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For a more direct comparison, we also train a more expressive model than the simple MTL-based model we propose. This architecture is based on bi-directional LSTMs {{cite:314cff9ae5cd404f30a00b978683d6b4a253f099}}. For this model, we input sequences of embedded words (using pre-trained word embeddings) from each query into independent BiLSTM blocks and output a vector representation for each query. We then concatenate the vector representations with the similarity features from our MTL model and feed it into a dense layer and a classification layer. This way we can evaluate the usefulness of the flexible, expressive LSTM network directly (as our MTL model becomes an ablation instance of the full, more complex architecture). We use the same dropout regularization and SGD values as for the MLP. Tuning all parameters on the development data, we do not manage to outperform our proposed model, however. See lines MTL-LSTM-SIM in Table 1 for results.
d
d56d51df774c0fce8ed12271fee25149
In recent studies {{cite:000cbd7adf4ebe6829271d2005324b28af95d3d6}} estimate that SNe Ia with early flux excess, such as SN 2015bq {{cite:b5e77c14b6cac58a992e64eb879dc98703196fd5}}, amount to {{formula:aa5aea3d-b2e8-4494-a398-96fe0cb36366}} of all SNe Ia at redshift of {{formula:65a7e5a2-c0d1-4240-a222-0b88a91d800d}} , and {{cite:ff03355597d772a28891c8fdf327e628036d4db5}} estimate this fraction to be {{formula:3db37b2c-3b59-4fa4-a887-69d159531ca9}} . My conclusion is that the inflated envelope and mass ejection by LTP/VLTP events might at most account for a very small fraction of SNe Ia with early flux excess.
d
eecfd0e8da21a5f7d97665a00ffb7e44
Following details in {{cite:59cbd0d2dc152eb819f46df02e54baf49f6f21c4}}, for simulation of (REF ) we use multi-order NDFp with {{formula:d141c512-3035-4caa-9b16-4c137357d14a}} (and respective {{formula:df1b7d63-ae48-4a29-b192-2631118b2936}} ) and these are {{formula:d14b7cf6-750e-406e-9cf5-40345bbf9abc}} -stable, with respective {{formula:b7a378e6-7608-4f27-94e8-f9af9c41a595}} . For {{formula:08d78d86-4692-4776-a48d-730726594af3}} , NDFp is more accurate than BDFp, however NDFp has slightly smaller stability angle compared BDFp only for {{formula:eaee3659-0c99-454b-8310-57a4441e6aa8}} (with respective {{formula:c730e9b7-ac3c-4107-b13e-b31d25445a2a}} ) and the same stability angle for {{formula:ca8ba843-b4e8-4bfe-8b2d-bb0e9a4c5c66}} .
m
e89f287b374f1e6ebf0fae5ab1146bc0
One advantage of the OutFlip is that the generated OOD samples could be used to train and improve the OOD detection performance of the models other than the reference model without applying additional OutFlip iterations. We trained the BERT-base and BERT-large models {{cite:b01b9b5793b6caeba5abe0af2de96c9855d37b9f}} with the ATIS and SNIPS benchmarks. As the same as previous experiments, the unknown intents are removed during training and integrated back during testing. Besides, we added OOD samples generated using reference models OutFlip{{formula:87c6e39b-df93-4a21-8076-5114f9cdc5de}} and OutFlip{{formula:806ab850-4037-4aa6-925a-29af7657b5d0}} with three OutFlip iterations and {{formula:cd8da57c-dfa7-4a4a-9ecb-7bf17b68817e}} value 0.3, while training the BERT models.
r
1adbb1afbd55f2ec6e67081d38eba1f5
where {{formula:f799d182-6853-4fe9-9572-7c8977303e30}} is another critical exponent associated with the M(H) at {{formula:dff9d954-fa79-4653-a389-9e35be6e7938}} . The {{formula:7125fb67-2af0-4301-84fc-dbc4efb2c5a8}} , {{formula:cdce9e72-7432-42f4-b35e-9e14d2079a23}} and {{formula:0209dce4-412f-4748-9853-17c13c8efd70}} are the critical amplitudes. In the critical region, right values of {{formula:ea668e27-c33c-4bbe-8fb9-21a306828144}} , {{formula:cdcb89f9-4b52-4003-b55b-2bba36e203f6}} , and {{formula:0ac3befb-e1d5-4f1c-ab94-c1a7337d9b82}} should generate a set of parallel straight lines of {{formula:fdf9b621-1822-407c-bbd2-89eba1e2e442}} vs {{formula:52bac4c8-a293-4536-91d1-0af445324b41}} in high field region. The normalized slope {{formula:e3f69aba-ad96-4892-a8c4-95670b6689f4}} with {{formula:3eeb2161-a3e2-43a6-9672-5fbd5d3f1b04}} enables us to identify the most suitable model by comparing {{formula:0bf040e8-4b14-49e1-8184-aa4577599664}} with the ideal value of 1 [Fig. 2(b)]. As we can see, the {{formula:00fba8ab-c3b9-4a4d-ba12-5f06e4d1459a}} of mean-field model is mostly close to 1 below {{formula:098ef2ef-d269-41b0-b93c-2cd944c43a3a}} , and it overlaps with 3D Heisenberg and 3D XY models within experimental errors above {{formula:66fbb741-c8e8-4f3a-b7bc-ea5484fb1ba0}} , but much better than 2D Ising and tricritical mean-field models, indicating a clear 3D critical behavior in 2H-Mn{{formula:1be7a1b2-b1c2-4cb3-94e2-817a5ee1b48f}} TaS{{formula:f84abb0b-9bf6-4537-acab-d95c0f15fa08}} . Figure 2(c) presents the extracted {{formula:43f02d43-cba6-4a44-98b6-2bea6c4715c3}} and {{formula:c1f9d442-8e94-489f-87a0-40e012d14f32}} as a function of temperature by using a rigorous iterative method {{cite:c39268eb670d05c9c7c1e9a66f0f8c3c47aef9a4}}, {{cite:6542295c55b5055a35eb3815d61f8bd8709700f2}}. According to Eqs. (2) and (3), the {{formula:068630f7-42d6-4a82-93cc-2967c45fa05c}} , {{formula:db72190c-cfcd-425f-80c9-18b6a9bc77a4}} , and {{formula:0541fea9-3bee-47ab-a4e0-dd0c37e07cdf}} K, are derived. The {{formula:55a87b29-0b54-406b-8a4f-32304293e6d2}} can be determined directly from the inverse slope of the critical isotherm in log-scale taking into account that {{formula:3ec24417-610d-4894-99d5-9058d22b51b9}} . A linear fit of log{{formula:cbf4e89d-1df0-42b1-80f3-718e6169cd75}} vs log{{formula:a1854d3c-d26e-4e0d-a3ca-3213fd59c6fb}} at {{formula:c02561d6-d992-4b16-a28b-1cc488457fa6}} K results in {{formula:b734fde5-e1ea-45c4-b4e9-666cc192d23a}} = 3.51(1) [inset in Fig. 2(c)], which is very close to the value of 3.41(1) calculated from the Widom scaling relation {{formula:352b6aff-6e8d-4d07-b855-ba424e5a6fa4}} {{cite:f78f28273e7ae6629f0cb14df71796910b78b795}}. In the Kouvel-Fisher relation {{cite:e9dabfe3d05fb01ce9d29c7f5f81eecd3fa9a888}}: {{formula:71f8a1ff-cf51-44fe-b32a-ac3ed3a9c99a}} {{formula:217c886e-af33-42e5-82fb-023ab96d7d04}}
r
e9367217ae51e26576abbee00fa27876
Huang et al. {{cite:ef829f4afa4ebd4844a2c059eeb20a057cb6a1d9}} proposed a complementary approach for proving local robustness to adversarial perturbations, i.e., proving that no adversarial example exists in a neighborhood of a given input. Their approach applies to feed-forward and convolutional neural networks and is not tailored to specific activation functions. It reduces the (infinite) neighborhood of a given input to a finite set of points and checks that all these points lead to the same neural network output. Specifically, the approach proceeds layer by layer through the neural network, propagating constraints that relate representative points between neural network layers. The approach is implemented in an open-source tool named DLV (https://github.com/verideep/dlv), which builds on the SMT solver z3 {{cite:873c6793ede76d5c312172724c4a507557fc0e9c}}. The experimental evaluation on state-of-the-art neural networks trained on the MNIST {{cite:c33b87c009dea829597147aa53cc35e90b016eff}}, CIFAR-10 {{cite:e27801b670284c4249eeec9c8f7335f4a9561436}}, GTSRB {{cite:f4436cee0fc7c9cdf2a83b4da05d068c176e85f5}}, and ImageNet {{cite:caff44d9c5bad5e9d0e4750350bd18a9dfda3507}} datasets shows that adversarial examples can be sometimes found in seconds but the verification has prohibitive complexity for large images.
m
3e15a033bcd63b3f7a78a2e73c2f1d87
The other goal of resurgent Quantum Mechanics is to find exact quantization conditions (EQCs) for spectral problems. The EQC is typically obtained as the condition that a WKB solution decreasing along one ray in the complex plane remains decreasing when it is continued along a different ray. To obtain these conditions, we have to solve the “connection problem" of relating WKB solutions in different regions. The correct solution of the connection problem was found by Voros in {{cite:5588ec6c0a368eb3c15c494309dd7cfcb605a431}}, {{cite:3fbb834af17ac5f00e9d88543fbb16797212bfc3}}, and independently by Silverstone in {{cite:6b05332473036368ea4ac770967f35e713e12873}}. Using the Voros–Silverstone connection formula, one can systematically derive EQCs for many problems in one-dimensional Quantum Mechanics. As emphasized in {{cite:840548c0bcebfb6365d148184b6c2299f6e4a443}}, they involve in principle all the (Borel resummed) Voros multipliers associated to the WKB curve, and they typically have the form of a single functional relation between them: {{formula:fa11c965-a8dd-4212-b531-272b1359dc48}}
m
721fa6d4687b8af2f649f81c748d4250
Artificial Intelligence for Software Engineering (AI4SE) is an emerging direction aiming to leverage AI-based approaches to assist software engineering tasks {{cite:a25e9332b7bcbde2b45b2f90a63794b8c75f7bae}}, {{cite:d83a45ecdc2be639f6738bc22bd9d3238daff933}}. In particular, binary codeIn this paper, we use binary code to refer both to executable binaries and assembly code because they are trivially interchangeable. comprehension is among the most challenging tasks due to the complexity and lack of semantics in binary code {{cite:1f740eee910662446a21b658d7a04d1a3f63a14c}}. Meanwhile, understanding binary code is an essential step in critical tasks such as reverse engineering {{cite:3d17b20029b92a8f9780a045a2e49ca491786b63}}, malware analysis {{cite:09f3130e7ddaa1d5850c2dcdb040bdf0a9dd1aec}}, and compiler optimization {{cite:3478c08f496aed3f03d0fb23bdc5c96f16a9aaed}}. In addition, AI is highly effective in revealing complex patterns from large corpora. For example, AI has been used for code search {{cite:a495f73769686e972590c70781843943305ebe0e}}, malware classification {{cite:1e2520ebdc52884abe45fca86d787cd0a742a43e}}, and code summarization {{cite:cbb15bbc1883255b20875b8efd1624c3131791f8}}. Thus, leveraging AI for binary code comprehension can help address complex problems while paving the way for new research directions in both the SE and AI communities.
i
cfe3341eaff6a76ec1a08e75d06eae09
However, FER is a very challenging task, especially in the wild. This is mainly because of the significant intra-class variances and inter-class similarities among expression categories, which differ from the general image classification task. For example, the same people in the same illumination and pose may have different expressions, while people with different identities, ages, gender, and pose may express the same emotion. In the past few years, with the development of the convolutional neural network, many methods {{cite:6cc0ae2b2ed3fa1581faa80e2635707cfedbf90b}}, {{cite:c231a8fa59731382522ca4137a907247de92e9b0}}, {{cite:e0df3fa5a71917cbd9eac0714880c5e0fd1f5d93}}, {{cite:cd6986aff9a0a5de962fea128ed3c8595cd1f9fd}}, {{cite:cc28fbf751d8c9487ef44fe79cc25ad1144573ac}}, {{cite:dd585f7b9ba7e1583927277f2f4f0332f989f7e5}} have been proposed and greatly improve the performance of FER. {{figure:73712ee5-789d-4a26-9d36-74c3b6c17176}}
i
02592ac3ee65095e635d05389332d5bf
It has been shown that many real complex networks share distinctive characteristics that differ in many ways from random and regular networks {{cite:bb548a50f2eee4b928f7dc12a0432d9efd6d1233}}, {{cite:a972d4d14a189c2f53637a96bdc646791b0248dd}}, {{cite:90ed16b7ebd70ab83f0c9c05244210757f97ca3d}}. Fundamental properties of complex networks such small-world effect and the scale-free degree distribution have attracted much attention recently. These properties have in fact been found in many naturally occurring networks. In Subsections 3.1, 3.2 and 3.3, we generate scale-free networks using the BA model of Barabasi and Albert {{cite:d20cd0714840a467bf81aa7cddba6684fbc34650}}, small-world networks using the NW model of Newman and Watts {{cite:4e8146b23ae2745f23e37ab10973de2a97ee3789}}, then random networks using the ER model of Erdös and Rényi {{cite:932180ade0d2cde805a9fb363833da771b36ece8}} respectively. We then apply our modified fixed-size box counting algorithm to analyze the multifractal behavior of these networks.
r
ecc9696813c29ba3e3894f12d413d62f
We compare three different representation learning methods: random projection (RP), principal component analysis (PCA) and variational autoencoder (VAE) {{cite:3bf89c7c9ff57c7e78f9d0b1f0eaa0623f5a2002}}. VAE was implemented with PyTorch {{cite:8dab0eff3301604b1ebc91a79ee3789977424393}} and uses 1–3 hidden layers with ReLU activation functions for both the encoder and the decoder. The learning phase uses the Adam optimiser {{cite:d64a4ae15faa1b52b65613e7bd33972f9138d15e}} and is given one hour of GPU time with early stopping. The size of the representation (for RP, PCA and VAE) and other hyperparameters for VAE (the number of layers, layer sizes, learning rate) are optimised with GPyOpt {{cite:a7f5d531c8e6147fbe4a03fdd989ebecf00554f8}}. We also experimented with optimising a much larger set of hyperparameters, 12 in total, but GPyOpt had difficulties in obtaining similar levels of performance.
m
2aff8717fb93d33d7a67d13b3799d9d8
The control of spontaneous emission in the multi-atom (or qubit) system that interact with a quantized radiation field in restricted geometries has received a great deal of attention in recent years (see review paper {{cite:113dafd85dbb2420802d076bd74efae0b62b30e0}} and references therein). This can be achieved in various physical set-ups, for example, by putting two-level atoms in an optical cavity {{cite:94ed84154ecc9e76e7929920044db9a1ef0de499}}, by embedding them in a nanophotonic waveguide {{cite:77dbd1ca23152f776ed91be34e918416326afcec}} or by coupling superconducting qubits to a transmission line resonator {{cite:b1843205a3a7eb7ab6cab8e1c9c214e66f1986cf}}, {{cite:84e9840d18a75a2b3744aee724aea2dd5467a1e5}}, {{cite:6494fca2f11d69a897350be0c348b31de0aadb17}}. Due to spatial confinements, these set-ups allow one to achieve an almost ideal mode matching which results in a strong coupling {{cite:3a09f967a1885478546df488e0b72ec8793c9cec}} and even ultrastrong coupling regimes when the interaction strength overwhelms relaxation rates {{cite:84af78c048ff613a82f56841a5cb4e37a2c33269}}. These experimental conditions are very challenging to obtain for regular atoms in optical domain.
i
66b1e53f89e573467278c9f225eb3b03
Comparison with the pseudo-labeled baseline. We apply pseudo-labeled (PL) method from {{cite:d11a30c01474e539e44a0f9ec098bce58b248851}} on our datasets (Table REF ). We use the same model HRNet-32 as in all our experiments for a fair comparison. Overall, the pseudo-labeled baseline is inferior to our method on all datasets used in our study. We explain it by the fact that {{cite:d11a30c01474e539e44a0f9ec098bce58b248851}} trained on datasets that are by order of magnitude larger than our data so models pretrained on the labeled subset are already good enough to generate reliable pseudo-labels.
r
288dec09726b204cba4e6c640df5d69e
The ATLAS and CMS experiments at the LHC have measured VBS processes as a signal, embedded in partonic processes of the type {{formula:b649cc14-f38f-4cc3-b05b-88c32cf64027}} , where {{formula:2e0df759-08a7-4cc3-a611-f6dea5cc09fc}} is any light quark. Numerical results have been presented in the form of limits on parameters within the SM effective theory (SMEFT) {{cite:ce5021b6e62773a5d849b4f2bf05aab4673c2d20}}, {{cite:8e698d776bbd1d5b593403cfe62d986047d4de44}}, {{cite:576446b69ffa6ee28b2e9fa7d136b391b373d071}}, {{cite:a8759b2731cc116b24cc4ef4882b76e2f05c7909}}. The usual application of the SMEFT truncates the power expansion of the Lagrangian at the level of dimension-six operators. A useful parameterization of VBS processes requires dimension-eight effective operators, the second order of the low-energy expansion beyond the SM.
i
be34c87f888975a3d2da586782d42f79
The superconducting diode effect can thus only be obtained if both time reversal symmetry and inversion symmetry are broken {{cite:5e314e4ea326a055c2c344fdaad4265105999125}}, {{cite:1696592d491452ae4d4b76d5205fae394ab1d01e}}. Time reversal symmetry breaking can be achieved by a magnetic field. On the other hand inversion symmetry can be broken intrinsically, such as in topological insulators {{cite:960f4630145a35d659bb5a46d6e45367368efb40}}, {{cite:e3474ee8f253a36ef586c63a3ff0d0d88f39132f}}, {{cite:6a48fa202ff33e6f4321b3f02ee57ba8c2fc9d98}} or superconductors with Rashba spin orbit coupling {{cite:11fd2a684a9a6eac816c53c1bc5d2eba8d063fde}}, {{cite:e584eafcc211e3aaf5c17f5a71c6ddad5b955988}}, {{cite:3e9373a46be56fe82ef727220a5be090ba29ed1f}}, {{cite:d4334570a5228aecb47e63f2fcf73d93954cc325}}, {{cite:9d78c01d95b4a9ca55c902343dde743ca9ce6d2a}}, {{cite:8f440e8f8678e40fbbd703e082bd09e45e45c19a}}, {{cite:a61fc23d1e7e91608b8ade2cb3e7b51d93387ca6}}, {{cite:769b6cfd7bf93f3763f2ddfbc9df2c9954c5b2e1}}. Inversion symmetry can also be broken by using an asymmetric junction geometry {{cite:2d342af35c17cd9797d8be9195d9fdb83716902a}} or asymmetry of the device originated in the fabrication {{cite:54b1c499249a7268c87234c9c28f9e708dcfceda}}.
i
6cb1a5f3d9b15258c05f1b2fc4bb4176
We also study the impact of the shadow dataset distribution on our BadEncoder. In particular, we consider three cases. In the first case, the shadow dataset is a subset of the pre-training dataset. In particular, we randomly sample {{formula:b5e091a6-a325-4b33-8faa-9834a6e07ebf}} images from the pre-training dataset CIFAR10 as the shadow dataset. In the second case, the shadow dataset has the same distribution as the pre-training dataset but does not overlap with it. In particular, we use the testing {{formula:ffdaedb3-84df-49ce-8bfd-644e066c85b2}} images of CIFAR10, which were not used to pre-train the image encoder, as the shadow dataset. In the third case, the shadow dataset has a different distribution with the pre-training dataset. Specifically, we randomly sample 10,000 images from the Food101 dataset {{cite:e7e9dad6f25bbebb502e47ff3660b481de99aef8}} which contains images of food and has a different distribution with CIFAR10. Table REF shows our experimental results. Our results show that our BadEncoder achieves high attack success rates and preserves accuracy of the downstream classifiers in all the three cases, though the attack success rates are lower in the third case when the shadow dataset has a different distribution with the pre-training dataset. Our results indicate that our shadow dataset does not need to be from the pre-training dataset nor follow its distribution. {{figure:a39fffad-d777-43cc-8499-317f4eae7683}}{{table:12b6c00b-612e-433c-ac47-d459c6224bdd}}
r
e3cfaeda442577be9122ee85fb524c94
where {{formula:c3d29ba5-20e8-4a61-8916-cf409affd144}} are the energy eigenstates of the left and right theories (for example two CFTs), respectively, with corresponding times {{formula:6b99d923-9c59-4a60-b35b-869b343c02bd}} . Moreover, tracing out either copy leads to a thermal state at the inverse temperature {{formula:a44a7123-6d78-492b-97f4-79dddcf0af7e}} for the other, {{formula:901d113a-4793-45d2-ab2c-1acda6615b86}} , {{formula:6e6ad7b9-6f19-43b4-819f-6795d23283e5}} and {{formula:56ed3a90-fd81-44b2-a9b0-96790dc238d5}} denotes the partition function. According to (REF ) and in the spirit of {{cite:9b12e95cdb50aca248353364e510b5545a2573e5}}, our setup to consider the dynamics of LN and OEE will be in a rather unusual quantum quench scenario{{cite:d9ef55a776c86faa289f22f54db813e72dac3664}} in which two decoupled subsystems are entangled via their initial conditions. Moreover, to have a mixed state, we will consider two spatial non-complementary regions. Since the underlying TFD state is a Gaussian state, we can use the covariance matrix approach to calculate LN and OEE. We will observe that their behaviors under the time evolution can be summarized as a linear growth followed by saturation which is similar to the expectations from the quasi-particle picture. Also, we will observe the oscillatory behavior due to the finite size effect as well as a logarithmic contribution in the intermediate regime due to the existence of the zero-mode.
i
67eebf5e00f70c4598c31d9bf9a1a522
Using Lemma REF and {{cite:a98fbaf974ed41bf45ea118d93413c1fff9dda68}}, {{formula:cfb2baf3-f79f-4e54-aa08-a67d50a604c1}} can be bounded as follows. {{formula:a75d85d4-859f-4687-8215-07ccfab0c275}}
m
30cdfbeb3bd7aa399e2afd84409dabf1
Typically, {{formula:86c8cb58-d11b-40fb-b6f4-41bf055dc265}} is related to the layer's input {{formula:94f02e79-a66a-49d8-af02-d946270256b2}} , and {{formula:cccaaef2-e1f0-479c-bf47-5742d2d94f9a}} to its weights {{formula:b35e2932-75ba-4743-8c12-70b5cc9380d0}} . LRP {{cite:2a01aee43d735fdb9dbde80bba7238e011cc4c49}} can be written in this notation by setting {{formula:92d5dfb3-bf41-465b-91f2-1e2370de0b9b}} and {{formula:cec6f92a-1f6e-4a11-9bcc-843472d0cd84}} , where {{formula:469c8e63-cc9e-41ed-bbb1-16ce0aa7101a}} for a tensor {{formula:ae3c42af-cdb5-4c43-9f70-05b292729280}} . Note that Def. REF satisfies the conservation rule: {{formula:99a29573-8591-494a-b03f-f1ac3efb6cbd}}
m
9f0e44b3e39b4be88187ba1d46b93e88
We employ two simple but important experimental methodologies which enable a more accurate assessment of performance in real-world scenarios. First, we provide timing results in the ONNX Runtime inference engine {{cite:fef8239b3d0ebae986fc96d05b1d84b906d58be2}}. Timing results are crucial because of the strict real-time requirements for background noise suppression. It is not necessary that reduced parameter counts give a faster inference time. For example, we measured no meaningful speedup for sparse pruned models in ONNX Runtime (see Section REF ). Benchmark results are conducted on an Intel Core i7-10610U CPU. Second, the model quality is evaluated using the INTERSPEECH 2021 and ICASSP 2021 DNS Challenge test set {{cite:35f1870e7849c8d0c90d7aa8985c8aaa5693356d}}, {{cite:39049e6d11774afe9b8db2f865a56bd8cb8db38e}}. We use a new non-intrusive objective speech quality metric called DNSMOS P.835 {{cite:0c5e3ce155bf0ce7d83762f133e96f75638037cb}} employing the ITU-T P.835 {{cite:46272c01ef24f86e03a37ebf48cb53cf04493354}} standard which provides separate scores for speech (SIG), background (BAK), and overall (OVLR) quality. DNSMOS P.835 has a Pearson Correlation Coefficient of 0.94 for speech, 0.98 for background, and 0.98 for overall compared to subjective quality, which gives sufficient accuracy to do fast pruning. {{figure:7f686a3c-d996-4687-ab91-0f539bc24571}}
m
e5494b6ed5af6fa88a747a9a11788be4
Therefore, evaluating recommender systems in offline fashion without running A/B tests is of significant importance. These offline approaches avoid serving experimental recommenders to users, and instead evaluates them using old online data, where users were served recommendations from a different system. Metrics such as Root Mean Squared Error {{cite:8fa64a0d9b55d455617002458b4ce74d3cab2112}} Mean Average Precision, Normalized Discounted Cumulative Gain, Mean Reciprocal Rank and Hit Rate have been used repeatedly for offline evaluation.
i
d4078fe26d923ccffc84ca664af423a3
1. View Selection: The first part of our framework aims to identify the standard 2D PC views used for the analysis of cardiac function and haemodynamics from a CMR acquisition. The manually classified data were divided as follows: 80% was used for training, 10% was used for validation, and 10% for testing. The training, validation and test data cohorts had a mutually exclusive subject pool, i.e. acquisitions from the same subject could only be used in one of the three cohorts. Prior to training, all images were cropped to a standard size of 192x192 pixels. We used the AlexNet network {{cite:9f2afe79ab4ce30723afe472ce80c74ce7a41972}} to classify between the ascending aorta, pulmonary trunk and other views. The network was trained with batch size 16 and learning rate 0.001 with stochastic gradient descent for 200 epochs with cross entropy loss to classify images into the three classes described. For the training data, data augmentation was performed on-the-fly using random translations (±30 pixels), rotations (±90°), flips (50% probability) and scaling (up to 20%) for each mini-batch of images before feeding them to the network. The probability of augmentation for each of the parameters was 50%.
m
66cd4bc182b861b73840632161527195
Some of those ideas can be extended to nonlinear problems {{cite:3fce9163181a8c8837bce15e8942ba9a1881f28b}}, {{cite:15296c8feec2785fbe38be1ec8d257c79e561ef9}}, {{cite:c27e2e2a6ccfcd655018e8027ab00caa60cf5c50}}, {{cite:77ad171791d05675fb8360dc323763ebefbc0266}}, {{cite:422fc88304738ace0b946e0f61657c1fb07e308a}}. These approaches approximate the solution of nonlinear PDEs on a coarse grid (see Figure REF for an illustration of coarse and fine grids) by using subgrid models. Some common ingredients in these methods are that local solutions are pre-computed over coarse patches, and coarse solves are performed over the coarse space spanned by those bases. The extensions of these methods to nonlinear problems use nonlinear local problems. For example, for the Leray-Lions flux {{formula:7b24a407-913a-48f4-94bd-fba20c87f315}} , one can use a local problem to compute a basis {{formula:dc45f739-f119-4b57-9583-c39e8ccc1a32}} in each coarse cell, such that {{formula:2147355c-9c3e-44c1-a24d-84ce48f19532}} , with boundary conditions {{formula:209fc8ec-11ce-411e-a9d9-ce34eef6eea1}} . The homogenized fluxes are computed by averaging the flux {{formula:8d4d4c1f-f9a3-40a5-a194-fff21e3dc97f}} . These approaches follow homogenization theory ({{cite:87ba20f373f1a2811f9c2162231fff039feb9b23}}, {{cite:0b6b38e6d4e9338f92bdf7deaa2a26fd7c2471f0}}, {{cite:b756b2034485737944e2e1b4179d58e60475dd76}}, {{cite:9c75ca68ca375e199bd77edd15e5eb5b1354974f}}, {{cite:9f496a2f0d596efdcf957c9c7249ad9bf87e4fbc}}, {{cite:1913be380723ae385b1bbd4a55b2a6f3ac06ab75}}, {{cite:ced3b9421079fbfbbf1562fa82aec29d4aeeb25d}}, {{cite:6dea34d309c0896118fa7e977fc3e6c353453b28}}, see also {{cite:eb84fe42d411be3e8a171dee75e8630ef68ecf66}}, {{cite:b756b2034485737944e2e1b4179d58e60475dd76}}, {{cite:30e73c1b3068e3652891d8c670d03b164a7833af}} and, the references therein, for numerical homogenization. Also, Desbrun et. al. have applied ideas from linear numerical homogenization to coarse graining and model reduction of heterogeneous and nonlinear elasticity problems, as well as Navier-Stokes equations {{cite:81a8f8f82aa86b9aab6efc773ee44e65bdfa35d7}}, {{cite:99ecbb8db0b3dd7518c3f69abfcd1bc9a9a92d97}}, {{cite:207ff7d7df4ee73a33ae70b377c0562f460d871d}}, {{cite:96dedd7845b377093ecf4eac3dd4a745abae6a58}}.
i
63ec922a8f8915fa14504764a0b021e6
where {{formula:ceaf93f3-5812-4f19-b0d6-abda29990fc0}} is the Boltzmann constant, {{formula:9415c920-75ce-428e-a8df-c8eb12ba5eb7}} is the effective exchange interaction between the Gd{{formula:478d8718-74ec-420b-8eb9-128e57cd08b1}} local moments and the carriers for the momentum transfer {{formula:25058fe0-a9f4-44b6-b4b9-ebac772fa55b}} = 0, and {{formula:daa36017-f8b6-4380-875b-89d4401b70c2}} is the average of the exchange interaction with momentum transfer {{formula:514928b5-e8c1-4cfb-a6d4-a89f5c0fc33f}} at the residual Fermi surface {{cite:0c93d00c3b39abf36f42de840a729796bb9393ce}}, {{cite:63d2f2dc2aca4a27d727171b911ff0d9cd2f0ebc}}, {{cite:1d9aedda8b2b07789e0fb02be376a1038a275676}}. Any possible relevant {{formula:7b42bb9f-ce28-4b18-a31d-afebb7a50687}} correlations are taken into account in the Stoner enhancement factor {{formula:f0e63c18-026a-4290-a281-dbeb85a43ff4}} {{cite:3f73e3271d06512dab73dc1d76a4587cef24ab6d}}, {{cite:1db0e5b6fd33c8c1694d3413cfff5cb3f574ed33}} and in the Korringa exchange factor {{formula:5caf83e5-31ea-495a-be79-990299206ca8}} {{cite:8b9af3d35ba9cf54f6d993f7911daedf670ba1bb}}, {{cite:30472a7e7ae8c3151ab88d3a689c0651b405ab82}}. As already shown, the {{formula:4f4a4069-03fe-4791-ba43-58e7e6a76dca}} correlations in the bulk does not seem to play an important role, therefore we assume {{formula:5b3cf842-584b-4e24-b1be-f1b4769fe972}} = 0 and {{formula:9596dfc1-ece3-472b-85da-735f2bea0291}} = 1. The estimated exchange interactions for each Gd{{formula:2d70b6a0-67b4-4443-8212-fc951f185bd3}} concentration and applied magnetic field are summarized in Table REF . Although we should underestimate {{formula:d3d5ae0d-6202-4baa-a499-b43686a5d35c}} and {{formula:58b1be37-fb91-41b9-a97c-7f0e3eb7b5b7}} due to remaining CEF effects and a local reduction of the DOS, the trend observed in our analysis qualitatively trustworthy.
r
d1f96b23819b9b49b6428b64847f432c
To reduce the inconsistency between the masked pretraining and the video prediction task and to speed up inference, we take inspiration from non-autoregressive, iterative decoding methods in generative algorithms from other domains {{cite:c957e099f0829a35edb04c528a9cc5ec92b1082a}}, {{cite:4ebab5d2ad47b7c22aeb9c17483ccd5323821fff}}, {{cite:4a2c1d9e87a4d266129f1d03751fb4e046a56335}}, {{cite:92fd364cbc90cc42beef0e190edf1bde6e3436c5}}. We propose a novel iterative decoding scheme for videos based on a mask scheduling function that specifies, during inference, the number of tokens to be decoded and kept at each iteration. A few initial tokens are predicted over multiple initial iterations, and then the majority of the remaining tokens can be predicted rapidly over the final few iterations. This brings us closer to the ultimate video prediction task, where only the first frame is known and all tokens for other frames must be inferred. Our proposed prediction procedure provides fast predictions without temporally increasing quality degradation due to its iterative non-autoregressive nature. To further close the training-test gap, during training we mask a variable percentage of tokens, instead of using a fixed masking ratio. This simulates the different masking ratios MaskViT will encounter during iterative decoding in the actual video prediction task.
i
f03feff56ce880a35bd5a02d35a93a36
In this paper, the problem of TL is tackled to with novel perspective. In the proposed method, samples are cast into a new domain via the process of Gibbs sampling while DA methods usually align features extracted across domains using a deterministic mopping, usually an ANN{{cite:4df044559028576b4135cf2dbf6a100ca0360df0}}, {{cite:8f4e4ccb670706bf1123d477968e397b0e8586e7}}, {{cite:a1ea2bfd0c2309d38e61e99e94207c3eef39079f}}, {{cite:3f5da3cea058c6f1e365f8f38d4a1b6687c56645}}. Furthermore, almost all DA methods require unlabeled target data for training domain adaptive models. Nevertheless, the proposed methods needs no target data during training of the models and instead it process target data during the prediction stage which enables the method to be employed in more challenging problems.
m
f73359b2c717d963e2e0e9e8f814ea0c
In this section, we quantitatively investigate how our M6-Fashion model compares to existing models for unconditional generative image synthesis. Particularly, in Table REF , we assess the performance of our model in terms of FID and compare to a variety of representative models for different generative paradigms (VAEs {{cite:c886640e905bff44aafd045258ff17562cf238a8}}, GANs {{cite:1f4f3f2c1752b393da539591bc56632c321e51d0}}, {{cite:18a68c05122b2a889babdcfafcb2b24077eff629}}, Flows {{cite:cc8f68a55ddb58b80366222c47c1615f80189c89}}, AR {{cite:ccf69c075f71fc89432617cf4008a3ec26b6ba0e}}). Although some highly-customized GAN model reports a slightly better FID scores, our approach provides a unified model that works well across a variety of tasks while retaining the ability to accommodate any conditional information.
m
3b83b8fe7730402f00aa96e8ad2f177c
It is also important to point out one caveat of our simplification. Naively, the double-scaled matrix model dual to JT gravity shares the same non-perturbative instability as the Airy model we considered; for instance, see {{cite:2bf07c50bdecc6b0fe5cc67b3dbd0d4b9c28bc27}}, {{cite:f12e8aab1e14f44ee498a38089e698fbb4788d29}}. However, there have been studies on how to improve the non-perturbative behavior of JT gravity and remove this undesired feature {{cite:f12e8aab1e14f44ee498a38089e698fbb4788d29}}. Therefore, it would be interesting to extend our work to JT gravity at general temperatures with the improved non-perturbative behavior.
r
a877b01fa68b59f109e12b0cd63b6623
Finally, we estimate the average fidelity of {{formula:6f6bc2dc-763b-424a-bb98-2e6dd5ed8853}} rounds of a large-scale quantum circuit.The Haar-averaged fidelity can be related to the entanglement fidelity {{formula:87d6cbc5-e6f9-408c-941e-068d68aefc57}} , which has been proposed as a means of characterizing the noise strength in a physical quantum channel {{formula:f0b9afb0-d2d1-4a6b-99b4-d05a82e4bda0}} {{cite:47b0cea97259d4a6c7fb95ead9901919dc68fe11}}, {{cite:dc907afd91bf3fd9b68be17f4bff6023222a36b5}}. Therefore, we obtain {{formula:37aa3428-2b7a-470f-bc25-3e8c51c64e70}}
d
14d001b0104dd29557fd8c0e5a9f39db
with an uncertainty of {{formula:d495ff24-ddcc-48b8-a431-3bdf54cda2f1}}  ppm {{cite:a975d3c9c0aa1bd8bdaa5d24fe906620ee6d48bd}}. The current theoretical estimate of {{formula:58a94330-a99a-4b10-a5a6-97f92393ad72}} within the SM has also reached a comparable precision of {{formula:1af716b4-8ccf-4fc7-9eb3-25546dd499ee}}  ppm, and is shown to be {{cite:f4c5cf8786e22fd04c6798653083ef795eb6f7eb}}: {{formula:3d440708-7663-48e4-b74c-59eb0439b078}}
i
260a3c5f2d14661b2430de030cff27ca
Likelihood Lower Bound - Since the data expectation in Eq. (REF ) is no longer in closed form for the DBM, data-dependent statistics must be approximated with a sampling technique over the conditional distribution, {{formula:528553a2-a147-43f9-a4a3-cc1d73eeab7e}} , where {{formula:1549b3c1-3a70-4f1c-b24d-07f5475b6350}} . In practice, a variational lower bound to the log-likelihood is maximized instead, which is tractable and is found to work well (as in the model term) {{cite:93beb29b085d7cf16a1908a87269d9437f130eec}}, {{cite:0a12a0594faa4b5c858945359185cb1ba1b7697f}}, {{cite:53e036c68a01f136755e8252e9b8bbae48c836af}}.
m
06554d97e912bfdca8d755fd9a497758
In all of our experiments, we tune the baseline, DDPG, and report its best performance. For exploration, we use parameter-space noise {{cite:fd818edde9db42f75d927751c9c39e39a8540182}}. Every experiment and each setting uses the same adaptive parameter-space noise standard deviation target, so exploration is controlled to be the same in all trials. We then add the MVE extension (we do not tune DDPG parameters to MVE performance). To evaluate the effect of the TD-{{formula:5c0ce6f1-ea17-477e-b298-5aacd77a292a}} , we evaluate against the naive approach of using {{formula:9c19667a-b379-4cf4-bdf2-17e4b76da67d}} -step MVE {{formula:899a70a3-bafb-4619-9bc8-3a3e3cddc491}} estimates for Bellman error on states sampled from {{formula:50e918ca-851b-474c-88dc-dd3369c6bb7f}} . This is equivalent to using only the first term for {{formula:cb0a8558-a0e1-46c0-8d9c-d8caf879d049}} in the sum of Line REF of Alg. REF , i.e., updating critic parameters {{formula:6c349506-c950-4641-a3e9-a3013d6c021c}} with the gradient {{formula:7b35da9d-2d0d-462b-9f41-3fab12c8acd5}} . Without the TD-{{formula:ef2356ab-1008-4303-bd9c-8497a92d3f45}} trick the model is still used to simulate to depth {{formula:128318ec-6cdc-4a9f-bfd6-d63bd4b2cedc}} , but the opportunity to learn on a distribution of additional support is neglected.
r
ab3a3b888cd5eb6bd272b4dda00b7487
Interpretability of deep neural networks has recently become a focus point in the deep learning community. The furthest progress has been made for classification networks operating on single images {{cite:a527f1fdfd2566a09e1e834ac014013d655261ae}}, {{cite:18a71b7d9463a7fc26b360cd3ad3003253dcb51b}}, {{cite:ba7f4f4de3df74722c9d7c181d7aff91d9f9646e}}, {{cite:903f8db23cd82f411f0d46a90e178333c98ae11d}}. Interpretability methods can be divided into two categories: network-centric and data-centric. Network-centric methods focus on specific units in the model, for example Activity Maximization {{cite:0db44c01327318d3591a25fb4560d53ce0d2f82e}}. This method aims to find what types of inputs would maximize the activation of a specific unit by using gradient ascent w.r.t. the general input space, not necessarily the current input. In this sense, it is more appropriate for examining network architectures and discerning the optimal parts in the entirety of the input space, as opposed to inspecting the actual inputs for a set architecture, which is our goal. Data-centric methods on the other hand, focus on examining or manipulating input data to determine which patterns the model has learned for the task. Some examples of these methods are Layer-wise Relevance Propagation {{cite:ba7f4f4de3df74722c9d7c181d7aff91d9f9646e}}, Excitation Backprop {{cite:b905636822b7b8a1ea3620f957f23aaebeefe846}}, and Grad-CAM {{cite:019e6fe0c14528c37d8633062a755d73cb0fcbfa}}. The first two utilize activations and weights which are normalized and backpropagated, while Grad-CAM calculates saliency maps using activations and gradients. A side-effect of how the first two methods operate is that they produce more fine-grained answers, in contrast to Grad-CAM which is more appropriate for detecting regions of interest in the input space. Because we are interested in considering the whole sequence of the feature (a row in the image), this is beneficial for the images we construct. In addition, in a work evaluating the scope and quality of explanation methods {{cite:f10912a26c403964fbfd7d6abbb4954a0ef92b50}}, Grad-CAM was found to be one of the few methods that take into account both the input data and the model parameters and do not operate similarly to an edge detector.
m
08242915a69df1929ea925eb1b968c96
We describe two closely related applications of a new rich class of strong homotopy algebras: (i) integrable models {{cite:bddef0d2d3c00b7d628902153bb042455a5ec3b0}} and (ii) three-dimensional bosonization duality {{cite:a4b1c32d52d04419c272169f4ec4ddeca061b37a}}, {{cite:d0a6291eaa043af272f8ac605d513052bb1464e7}}. A cornerstone of these applications is a new approach to constructing strong homotopy algebras {{cite:a4b1c32d52d04419c272169f4ec4ddeca061b37a}}, {{cite:dafe29efd77502e14a2486747bcf055d9f3e0b1d}} via intrinsic deformations. On the physics side, the {{formula:2d1b314f-4ec5-4251-b4d1-1f1461b05e34}} -bosonization duality conjecture {{cite:11d8859f4a8c2f6022bab09061b385f638e6682c}}, {{cite:ee77fcb701dac4b5db73df7a38864426dd25b8f6}}, {{cite:bcf27bc4fc69e69fadf2f4f6411d8b2ab34d7c95}}, {{cite:7edf164228fee28856474080dfcdcec9dca0534a}}, {{cite:6b314baaeddd78e368693b8e9ec6d357d798f1ee}}, {{cite:3d6efba7fabff9e84e64b40a3b2cd1d8d03a5585}} takes place in (Chern–Simons) vector models that describe various second-order phase transitions in {{formula:47dfb542-607d-4211-b02b-1ade65d11120}} , i.e., in the `real physical world'. The class of {{formula:b5c4d5ec-75bf-40b7-a803-f9f068971566}} -algebras, to be described below, allows one to give rigorous mathematical grounds to the idea of the slightly-broken higher spin symmetry {{cite:dafe29efd77502e14a2486747bcf055d9f3e0b1d}}, {{cite:758f900af4678f7130baa0984e340dff3f9cba83}}. Correlation functions are then invariants of this symmetry. At least in the large-{{formula:bd7333c1-8d7b-4534-b9e3-9ba1dabd05cf}} limit the bosonization duality can be reduced to the proof of uniqueness of these invariants.
i
d375fdc5c3fa3de9797cf82aa9c1ab2d
From the perspective of numerical practice, the execution of this work consists of three main steps: (1) MHD turbulence simulations to generate data cubes including the information of both magnetic fields and velocities; (2) implementation of wavelet transformation to decompose MHD modes into Alfvén, slow and fast modes, and (3) test particle simulations to study the properties of particle acceleration. The cost of simulation time restricts us to use a numerical resolution of 512 along each dimension of coordinates. Especially in the process of test particle simulation, the time-consuming is strongly dependent on the number of injected particles and the terminal time of simulation evolution. The 10,000 test particles we injected have ensured the reliability of the numerical results, which is an order of magnitude higher than the earlier simulation of 1,000 particles ({{cite:51655708dec099cca4d3921af73056d3eb1fa4ac}}). As shown in Figure REF , the inertial range of the MHD turbulence cascade revealed from the particle's maximum acceleration rate is narrower than that displayed by the underlying magnetic field (or velocity). Nevertheless, the execution of higher numerical simulations is necessary to confirm our research results.
d
3a09980efd9c45e1d7e3005858385ed6
In this paper we report the results of the first joint observation of a new detector in the global network: KAGRA. The KAGRA detector {{cite:04a1c3240a3d86e97e71ebae003f6a29be046f70}} took scientific data from April 7 through April 20, 2020, at the end of the third observing run (O3) of the LIGO–Virgo–GEO network. The LIGO and Virgo detectors were forced to terminate operations prematurely due to the COVID-19 pandemic, but the GEO 600 (abbreviated in this paper as GEO) detector continued operations and collected data jointly with KAGRA over this period. We present the results of analyses of this joint GEO–KAGRA run data for transient GW signals. We perform four of the searches that are standard for LIGO–Virgo observing runs. Two of these scan all of the data for signals arriving from any direction at any time: a search for BNS coalescences {{cite:ccf5db39d005c7615e6bbe60335dbe7b4ea599e3}}, {{cite:11bea4d5b7143468d7dabbaa9749ee560c69ae40}}, {{cite:c0db48621e425133cd40c253b4a6c74c52cbafe1}}, {{cite:15c7b5a655d22e1247368df82b7224ec90a013ec}}, and a search for generic unmodeled short transients (bursts) {{cite:cdc3f46990c0d1327ce5d5a806a18f6cf3b11224}}, {{cite:abab3bbeccb6166c1d56c0e66249eddcb4d29fe3}}, {{cite:85a47f08d2b409a3f3372392887a135e14d85ea6}}. The other two analyses are dedicated searches for binary coalescence signals and GW bursts associated with GRB events observed during the joint run {{cite:595672c07087720a144c4c7f70f23a7204a1baee}}, {{cite:29c085d92981bed99f84ec028cf1e05a00c8222b}}, {{cite:1570edb9d3e886e33af32b036f8ebec2a91fa700}}, {{cite:abf1df8ed87a68a1e77e33c080081973883caa4a}}. No significant candidate GW events are identified, which is expected given the sensitivity of KAGRA at this early stage in its commissioning. However, the sensitivity of KAGRA is expected to improve by more than two orders of magnitude over the coming years as its design sensitivity is achieved {{cite:724edf1ffd8fa0e44fe82727daf89332dd30d855}}. These analyses demonstrate the value KAGRA will have as a member of the global network as its sensitivity increases.
i
bf942e8281fb389035de73539fcf903e
We compare our method with the recent baseline: Next {{cite:a1fc82a5e6b575238b257d816edbca8dc9b3afed}} is an end-to-end model utilizing rich visual features about the human behavioral information and interaction with their surroundings to predict human actions, which is similar with our work in this paper. This method uses LSTMs to extract features, and directly splits different types of features into a long vector. And based on the conbined feature, they can get the prediction results.
r
11f9f406278091123bdbb1414d0d9dc4
Let us compare our results with the {{formula:7c4b9523-3479-4bef-9dac-a457b6eb85b1}} measurements available in the literature. Our limit is a factor of ten worse than the Planck 2018 constraint, {{formula:54e035fb-9bfd-44e4-bdb7-449de65475ab}} (68% CL) {{cite:76ae855d3f729657e6c77a5c37f504d2a43125e0}}. As we stressed before, our limit is better than the one obtained from BOSS DR9 {{cite:b8db8f858dc8d3d5649c951205bfee6e7046f1c8}}, which is equivalent to {{formula:12e59dc4-c4a1-4970-9cbd-f5a9bc9ae169}} . The main reasons for this improvement are new data, the complete theory model for the power spectrum, more accurate priors for LPNG bias parameters, and the large-scale galaxy bispectrum, which is quite sensitive to the scale-dependent bias signal. Note that our measurement has a precision somewhat worse but comparable with the eBOSS quasars {{formula:5320e6bf-8277-46e8-84a8-1888b0a57ed0}} (68% CL) {{cite:9aa45717f7f673a0572d57fac53e335b260f4754}}, {{cite:8ec1e9f876969d3bdefae9c12266415f3f7ff8a6}} (which boast a much longer redshift baseline, and thus a substantially lower {{formula:36a83db6-5255-4012-842a-255ca1984059}} ), and with WMAP, {{formula:19fe2239-2f57-44d1-8d7e-ca7c162e9e56}} (68% CL) {{cite:4c3a7a3228324ecc7fd07de69bff10dadb56dfb4}}. We find comparable results to those from an independent analysis of the BOSS power spectrum and bispectrum (using a partial one-loop theory model for the latter statistic) {{cite:25a5f5b39a405ac1e44ba7112c9c0c38ebdabf52}}: {{formula:2a4558fb-6e96-4ab5-a583-7455f8337ac0}} , though, as noted above, our analysis differs due to the use of a fully consistent theory model and complete treatment of the survey window, allowing larger-scale information to be robustly included. Finally, our measurements are somewhat better than the ones coming from the UV luminosity function {{formula:fc81859f-305a-4816-88d0-a8107105481a}} (95% CL) {{cite:ab7d2509fee0331e091ab347d68a38055d8e6445}}, {{cite:4886ded8a04bf75c4867b00cd72eecaa59ed83b6}}, {{cite:d21e302610a9fa753f3369f03a736ad3bf6b10b6}}, although they include information from scales with {{formula:b79f0e16-ef5a-483c-88dd-254e1718df63}} , which we do not consider in our study.
r
12b2dd984e6d1e782265ffa902651ce5
Another challenge is the thermodynamic uncertainty relation (TUR) for discrete-time systems {{cite:fac05c3547e6d1a703e2337d5d2887a01706a10c}}, {{cite:79b997faa6241fb9b37f77fb30708b4f1e7e3060}}. TUR is an inequality in which entropy production is bounded from below by a function that depends on a quantity called current. This is a tighter inequality than the second law of thermodynamics, and can be used to estimate entropy production {{cite:581a3c5624a873aa6fe8240bd7e698141dafa0d0}}. It has been pointed out that TUR does not hold for the steady state in a discrete-time system {{cite:541151ada530b28ff7db460e50c542de64d0b556}}. Subsequently, looser bounds were derived for time-reversed entropy production {{cite:c784a738606f844b5bf04a291291e0d106601a4f}}, and after that, tighter bounds were derived for the steady state {{cite:2cf967c70f4693d372c18012247399dd6d3e181e}}. In recent years, an even tighter bound has been derived for backward entropy production {{cite:9c8ac3d27a75d190184146cb6f7cada900373d2d}}. However, these studies made no distinction between time-reversed entropy production and backward entropy production, and their discussions were limited to single systems. For continuous-time systems, TUR in a composite system has already been derived {{cite:c22bb76c05811fd9a191c177bcc8163b57af5ad7}}, {{cite:6f090b3479c17d0e8d739cb0344ab0b3092ed6c3}}, but it is not clear whether TUR holds in a discrete-time composite system in the same way as for a continuous-time composite system. Based on the results of this paper, It might be possible to derive TUR for discrete-time composite systems by drawing distinctions between different definitions of entropy production.
d
ccfc1296015fcb43a2e172c07a3f1085
The following lemma will also prove to be very useful in our study of solitons. This extension of the Bochner formula can be found in {{cite:32c71c82c2871340b7681a5e2b781afa185d4e0a}} and was originally shown in {{cite:64796d418488976873e4389ab7741b1e2d0e2b71}}.
r
8a10aea1171c44a9d873ac9ce6f47d1b
Further, and to ensure that our approach does not cause the well-known obfuscated gradient problem {{cite:c624b4e4f69f8bef702c5858e9b64f0f5b9a16ed}}, we resort to stronger parameter-free attacks using the newly introduced AutoAttack (AA) framework {{cite:88f17a4a55e7ee62afbb13f3e24c49a36ae0039a}}. AA comprises an ensemble of four powerful white-box and black-box attacks, e.g., the commonly employed A-PGD attack; this is a step-free variant of the standard PGD attack {{cite:abd42f5b9a236d0ed76318a9f6461b6cbb4cd513}}, which avoids the complexity and ambiguity of step-size selection. In addition, for the entailed {{formula:5b7ab135-388a-4027-89d9-909b39892a3b}} attack, we use the common {{formula:8c6519b5-098d-4f92-8d92-a6927e42b3e9}} value. Thus, in Table REF , we compare the LWTA-based networks to several recent state-of-the-art approaches evaluated on AAhttps://github.com/fra31/auto-attack. The reported accuracies correspond to the final reported robust accuracy of the methods after sequentially performing all the considered AA attacks. Once again, we observe that the proposed networks yield state-of-the-art robustness against all SOTA methods, with an improvement of {{formula:b43e8498-921f-4fd7-a6c2-b755b1f5445b}} , even when compared with methods that employ substantial data augmentation to increase robustness, e.g. {{cite:4dda3681efbf7a11a179caf3aaa77ab740ec2c80}}. These results vouch for the potency of Stochastic LWTA networks in adversarial settings.
r
ab06375ec233ed94606a4a8a9fc0c378
The simplest model that can incorporate baroclinic processes together with diabatic heating and surface friction is Phillips' two-level quasi-geostrophic model on the {{formula:b784891a-2b7d-4f8a-bb0c-02315265f177}} -plane {{cite:fe636f4619b4a600d8692c6ee1490119350d0714}}. The present paper uses this model to derive a set of ordinary differential equations that are able to provide a minimal yet meaningful model of the above described interaction between mean flow and eddy activity. The novelty of this work is how the stability properties of the derived models are determined. In contrast to the usual approach of normal mode instability analysis (see e.g. {{cite:6a52de85104cb67f998f5bef02d9126bfeaaeee1}}, {{cite:1c8bfbba4b799a22f6e71941622242f8ec0dd4ad}}), which focuses on studying the stability properties of the zonal flow, we use here methods of dynamical systems theory, which allow us to show the existence of a second attracting steady state instead of growing normal mode baroclinic instabilities. Another novel aspect is that this second steady state exhibits the above described eddy saturation properties in a model with parameterised eddies.
i
c24d76446996ba1724b7846baf2d0957
For the last passage time from {{formula:e5d72469-8c88-49d2-a350-b515675b472b}} and {{formula:a743e38f-daab-4293-ba83-fa4bf25c96b0}} , we have the following one point estimates by the connection with random matrices. For any {{formula:39164ce1-3b5e-4d8c-8775-3655f9963531}} , {{formula:60be0a6e-fc88-4252-bb1c-b3d15cd46c9b}} has the same law as the largest eigenvalue of {{formula:e466bf42-112d-4d34-9ebb-f6e6df89fcbe}} where {{formula:89c30815-c10a-40a8-adae-4d356e45c2ea}} is an {{formula:16409c33-83e7-4882-9111-4b653dd57ab3}} matrix of i.i.d. standard complex Gaussian entries (see e.g. {{cite:6197c0f08e4cf8562f4045b35b69470605b93ec0}}). Using this we get the following one point estimates from {{cite:3dd30b2bac06eb3f037a650ec937220b4961b589}}.
r
15b4b97c100680d88f805ab1a2dc6c19
Fixed-length skills {{cite:2ce20980bf6fa5054ea0f5abac773445fe7cddfa}}, {{cite:f4c1fc8251d52a84de00ef3db9ae2bf9ac6011d7}}: A simple and common HRL approach uses the high-level policy to choose a discrete low-level skill to execute every {{formula:4fbb6328-f0b1-4ab1-b691-7fb375124a62}} timesteps, where {{formula:6276eaaa-8abe-4dbd-b531-632623731903}} is a constant. Both the high and low-level policies are optimized directly using the environment reward. We choose to optimize the low-level policy using discounted environment rewards as learning was unstable with undiscounted rewards. However, as the high-level policy essentially faces a shorter horizon length due to actions being temporally extended, we optimize the high-level policy using undiscounted environment rewards to avoid the issue of objective mismatch.
m
5afa66c07041d9a56d8eff0066c91d84
We considered dynamic mode decomposition (DMD) {{cite:fe4ba1ac14bf5af8ac9bbf56f318fec905fa88d5}}, {{cite:18c594dba00ca2ba75ca1051b4fa7f545cc1ed19}}, {{cite:486a951afce34c229175c46fb2a56e5882b559b0}}, {{cite:f59540b3ff27bfdda76f75cf275d9d29d15eff27}}, {{cite:7e839752b54557f0b6c50394906b14d3c76647dd}}, a popular approach for performing KMD, on a data three-tensor, with one dimension being the elements of the state space, one being time, and one being the initial conditions. We proved, in Lemma 2, that when the data is linearly consistent and the Koopman operator, approximated via Exact DMD {{cite:f59540b3ff27bfdda76f75cf275d9d29d15eff27}}, has a full set of eigenvectors and rank R, the DMD modes are an R–optimal TCA decomposition of the data. Motivated by this, we then formulated a correspondence between the TCA and DMD modes (Eq. 17). We proved, in Lemma 3, that this correspondence was exact, up to scaling and permutation of labels of the modes, when R is equal to the tensor rank of the data and when a certain inequality (Eq. REF ), known to be sufficient for TCA uniqueness, is satisfied. When the modes of the two methods are equivalent, there is a strong implication about the dynamics of the data. Namely, the data comes from distinct sources with single exponential growth/decay and/or oscillatory time dynamics. On a simple example, we showed that modes computed via a numerical implementation of TCA{{cite:b9bf4c296016531701b5ba1aae9465d761afe4e3}} very nearly matched the modes computed via Exact DMD {{cite:f59540b3ff27bfdda76f75cf275d9d29d15eff27}} (Fig. REF ).
d
9d167c5efd123453a220cfd39cb4d151
For a source-target pair, choose a related higher-resource language to the low-resource target such that there is sufficient source-related parallel data to perform joint mapping. {{cite:118a2cdd1c25d5baed3f5ff13d7d4e701f77c43b}} Use offline mapping {{cite:f55710a77cc6c1ff2a712d10a226de245f92e4d2}} to align related and source language into a shared embedding space. Due to their relatedness, these resultant embeddings remain isomorphic as the assumption in mapping methods hold true. Use joint training {{cite:411b60ba996506ec2309fd1425d971113d0bf44b}} to map related and target language into a shared embedding space using the higher-resource parallel data between them. As this is the highest level of supervision possible, we ensure that the embedding spaces remain isomorphic. Lastly, map the aligned-source and aligned-target embeddings using unsupervised mapping methods as they are now isometric in nature following the alignment to the related language for both the source and target.
m
79a49912916d4127648a0c54995bc94f
Tree Parzen Estimator (TPE). We apply the TPE algorithm {{cite:7815b548a0efb2fdd0c0e40a819da9fe6243cc98}} by formulating the problem as a hyper-parameter search where the hyper-parameters are the sparsity values for the attention heads and FFN of the 4 encoder layers. Reinforcement Learning (RL). Our implementation follows the well-known ENAS {{cite:98b456d26fe4acd55500f2c581af46044da1ffdb}}. We design and train an RNN controller to predict the sparsity for each layer. The controller consists of 4 LSTM sub-networks, where each sub-network predicts the attention and FFN sparsity for a corresponding encoder layer. Aging Evolution (EA). Our implementation follows the original algorithm in  {{cite:b34864d8567c3779addcc3586d97b03fbad38486}}. EA is conducted with the same setting to SwiftPruner, except that the mutation action is made by randomly sampling a layer and its new sparsity setting.
m
bd6fbff99b02bf7367258f3e4cbb16b1
Neural Implicit Functions are gaining popularity as alternative 2D image and 3D shape representations. Using a simple MLP encoder, these networks approximate a function mapping between spatial coordinates and a quantity of interest such as colour, occupancy or SDF values. They have proven to be very effective at fitting natural images {{cite:bba2276cd0e1f296ee87d423820e174774884b84}}, {{cite:fee93f4e3932f428202d4d62c6e0587760c7e499}} and 3D shapes {{cite:e15b70889410d7d01d380bddda19781d1d257168}}, {{cite:f44d140f0c1ada1b7585c6e459883c3a94390987}}, {{cite:4b11358a583739c99458f0327a5fc604e2813fb5}} and have been applied to various computer vision tasks, including novel view synthesis {{cite:21cd54d68da5c579b622d48e1737bf1a5a695481}}, {{cite:b6e2934ac2d894919a987a27745e6b53b53e8a28}} and generative shape modelling {{cite:99c27e7fb62c917fa03ea17fca77b41e93279c78}}.
i
6954b8832425a86415e9977bf31cea01
To describe the stochastic ensemble of networks, we must design a measure for the probability space and define the fluctuation size with its given statistical properties, (i.e., its observable quantity). Following the well-known methodology of Jaynes {{cite:090943f061f94fc8fc22391300d6d212cb36410a}}, we can write a maximum entropy argument that allows us to obtain the maximally unbiased probability distribution. Motivated by dropout, we define an ensemble that is defined by the full NN and its associated thinned NNs. Our observables will be the average loss and for a changing number of neurons average number of units.
m
b8c3aead52ebffc5e506dd922543de4a
Any statistical distance function that measures the difference between two probability distributions can be used for the discrepancy module {{formula:9ec5276d-744e-401a-8369-c78ac349a0ad}} . The algorithms such as Maximum Mean Discrepancy (MMD){{cite:1ca0ad9e42809afe58377a7904cce3724e11c98e}} and Wasserstein metric {{cite:207f71916e288e2967e3d407ad7639f60f6b30ed}} are commonly used for diverging two distributions from each other. Since it is shown that MMD can be used to disentangle probability distributions {{cite:ab8fea177621581d367682f75ab15577d59f0584}}, we exploit the same principles for MMD in our discrepancy modules. Formally, the MMD for two distributions {{formula:2ca2233d-79c3-49d0-904a-fdcfd35a52f4}} and {{formula:999f0e2f-04e6-4943-850e-5174a37bf58c}} can be defined as: {{formula:316a45a5-a5da-4c86-8530-ebb59c5586b0}}
m
a51a6e4229a82a7d045a4f52406abbfd
Results for exactly the same experiments, but for the ASVspoof 2021 DeepFake (DF) database, are shown in Table REF . While neither SA, nor DA improve upon the baseline EER of 21.06%, consistency improvements are obtained for the wav2vec 2.0 front-end for which the EER drops from 7.69% to 2.85% using both SA and DA. This result is also statistically significant. To the best of our knowledge, this is the lowest EER reported for the ASVspoof 2021 DF database. These results, while determined with the same wav2vec 2.0 front-end used for LA experiments, relate to a DA strategy optimised for the DF database (stationary signal-independent additive randomly coloured noise – see Section REF ). Results for exactly the same setup, using the DA strategy optimised for LA (linear and non-linear convolutive noise and impulsive signal-dependent additive noise) are shown in the last two rows of Table REF . While the EER increases to 6.64%, this is still a competitive result and is 67% lower relative to the result of 20.04% for the sinc-layer front-end. Whereas a component of the DF database originates from the same VCTK database as the entire LA database, other components are sourced from multiple different corpora (Voice Conversion Challenge 2018 and 2020 databases) {{cite:96bc99f04ed8eff866b01d588b4534449e854033}} including spoofed utterances generated with more than 100 different algorithms. With the ASVspoof 2019 LA training data containing neither codec or transmission variability (LA evaluation data), nor compression variability (DF evaluation), results show that the use of better pre-trained models leads to consistent improvements in generalisation, here being previously unseen spoofing attacks. Results for the DF database show that the benefit extends also to the case of domain mismatch. {{table:48c17dab-9149-47fd-a825-2a039252e819}}
r
e29d53ee2e2645f2101f939fa9012ee3
Note that we do not compare against simple baselines such as BiLSTM-CRF {{cite:d19bfe8f1ae76e0a0a471bc0c83d7ca45d9378b9}}, LSTM-BoE, and CRF-BoE {{cite:971bf96fb6aa5fee781d30b6f7337ac15b82556f}} because they have been outperformed by the previous works we compare against.
m
c5003806af7397d46d8c037fc236e3f7
where {{formula:a8a6f6c6-0a79-46e5-a152-29b3d5f76f88}} is the observed shortest variability timescale, and {{formula:6c04a917-13d6-4be1-9d78-18f4595bc30d}} is the redshift. By equalling the minimum zero-crossing time of the ZDCF (in autocorrelation mode) to the shortest variability timescale approximately {{cite:123c037632343df9858d6e060f5f64e8dd416211}}, the {{formula:d2e9e817-92cf-441c-abd5-64b8de547689}} is calculated to be 2.8{{formula:18284cbd-bdda-4492-913a-b43000c2e0e7}} for 1ES 1218+304. If the variations arise in the jets and are not explicitly related to the inner region of the accretion disc, the BH mass estimation is invalid {{cite:b306d37aa7938dd53b3efc7291468bdf6155e855}}. {{figure:7db05e56-9556-4507-959f-f195d129463c}}{{figure:4e4be185-b2e1-4076-935d-ed5da26068f4}}{{figure:1dc45160-4c2a-45d4-8feb-67e3b1f70ef4}}{{figure:8a5ae778-0939-427c-879c-0ee238ee7b6a}}
d
14bc894537c9f19b4dbc95de5b2ace40
Our proposed perturbation bootstrap leverages a first-order multiplier bootstrap distribution using a percentile approach. Studentization often can improve the quality of bootstrap approximation {{cite:7c59587c136810a58fc80df8947543c35c8573be}}, although, in the case of the {{formula:60ac4b36-12ff-4f32-bae7-31d6b469ff1d}} , such a technique requires a variance estimate of the sum-product estimator {{formula:3c9cfe38-3bb1-4747-b9b0-f96ba72f42f8}} . Such a variance estimate might be furnished by a Delta Method approximation with a Heteroskedastic-Consistent covariance estimate, although the resulting performance is unclear. A recent proposal by {{cite:6c3382485c78cf76c0a86f9beae54ba7439b1792}} used an Edgeworth-expansion approach to arrive at a bias-correction to the {{cite:6527cd474ee25a6782b15ddc4e1957342ba70caf}} approach. A higher-order study of our bootstrap approach with the Edgeworth-expansion may provide a bias correction, although it is unclear how this study might accommodate the nuisance parameter estimation via Robinson's transformation. Simulation studies did not show an improvement when applying the Das bootstrap to our setting. Developing a higher-order-correct bootstrap deserves further study. {{figure:f2fa8cba-8fed-42c1-be34-6ffaf24c4b9c}}{{figure:1f33d2ff-a5f4-45de-83ca-9c37bf2f140f}}{{table:82981983-9550-4d65-a7f2-3c94f4cbc577}}{{table:f003e2c9-1027-4062-8e24-68cfa4c9d8b2}}{{table:eb76dc17-0acf-47ec-88d8-2b5230516474}}{{table:c23edcc1-6ee4-431f-ab1e-ec8bf382b3f7}}
d
37e4fee4ac39de1c3669ff9e9e269d98
Some efforts have been made recently to reduce the cost of model training, e.g., ClipCap {{cite:8e76a690823091e7268fdaaf3c8563247edc00ef}} and I-Tuning {{cite:bc730b83277087952f7344ae1a0d734b85c2c628}}. These models use an off-the-shelf pre-trained vision encoder and language decoder. The parameters of these pre-trained components are frozen and only a mapping between the two is trained for the task of image captioning. This results in a highly reduced number of trainable parameters ({{formula:2ced8988-f0ac-4d1e-bf47-da54e37dd118}} 43M in each case) and faster training time. While these models operate on a much more manageable scale from a research perspective, they can still be unsuitable for the aforementioned practical applications, as both models require separate training for every use-case. {{figure:52d83d7d-fad9-44b5-843a-514fdc84e812}}
i
94290e2c1a5625571e22b06ed43bb895
Modifying {{formula:93dd59a8-2d05-4b3a-bafe-fd87361a244c}} helps improve the efficacy of DL models; active learning (AL) methods introduce querying a user to label unlabeled data to help the learning model develop a map. The modification has shown impressive improvements on CNN models {{cite:4dbee20b6e7b716e5a3e22282e3ba080df914c1b}}, {{cite:a7afee96685f280a2d54ce81ba0439c4b2cc7225}}, {{cite:e6076a675c546221104ccbaf3fd1892acb128633}}; however, AL still has long training times due to large training datasets. Thus, we introduce HARDLearning, which modifies {{formula:9eb0b3a9-e256-465f-b6f6-59ccb03b16ba}} by appending versions of {{formula:8f9ff280-7e4a-42da-81e5-d7c4b10150b8}} , {{formula:48fea75a-f534-497e-8ff8-e9a793712efc}} , and {{formula:2ceac708-89cf-40e9-a091-ec3b34c03ff0}} that mimic {{formula:c84238b1-7ad1-4f3a-9855-bd7b9648e4a9}} , {{formula:d9c9fcdf-204a-425c-9980-be8e45340be4}} and {{formula:99488ecb-059b-4bc3-bfee-a060d7ea498c}} of {{formula:f994aa03-1b54-4ad8-8283-2ee12232cfee}} to provide the most useful data for maximizing the accuracy of the approximation of {{formula:b2dc4f57-6977-4907-9997-30b801d33652}} and reducing the training dataset size to minimize training time. We suggest the optimal modifications drive {{formula:36966573-1c56-4633-9075-5838b923f370}} closer to {{formula:23980d75-cd54-4221-a46a-97f285e76bef}} .
m
6e0204799d42ab808b632226eadfff3b
Electric polarization was calculated within the Berry phase theory. {{cite:2762061731c912f82ce9548f41b48ca081f81481}}, {{cite:4a9e55179b2010f7e159067fefe4879c46ef705a}} For the results shown Fig. REF , we have considered the T{{formula:bea0db24-f43c-4c2c-a6bc-704c2865d7ae}} phase modulated along the {{formula:51e76554-d0db-4b38-8006-956312abec1f}} mode while keeping fixed the unit cell volume and atomic arrangement in each trilayer. Electric polarization of the fully optimized T{{formula:478068aa-8b4e-41cc-a44f-7aa97c957908}} phase obtained within different approximations for the exchange-correlation potential is summarized in Supplementary Table 2 and Supplementary Figure 7. The analysis of electronic charge centers was carried out using maximally localized Wannier functions as implemented in the Wannier90 package.{{cite:1c0ed3fe55b5f36d07a172a50ad10515e64554da}} The resulting Wannier functions are obtained by projecting the states below the Fermi level onto the Zr {{formula:9bf4719d-016f-45a7-81a7-4dcbeabd9ec5}} and I {{formula:a8b24cf1-3bef-46a4-b7a4-0a25d4659fb1}} atomic orbitals. Contributions from all sites to the net dipole moment can also be seen in the non-diagonal components of the Born effective charge tensors (see Supplementary Figure 8).
m
78278f6b247dcfbaf47c24bda9bf48b0
An alternative way to generate {{formula:ce87743d-394a-4dc8-be5c-9cd0fe96ff7b}} is to generate first the partition and next attach to each set in the partition a value generated independently from the center measure {{formula:bfe5b50e-8dff-4357-a71d-00c24d2a2460}} (see e.g. {{cite:4e28a774ae7348fad426cd46f976b5967a427f12}}, Lemma 14.11 for a precise statement), duplicating this as many times as there are indices in the set, in order to form the observations {{formula:8aeb85d3-96a9-4256-9e1b-17259ec50333}} . Because the parameter {{formula:05a542ae-8683-4619-ac08-8fe562e27e4b}} enters only in creating the partition, the partition is a sufficient statistic for {{formula:6a3a0d9f-4a29-4eea-9416-14d42b533c60}} . Because of exchangeability, the vector {{formula:d3e5a9de-b3dd-4542-b7f1-1bbab41947dd}} of the number {{formula:fae6add8-ae79-4a4e-912c-22c6b83af00d}} of sets in the partition and the cardinalities {{formula:f2500b40-b860-47bf-baa8-dc3ee00149a6}} of the partitioning sets (i.e. the multiplicity of {{formula:f82cd3ba-0fd3-445a-8771-d7322cdd3ba5}} in {{formula:e2e888fa-8d24-4316-92cd-490484419714}} ) is already sufficient for {{formula:21b867e2-02c4-478a-a094-7d11da2b4a35}} and hence the empirical Bayes estimator and posterior distribution of {{formula:af8e9813-ca93-46cd-9ead-4cb5695489c6}} are the same, whether based on observations {{formula:5ca48ce9-8367-4f57-8212-1c0e751146b7}} or on observations {{formula:e3379d66-da2f-4e97-9174-1f794342147c}} .
r
36310522ef4b354fb9ef460e01acd8f8
The results can be seen in the first two rows of Table REF . In all the cases, our approach is more efficient as can be seen from the shorter average trajectory length and duration, which is more evident as the measurement noise increases. We also provide a comparison to center point approximation {{cite:fa2ffd223d7af41bde7ad6fc5eafb174310c6f42}}, which is also computationally less intensive. However, as recognized in {{cite:ecebde2b8708ec35a2542dde4e93526c5a6286b8}}, if the covariance is small, the approximated probability can be much smaller than the exact value. Moreover, the approach works well only when the sizes of objects are relatively very small compared with their position uncertainties {{cite:b02675f3959e48e858923812bb23d2b0c245429a}}. This is seen in the last row of Table REF . For measurement noise {{formula:9bae90a4-41b3-47e0-b5be-6801cb7c06b1}} and {{formula:25673bbd-db39-4998-9e75-820e29c04b2b}} the approach resulted in collision for all the runs. For measurement noise {{formula:023bda38-d443-4209-be80-3fd0ebeec8d1}} and {{formula:e8ebde33-8307-42f1-b740-2451a5040c0a}} , the approach succeeded in 55% and 35% of the runs, respectively. This reduced success percentages are due to lower values of the collision probabilities computed. The executed trajectories for all the three approaches in Table REF are shown in Fig. REF . For a given {{formula:36366bae-976b-4c96-b1ce-59f163f7e8b3}} , the metric d allows us to define a measure of risk— distance to closest obstacle. However, increasing {{formula:bb944a1c-cd38-44ed-8334-3a801088bbbe}} , increases risk as we solicit controls such that the collision probability is at most {{formula:f7cbd7e9-f6d1-4878-94e2-49930c0dd65a}} . For example, in the scenario considered in Fig. 1 (b), an {{formula:98709c8d-ed98-474d-9ea4-3d5e3ca18077}} lead to collision in 80{{formula:049a4b01-d2e5-4219-b2d2-fff7183d3a03}} of the experiments. {{figure:b2f6220e-c8b2-4b78-83fd-4f0340c20697}}{{table:06b4494f-d4ae-4a10-bbe1-8953c8cf9381}}
r
eb575c40bced084dda469f9b6fb9a5b9
Baselines. We compare our method against the following state-of-the-art talking head generation baselines: 1) Wav2Lip {{cite:c4faf3a9ac1e54a1ea90d1efb221e764a75736d9}} is a lip-syncing model for videos in the wild. Wav2Lip generates the lower half of the face given the upper half of the face and a target audio. 2) MakeItTalk {{cite:071dbcdb41ad69036ca92806ec5e8a3f7a1ba159}} is a audio-driven full-head generation model that drives lip movements and motions from audio with 3D facial landmarks. 3) Audio2Head {{cite:2cbcff6408f9d591f21c38b082c6129f0959e1f2}} is a audio-driven full-head generation model that utilizes key point based dense motion field to warp the face images using the audio. 4) PC-AVS {{cite:4de3c783e0938ea04c284b5f3cc905a0f6c8a8b2}} is a video-driven full-head generation model that enables pose-controllable talking head generation using the other video as a pose source.
r
3e83820168d33929538646e6f1f196db
This section is devoted to the proofs of Theorems REF and REF . Let us begin with some useful lemmas. The first one is the classical Euler-Maclaurin formula, see Theorem 7.13 in {{cite:e64751f7b23e5a058c3e64ec3970725634117989}}.
r
86956c497b8f1b74e7f23856573b851e
2D Instance Segmentation. We compare BoxeR-2D with Mask R-CNN {{cite:c62f306c228580e0081b446269ae45458b50dd4d}}. In order to have a more fair comparison, we attempt to make the Mask R-CNN baseline stronger. We add generalized IoU {{cite:9c9bf60dafeedf6d20604239449572047de800b8}} to the box loss of Mask R-CNN and train the network with the scale augmentation as in {{cite:a60ae7659317840e9c83942655e9d3375783ff3d}}. In Table REF , the 3{{formula:540f4448-9f80-4416-a631-740d5e9b4e4d}} schedule is used in both networks with a ResNet-101 backbone. BoxeR-2D improves on all of the bounding box metrics against Mask R-CNN by more than 4 points. For instance segmentation, we conclude BoxeR-2D is competitive with Mask R-CNN with less number of parameters (59.0M for BoxeR vs. 63.5M for Mask R-CNN). To be specific, BoxeR-2D is lagging behind in two of six metrics (AP{{formula:971ac2f6-6481-4b91-8982-6ad11f90d664}} and AP{{formula:9b5bd4eb-fbf2-4ded-b637-800c40b06913}} ) while improving AP{{formula:d9f5900a-bf01-4d1d-839a-3fdc12570aa7}} and AP{{formula:501d9a0e-a085-4d10-9c13-1740a04dd46a}} by 2.8 and 1.7 points. The visualization of the BoxeR-2D prediction can be seen in Fig. REF .
m
78c466162317689ed82c73edf2322dad
Training and Inference Details. Our learned affinity estimation is implemented in PyTorch {{cite:5a44d82430550a9243ca1f84083ecb67c8bd44b0}}. We use OpenPCDet {{cite:29e9e9b7c985b158a3354eabb228a8478535081a}} for the Voxel Backbone described in Section REF . The network is trained on a NVIDIA Tesla V100 (32GB) GPU. The Adam optimizer {{cite:03f689b17e206d837b1f7cfcdd12f081e1c14e88}} is used with an initial learning rate of 0.03 and is modified using the one-cycle learning rate policy {{cite:6f15680b538c07f09b6df8fde4d425329be4f13e}}. We train the model for 20 epochs on the nuScenes dataset {{cite:67d0aa78ca9cccdea178dd9c8328752efe9bdc26}} and 100 epochs on the KITTI dataset {{cite:0a89596268719c25321ab4b5bc04dcfa1995457d}} using a batch size of 4. We use previous detections {{formula:f7bd8431-f63b-48b0-a2c5-eaec3c1358a4}} to represent tracks {{formula:cb2d12a7-2209-40c3-b693-f5f4f55d8931}} during training. We use the 3D Kalman filter for track prediction on the KITTI {{cite:0a89596268719c25321ab4b5bc04dcfa1995457d}} dataset due to the lack of velocity estimates in KITTI detections. The values {{formula:64e43ccb-bba0-4824-b8f4-47fc804f01b8}} and {{formula:d4da0c28-47e1-4f40-972f-acb3995da1a4}} are used for the focal loss parameters in Equation REF . We set {{formula:797e8660-c5b6-4843-a0a5-59a4ae295707}} and {{formula:847d69c8-f8bc-4c05-a12a-9e22f7735193}} for the IoU thresholds in the track overlap rejection and affinity label generation steps, respectively. We set our detection perturbation standard deviations as {{formula:da2fe704-89fe-4e13-872f-3f352b06535a}} , and set our detection drop fraction range as {{formula:79c5f020-e6e3-4618-8847-ee151310a1b4}} . We inherit all tracking related parameters from EagerMOT {{cite:36ea152d8da4b10fbfd5f20cd7ea6286cd72ac25}}.
r
f15b8ce1861b171821334897d2981905
Controlling the Type I error rate of a test is, of course, only part of the problem, and designing tests with high power is more complicated still. In Theorem 3 the proposed test is shown to be consistent, in that its power converges to one as the sample size increases and the resolution becomes finer, for each fixed distribution that does not satisfy the null hypothesis. This is a very desirable property for an independence test, but the power does not converge to one uniformly over alternative distributions. While it is possible, for example with permutation tests, to control the Type I error uniformly over the null hypothesis space, when data is continuous it is impossible to design an independence test that has power against all forms of dependence simultaneously, even after fixing the strength of the dependence {{cite:df1b14f39c2142f8a9338ca3af92c2b2464bf475}}, {{cite:8b06f090acc7c924eb1a3aba8daa0d739fc15923}}. This is another reason for the great many different test statistics in the literature, each of them making implicit or explicit choices about which kinds of dependence are prioritized for detection. The authors assume that the maximal resolution at which exhaustive testing is applied {{formula:045c5087-3559-4d21-a623-a7900b0d44d6}} , so the current method naturally focusses on dependence occurring at the coarsest resolutions, progressing to the finer scales only if enough data is available.
r
ad343f1206e67af7b7393544dad91e1a
Implementation details. The network is implemented in PyTorch. The weights have been determined empirically as {{formula:04523c0b-e91c-41db-b831-d9e120d1762e}} , {{formula:c3ab2bc2-8d6f-4f99-be72-942ae9060d81}} , {{formula:8ecd8796-533f-481a-9f9c-4bdffea81f36}} , and {{formula:d5623e55-ee5d-49e6-958b-6910cddbac51}} . We downsample the ground truth GS images to obtain the supervision signals at different levels. The desired level {{formula:75b4d19a-9d45-4142-92e7-c7d5c4898fa2}} is set to 3 and the top pyramid layer {{formula:3e80851b-9533-4a0b-bded-d47a0a5de3b7}} is set to 5, i.e., we only work with the feature representations captured by the second to fifth pyramid layers to estimate the undistortion flow and correct the RS images. We set a search range of 4 pixels to compute the cost volume at each level, i.e., {{formula:8dcb4fb7-15a3-456d-8494-76cd38ab0771}} . We adopt the Adam optimizer {{cite:67c4b41da8aa0a8c4c4ef367eb18fa07c9838258}} with a learning rate of {{formula:ce38d15b-0b3b-4622-8e8a-ddd47ccec16f}} . The chosen batch size is 6 and the network is trained for 400 epochs. We use a uniform random crop at a horizontal resolution of 256 pixels for data augmentation. Note that we do not change the longitudinal resolution to maintain the inherent characteristics of consecutive RS images, which can help to better learn to accumulate contextual information of two consecutive RS images. {{table:7589981d-a678-4a6c-bc13-2cc46f3135fc}}{{table:60e8f221-4226-4620-b4e4-9e06b4f59726}}
r
93d0589e81e34fe4ec57dc0c513d3fb8
Remark 3.5 We can see from the proof of Theorem REF that, when {{formula:15787fbd-91a1-42ea-b2ff-6699914709b9}} is an integer, the above convergence results still hold for moments without the modulus. Absolute moments of the limiting distributions can sometimes be given more explicitely, for example, it follows from {{cite:8b9d9a7e6afef74ec14a4ab01c4a61a61ee14777}} that {{formula:3e6a8587-a3e2-4f03-9543-ce1394f481f7}} with {{formula:5524a51b-e8a2-4bc3-ac26-9f7fc8af3a6e}} the Gamma function. Furthermore, by a change a variable formula, we can obtain {{formula:f8bb247c-f71e-41a5-93f2-633c212a886d}} The formula for other distributions seems to be complicate and thus omitted here. Moreover, these moments can be easily approximated by using Monte Carlo simulations.
r
c73bcbf6a83b2ccc034ca77d45477429
We comment that the reversibility of {{formula:e91a1689-bfd1-4f44-b7c1-8ecb2896bef4}} processes can also be treated via the conformal welding of Liouville quantum gravity surfaces (see e.g. {{cite:1aa0a0ed9749d95739bb29a75cb4ee530b3d6ca0}}, {{cite:d1ecd25decb45135712df99545fa8b83760d83b5}}, {{cite:117ad31d52a7720bb532a997dd71b399ad5879c9}}). For instance, by viewing the welding interface from the opposite direction, Theorem [thm:igII]A is a direct consequence of {{cite:d1ecd25decb45135712df99545fa8b83760d83b5}}. The time reversal of {{formula:1c22550c-a447-48f3-9012-f1e628e9ccbd}} with force points {{formula:c30ff1f5-357f-4c93-a17a-cc63bb7db1a5}} has also been discussed in {{cite:117ad31d52a7720bb532a997dd71b399ad5879c9}} via the conformal welding of quantum triangles. We expect that this method can also be used to describe the time reversal of other types of SLE curves, such as radial SLE with force points and SLE on the annulus.
i
3812d231d7d8cc3b4d256f86d0a384cb
However, in many DL-based communication studies, DL technologies in computer science are directly applied to wireless communication, ignoring many essential characteristics of communication. Actually, the features of wireless communication channels and the theories of wireless communication are very helpful in the design of DL networks in {{cite:cc9302d34c85f41cbc088c164dd608487efc460e}}, {{cite:17cd1d1b1bd626f36e0fedce28dcda85585fb583}}, {{cite:ef8737dafe75c0c2fc7d01e7791a0685cbf71132}}.
i
2fd0e69cf10df3b90e926b9c7ecc6364
PointNet++{{cite:eb7fe4922d5eac7179ad2047e2a982c9e75e3d61}} - Qi et. al introduces a hierarchical feature learning alongwith the PointNet architecture and thus enabling a better understanding of the local neighborhood in point clouds.
m
ce7200155f68c9ce8edde4b6705b3196
Parameter-isolation based methods allocate different parameters to different tasks to prevent subsequent tasks from interfering with the previously learned parameters. This family requires task-id in both training and testing so it is mainly for TIL and DIL settings. This family also usually suffers from the capacity problem and makes KT challenging. Like regularization-CF and replay-based methods, parameter-isolation based methods are also originated from CV {{cite:c5d1cc5b5cf33d5228328e5efa9134fd99743cd7}}, {{cite:922e957e1336ceba60c96bfe64f8638b429b661c}}, {{cite:4fa37f82f68187b10003c18eddf6c194cce1fbd1}}, {{cite:6816eb7052e67667a873a91b3b7f5c4d6bcebb2d}}.
m
660b5f24c4a38e91aad6ed34062e2493
which e.g. generates the state with {{formula:65561def-4ff2-4f22-b0c7-27a6b2671e42}} small and no large excitations {{formula:a0648c9c-c87a-40fc-94d9-eeafb23e6ef6}} and the state with {{formula:24cfb2ba-81a3-41ff-9f94-ba922c9fb801}} large and no small excitations {{formula:d937967a-573a-4e94-873a-4709bc65c698}} , and many others in between, see Fig. REF right panel. Correspondingly, the transition rate from {{formula:d41f1ba0-de60-437a-abd3-7d54e24f5633}} to {{formula:da35244c-3c49-4164-8048-02d720ea5ed2}} is given by {{formula:99e9d05c-2ce5-4028-8fda-0f891957c8a9}} . As this approach is just a special case of LGKS equations obtained using a secular approximation (exactly valid for non-degenerate {{formula:8bb56afd-4586-42e8-93e9-8247a4bc9189}} , here applied to isolated subspaces), it also obeys its favorable properties, manifest e.g. in the fact that the rates for every reservoir respect local detailed balance {{cite:687e9c9143f53d0ef7c957df5f139ff95110bc6a}}. To obtain the coefficients in Eq. (REF ), we require the action of the collective ladder operators in the symmetric subspace, compare Fig. REF right panel. They can be evaluated by representing the symmetric subspace with two bosonic modes by means of a generalized Holstein-Primakoff transform, see App. , which yields {{formula:6f19dec7-d802-4783-96a3-77d37d589053}}
m
52f3dc10b4344433397f5180bb9b940e
We assume we are given an RGB-D sequence with camera poses and intrinsics. Depths and poses could be acquired, for example, using a dense structure-from-motion pipeline {{cite:fc6457ef5221396737824280822a0a00a58e553f}}, {{cite:4b5d58cf29c22678743fe2550936dbcb3e8fae81}}. For most of our experiments we capture posed RGB-D sequences directly using Apple's ARKit framework {{cite:c48dff2fde564075b0d779598f5fdc90f54a2240}}, but we also show that we can relax this requirement through use of a multi-view stereo method to estimate depth for an RGB sequence. Along the way, we also assume access to a per-frame mask of the object to be removed. The goal is to learn a NeRF model from this input, which can be used to synthesize consistent novel views, where the per-frame masked region should be plausibly inpainted. An overview of our method is shown in Fig. REF .
m
d9fe8ef05ca15378e60cbfe3d7fc652e
Dataset development: We developed an Architectural Design Patterns dataset, named as ArchPatterns dataset, comprising 2,035 architectural design images from fourteen different architectural patterns viz., broker, layered, event-bus, pipe-and-filter, repository, microkernel, microservices, model-view controller, peer-to-peer, presentation abstraction controller, client-server, space-based, representational state transfer (REST), and publisher-subscriber. We considered more than 100 design images in each pattern category. The images were collected from online sources such as official blogs and technical write-ups with ground truth. After collecting these images, we manually filtered them to remove the images not projecting the relevant design patterns or not of the desired quality. Ground truth for the remaining images is manually annotated for the training. Images are of three channels with RGB color coding of different resolutions and sizes. We consider the QAs and sub-QAs listed by ISO/ IEC 25010 standard as a reference point for our study. The necessary tactics required to achieve these QAs were derived by reviewing some standard software architectural reference books {{cite:84b81ae6e4ef2f9d88c66d564e5c6b224547dfee}}, {{cite:bf2719757dd730f0881b51e6d4b4f62c50c2fdea}}, {{cite:ad4212134541213f9b792fb9938dce5f36433eaf}}, {{cite:28ae57e5675c3c68cf0edcae7021f55f26a05fde}}, {{cite:bf2719757dd730f0881b51e6d4b4f62c50c2fdea}}, {{cite:a871d48677f594d1774fadc14881e9e9d57bc32a}}, {{cite:dff91d4a8cf67ec1ef7b7aeec2693747b3dddb48}}, {{cite:e2a2be59893c953af19e2a9e135d7a8c3e7948a7}}, {{cite:bedc37ef992e11fd8ffa313676b54a20c2152189}}, {{cite:fbba561903bc831eee3365c72794a1c094498cc4}}, {{cite:ae585b615ca14a50a6bbb4add556fd847c115ac2}}, {{cite:34b3b8700b14f67d909d40d1d65b998600392b3c}}, {{cite:9daa601922134acf9841261ceb1c8bc0f2626b75}} and the information is stored in the form of structured tables available at https://doi.org/10.6084/m9.figshare.14623005. Our ArchPatterns dataset is publicly shared at https://doi.org/10.6084/m9.figshare.14156408. Image Preprocessing and Enhancement: To improve the quality of our images and remove noise, we preprocessed all the ArchPatterns dataset images and scaled them to same size. We considered the images of only a considerable resolution ({{formula:d4f1465b-8f61-4059-b2d4-6c93694aa888}} pixels) to have an effective image detection and matching. Feature Extraction: We extract the image features, software components, their interconnections, and component labels present in the ArchPatterns dataset. To speed-up the image matching (or lookup) task during the evaluation stage, we also store the similarity of an image when compared to all the rest present in the dataset. We store these image features as a structured dataset, named as ImageFeatures dataset. We used SIFT {{cite:5fcba51155a58d253d2cde58294b5af8f176c92e}}, a scale-invariant interest point detector with corner properties at different scales for feature extraction. SIFT also devises a suitable feature descriptor to uniquely represent the interest points. Image matching and Similarity detection: Every image has multiple and different numbers of interest points. Interest point descriptors across different architectural images are subjected to achieve a mutual similarity, and then the count of matching interest points is used as a similarity measure between the two architectural images. For instance, if the images A and B having {{formula:bf2e8675-da9f-4d71-98c1-f53d876f93fa}} and {{formula:3c7f9542-7724-4f93-a2d3-ae4470936a6b}} number of SIFT interest points have {{formula:10c9f478-52ff-44bb-a5db-2361509783b9}} number of highly correlated descriptors in common, then the match score is computed as: {{formula:936a4445-54f2-485b-a016-3816a47f0faa}} Each image in the database is matched with all other database images to obtain a dis-similarity score during testing. The images belonging to the same architectural pattern are expected to have a low score, whereas those belonging to different pattern classes have a high score value. The matching score of every pair of images is obtained, and the score list is sorted in increasing order of dis-similarity. Further, for a given query architectural image, the most similar architectural image in the database is determined, and the corresponding label is assigned to the query image. The suitability of SIFT lies in the fact that the method builds a scale-space pyramid and only chooses prominent feature points that appear in all scales. By this, it achieves scale-invariance, which is a much-needed property for the architecture images. The same is evident from the result of achieving a higher correct recognition rate (CRR), which is defined as the percentage of images, out of total images, for which the recognition is correct at Rank-1 retrieval. Suppose out of {{formula:6482eb77-d101-40bf-b4ad-58cdfa355994}} test images, {{formula:300b5b4d-defd-431b-9391-3cf24b383618}} images are found to be true matches at Rank-1, then: {{formula:0e9c8e49-fea1-459c-abe1-06abf292362e}} Software Architecture Design Evaluation: When a software architect starts evaluating an architectural design image using our framework, the steps involved are: Feature extraction of the image as described in Step REF . Using the extracted features, the image matching and similarity detection is performed to determine the top-similar match from the ImageFeatures dataset. This step provides the necessary information about the most-likely architectural pattern prominent in the considered design image. Architectural Evaluation: The software architect can then conclude about the strengths and weaknesses of the design (in terms of QAs) using our knowledge-based provided in the form of tables (discussed in the Section ). The software architect can then work in the direction of improving the design by implementing the necessary tactics as listed by the tables.
m
ee91a956869763abc938d07f017844a5
Separate Learning (SL) is the standard in BIQA, which trains the model using a single prediction head on one of the six training sets. Joint Learning (JL) is a recently proposed dataset combination trick {{cite:482fa4da771452948e0380bb031022a480af28a3}} to address the cross-distortion-scenario challenge in BIQA. As an upper bound of all continual learning methods, JL trains the model with a single head on the combination of all six training sets. LwF {{cite:33f3489c63c10da968ce29da6c130e398145c54c}} in BIQA is based on a multi-head architecture, which introduces a stability regularizer that uses the previous model outputs as soft labels to to preserve the performance of previously-seen data. LwF relies on the newest head for quality prediction. We also leverage the task oracle to select the corresponding head for quality prediction, denoted by LwF-O. LwF-AW {{cite:2a80afbd361bf26a88edf6d99b42027d4d25a19d}}Our implementation slightly differs from that provided by the original authors {{cite:2a80afbd361bf26a88edf6d99b42027d4d25a19d}} in that we use binary labels instead of probabilities. is the first continual learning method for BIQA, which can be seen as the combination of LwF and vanilla adaptive weighting. SI {{cite:f9c168b39a6ae80d88f8ed189e13521c4074594c}} is also a regularization-based continual learning method, which estimates important parameters for previous tasks. When learning the {{formula:1df5e8cc-a608-471d-96c0-0ba6946b42e6}} -th task, SI maintains an online estimate {{formula:f6a2d41b-8706-4590-99ab-e2514cb16c57}} where {{formula:539186cd-b5b1-4502-9bfd-d1ef45a9283c}} is the learned BIQA function, parameterized by the vector {{formula:2b9b60a1-a55b-4113-a7af-ea449519a61b}} and {{formula:94c7c9e9-6bbb-4f64-a4f3-6ae4a4048b72}} is the Hadamard product. {{formula:2b8a4319-caa6-4985-9310-d98d01e1ca10}} records the values of the parameter vector before learning the {{formula:619d9feb-a7d5-4580-a6e7-0171e8d1e335}} -th task. A cumulative importance measure is then updated: {{formula:e30fdf02-fe59-4129-aa9b-92b978dd0c67}} where {{formula:65fd377c-7dac-4659-a58e-0699fb6341a6}} denotes the initial weights and {{formula:5709dd00-4b31-4243-b841-52426303c42f}} is a damping parameter to avoid any division by zero. Similar to LwF, we implement a multi-head architecture for SI, and rely on the newest head to predict image quality. We try to improve the performance with the adaptive weighting mechanism, denoted by SI-AW, and leverage the task oracle as well, denoted by SI-O. MAS {{cite:f9c168b39a6ae80d88f8ed189e13521c4074594c}} shares a similar philosophy with SI to penalize the changes to important weights. The difference lies in the calculation of the cumulative importance measure. {{formula:c48f7793-3383-4844-8673-b48ccdef8536}} Similarly, MAS uses the latest head for quality prediction, and has two variants that include the adaptive weighting module and the task oracle, denoted by MAS-AW and MAS-O, respectively. The proposed method makes use of task-specific BN to handle new tasks, and enhances the adaptive weighting in {{cite:2a80afbd361bf26a88edf6d99b42027d4d25a19d}} using rich feature hierarchies. We also replace the enhanced adaptive weighting with the task oracle for quality prediction, denoted by Proposed-O. {{figure:d3a6051e-fb2d-4834-a758-acbdf96755d9}}{{figure:6691cf1e-dd78-4377-abb2-e53f647cee10}}
m
115a9e56a8949d456236f8454d0bf616
Remark 1 The argument for non-collision in {{cite:7ab874a4ce99a7a958a1fd3e82f83ed5f663ae80}} is different. For {{formula:a0880ec6-8b1e-4913-9670-aa2a7a93d450}} , it is shown that the first time for {{formula:636effa7-309f-4e16-98d3-270a3a98851f}} with {{formula:0a1d6257-7eaf-4133-a20c-211285c2b2e1}} replaced by the {{formula:e8a9413c-0e4b-4378-9f7f-1f5520ea34ee}} to exceed {{formula:fc04d0f4-e2ee-482b-ac30-13dae23055ba}} is greater than any positive number almost surely via Markov inequality and Borel–Cantelli Lemma.
r
67f16b162c5e513562bf03d6dcc859b6
Partial Connections. FPN {{cite:8918c394013b0534c59d47d093a726e148f8c44c}} first proposes lateral connection to merge features from adjacent scales in a top-down path. PANet {{cite:7121479f3ac03e945c4f0ba85ebffc0255947af3}} brings an additional bottom-up path on the basis of FPN to supplement the missing finer spatial information from smaller scales. NAS-FPN {{cite:14708f92e5aabd285dc2ed75b2d4d1aee4819028}} introduces neural architecture search (NAS) to discover a better scheme that merges cross-scale features from any scales instead of only adjacent ones. These methods enhance the original features with semantics from other scales, but can only obtain information from limited ones.
m
e01cd30fb55cc3fce918c5f1f90d32f2
Next, we recall the following approximation result, which is an analogous bound presented in {{cite:29ea32d57c4bf2045deb2f8acf80b37e0d7f57b4}}. Let Assumption REF be satisfied, and let {{formula:53ad976d-910a-4224-9876-c10e98e39dfb}} such that, for some {{formula:93062d47-684e-426b-bf48-079b59a68287}} , {{formula:023cc7d2-930e-4f26-aada-2a33b2b29ac9}} for each {{formula:5ab45783-2f95-4e22-8dd1-5d1a5ab2ed55}} . Then there exists a projection operator {{formula:c7e244b5-b033-4dd2-ad14-da010b05b3fb}} such that {{formula:12636c73-3f35-4938-a63e-6e38042238fb}}
r
3c60086333bad4df902521524e0294e0
(i) If {{formula:a1247013-85c8-407e-b00c-c0ae52803435}} then moduli spaces {{formula:2cd21dd9-9bbb-4bbe-a711-b922d6dd2714}} are smooth {{formula:5964029a-5edf-45f7-8e5a-9794a271b716}} -schemes. If {{formula:a718595c-319b-4770-b2aa-b1eb7b2e8541}} then {{formula:7c948c23-557d-45b8-b26c-38ec3f5a1185}} is a compact complex manifold, and thus has a fundamental class {{formula:38f32e43-b6f5-4a20-be3c-51bbcce18fa6}} in homology. This case includes {{formula:c3f6bab1-ed54-4a82-8a43-aebbb0ebd132}} for {{formula:6b770dc9-a2a3-49e7-a2b8-e507774841c9}} a projective curve, and {{formula:243f3b99-1900-414d-8341-3ceb01b2aeb7}} for {{formula:98a98ab8-4912-4dc1-b09c-977f1905e02d}} a quiver. (ii) If {{formula:d4947a5b-2af4-4257-afd3-6b49c9cbbe8a}} then moduli spaces {{formula:eb6f250b-5492-425d-9edb-8077ca121c7f}} have perfect obstruction theories in the sense of Behrend–Fantechi {{cite:1080d7ae65c397e07a874c99837a1b47ba2a5a92}}. If {{formula:0d43357f-ef50-4004-9792-842c0a5acf3d}} then {{formula:883d691d-6ae6-480e-9e82-ce229bf0b45a}} is proper, and thus has a virtual class {{formula:9db76901-17ee-4156-aa14-4f18fa4ad87c}} by {{cite:1080d7ae65c397e07a874c99837a1b47ba2a5a92}}. This case includes {{formula:f96d0ab1-8cfc-4472-86b6-86d28a3823c9}} for {{formula:362c23b2-e29b-495b-817b-cd961d1db19a}} a projective surface, and {{formula:2231bfae-943f-40e6-9bc4-1723a2399c6b}} for {{formula:a82ce587-f4d6-447b-9986-0cc67fd2ba2b}} a quiver with relations (though see Remark REF ).
d
1339e7538c8efa74ed5fd964247bb527
In contrast to the formulation of the effective reproduction number {{formula:045fd97e-8a0c-4b48-8f13-3cf68ca9b712}} as a time-dependent parameter in the reparameterized SIRD model and its estimation using e.g. the SIRD-AKS method, the reproduction number can also be calculated directly from incidence data {{cite:8fca6987edd6a7090a21574a43bcd231f777ae97}}. In its original formulation in {{cite:8fca6987edd6a7090a21574a43bcd231f777ae97}}, this incidence-based method requires not only incidence data, but also the empirical serial interval distribution, i.e. information about the time period between illness onset in an infected case and illness onset in a consecutive case. Since reliable data on this was not available in the beginning of the SARS-Cov-2 pandemic, the German federal center for disease control and prevention, i.e. the Robert Koch Institute (RKI), chose to use the incidence-based method from {{cite:8fca6987edd6a7090a21574a43bcd231f777ae97}} and assumed a Dirac {{formula:9193515a-1ade-43ed-ac9f-4445a838add3}} -distribution at {{formula:c0fcf0f3-6ee4-49c5-86a5-47fc2da588e1}} days for the serial interval distribution {{cite:e1d8020e90df7e60921eb15fe1e48526bef9fc0e}}. This assumption of one single applicable value for the serial interval time {{formula:68c77d8e-ba01-4514-95b5-9cd337869551}} leads to an easily interpretable calculation rule for the effective reproduction number as the ratio {{formula:e34506db-376a-4fcc-8b74-d02def10edc7}}
m
33a8941d84e122cc3ca9572432731bc6
At this point, we have experimentally shown that our proposed detector outperforms OS-CFAR, OR-CFAR, TS-LSCFAR and CHA-CFAR in our specific indoor sensing scenario. The reason for this is twofold. First, conventional CFAR methods and their state-of-the-art derivatives (see sections REF and REF ) perform detection by ML estimation of the clutter statistics given a prior clutter distribution model {{cite:e7de227f8d16422a89524e5c83f091d1a02b3681}}, {{cite:fc22ed21f1c1142f0613f839ea1b40bfacbf2f30}}. Therefore, the performance of those conventional techniques degrade when the clutter distribution severely deviates from their prior hypothesis. In outdoor scenarios such as remote earth sensing, clutter distribution is often analytically well modelled by distributions such as Gaussian, log-normal and so on {{cite:7cd0bebf66a07a46c5209c6cf2b84c706ec49b73}} as the wave propagation paths are simpler. In contrast, indoor scenarios lead to severe multi-path effects as a large number of reflectors are present. In addition, floor reflectively is not always uniform which can lead to an increased number of clutter edges. Finally, compared to satellite SAR radars (as used in {{cite:e7de227f8d16422a89524e5c83f091d1a02b3681}}, {{cite:fc22ed21f1c1142f0613f839ea1b40bfacbf2f30}}, {{cite:ee97dc671b93f63281e96b46e083485c9ed6192c}}, {{cite:dbb8dfc3be8b99a437b4351d532511afd07ee9b0}}), our radar setup provides a much more modest resolution which may lead to residual correlations between the bins in the RP, violating the assumption of inter-bin statistical independence {{cite:090f1325aab9a79d4b2091babb1c2fff44a6874d}}. Fig. REF and REF show the goodness-of-fit of an RP data distribution against the log-normal and the exponential models, which gave the smallest Kolmogorov-Smirnov (KS) distances out of a set of typical hypothesis distributions (log-normal, Gaussian, Exponential, Gamma and Weibull) {{cite:090f1325aab9a79d4b2091babb1c2fff44a6874d}}. For both hypothesis PDFs, the KS distance is above one order of magnitude larger than what is considered to be acceptable in ML-based CFAR estimation {{cite:e7de227f8d16422a89524e5c83f091d1a02b3681}}, {{cite:ee97dc671b93f63281e96b46e083485c9ed6192c}}. {{figure:bea16c6f-02a5-442e-ad9a-9a312e7affed}}{{figure:2697cf0b-fb6c-4eb8-8680-655bb957d65b}}
d
2e81d765798734dca7ec2d042b6ee908
Point clouds, which are widely utilized to represent 3D contents, have played a vital role in immersive applications such as virtual reality {{cite:48d8f9a9c4366e147a4454b9ffeb58221c1a55d8}}, mesh representation{{cite:0f8e1586d9c3e7bb4704ce1423bc41cee212ad7c}}, 3D reconstruction {{cite:047e520c9701b119da9c871cea5017ade83d718a}}, and metaverse {{cite:834f6d30de2dbe7d1b3419f67e3ad152b75a34df}}. However, limited by the storage space and transmission bandwidth, point clouds inevitably undergo lossy processes such as compression and simplification. Such processes may sacrifice quality-aware information to compromise with the bit rates. Additionally, affected by the sensor accuracy and rendering techniques, unintended distortions like noise and blur might damage the visual quality of the point clouds as well. Therefore, mechanisms that can effectively quantify the distortion of point clouds are urgently needed to provide useful guidelines for compression systems and improve the Quality of Experience (QoE) for viewers{{cite:42a591224e0fab0e8429288fe189b34fd2690bb2}}.
i
2efb4509050c798ebf3a82ef65e8bc76
More concretely, we attempt to analyse a version of BERT, DistilBERT (that was shown to attain 97% of “vanilla" BERT performance {{cite:5f0f184ce386042e6faaddc9d45bac4a437fddd0}}), fine-tuned on the TREC 2019 Deep Learning track datasethttps://microsoft.github.io/TREC-2019-Deep-Learning/. We extend previous work {{cite:460a2ed4de71c146b55b83c7481bcdbf1188dc08}} by incorporating additional axioms (moving from term matching to semantic axioms). We find that DistilBERT to outperform the traditional query likelihood (QL) model by 40%. In contrast to our expectations however, we find that BERT does not adhere to any of the axioms we incorporate in our work. This implies that the currently existing axioms are not sufficient and not applicable to capture the heuristics that a strong supervised model learns (at least for the corpus and model we explore); it is not yet clear to what extent those results generalise beyond our model and corpus combination but it opens up a number of questions about the axiomatic approach to IR.
i
7da9d489c91e4683c795412934039a36
Variational inference provides an accurate approximation of the full posterior distribution. Still, it is generally not recommended to infer properties of an underlying distribution beyond the expected value due to the difficulty in verifying the assumptions regarding the factorization of the posterior distribution. This begs the question, why not simulate BN{{formula:b285cbd5-eaed-487b-97e6-9062db554e2b}} MF's posterior distribution with a Markov chain Monte Carlo (MCMC)? Several considerations led us to prefer variational inference over MCMC for BN{{formula:223ca723-d9b5-497f-a887-89572b8392dc}} MF. First, we developed BN{{formula:37fe64fc-fe8c-4c5e-a511-e94913daafd2}} MF primarily for use in environmental mixtures analyses, often performed by environmental epidemiologists. Variational inference is a more approachable method for many researchers. Pragmatically, by converting the inference problem into an optimization problem, variational inference outperforms MCMC in terms of analytic efficiency. An MCMC is more computationally intense and often assumes access to higher performance computing resources. Additionally, research on bounds for guaranteed MCMC mixing time is, in general, an open area {{cite:1fb5482042f79ac499e3205bf48a4b376d641c85}}, which places the burden of assessing convergence on the end user. This is not a trivial task, especially for users without formal training, and variational inference avoids it by converging to a local minimum. Multiple runs of variational inference are easily ranked in terms of performance; the model that obtains the highest objective value is the best approximation of the true posterior distribution. In this way, variational inference is more widely usable.
d
a3aa463f7d359414e7e461b53104e36f
Given a corrupted input image, our aim is to predict the missing region in such a way that it looks similar to the clean images to human eyes. In this paper, we propose a frequency-based non-blind image inpainting framework that consists of two stages: i) frequency domain deconvolution network and ii) refinement network. The overall framework of the proposed method is shown in Figure REF . In the first stage, we compute the DFT of the masked image (both magnitude and phase information) and the original RGB image and train a CNN for deconvolution to learn the mapping between the two signals by minimizing the {{formula:4bb247f3-1170-402c-9d4e-34926f1c59ee}} loss. Here we formalize the problem of inpainting in the spatial domain as deconvolution in the frequency domain. We employ the feed-forward denoising convolutional neural networks (DnCNNs) {{cite:605d4e68b13e5e144a3ecdb66957c10c6dbb6e18}}, a manifestation of deconvolution, which uses residual learning to predict the denoised image. The motivation behind this DFT-based deconvolution operation is to learn a better representation of the global structure that can serve as guidance to the second network. In the second stage, we use the spatial domain information (of the masked image and the mask) and train a generative adversarial network (GAN) based model {{cite:9d11268eadbc7dede04ff825f19a630d90436083}} by minimizing an adversarial loss along with {{formula:d9475a82-a585-4fc7-9f6b-cd3578a55d9f}} loss. The motivation to incorporate this stage is to fine-tune the output of the first stage by refining the structural details and matching the color distribution of the true image in a local scale. The various components of our model are explained in the following subsections. {{figure:01e50b84-b087-4130-9789-3fef9ab4c151}}
m
e09146279d99a98e0becf094c861c0cc
In this work, we demonstrate the feasibility of coarse, low-power depth estimation of real-world stimuli using event-based, mixed-signal neuromorphic hardware. Given their massively parallel, asynchronous, real-time computing features, and their explicit representation of time and space {{cite:14cacddec09996cb9f57e679047bceec342da03e}}, as opposed to their fully-digital time-multiplexing counterpart, these systems have the potential to achieve higher energy-efficient computation in a reliable way, despite the inherent noise and variability in their individual neural CMOS circuits. The major contribution of this work is the validation of a neural architecture for coarse, real-time, stereo vision with events from real-world stimuli. Unlike datasets such as {{cite:b9a9fdd830e2a23c44b7e54887389d5e49fe6571}} and {{cite:b167f6c124c25e3f04e10f194e917a44d79cbdb1}}, which can be used to compute the ground truth on a per-event basis, the Vicon marker-based motion capture system provides ground-truth depth information directly with sparse data linked to point labels attached to specific body parts. This approach is therefore suited for validating current small-scale analog implementations of event-based stereo vision and provides a compelling benchmark for cross-platform comparisons. While additional analysis of more samples from the DHP19 dataset can be useful for a full characterization of our event-based stereo-vision setup, this work sets the stage for using the proposed approach to validate novel low-power, coarse depth estimation systems that could be deployed in applications ranging from robotics to surveillance.
d
db0bdb97a15ccb9fb777f1bfd564603a
We compare our approach to several state-of-the-art methods: the out-of-distribution detector method (OD) {{cite:854af9ffb99e1a41786cfca0a4b416f798f25cb5}}, a generative approach to zero-shot action recognition (GGM) {{cite:5342cec3ef2ec1505dee125a2bc614fec31a6a21}}, the evaluation of output embeddings (SJE) {{cite:b4eb4c6e9224fd69b5117d42273f607993fe4d3f}}, the feature generating networks (WGAN) {{cite:e54a98db783c8f40f8d2ea9940f0ecdb48b69641}}, the end-to-end training for realistic applications approach (E2E) {{cite:9285735e3bc0cf2d8c2a776a7fc3903337499493}}, the inverse autoregressive flow (IAF) based generative model, bi-directional adversarial GAN(Bi-dir GAN) {{cite:99fb88681af2b361cd36dd488f2a8c9a20a816e4}} and prototype sampling graph neural network (PS-GNN) {{cite:dd4ae3868b43e90451069edccc92764e6db220c8}}. We use a pre-trained model on Kinetics.
r
ffe4d5c620ad9e2f7feccd205df7f645
In this work, to address these issues and limitations, we propose an approach based on self-supervised speech representations using wav2vec 2.0 {{cite:4b478c7d6196db22cd2806c41338dc090ffb321f}}, {{cite:578c4ac08792579be01b78885162582d3ab49692}}. Recent studies have demonstrated that self-supervised learning (SSL) is an effective approach in various downstream tasks of speech processing applications, such as ASR, emotion recognition, keyword spotting, speaker diarisation and speaker identification {{cite:4b478c7d6196db22cd2806c41338dc090ffb321f}}, {{cite:13f4f1aae90f2b8bd77fe7706530682a84c2eb86}}. In these studies, contextual representations were applied by means of pre-trained models. Specifically, it has been demonstrated that such models are capable of capturing a wide range of speech-related features and linguistic information, such as audio, fluency, suprasegmental pronunciation, and even syntactic and semantic text-based features for L1, L2, read and spontaneous speech {{cite:57ccb8281a3deb3823eee73f08bd11080d7a970b}}. In the field of CALL, SSL has been applied to mispronunciation detection and diagnosis {{cite:fa136f994d12286dde1e45e1a82ed410f64e4f69}}, {{cite:dc1050b4d5f2f07c5fe48630703e5d177d356a0d}}, {{cite:0a7d05623328e4eb6c8128925d13424031c48215}} and automatic pronunciation assessment {{cite:d96d36ede679cb1e6316ab790db5a678211275f6}}, but, to the best of our knowledge, it has not been investigated for the assessment of overall spoken proficiency nor of other specific aspects of proficiency, such as formal correctness, communicative effectiveness, lexical richness and complexity, and relevance.
i
bec34bf679d2284df28133e414e14310
The CCA between two subnetworks for individual {{formula:725fcb95-3e2a-4f86-a811-bbe97998979a}} is a stochastic Poisson process. The time interval distribution between two successive actions of {{formula:0e472b69-0233-448a-97a3-3b312965ea70}} in subnetwork {{formula:5078fc8c-c51f-43c5-bd95-3ddbc643792e}} is {{formula:f4fd55fd-ee9e-4c4f-8e6f-22dec982b49d}} {{cite:2fd1d90a91d1624a61feae5918f2e64ca6d4f0c4}}, as shown in Figs. REF (a)–(b) and (d)–(e) where {{formula:15bff0fe-51ec-4c44-9ace-efedad05fc6d}} is the probability that {{formula:ab0f0ebe-fa24-4726-829e-8b7b200c3bf3}} is active in subnetwork {{formula:79b0113c-73d4-4c53-8de5-f31e65307015}} . Note that we use random regular (RR) {{cite:6999c9a9ce29d93ec607f346216a69c4426625db}} networks to describe the two subnetworks {{formula:07298c60-af22-47bb-ab3e-48bbff9957e2}} and {{formula:98c525dc-2eff-41ce-951f-ea5f295d9dd9}} in Fig. REF . All nodes have the same degree in the RR network, i.e., {{formula:54a27bba-c150-4a1b-b091-afdec90d9a77}} if {{formula:b1b586cf-0004-4d6e-81e9-72b1c5ef183c}} . Each RR network can be built using an uncorrelated configuration model {{cite:635fed9698a99a3fc30a2a91efefae7ed28e53a8}}. We find the approximate average time interval of all individuals active in subnetwork {{formula:c85e7a8d-72b5-4837-801f-f663a87acc85}} to be {{formula:73e0063e-3356-4975-8e8e-d8c8002dd497}}
m
4e4613eea3f945d4c67423ca7bef9d9a
In this work we demonstrated empirically that the model randomization tests proposed in {{cite:e9d371bf147878770393d42e9cca9d2e9bb00caf}} are distribution-dependent. We have proposed performing the sanity checks w.r.t custom tasks in an attempt to control for factors that may confound the results. Our simple experiments demonstrate that doing so reverses some of the initial observations of {{cite:e9d371bf147878770393d42e9cca9d2e9bb00caf}}. We emphasize that this does not challenge the basic idea, which is that for debugging or explainability purposes, one should not use saliency methods which are independent of the model to explained. What it does highlight is that when performed carefully, the necessary condition this perspective proposes may be too weak to provide meaningful distinctions between the existing plethora of saliency methods. For example, as we have shown in this work, both vanilla backpropogation and guided backpropgation pass the modified sanity checks – and hence there doesn't seem to be a reason to prefer one over the other on the basis of the sanity check methodology. It would be interesting to explore whether semi-synthetic, engineered tasks, as we used in this work could be used to compare the utility of different methods on a per-task basis.
d
63333c9820a60aa0e8fe485d9a0aa25b
We first would like to highlight the fact that in this work, we do not propose any novel network model. We rather show that the state-of-the-art models (e.g., EfficientNet {{cite:a617b48ec542754a22bc2de7da5609916e71a222}}) can already handle the challenging state estimation problem with the help of transfer learning. Our reported high accuracy scores in Table REF already show that there is no need to focus on designing new deep network architectures. Instead, we should address the domain shift problem. Our results show how the network loses accuracy very fast when presented with new unseen deformations, due to the high dimensionality of the cloth state estimation problem. We, however, show that fine-tuning the network with very few new frames can again boost the performance. Despite the domain shift, the class activation heatmaps in Figs. REF and  REF also clearly ensure that our network focuses on similar manipulation relevant regions such as the grasp points, cloth edges and corners instead of the cloth textures and patterns.
d
c0f6c50edb0442b24b1893b800f3b0da
In this paper, we also show that if a {{formula:5771c0f2-415e-4b34-bb0d-6f08a144ba84}} -dimensional BCFT can couple to a {{formula:ff5e56ff-6e5c-4461-8d41-f6ac7ef5b789}} -dimensional gravity with a boundary, the energy-momentum tensor should satisfy nontrivial constraints other than the ones for the boundary conformal symmetry.Note that even if we consider the AdS/BCFT, this {{formula:f8602900-9f93-431d-8ddc-560242bf08ad}} -dimensional gravity is different from the {{formula:dbcd5711-728a-4356-956a-6f27c6217164}} -dimensional bulk gravity. More precisely, we need to choose the boundary condition of the gravity. We consider two known consistent boundary conditions, namely, the Neumann and the conformally Dirichlet boundary conditions. We note that the Dirichlet boundary condition may be incosistent{{cite:18e4bbbbe09457a9bcc6306f786b8a5db61916fa}}, therefore in this paper we do not consider the Dirichlet case. We find that the necessary conditions for energy-momentum tensor in the BCFT which couples to the gravity with the Neumann boundary condition are {{formula:788ae235-f123-4be9-aa8f-e9dea2b5a29e}}
i
7b54fb0363d0f69872531c0e298c3bc2
 blackLastly, we mention that in some communities (optimization for example), the algorithms that avoid or use gradients are termed zero-th order and first order methods. Similarly methods that use hessian information are of second order. The method we propose in this article can be viewed in between zero-th and first, since it eliminates a large portion of gradient calculations. Compared to zero-th order method, the advantages are obvious. All zero-th order methods converge slowly. One such example is the random walk Metropolis (RWM) that converges in {{formula:9fc6ab27-5109-4f63-9926-59ac82a44efa}} iterations {{cite:ca99ef182001bf1acbcf7cc43716d01e2bdd6a5d}}. On the contrary, LMC converges in {{formula:dbb5fc02-cb34-45f9-a6bd-db9c17170f4f}}  {{cite:6542532473bd7ac83d63499c2b8c2843d625ef7f}}, or sometimes {{formula:ef1315ee-10a4-4182-9988-f37a4c17cb65}} iterations when {{formula:9c451e57-1dbe-423d-9cbb-13794b6f84c4}} is sufficiently smooth {{cite:fa6fd33e5d100591f911ad858931e7d3457d1ecf}}. Our method matches the convergence rate as the classical LMC, but eliminates gradients, meaning it achieves the first order convergence with a zero-th order cost.
i
5ce5634b472697d3c1b47428c06bcefc
Under ideal convergence, these two discriminators help to ensure the realism of generated images and the reliable random combination of content and style representation to create a hybrid imageWe use hybrid image to represent the generated image whose style code and content code are not from the same source.. More training and architecture details can be found in {{cite:62a191ef9a3bb9047185a72d3d11033ed410b5ce}} and our supplementary materials.
m
9e01bbdc3877f09d351880b11189485c
Observation of superfluid to Mott insulator (MI) transition in a system of ultracold atoms in optical lattice {{cite:b70dc0a19bc36d890ef2c00aeebdd3e04207b9b2}} as well as the advancement of quantum engineering techniques has opened up the possibilities to realize various exotic phases of interacting quantum systems, which are otherwise difficult to observe in usual materials {{cite:2f8a709f2bd68c95fc42aea6616399c5d25a102c}}, {{cite:e19ccde8e17a3a4511611b402e5545734730e483}}, {{cite:cd8257abf30f3e3e3c0f528ed07a44aa9eb8d974}}. Supersolid is one of such phase which has been speculated since early 70's in the context of superfluid {{formula:1e0b0f40-93f3-4752-aab2-41684dbdd13a}} {{cite:e519a050104f7d605c5584b93578c3a02da19ba7}}, {{cite:c32acad0a296ef99e6296b3bfa8c94fbd2e90037}}, {{cite:d588f28c17ae5476a05ff4924a4013e9f591da11}}, {{cite:3a87c3db7131c3be5fb350edd0e1c82f80919ffe}}, {{cite:7c7de2fe6cd75131692d2468f6716b8306bf6775}}. It is believed that, in the vicinity of solid phase, the density ordering can coexist in superfluid, resulting in a supersolid phase, which has not yet been confirmed in case of {{formula:d31d1e7f-c92d-43a4-b5e9-639bf0dccfc6}} {{cite:e9b0fe47ca4458e25df13828659f3a64319331a2}}. However, ultracold atomic system has become an ideal setup to study such exotic phase of matter. It turns out that in addition to the short range on-site repulsion, an effective longer range interaction is a key ingredient for supersolidity, which is present in dipolar condensate and ultracold Rydberg atoms {{cite:91a72428af2849827d6a64cc635c6763f478d6ee}}, {{cite:b6f7d238abaf0795ee062a47a4bbe72513e7caa1}}, {{cite:38485cf03a4ae3c1916fddc3bff77a9b3c05543a}}, {{cite:63766bebaf505b624c241978924c71aec7955a79}}. Remarkably, the evidence of supersolid phase with coexisting density ordering and superfluidity has recently been confirmed experimentally in ultracold dipolar gas of {{formula:f85746fc-4de8-4ba9-b742-78e584989a77}} and {{formula:f98b5737-895f-490f-ab00-c6c8eeaeb2ab}} atoms {{cite:491d06215fe351dccc5185ac13779725142831bb}}, {{cite:4522f255c9cab84c4d41b90b2b93a0252c18a301}}, {{cite:582e48e5e9f11ce8f5546b614dd57fdb55915512}}, {{cite:7ab9cbaf7c478caed1da334dc72ca6043c85b39d}}, {{cite:573aeb2ecc0a03118a0383941f77a1f4d7ac34a0}}, {{cite:23826243357c8f2c5fae7fb4e815b51c7a54b2b2}}, {{cite:159ffd249a30ff95f34eae040b48c18ccd8326bf}}, {{cite:37e9acd23cd6dc6c68a01874e65c559094a54855}}, {{cite:a714f49e0f87c702ce98b7bd0048cb8650e0b000}}, {{cite:87f469043615e379ac6fe41398d1736faeb393a0}}, {{cite:1b3c56f937da62392c667e60dd7a0424288455b5}}, {{cite:94b6e5da8e5bc9fab2996a10266314bb0b0c3b76}}, {{cite:84644ccfde5016b07a45b1a0b492e46771b25510}}. Apart from the dipolar condensate, supersolid phase has also been realized in a recent experiment by coupling a condensate with external cavity field {{cite:c219af9de8fe0af6ef4ede88f07cd7b8693ad391}}, {{cite:210a39012ebb21b64bdefbe4aba3911d6e5a8dff}}, {{cite:2599496a5d6003c4f79f0941744a3b9caed7b2a7}}, {{cite:0f7323ee6a7ecc64d209282486ab5ad8ff29a718}}, {{cite:5b21ca6cf6a4bb71910db6a93a8b377944657600}}, {{cite:10a487948f49ef2138d50c2deb2c172af9da5e71}}. Moreover the superstripe phase of condensate with spin orbit coupling also exhibits density modulation similar to the supersolid phase {{cite:342b45ee6d894bf4424abb9050fd978c66b331c4}}, {{cite:193df5ba7663bb9f5fc84a7952690e617c35f3da}}. However, bosons in an optical lattice is an appropriate candidate to investigate the original idea of supersolidity arising as reminiscence of solid phase, where the defects of the solid can condense to form superfluid. Formation of supersolid phase in strongly correlated bosons has extensively been studied theoretically for various lattice models using different techniques {{cite:d115c2d3721f20e4c589c07d0d6d55f7f2d426d1}}, {{cite:37db7a98cc22f86c9606f5f6f34c8388416297e0}}, {{cite:546a2dc83af7d6a3bc33c8184da6f5523425306c}}, {{cite:2623de0f5b6fa9aa9bc12d4120fc9d92989309db}}, {{cite:6c74fc02f47413bc79e9af23d8bf4f64a464b8a4}}, {{cite:bf93e649121eef0af91b3b896e3716bb32b1400a}}, {{cite:36ebdf26889950cea78d010697b60f33d31a307c}}, {{cite:99b23d3ced48e9242955ac1ce6be1bf138e38fcc}}, {{cite:14f169c49dd3a1fa8490ed4b85e08673dffcd132}}, {{cite:01fcaf0487588c59546050317a86bcb1d9d0bef7}}, {{cite:2be304c0139c6eb7e5141acef653d9f350e5ab4c}}, {{cite:8f8c8e9886e3dadd463545592aa0a7ad19d50d68}}, {{cite:f51b48116ad6370a241647c6fa2b833303758151}}, {{cite:9ad2e2cf4adcfe12d84e327088d382d9ee9e469e}}, {{cite:93c6fe40a33f4e9d8bb848f3a461c60f54712d7e}}, {{cite:07b23a777017391a20bcc172e94067e11f04dd4b}}, {{cite:000891780fc50b04503694ad77c8bf2a9bfdc53f}}, {{cite:88dbc4c7b72e8f95804e121520046ee37bd696e7}}. In strongly interacting systems, particularly in one dimension, stabilization of supersolid phase with coexisting ordering is a delicate issue {{cite:ae0a5e4eeee70435c50836b0a189eba700d062cd}}, {{cite:b7e95601017b09983eba2e0d79c2d097410d931a}}. On the other hand, frustrated lattice such as triangular lattice favors the formation of supersolid {{cite:3b4b6bbdda2cde652393e51d0f5c52db83391cf9}}, {{cite:144da52ce4e1ab1c271995f44dc05b0d2887d0b4}}, {{cite:00254c727792add0b9d6502604570ebb8e4c78f1}}, {{cite:9c4df0946675e9b4bdb661c5603f248bb3c8f354}}, {{cite:29f5f5795151c95cc3e4367231e03ee5ef97ff02}}, {{cite:dd9d5604ff4702e23682a48e07ae2816399c3994}}, {{cite:96646968b6c308b13bc85e1505f6115ff702f941}}, {{cite:53cea054578223859beefbfb17645aa42d5e71b3}}, {{cite:d9bedd96d831c5f059c3435f8816635f5b617568}}. Apart from the gapless sound mode which exists due to the presence of superfluidity, the supersolid phase has an additional Higgs like gapped excitation, that has been recently explored in the experiments {{cite:210a39012ebb21b64bdefbe4aba3911d6e5a8dff}}. Such excitations can serves as an important characteristic for the supersolid phase. Moreover, the nature of density ordering in supersolid can also be probed from the excitation spectrum.
i
25ec11b48e1e0aad493b57ca49c334b6
The ring here is the 0 ring, whose set of elements is {{formula:24681ea7-e157-491f-9838-37a70697b1b3}} . The definition of the operations {{formula:95dba085-f343-4592-aecf-7e952167bb47}} is immediate. A proof of this fact can be found in any undergraduate textbook on linear algebra for mathematics students, as long as that textbook covers the spectral theorem and SVD. A proof of this fact can be found in any undergraduate textbook on linear algebra for mathematics students, as long as that textbook covers the spectral theorem and SVD. See {{cite:448f9cedbd7da74f86eac58ff8de2773a33dbe94}}. See {{cite:448f9cedbd7da74f86eac58ff8de2773a33dbe94}}. Consequence of Theorem 2. This follows from Theorem 7.2 of {{cite:b7229a7ac9a0c812c4178dc29948eea865b5e29b}}. See {{cite:ab2f2b4b1df2b92e62a1e07c8cf2e666d6849e47}}. In this case, we haven't stated the result clearly enough that we can prove it. If we wished to, we could state it rigorously and prove it. Note that a unitary matrix {{formula:98f286db-b627-4fbf-b5a3-2f13d896a321}} that is also an integer matrix is precisely a signed permutation matrix. Two undirected graphs, represented as adjacency matrix {{formula:bb4793b6-e1e6-4f0c-98b6-2614619f9aff}} and {{formula:4bfb2ac5-bcca-488c-a85e-75f68fd0f58a}} , are isomorphic iff there exists a permutation matrix {{formula:cb1022dc-f657-48c1-9d01-504202855d3b}} such that {{formula:ab7b84e6-451b-43e5-a1a7-24cc9b84deb1}} . The generators are therefore connected graphs which are combined by direct sum to form unconnected graphs. See {{cite:a65b5d3ef3725fbd43a8388b697696ec0355b69c}}.
r
27f47c2b0197965feaa17413d4552711
Existing person Re-ID approaches are mainly divided into two categories: image-based methods {{cite:57c434a944d4bf7d0f86155950e2cc83fc82fe37}}, {{cite:dadeb0bf1340e20b5221271135ff24c6b16033b3}}, {{cite:e9a2356895bec1e658863603fac76af091f8c96e}}, {{cite:47174ef90a55988eeee66d9f75c66fd634661da3}} and video-based methods {{cite:f2cd842daadf3e65fa045b4243da4bfd1f7d1236}}, {{cite:622675ade41d296fad024f0f253ec728381016ec}}, {{cite:dbb993ba8185cb9fcff8320b9af861901117d98f}}. The former exploits static images without temporal information to retrieve pedestrians. It has achieved impressive advances with the surge of deep learning technique in recent years {{cite:2de6ea42adf8ace979f81d77a9acb4a5934869f7}}. However, image-based person Re-ID heavily relies on the quality of static images, which are sensitive to noise, occlusion and viewpoint variation, etc. Different from static images with limited content, video sequences contain rich spatial-temporal information across a long span of time, which can provide clean and informative clues against these problem {{cite:dbb993ba8185cb9fcff8320b9af861901117d98f}}, {{cite:8bb5bdf427f6321c1bc1cdf56a344cb72191beed}}. Thus, video-based person Re-ID has the potential to solve the restrictions in image-based person Re-ID.
i
049a7dbf2ac76f5faa713434cb961401
In this study, we obtained the light curves of an eclipsing binary system, DK CVn, in two observing seasons, and we analysed the BVR light curves obtained in 2008 to find the physical properties of DK CVn. In addition, using Kepler's third law under some assumptions, the possible absolute parameters were found. The observations demonstrate that the radii are generally larger than the expected values. We compared the radii of DK CVn's components with the known active stars and a model. The radii of the active stars, which exhibit spot or flare activity or both of them, are dramatically larger than the values given by the model developed for the stars with {{formula:89230ea8-c1d3-47a2-8a28-68593a2c583e}} by {{cite:e63c1812a12616afa8fcb89fddf5fd4a1410f4bc}}. The components of DK CVn are also in agreement with the other active stars, listed in the catalogue of {{cite:9bb921288da42d0f431ad6d530c615e872f0f85c}}. According to several theoretical models and observational studies {{cite:9d7b7ff3b13b3bf93e09726100154f150abc7c37}}, {{cite:1d00fe2ff793c4c2a6d15be7f6d6da4750f6f175}}, {{cite:097dc302e56106b8e26b5f8e177325a81b84803a}}, {{cite:b7ea684e6be0a6c00f3ac625109636aee69082a5}}, the case seen in Figure 7 is a well known phenomenon for low-mass active stars. For instance, YY Gem {{cite:6949ee812ea3875116b117f48e03650364f16fe2}}, CU Cam {{cite:e8571edc1c4d71d93c6b64780f494e13163bc6c4}} and CM Dra {{cite:a873d303e65369f5bfa057eb364e8b315909c0b6}} are the most popular system for this case. There are several similarities between these three systems and DK CVn. Firstly, all of them exhibit the spot and flare activities, and they consist of the low mass components.
r
e4d7997d9a6d71ac07c449c726211a48
Access to reliable information has always been and will continue to be critical to people's lives and rights. Diverse ways to retrieve information include text, voice, and image queries to search engines, which systematise human knowledge and provide universal access to hundreds of billions of worldwide web pages (or simply web pages) daily {{cite:33153746d6e70fdea0b46baf09ff44072e720b7a}}. At a query time, the most relevant pages are returned in a fraction of a second. Behind such impressive time performance lie significant computational resources that can be divided into two categories. First, the semantic meaning of a query is analysed by applying traditional information retrieval techniques, combining advances in computer science and statistics, and machine learning methods, including the latest natural language processing algorithms for context analysis {{cite:821a514efce84b493ea491a58a077e70b0bc2986}}. Millions of pages are retrieved with potentially relevant information to the query. Second, before the search happens, the database of publicly available web pages is precomputed and organised by applying hundreds of ranking metrics covering the linking structure, keywords, location, and content freshness of each page. By combining the ranking scores of these two steps, the final order of the most relevant web pages is determined in response to the query {{cite:84cc4eb209ceed5ecc2849838c65de1e8269190d}}.
i
8bee8b3b5930e0c0408f411c94135b99
A cornerstone of the field of quantum phase transitions in magnetic materials represents the development of a continuum quantum field theory using a Landau-Ginzburg-Wilson functional, taking into account quantum fluctuations of the order parameter. As established by the seminal work of Hertz {{cite:93ff41d7f571a257dbd99b6e9603a773a3e168d5}} and Millis {{cite:05d19073eabeb088b24c43a95b10315debc347a8}}, in this approach the time direction may be interpreted as an additional space direction, such that the quantum theory of the zero temperature phase transition in {{formula:ebfd3125-1082-4a2e-ba93-c76c5bc5288b}} dimensions is equivalent to a classical theory in {{formula:a376fe99-cb83-4591-b661-4d7428cfe95f}} dimensions, where {{formula:c4c02254-ea59-4f7b-834f-c3b954682941}} is the dynamical exponent. In turn, mean-field critical behaviour is expected when the effective dimension is at or above the well-known upper critical dimension {{formula:e29674b1-b387-4f38-bef1-247248e9ee29}} . These mean-field predictions of quantum critical transitions triggered a large body of developments.{{cite:047b8dfe00a0f737f01a8e73527503c98e8ec174}}, {{cite:71f9e661503e615d44ebcff0092c55cd1773b9b7}}, {{cite:e14aa32b9c64a7fb24ce7c08de81aa318fa691ab}}, {{cite:12d13809ca3cc87fef94d388ba9661758028d905}}, {{cite:b00e9651e388b7e717d06ef10bc080c4016e17c5}}, {{cite:0c7a163f215b0c1eb91c06e1bd1a16a4a0dddb35}} Theoretical work in the preceding decades that took into account material-specific properties revealed corrections beyond mean field behaviour. For instance, in itinerant-electron magnets the additional presence of fermionic degrees of freedom was found to cause additional soft-modes {{cite:34f57289759f571e3c27302ffbf74a7b516d2ae6}}. Another example are Berry phase contributions, which were found to be important at quantum phase transitions of frustrated spin systems.
m
217ab53e48d8c83cefb420bf990b6bdf
In its introduction Ref. {{cite:a691189d6d1e44832cdf6272b51a6df3e4b08aaa}} asserts that a {{formula:55add2f0-155a-4b52-a076-be82cf83b634}} spectrum “carries information of the dynamics of soft and hard interactions.” As noted “The aim of [Ref. {{cite:a691189d6d1e44832cdf6272b51a6df3e4b08aaa}}] is to investigate the importance of jets in high-multiplicity pp collisions and their contribution to charged-particle production at low {{formula:043b26d9-aea0-4949-8898-5c4820389b6a}} .” It is proposed to “disentangle the energy and multiplicity dependence” of {{formula:f40f09a5-e024-47d3-8421-e816461d9a14}} spectra.” The TCM has been applied to {{formula:7f1e9a79-20f8-4b70-ae7f-1f3893a60cac}} -{{formula:7d762b3c-0b6a-4756-81fe-5d832fcd0ddf}} {{formula:7e957b2c-d233-4c51-9f9e-fe971a218a22}} spectra over three orders of magnitude of {{formula:6c305f5a-6be3-4dc9-b90d-e39aa7b5d939}} -{{formula:b87b2d7d-a3eb-4a8b-bc7e-3e57db4d2400}} collision energy, and after fifteen years of development arguably extracts all available information from {{formula:719096b1-8e26-4ef5-80f5-d1f50bb58110}} spectra {{cite:a0e89294967f166c0c530b68f6e070c7c0cf277e}}, {{cite:184a0d1d268bb4f7573cb6f25c024077f3e91920}}, {{cite:c94b09cb2cead7f04b334933963166348a0cfa3b}}. The energy and multiplicity dependences of {{formula:29a96692-e5c1-491d-b548-93e68682026c}} spectra are indeed factorizable, but the energy dependence requires a large energy interval to identify systematic variations accurately; the interval 5 to 13 TeV is too small to do so {{cite:184a0d1d268bb4f7573cb6f25c024077f3e91920}}, {{cite:049140b7fe9455a3861c86f4d112b127882f1e9b}}. Given those observations it is instructive to consider certain comments within Ref. {{cite:a691189d6d1e44832cdf6272b51a6df3e4b08aaa}} relative to TCM results.
d
893e2df1ede5aa4abd33f2366a772d80