bb4cbc3a2b0065fc272379fe35ff6ec2ca402f}}, {{cite:cc1cc760d5060db1f856abc5ed52a7feba0c644a}}, {{cite:315cf6311e8856c32d275d1d1f314abb61d935bb}}
However, in the time-continuous systems,
the critical number of the colors, degrees
of freedom, is not {{formula:c89141a9-ec66-4f73-83ed-8d978fd47f7f}} but {{formula:0276e647-bc70-4374-8908-2e0b0b9f2354}} , unlike the periodically kicked quantum maps
such as KAM and KHM.
{{cite:f964a4107321e366a136f1e8594a9556a84bc6b8}}, {{cite:8aba8909316cdd45f1ea49f5a9e90c2cea5ae70a}}
We hope that this study will be useful for studying the long-time behavior
of the dynamics in high-dimensional random systems and multi-degree-of-freedom
quantum systems that cannot be calculated directly.
| d | 9cd94a2575c094c77518197a771cf421 |
The Schwarzian derivative (REF ), or just the Schwarzian appears in apparently unrelated fields of mathematics: from classical complex analysis to integrable systems {{cite:cab2f769903d686526ebd251efbcbf31f136deff}}. In contrast, in the physics
the Schwarzian appears either in the transformation properties of the conformal (supersymmetric) stress-tensor {{cite:398d88ccbf072a91e893c850f1c029b189e6ad37}}, {{cite:2355921f1bcd1a7e5f6d07c428ead360fd22cf9f}} or arises as the low energy limit of the SYK model {{cite:f97be0dd48fe008d50e73ef9c84648ecb1888e17}}.
Therefore, it is not strange that the possible generalizations of the Schwarzian are mainly related to its supersymmetric extensions where the supersymmetric Schwarzian naturally appears in the superconformal transformations of the super-current {{cite:0d8fe90d93391baf8e9dcc37d8411eed4373aca3}}, {{cite:03daeb3afb9b916f048371f919ed2978cca13768}}, {{cite:2355921f1bcd1a7e5f6d07c428ead360fd22cf9f}}, {{cite:a1e2d7ca4f6a2e9c548c3ed64e9bce67a08f6fe1}}. However, this generalization quickly stops at {{formula:e84ab5e7-98be-4fd7-8db7-e0d5208c985c}} supersymmetry due to appearance of components with negative conformal dimension in the current superfield {{formula:5b2e900a-27cb-4cb9-b8a3-18b7a970b077}} for {{formula:8fb59190-73c8-48f0-8c5a-9f142e4b5a54}} . In addition, the recent
construction of the “flat space” version of the Schwarzian {{cite:92d66bc7a392f873257192132af4024b55702d23}} raised the question about
existence of the systematic way to build the generalized (bosonic ones or possessing higher, {{formula:54e84a27-60a1-448a-90aa-90c901d2df7c}} supersymmetries) Schwarzians.
| i | 4973b3ef9af945e1bc259acf0c5f064c |
We first provide background on spatial and spectral pooling, and propose DiffStride for learning strides of downsampling layers. We focus on 2D CNNs since they are generic enough to be used for image {{cite:0062ceff4a7c4881afec398d9d206b0e4241cddd}}, {{cite:ca1373c399fa774e3e669c9caac258302ebc5920}}, {{cite:f1285a097e8638602dbed06428bf04c333a3dca7}} and audio {{cite:9db6c1225998164d70bd731f5eabec49a9df93f4}}, {{cite:80b159c865bda88c3c6e0e1e13f9016e98186942}} processing (taking time-frequency representations as inputs). However, these methods are equally applicable to the 1D (e.g. time-series) and 3D (e.g. video) cases.
| m | 0cd34ef6aa3ec6fd351137b874ab3e02 |
One common problem within neuroscience, in general, and for the specific technical challenge of creating a robust model of cognitive load, in particular, is the limited availability of EEG data. This is often due to the difficulties in recruiting participants, or faulty recordings, or the presence of various artefacts in the EEG signal, leading researchers to discard significant portions of collected data.
Unfortunately, when employing machine learning methods, in general and deep learning methods in particular, limited training data might often not benefit a robust model formation.
For these reasons, this work proposes to use a sliding-window technique {{cite:a6965752e79e771f7a712b44838e04a3f339397a}}.
The available EEG data are segmented into windows of {{formula:ba54fd10-8e40-4d6d-8095-344bf098d22a}} seconds, shifted by {{formula:0993ca4a-7102-41e7-9b7e-52012dcfe436}} milliseconds. For each window, a pre-processing pipeline has been designed for producing 2D spatial-spectral preserving images, as summarised in figure REF . Fast Fourier transformation is run for each EEG channel in each window, obtaining a power spectrum in the frequency domain. For each spectrum, the five EEG bands (delta, theta, alpha, beta, gamma) are defined by employing the same boundaries used to compute the brain rate. For each band, the centroid (geometric centre) is computed, which equates to the arithmetic mean of all the power values within that band. For a given band, all the computed centroids, one for each channel, are positioned in a 3-dimensional space, following the coordinates of each electrode position on the scalp, forming a scattered 3D spectral topology-preserving map. Azimuthal Equidistant Projection (polar) is subsequently used to transform this map into a scattered 2D map, preserving the relative distance between adjacent electrodes. Eventually, the Clough-Tocher method {{cite:6f20a47b1ab2be5e63f7976becc65782ae0554c9}} is applied to fill the scattered 2D maps by estimating the values in-between the electrode over a new interpolated map, an image of {{formula:462d2585-ce73-45fd-b55a-9332b6ef5cdc}} .
The aggregation of the five {{formula:51a14e53-7e01-4fcd-b107-0e3b95bb485b}} maps, one for each EEG band, creates a tensor of {{formula:5f786609-bf3a-47b0-9dc8-466c14c288b0}} .
The sequence of these tensors can be seen as an `EEG movie', a stream of data over time in the frequency domain that preserves information in space. This stream can then be processed with deep learning methods, inspired by state-of-the-art video classification methods for spatio-temporal feature learning {{cite:18567c49b2b84627cea5ef3cfd47746725ff0ccf}}, {{cite:208951bbeadfbfce8b3545a6a14e86ed17634264}}.
| m | c7b2c9edbede7fca369409ae487d3a18 |
The intuition behind the proposed method is that the known distribution should be uniformly distributed in latent space in order to effectively minimize the distance between new samples and known samples under the constraint of a limited number of known samples. This can be done by relying on learned feature space representation. A self-supervised method for learning representations is shown in {{cite:7afde21ef603b760609c83ef2eecf70cb263f17a}}, but representations can be extracted from any relevant DNN. In this case an Autoencoder is used to build the feature space transformation in a self-supervised manner. For visualization purposes the dimensionality of the latent representations is reduced using Principal component analysis and only the two foremost principal components are used in the following plots. Figure REF shows a comparison between the samples selected using random sampling and sampling maximizing distances in feature space. Figure REF and REF shows the first {{formula:19074a72-2ff9-437c-b2d9-92c8efc1b7e8}} of the total number of samples, sampled using the two different methods. Figure REF shows a more uniformly sample (green) from the data set(blue) using furthest point sampling. Training using this sample should provide better coverage of the input space compared to the random sample shown in Figure REF .
Figure REF and REF shows the last {{formula:872e107a-52f4-4e73-b73b-a5b008104da1}} of the selected samples. The random sample shown in Figure REF is clearly better distributed in the feature space compared to the sample using furthest point sampling shown in Figure REF . The result is that furthest point sampling provides the most significant samples up front, while each batch selected using random sampling is approximately equally diverse.
{{figure:b38e1ff3-497a-42d4-b497-3e39d5325a12}} | m | 8451a6b8f09efdc138a2b8bdf2bf2652 |
The total decay width {{formula:204f9213-a728-4651-9f87-b85b81e34aff}} of the {{formula:7ef23836-7f66-44b0-b439-f83701137ac9}} meson in the free
space is composed of the partial widths of the {{formula:0302fccc-bdec-4dce-9cb0-806ac9c0e871}} meson decaying into
various channels, i.e., {{formula:2c1491fb-2b18-410e-9364-c2c1696a2875}}
{{formula:52dd4fe7-6c03-498b-93c9-b9e45020d517}}
+ {{formula:6a0bf10b-9862-4211-9dc4-96af1755aae0}} {{cite:4d56df9a03b7e163dfda8894d7331c5adc0456c5}}. The
two body decay width of the {{formula:b46abc6c-b1d5-44ee-a195-83a1a88fca85}} meson {{formula:0b708098-da1b-47dd-b5a0-4c8a854b78d7}}
{{cite:c7fad47a9cb30ac9e43c618fdeffdf46ca1f35f0}} is given by
{{formula:a1d5110c-502a-47bf-9c3c-d69adca4c62d}}
| d | da508325bdc9c138003069b556f81687 |
In this subsection, we do not aim to describe the mathematical models of dynamics in open and closed quantum systems – the details concerning this subject may be found in {{cite:2497a9f774b1453d8a01e08f362df205b9fb7a6f}} and {{cite:3118fb5d0dc97fbe096e35a66f0e1a1abf34ba74}}. For clarity, it should be recalled that for closed systems, the evolution is a unitary operation, and it can be denoted as Schrödinger equation:
{{formula:b49e69f0-3ae7-4523-9897-4d6f50a0853c}}
| m | cac4036eac5a8b082b9f0ca1b291c40d |
The persistence of a periodic solution under perturbation for retarded functional
differential equation (RFDE) is presented
in Chapter 10 of {{cite:5c98cecf1e2c25247874fa70a8fcc755472da627}}, notably Theorem {{formula:759096c7-2890-4247-98cf-56cb8cd0dd48}} . In this section, we present some remarks that can help the specialists to compare our results with
those obtainable considering the time evolution of RFDEs.
| r | 4b0d7a55852f487555d7d9ddd0a52b61 |
Recently, the theory (REF )-() has attracted a lot of attention for many reasons, one of them is the simple way to add new degrees of freedom through the introduction of a scalar field {{formula:34121f84-6833-41cc-8d33-1ed28f3e0b55}} and avoiding Ostrogradsky instability (see for example {{cite:bf05678e0256f5af4e60ee876ef67768fa9577d7}}, {{cite:aafb0e54a72d31a94ea45e3bb9f873f6ed4310a4}}), as well as allows us constructing regular black holes solutions via a Kerr-Schild transformation {{cite:e3e3f970f618435d38c9562271b64de96d0f8ac4}} and three-dimensional spinning configurations {{cite:966da4407eb62b89ca673cb6f669f6b27eceed32}}.
| i | fa0ff6fdd3b58201a186252d8f8a1566 |
This section describes the methodology to predict the spatio-temporal dynamics of physics-related quantities using a convolutional neural network. The trained network follows a typical auto-regressive strategy {{cite:cec153f2cde216dd132b46dd12a6265c9e5ee007}} to produce time series of high-dimensional state vectors.
The focus is put on the treatment of boundary conditions in the context of convolutional networks, in order to reproduce the desired physics. Several algorithms for the treatment of such BCs are presented and later evaluated in Section .
| m | 531ac11295d36dfc5943f1f9987ed373 |
Creativity support systems have been extensively explored for both professional and common users in computer graphics and human-computer interaction fields. In particular, the production of character animation is a common creative process in both entertainment use and industries like game and film developments, sports, and medical applications.
Creating natural character animation requires expertise and manual labor, which prohibits novice users from even casually producing some simple character animations.
In practice, motion captures are widely used in the industry to create natural character animations.
In the motion capture process, one or more motion actors who are equipped with sensors in their body parts act the desired motions.
The word “natural” means to convey the credibility in the animation that there is really a virtual human there.
At the same time, the cameras in the environment sample and record the locations of the equipped sensors many times per second.
In this sense, the cost of motion capture process, which includes labor, site, time, and equipment, can be expensive and time consuming.
A big volume of motion captures have been recorded and many motion capture databases have been released for open access, such as {{cite:7ea5ebb2eb0a8f38bfc20ac77990531f3e94075b}} and {{cite:83c5c0872b898e5b7a1fd9a3b7885969246ae435}}.
However, the reuse of existing motion capture database is still difficult for novices:
for specific applications and stylish motion details, animators still need to record motion captures from scratch.
Although existing motion capture databases usually provide keyword-based motion search, the subjectively defined keywords can not represent all details in each motion sequence and thus prohibit animators from retrieving desired motion sub-sequences from a large scale database.
{{figure:6c568b93-1c75-4ab6-95c5-8485645d4a3a}} | i | f33ebafdf5614a35a2173e9cc8f6ed85 |
In the experimental realizations of the auto-thermophoresis {{cite:c3ec244d0bc458840e9546da5b1352db1fd1f540}}, {{cite:8ba36b2768783be45df07632051821f3ac967d2b}}, {{cite:db04df88551e0bf1f12bf4c7ae596f34b9ba4581}}, materials that have been used so far to fabricate a thermally asymmetric particle include microspheres made of ceramics, such as fused silica; and polymers, such as polystyrene, while the continuous fluid medium has been commonly taken as a mixture of water and glycerol. The typical thermal conductivities of these materials are given by: 1.3 W/mK - fused silica {{cite:0e628277b6a42d3dd90c3474934e11fe43889bac}}, 0.13 W/mK - polystyrene {{cite:40c4f9b3d4adaf57b711381602b2c0d4f8f46e95}}, and 0.54 W/mK - water-glycerol mixture {{cite:7b904cfbd3b4a2098526666bfdf641692c5b1458}}. Considering these materials, the thermal conductivity ratio becomes {{formula:707f9314-936f-429e-bf88-0137620cf521}} (polystyrene-water) or {{formula:eff2da9f-4d87-421f-927d-40a03cbf4b9d}} (silica-water). However, a plenty of other materials have also been used to produce Janus particle with different functionalities {{cite:bb753b652b60359690a207fd853ec03edbb01ff9}} and are yet to be tested for their performance in auto-thermophoresis.
It should be noted that, in the previous theoretical treatments of an unconfined self-thermophoresis {{cite:c3ec244d0bc458840e9546da5b1352db1fd1f540}}, {{cite:789b10c47f9c01f1d065dee292e638d9dfb0ac1c}}, the parameter {{formula:c21505b9-a5f4-45dc-a508-79f4082c78b5}} has simply been chosen as 1 considering the same order of magnitudes of the particle and fluid thermal conductivities. Thus, remaining consistent with the practical values and from the theoretical interest of capturing the key physical aspects of the thermal conductivity variation of the particle or fluid, we vary the thermal conductivity ratio {{formula:976030f1-1d94-4be6-85c4-3aa0d43ab58a}} from 0.1 to 10 during the illustration of results.
| r | 7082f26de0eed972ad2261532d79abf4 |
Beyond this first bifurcation, our mass-conserved RD model predicts different dynamic behaviors depending on the regulatory motifs. These include sequential pattern formation, transient pattern formation, pattern scaling, and pattern splitting in growing systems. In line with the well-established literature on domain size in Turing patterns {{cite:1f6c9fc3780b6ef9792ff74bb04168a692221f30}}, our model predicts clock-like sequential pattern formation (Fig. REF -REF ): as the system grows larger, given patterning wavelength is intrinsic to the system, the domain can accommodate multiple structures. An important dynamical consequence of this is temporal ordering: growth elicits consecutive bifurcations, resulting in sequential patterning, shown to be instrumental in neuronal cell (bi)polarity {{cite:55b6b24611343f0dcf94a46256e2b96eae9391ec}}, and joint patterning in digits {{cite:2440efe3649aee8a4f2321acbc9e7a650892dafb}}. Alternatively, growth-induced pool dilution can drive systems back towards an unpolarised state, allowing for transient pattern formation at intermediate size (Fig. REF ). Thus an alteration in growth regulation can yield timer-like dynamics, which we hypothesise may be important in orchestrating switches between asymmetric and symmetric stem cell division modes. A qualitatively different behaviour upon continued growth is scale-invariance, whereby the proportions of the pattern are maintained upon domain elongation. Scale-invariant systems show switch-like dynamics, becoming time-independent after the first bifurcation. We argue that such behaviour could allow patterned tissues to maintain proportions upon proliferation, where self-organisation continually refines boundary position instead of stretching noise in initial specification.
| d | 6d6db321391424354106314d04d68648 |
At the stage of direct coding, the encoding rule of ANN is to convert it into a genotype {{cite:31f043d06b76fa0dcf77fc8cf13ba0f77672ab23}}.
In order to generate large-scale, functional, and complex ANN, some indirect coding {{cite:3cb2d516ea6e510b0f94b372c8da7c59d238507d}}, {{cite:e772cea5dbb1bf5df3123e919386aab6f1065329}} techniques have been proposed.
However, they are not efficient enough for the evolution of local networks, because decreasing the granularity of coordinates leads to a decrease in resolution {{cite:cfcb2537dea2f9bfa514fad93161af59281778d9}}.
The above encoding is a kind of cellular encoding {{cite:15f6f358d12c45a45472d158a13669f4bc213ab3}}, which uses chromosomes or genotypes consisting of trees of node operators to evolve a graph.
| m | 7f1c13ace2f23ee1a90fcabbce41e0c3 |
In comparison, GAT-based recommendation techniques outperform the baselines in terms of both metrics. For these models, we experimented with different numbers of hidden units, attention heads, several dropout values, as well as residual connections. The models were trained using an early stopping strategy after 100 epochs with no change in the loss. Adopting the inductive parameter settings proposed in {{cite:45dada828de5b80d9ba19fedab3b55838a126292}} (i.e. two hidden layers with 256 units each, 4 heads per layer, for a total of 1024 features, followed by a layer with a single attention head which computes 1171 features, no dropout or residual connections) resulted in a lower performance than that of GraphSAGE Classifier (co-authorship graph). However, GraphConfRec's best performance (recall@10 of 0.580 and MAP@10 of 0.336) was obtained with a GAT model with only one hidden layer with 8 units and 8 heads, for a total of 64 features, dropout of 0.5, and residual connections, trained on a directed heterogeneous graph. Increasing or decreasing the number of heads, dropout value, training only on the citations graph or an undirected graph lowered both recall and MAP. The findings show that adding residual connections alleviates the vanishing gradients problem which might have caused the sudden drop in performance for the first configuration of the model. Moreover, a directed graph better encodes the structure of a citation network, which is naturally directed.
| r | dabe707699b81db927a230811724b7f7 |
We also conduct experiments on Waymo, as shown in Tab. REF . Following {{cite:33cc536970573668ef2fca1871f24746cd4db63f}}, we evaluate the vehicle category with IoU criterias of 0.7 and 0.5. In addition, We also adopt the nuScenes metrics to evaluate the results since the IoU-based metrics are too challenging for camera-based methods. Due to a few camera-based works reported results on Waymo, we also use the official codes of DETR3D to perform experiments on Waymo for comparison. We can observe that BEVFormer outperforms DETR3D by Average Precision with Heading information (APH) {{cite:55a64e5eac8f149b05425374f42c4a2a9ad1bb36}} of 6.0% and 2.5% on LEVEL_1 and LEVEL_2 difficulties with IoU criteria of 0.5. On nuScenes metrics, BEVFormer outperforms DETR3D with a margin of 3.2% NDS and 5.2% AP. We also conduct experiments on the front camera to compare BEVFormer with CaDNN {{cite:33cc536970573668ef2fca1871f24746cd4db63f}}, a monocular 3D detection method that reported their results on the Waymo dataset. BEVFormer outperforms CaDNN with APH of 13.3% and 11.2% on LEVEL_1 and LEVEL_2 difficulties with IoU criteria of 0.5.
| r | 4d46bf2d3e882bb4c9e938a02517a00f |
Using the classical Gibbs variational principle {{cite:f0890cc3c9bdbb58840b51b66a0fa395e7d44ced}}, one has
{{formula:3608a423-d3d0-4fe4-b7f0-24ae4cbfcc6b}}
| i | f1ecbc837e3c05c050aa38eaf2409b08 |
Experimental searches for lepton flavor violation in muon decays date back to the late 1940's {{cite:787b44d23974534280108c5ad6d437acd2658d18}}, {{cite:355d16179fe8aaf68e0274cd203d6377cd1725c7}}. The most sensitive searches as of today have set the upper limits {{formula:c42f3dde-9c9e-4787-918f-cae97cdef133}} by the MEG collaboration {{cite:7ecfec5716eee3c86483dc961de978c2427c55fc}} and {{formula:dc69adad-aea7-41e4-986c-725955c7545c}} by the SINDRUM collaboration {{cite:6c88324cdf09fa919cda4466e9f714c937d11857}}. The searches for rare muon decays are complemented by those for other lepton flavor violating processes, such as {{formula:a3ba4c8e-e5ce-49a8-9d9b-628f50bdc13c}} conversion in nuclei {{cite:d72baa3b62d9283bae073825a30343b5e1027328}}, {{cite:8c8d9dbb5b9d725477032c1f902bd938a16a05db}}, {{cite:bacdc619641cea7439934627496abfc8156dcf9c}}, muonium-antimuonium conversion {{cite:3849e24a1464f04869e58189e12c53f7abc0d0b5}}, or in neutral meson decays, such as {{formula:07b63cc0-b21e-4acd-ab45-04c22701515d}} {{cite:27a39a2c3505c9c0ba9aca05ca0c61f9a3c2cead}} or {{formula:eac02e98-37df-4c68-8e57-903cb77bd148}} {{cite:6a4d4ca005121483e380f2324c0b5a4f0330d32b}} among others (see e.g. {{cite:7bc437ebf0f709f9e3768061551ad4e2a5c0dc71}}).
| i | ab24705b4c025099adaf53f935abd429 |
Astrophysical probes. A striking prediction of wave dark matter
is the interference substructures inside a halo. These are order unity
density fluctuations on the scale of the de Broglie wavelength.
The density can even vanish, where
complete destructive interference occurs. These are locations of
vortices—a unique wave phenomenon (Section REF ).
Such interference patterns are distinct from subhalos as a form of halo substructure.
Some observational signatures, for ultra-light masses, have been worked out, such as the
scattering of stars and gravitational lensing
(Section REF ).
Recent measurements of the density power spectrum
along globular cluster tidal streams GD-1 and Palomar 5, from Gaia and
Pan-STARRS data, suggest consistency with
scattering by subhalos in conventional cold dark matter
{{cite:998d842874f1511729b89e05d06254900335a256}}, {{cite:7990c5ec5c43655249528ee6acdcf70c5198dbea}}, {{cite:7a2e1f4779fdec2f29e77f2ce05bdf37e4a462c7}}.
For more background on the streams and the data, see
{{cite:6e0b72c681d1d075bd998e652ac0d3d5da9349e4}}, {{cite:a725de6439a78d8c072125d4c0fe852d65ca4e69}}, {{cite:cc6dd6452d9c9772504b13d78546a66b7ed64366}}, {{cite:acdedd451d986a7f4086941e131e0d3fdb7da9cf}}.
Are the same measurements consistent with
fuzzy dark mater? To answer this question, one
must account for scattering by both the subhalo
contents {{cite:9b25c20dd2f0d0d4dab3571038f08f18880dcf5f}} and the
interference substructures {{cite:e4dad45e112fecd554cff14474a7744c500cb2cb}}. In addition,
it is important to clarify to what extent the tidal stream
density fluctuations can be attributed to the tidal disruption process
itself {{cite:d30d2d4f5e8ac72ec5a945749cc56fa336cef23c}}, {{cite:775b1eefacb7b57dba418b79bb02a506c1f5587f}}. More measurements spanning different
orbital radii would be
helpful in differentiating between models: scattering by interference
substructures is expected to be more important at small radii relative
to scattering by subhalos {{cite:e4dad45e112fecd554cff14474a7744c500cb2cb}}. It is also
worth noting there are
other statistics that might have different sensitivity to the
mass and compactness of subhalos {{cite:c926b314fa68b587bb4aac90c9b9f712de54da7a}}.
Improvement in stellar stream data is expected from further Gaia data
release and the
upcoming Vera Rubin Observatory {{cite:3b1c838f63156605edbb7472c8865474ae787d86}}.
| d | f2e21ada71f67fe560a4bf570c03d181 |
Recently, several works proposed biologically plausible supervised learning algorithms {{cite:5ba8812487abe89789fad2a1c80801b2162848aa}}, {{cite:11a1c3887cade35604cac9c7c8df04660602d70f}}, {{cite:072d5016d543ce8486da8d9458e9719a53445164}}, {{cite:7b867dad3baf819a1a8f0a3ebddd98e308de00e2}}, {{cite:e4227d1ebd42e2dfd8720e4c3012c9e16538e72e}}. Combining these with ICA and unsupervised learning algorithms in general would provide a more comprehensive description of cognitive processes.
| d | 6f5ca85ee6138fb26ec6468255bd3dd1 |
In order to write a spectral approximation which avoid aliasing, it is sufficient that the distribution function {{formula:fb983f79-acf1-4635-ba62-7d172e75a6fb}} is restricted on the cube {{formula:1c5f7703-02e0-4a40-b199-1277f5524777}} with {{formula:9a5371d0-eed7-4600-b95d-203ca79ff87f}} . Successively, one should assume {{formula:af5f8af1-f842-40e0-a244-e2b0c0699be0}} on {{formula:c421e148-7d8b-4f23-8416-954574debf32}} and extend {{formula:697e1912-de40-4998-af8f-09f8aa2c45fc}} to a periodic function on the set {{formula:d3547c80-6970-4c03-a667-7b4febaa9c6e}} . Let observe that the lower bound for {{formula:643b2a8b-65b8-49ac-9f2f-c4433e0bac94}} can be improved. For instance, the choice {{formula:65e5edd1-5cc7-4619-9a8c-faa80779840b}} guarantees the absence of intersection between periods where {{formula:d936facc-325c-4dce-9111-f89b5c3966c7}} is different from zero. However, since in practice the support of {{formula:dac497f2-5f82-47c2-a6ee-64150fa84898}} increases with time, we can just minimize the errors due to aliasing {{cite:191210df848dcd26d36f617371fcf932fb9b732a}} with spectral accuracy.
| m | 8ae14a4c62464a100f1705874089d568 |
Preliminary analysis of the experimental data suggested the coexistence
of negative and positive parity pentaquarks in the same energy region {{cite:b87fdb48b540937c3e4fbba6caab822ee6bb741a}}.
We have studied such possibility within our model.
For this purpose, we have calculated the mass of the lowest positive parity
state, the first orbital angular momentum excitation of the {{formula:6444a729-bf0b-438e-8276-d852dc7b8e8b}} state.
The technical details have been described in Sec. REF .
We chose this state because it is made up of the most strongly correlated structures,
{{formula:65b34beb-f916-48bf-aa90-b96a44da5593}} {{formula:775a32d2-85c5-420e-a606-c8f11cf89d22}} and
{{formula:73dc7e52-b8ba-4b69-80fc-405cafc4cf14}} {{formula:21bb6980-7952-474b-8b9f-4efb20d13de8}} .
Then, it might have a similar mass to negative parity states
made up of spin 1 structures. We have obtained an
energy of 197 MeV above threshold. By using the values given in Eq. (REF )
one obtains a mass of 4518 MeV for two degenerate states with quantum numbers
{{formula:568cb22a-dfb2-4c06-bdc7-bbc6be9d7b31}} and {{formula:4dcfd709-cd3f-4e8e-a279-2a9fe2d5f0a0}} . Therefore, positive parity pentaquark states
would appear above 4.5 GeV, a mass slightly larger than that of the states measured so far.
Similarly, most of the theoretical works prefer to
assign the lowest lying pentaquarks to negative parity states.
Almost degenerate negative and positive parity states
may occur for hidden-flavor pentaquarks that have been detected
in the same channel but that were formed by different pairs
of quarkonium-nucleon states {{cite:3ef6153175550bbceabbb550fa8242e281ba0849}}, one of them radially excited. Thus the negative
parity pentaquark of the {{formula:50f4597b-d143-4725-98d8-c333a11ab3ec}}{{formula:ff6d9083-b10f-4b31-8e39-a873a6d0a28e}} stands for the
radial quantum number of the {{formula:62c1f9ff-3419-46c2-a358-648117e55e19}} system. system would
have a similar mass than the positive parity orbital angular
momentum excited state of the {{formula:0904c06d-f2ce-4e23-a311-e6eea8c8dde1}} system. The assignment
of negative and positive parity states to different parity
Born-Oppenheimer multiplets has already been suggested as a
plausible solution in the triquark-diquark
picture of Ref. {{cite:ffca79c484971c58a31acf1dfd6a347276add767}}. Nevertheless, this issue remains
one of the most challenging problems in the pentaquark phenomenology
that should be first confirmed experimentally.
| r | 3b5e50af5d86a0f6ae4f1e931851c702 |
Recently, In Ref. {{cite:1a6204fecc4bd10ddb791b436652c0986b404c98}}, Jusufi et al. have discussed shadow images under an assumption that a supermassive compact object at the center of our galaxy
is the Bronnikov-Kim wormhole
and, from observational data on the orbit of S2 star {{cite:884ea1a5f124352c138597a88b90715d5c61ace1}},
they have concluded that the parameters of the metric {{formula:e6fd1598-7755-4a56-a72d-3999b870a8cb}} and {{formula:e2bb4d0f-a709-41c4-bb7c-bff26bc041af}} .
Note that a Schwarzschild black hole with and an ADM mass {{formula:e0aee573-d6a2-4a7d-8825-571f39be24f3}} , which matches the observation of orbit of S2 star,
can form an Einstein ring with a diameter {{formula:53073211-21c0-40c4-b5ce-d7d82fd14a1d}} arcsecond and an photon sphere with a diameter {{formula:1a73ea48-6fec-4c99-92a1-829d704f72aa}} {{formula:07ff8530-7d95-4d97-b370-d34661655230}} as
if we set distances {{formula:fbe1219f-b6d0-46f1-a766-a013cf20eb52}} kpc and {{formula:2563cdd7-8904-41e9-89da-a3089e5e26d0}} kpc as shown Appendix B.
On the other hand, the Bronnikov-Kim wormhole with the parameters {{formula:526a6eed-a13d-482c-84f9-afed1c2ead07}} and {{formula:fed0cc3e-8aec-41d6-9ce4-f8aa3f97a90a}}
has {{formula:5f13a0e7-5fdd-41e1-a314-f26b1ad31a36}} arcsecond and {{formula:b025ba1e-f942-4f92-876a-addcd3a293d6}} {{formula:c160b2a5-fe81-4332-b034-00ed6c81cd45}} as as shown Table I.
Therefore, we would distinguish the Schwarzschild black hole with and ADM mass {{formula:0a890949-ee48-4e7a-b333-66683bee915b}}
and the Bronnikov-Kim wormhole with the parameters {{formula:b295c084-4ce1-4330-8687-1e1866120254}} and {{formula:50537728-d42c-4907-92c6-4aadf560db4d}}
at the center of our galaxy
if lensed images under the weak-field approximation and {{formula:acb1ae51-f7fc-4bb5-acb0-7e79d3f975c7}} are observed or if lensed images in the strong deflection limit are observed.
{{table:ceec6d01-8ac0-43e2-951a-5be28139ce32}} | d | a3e7a43e1e63b7b28f7f80b8fa4d20a4 |
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