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Quantitative results.
Tab. REF shows that our proposed method outperforms other baselines by a great margin in LOL test-set. It achieves the highest PSNR on the MIT-Adobe-FiveK dataset, but slightly lower than MBLLEN {{cite:bee447fde11d9e7acf473c80ad9f2cdd707448fa}} in terms of SSIM and LPIPS.
In Tab. REF we report the NIQE and SPAQ scores on the LLIV-Phone-ImgT dataset. As shown, our method outperforms some of the methods including LLNet {{cite:1d9ff405d5b878b83669636db2f02a9adc73b9b5}}, LightenNet {{cite:f02d0c1e099e7d5838c8ea86852f06c35f72595a}}, DRBN {{cite:51c01d667210604a74bc8255a9d0b04c89eaaecc}}, ExCNet {{cite:f01b2458c60fc8c3e06b0b85f906e764e843c84b}}, Zero-DCE {{cite:011d53c46c8d6aa9d499f8f804890280276650ed}}, and RRDNet {{cite:8eb03c612445aae18ebcd1aedfe15227bd912b91}}; however, it achieves slightly lower than comparing methods RetinexNet {{cite:39a3422d7d1c9dc6096bbb932d778e5a85a7cfff}}, MBLLEN {{cite:bee447fde11d9e7acf473c80ad9f2cdd707448fa}}, KindD {{cite:6871dada344d476afb10453e4f03b75cbe83ee08}}, KinD++ {{cite:4d47595f8287ea46640cb266aa4c49b7aaa06f5d}}, TBEFN {{cite:f64ee5b75afa40feb222fa04364764f3564fd98e}}, DLSR {{cite:e2b1150873178b40777980fe580aedebc8e4bfb4}}, and EnlightenGAN {{cite:95a68e6ce1f03a318e155ad099b62dea057bdcaf}}.
| r | 4fdb310e66ba3165459aeef09c952d7b |
Our results demonstrate that self-attention is competitive accuracy-wise when training on ImageNet from scratch.
Figure REF shows that pure self-attentionBy pure attention we mean models that use self-attention in all layers except the stem, which is convolutional. based HaloNets are currently slower to train than the corresponding EfficientNets and require further optimizations for large batch training. However, our hybrids have the same speed-accuracy tradeoff as EfficientNets. On transfer from ImageNet-21k, our models outperform very strong models such as BiT {{cite:7de4d7f0d79830843a7431e17c10676b95e1070c}} and ViT {{cite:07c56a250b028f47a9a135cf3cffc83da1c659bf}}, on both accuracy and speed.
Model optimizations, such as using architecture search methods to find better speed-accuracy tradeoffs or different forms of more powerful and/or efficient attention forms {{cite:a94fbe453207328cbbda8c875993473d9ce5196b}}, {{cite:212de8cdfe2199ddb63b8b8be6c2758737760e06}}, are promising directions for machine learning researchers.
Implementation optimizations, such as better memory management, can improve the practicality of these models. Also, scaling up our models to larger widths might cause our operations to transition from being memory bound to compute bound, and lead to better speed-accuracy tradeoffs. We leave this study for future work. Overall, our work shows that self-attention can be competitive in regimes traditionally dominated by computer vision.
Future work can push these boundaries further, both in terms of scale and efficiency.
| d | 3e545937daecc141a82dce9a93cb6e15 |
where {{formula:01e79064-d586-4eeb-9353-2faaca228403}} are the observed data and {{formula:e5ba2716-6f11-4c5a-a4d9-c02148e5c469}} is the {{formula:214077da-f135-4a49-99d3-983416ef93de}} -dimensional deterministic signal with structural changes at certain points. The signals that we treat in the current manuscript are those that changes appear in the mean structure or in the vector of the first order derivatives. The diagonal matrix {{formula:f95b0cb7-4b4a-43c6-8297-1d4d9fdde560}} has diagonal elements denoted by {{formula:a1ac6d11-7adc-4f13-9276-e636c8f91157}} , while for any {{formula:21985ec9-4b4e-4b1f-ac24-3ef442294c3e}} , the noise terms {{formula:59ba84b1-b2ed-444c-9fa8-0c3606040b9b}} are random vectors with mean the zero vector and covariance the identity matrix. The elements {{formula:2f8d4e4a-4382-4412-83b9-aed6c280a697}} of the diagonal matrix {{formula:405be90a-c552-418e-9d3f-64bd7ca5d2b5}} might be unknown. In such cases, {{formula:cdc288fd-a6f4-45b0-b6d7-c05c4eab8e1a}} are estimated using the Median Absolute Deviation method explained in {{cite:0cc351126cf432a30f9b9ae93ae9aef94bc63145}}. The true number, {{formula:0793ef26-ba40-4716-bdfd-2a15abdd10f0}} , of the change-points, as well as their locations {{formula:63ec6599-aece-432a-a2fe-f2ed4062f61e}} , are unknown and our aim is to estimate them; {{formula:0f9cdb5c-bb66-4eae-a788-e5df15156ab7}} is free to grow with the sample size {{formula:7029b895-0c39-406a-a551-4a6235f00091}} and the dimensionality {{formula:2f77e009-fb70-4d7f-8a3f-695bdb15727a}} .
| i | 13b5507ad55d455e4cf6a54bfa7b7588 |
We have shown how recent dispersive results for exclusive-mode
contributions to {{formula:231b6bfa-16d7-4bdd-87c8-fcccee5e0de9}} can be used to provide a
determination of the corresponding isospin-limit, light-quark-connected
contribution, {{formula:4e9390df-f547-467d-99a6-3db0dfb7376a}} , the precision of which turns out to
be of order {{formula:312935e2-350f-4538-bd18-95bf50e91687}} . The determination employs lattice input for a small,
{{formula:2c262ff3-54ac-45ed-8b9c-57797132b873}} , EM correction, but is otherwise purely dispersive. The result,
of course, depends on the choice of exclusive-mode input, and small
differences in the KNT19 and DHMZ assessments of individual exclusive-mode
contributions lead to an associated {{formula:b79ba10e-e6aa-4dad-8f03-2159f0b2a2e9}} difference between the
{{formula:8d2f273a-6cf1-496d-8d82-6b39ab0bc9a5}} results obtained using KNT19 and DHMZ input,
given in Eqs. (REF ) and (),
respectively. This difference is similar in size to the errors on the
individual KNT19- and DHMZ-based determinations, and sufficiently small
to allow meaningful conclusions to be drawn from a comparison of our
dispersive results to those of recent lattice analyses. This comparison
is summarized in Table REF and Figure REF .
Our dispersive results
lie lower than the majority of central lattice values, though some
variability, at the roughly {{formula:142b1f1a-0aa3-4491-ba1b-23e4a0d997a9}} level, remains in the lattice
results. Among the lattice results, that of Ref. {{cite:0e8b2cabbb9d714cae0c724f15dd977a2693b2fc}}
(BMW 2020) has, at present, by far the smallest error, and would strongly
dominate any putative lattice average. Our KNT19- and DHMZ-based dispersive
results are in {{formula:556a84d9-3974-44b0-beab-4f4c929e0a72}} and {{formula:999e6912-81a9-437b-b84d-8e5aace6ac9f}} tension, respectively, with the BMW
2020 result. Other lattice results, from multiple groups, with similar
or smaller errors, are anticipated in the near future,
and our dispersive results provide a useful comparison target for
such future lattice determinations.
{{table:c174c22f-98d4-4910-9d58-e215c06c3a03}}{{figure:e48fcf20-34b4-41c8-95e0-c5a13fb39ce6}} | d | d22f2b2ba315083d9ba4fc83c532ea57 |
The most common approach for associating neural network components with linguistic properties is to predict such properties from activations of the neural network.
Typically, in this approach a neural network model is trained on some task (say, MT) and its weights are frozen. Then, the trained model is used for generating feature representations for another task by running it on a corpus with linguistic annotations and recording the representations (say, hidden state activations). Another classifier is then used for predicting the property of interest (say, pos tags). The performance of this classifier is used for evaluating the quality of the generated representations, and by proxy that of the original model.
This kind of approach has been used in numerous papers in recent years; see Table REF
for references.A similar method has been used to analyze hierarchical structure in neural networks trained on arithmetic expressions {{cite:c45becd7e07e371c3b9d804139f754a6263d8e95}}, {{cite:0973d78f557d6e315462567883d27281cc90e575}}.
It is referred to by various names, including “auxiliary prediction tasks” {{cite:59628acf8990b9f993511651697c08be0a22ceed}}, “diagnostic classifiers” {{cite:c45becd7e07e371c3b9d804139f754a6263d8e95}}, and “probing tasks” {{cite:4b9c7fff66a871d52bba87bc30a4b26bf8b5f812}}.
| m | 08844bde6e05359997233f5eebb0d0ca |
In this work we address two long-standing challenges that arise in the context of neural networks, and dynamical models of biological systems more broadly: i) how to implement a memory for continuously varying quantities without using special symmetries of fine-tuning parameters; and ii) how to generate long timescales in the collective dynamics without fine-tuning parameters. The ability to implement memory and generate long timescales underlies several functions critical for survival such as evidence accumulation from a noisy signal {{cite:19eb01045ba74f6d19366f980892a4120280f679}}, {{cite:4039142230ae30a24ecd7b3c2e8c335a9f05c1a2}}, path integration based on velocity cues {{cite:d98b067c376074d553dc919ca461389736d8cc69}}, implementing cognitive maps {{cite:1c4b7337a862c2c6f37d1f6c2dc4403e69e804a7}}, {{cite:c3d0f5b8129898655cd3c17180d8b773a0e9d050}}, just to name a few. Implementing memory/long timescales requires the system to be poised at the edge of stability-instability, and prior approaches to this problem have typically relied on systems close to a bifurcation point, thus requiring tuning parameters to a special value. Marginal stability without symmetries or parameter fine-tuning requires the system to dynamically self-organize into a critical state. This is a highly non-trivial phenomenon, and apart from specific models , more general principles are hard to come by.
| d | 669d40a256175c460213614244de1546 |
In this section, we briefly describe the numerical methods we employed to solve the differential equations in this work following {{cite:877afa9ff8fb6fec7eb67a03977d4edfe31b0647}}, {{cite:f80920c138c6bb3248efcb8a948b1ccd4a69de7d}}, {{cite:5595c0dd0c3a94fbbf6fdd394e36b794d8a96777}} (for a detailed introduction see {{cite:ea0e91ba37f29873b6ebd06e392017d47350155d}}). Both, the background equilibrium solutions as well as the solutions to the linearized perturbations about the equilibrium state are obtained by means of pseudo-spectral methods. The idea of spectral methods is to approximate the numerical solution in terms of basis functions on a discretized grid. Throughout this work, we choose Chebychev polynomials as basis functions and a Chebychev-Lobatto grid to discretize the radial direction. Spectral methods solve the equations of motions globally which is a big advantage compared to shooting methods or finite-differences where we have to vary the initial conditions on one side of the domain until we find the desired boundary values at the other end of the interval. More importantly, spectral method are highly accurate and have a fast convergence rate and are thus perfectly suited for problems in numerical holography.
| m | 58591df5ddd316d8ce081b28729c566f |
To solve the above limitations, we propose the HD-VILA-100M dataset (i.e., High-resolution and Diversified VIdeo and LAnguage) that consists of a wide range of video categories and will benefit a plenty of VL tasks, such as text-to-video retrieval {{cite:9bee4caa7230ed62a529694c9d592a50922a3e5f}} and video QA {{cite:cf9f2bcd9351aaced1583d5e16b0563f19227012}}. This dataset has the following key properties: (1) Large: we have collected one of the largest video-language datasets, which consists of 100M video clip and sentence pairs from 3 million videos with 371.5K hours in total ({{formula:5b692c6d-7d1b-4cb4-adb7-e25ae6442f8d}} video hour and {{formula:05b513a1-12fd-4e87-b6d4-858d28b9e274}} average sentence length than HowTo100M {{cite:6e3ebb62da129cdefae0bcef8f88ccd5035265e9}}).
(2) High resolution: all the videos are 720p which is much higher quality than existing datasets that are mostly 240p or 360p.
(3) Diverse and balanced: we cover a wide range of topics from the YouTube, with 15 popular categories (e.g., sports, music, autos). Meanwhile, we ensure a balanced video clip number in each category to ease underfit problem.
| i | e7f6571598f6ad0f07c14c159d11e110 |
An interesting application of the perturbation bounds given in Section is community detection in bipartite graphs. Community detection in networks has attracted much recent attention. The focus of the current community detection literature has been mainly on unipartite graph (i.e., there are only one type of nodes). However in some applications, the nodes can be divided into different types and only the interactions between the different types of nodes are available or of interest, such as people vs. committees, Facebook users vs. public pages (see {{cite:4d734afc62936a9e0a16b232ed16c8b4c46b785d}}, {{cite:bdbcaeef67403aa817097486af6480c4464402b5}}).
The observations on the connectivity of the network between two types of nodes can be described by an adjacency matrix {{formula:43df436d-aa4d-4ece-9ca0-6492c6bafff7}} , where {{formula:a7748a92-764c-4a9f-8f11-eb568cde7831}} if the {{formula:540b12d6-1ceb-4bd7-86da-106e6c4767f4}} -th Type 1 node and {{formula:3548d799-4496-4ca4-9e84-3761f9df5f49}} -th Type 2 node are connected, and {{formula:d80c0306-821e-4129-ac81-c6c50bc26923}} otherwise.
The spectral method is one of the most commonly used approaches in the literature with theoretical guarantees {{cite:9c0441d4697793b459e483aaa47f51902ab97651}}, {{cite:6df6196d772b01ff0b39b7aeaca5e705425f97d1}}. In a bipartite network, the left and right singular subspaces could behave very differently from each other. Our perturbation bounds can be used for community detection in bipartite graph and potentially lead to sharper results in some settings.
| d | b1d2df892024eb80deda7bd2fb39f9f6 |
On datasets featuring a single foreground object, we use the 2-slot version of IODINE and Slot-attention. Since ReDO, IODINE, and Slot-Attention do not distinguish foreground and background in output regions, we choose the best-matching scores from the permutation of foreground and background masks as in {{cite:4b7791768752ecea81996a428e746eff2636a5ec}}. We observe that the proposed method and Grabcut are the only two methods that provide explicit identification of foreground objects and background regions. While the Grabcut algorithm actually requires a predefined bounding box as input that specifies the foreground region, our method, thanks to the learned pixel re-assignment (see sec:model), can achieve this in a fully unsupervised manner. Results in tab:extresults show that our method outperforms all the unsupervised baselines by a large margin, exhibiting comparable performance even to the weakly supervised baseline that requires additional background information as inputs {{cite:6a20e00f3fb56c8f76d8f9f88e9a49bec3ad56b7}}. We provide samples of foreground extraction results as well as generated background and foreground regions in fig:viz. Note that our final goal is not to synthesize appealing images but to learn foreground extractors in a fully unsupervised manner. As the limitation of our method, drc generates foreground and background regions less realistic than those generated by state-of-the-art GANs, which hints a possible direction for future work. More detailed discussions of the limitation can be found in supplementary material.
{{figure:f79f67b2-bc1f-48fd-8f8f-bc2b88977eb2}} | r | 11987e78dec2a02582bf22580553bea4 |
We compared our method with the existing unsupervised LDCT denoising networks {{cite:45364383697e6f397f6e97bf3c94d5e5658b2afe}}, {{cite:7c92c5df074ce819fd94dd601f7cff9553525597}}.
For AAPM dataset, we compared our network performance with the conventional CycleGAN{{cite:45364383697e6f397f6e97bf3c94d5e5658b2afe}} whose the generator is based on U-net{{cite:b64b1d194887db79b1201569ecdf6e884f097974}} architecture. We also compared with AdaIN-based tunable CycleGAN {{cite:7c92c5df074ce819fd94dd601f7cff9553525597}},
which shows state-of-the-art performace for LDCT denoising.
For unpaired 20% dose CT scan datasets, we compare our method with AdaIN-based tunable CycleGAN.
| m | 2684581e8fa768429bfb9bf5fd7b4e85 |
One of the possibilities to modify GR by considering a massive graviton also attracts the attention of various people. For instance, a ghost-free theory with massive gravitons is developed in Ref. {{cite:fe1bb3d1e6af2b51cd55470422eedcbe0bc6386e}}. In curved spacetime, this causes to the presence of ghost instabilities {{cite:4273cc18d06f1c34d4c479bae1aeb8124be11da6}}. The black hole solutions in the presence of massive gravity with their effects on the geometrical structure is also studied {{cite:15c2f6b8305837a582dc9eb71d8266d54cde33fb}}, {{cite:31efa5e78f2582e0f058a22de7e170f8bd6d236e}}. Hendi et al. {{cite:47f2e8670f1fb877e40da9209d83060a29b80374}} investigated charged black hole solutions in GB massive gravity and their thermodynamics in {{formula:ff3b548b-37fb-447c-81ae-24601ddd79fc}}
dimensions.
| i | 387f81dea1591f19056bccac95b55426 |
With simulation in hand, we aim to train a SBI method to estimate the posteriors of the SN parameters given the observations (and redshift) and compare this SBI method to traditional Bayesian inference. In our baseline comparison, we will use the affine invariant MCMC ensemble sampler implementation in the Python module emcee {{cite:8a10b91a7d71f3d91eb02320f7d226e2f07cc18a}}, arguably the most common sampling technique used in the subfield. For a typical SN with {{formula:531cd5f7-2456-4266-a014-65214a987037}} observational data points, it takes roughly {{formula:a3ff1421-df91-4df0-bb69-8accf4dc7e16}} minutes on one CPU for 50 walkers to take 5,000 steps (at which point the MCMC is typically converged).
| m | c68b9e36b44f7b27ac8ab2876f9bfa49 |
In our experiments, all networks are trained on the Extended Cohn-Kanade dataset (CK+, Figure REF a) {{cite:e06414a3d12f349f10f17d3de566ab0726bb49f5}}. CK+ is composed of sequences of images, starting with a neutral face, and ending with one of seven universal facial expressions {{cite:231ff43bda8c6ea1bfdefd04a8102673f40a0341}}: anger, contempt, disgust, fear, happiness, sadness and surprise.
| r | db39637cedbdbee7c5f645c05c11f3a7 |
The experiment in Section REF clearly shows the benefit of initializing the network parameters by (REF ) and (), respectively. As seen from Fig. REF , the optimization process is able to offer around 8-9 dB improvement in performance over the SToRM initialization. We note that the proposed framework of recovering the bilinear representation from 10 spokes/frame is significantly more challenging than the traditional DIP strategy in {{cite:4b9f9e1d3e11080539cbe5c854cc5a6ac3346383}}. A reasonable initialization of the network can offer improved performance compared to random initialization. Fig. REF also shows the need for early stopping of the unregularized setting in (REF ). In particular, the performance of the algorithm decays with increasing iterations, indicating overfitting to the noise in the k-space measurements.
| d | 3fbd1433d88bfd2be70b687247f6fa9a |
Our proposed booster method can be extended to prepare excited states.
Using existing near-term methods for estimating low-lying excited states {{cite:675f332c14f96655211b69965be61f6676308694}}, {{cite:7047fe5d931d628921d50128e313fc8db6030be6}}, {{cite:38b22b06ee5c7f3984a95ebe421bcf290bd778ff}}, {{cite:3c16c50e1557da57db7d397ac7fb88a6c11d1816}}, {{cite:9982c6e3f80659c03fd77b87167703a8f0e2d1a7}}, one can obtain an initial state that approximates an excited state.
Then, with the estimated excited state energy, call it {{formula:2b136a2e-ef8a-45be-b5ee-2ea360da194f}} , one can construct a shifted Gaussian booster {{formula:a613073c-b66d-439c-a7c2-d539232882d0}} such that the booster function peaks (approximately) at the excited state energy.
We note that many of the steps to implement the booster method for ground state preparation carry over for excited state preparation, including energy re-scaling.
| d | b8f1cd18f5322a8d909a4b06530c4d10 |
It should be noted that in more complex, an-isotropic, in-homogeneous systems (e.g., channel flows or ocean circulations), spectral analysis using other basis functions, such as Chebyshev or wavelets {{cite:fa45dc0752dfa6a3beb62f99deca8110c132f30e}}, {{cite:a8d12956fc0d84e4cd50ef30cdbd72f635289f66}}, might be needed.
| d | 8a4f27bf7a1682a0f4f2562782ac7c10 |
To compare the efficiency our proposed IGSAM with different sampling methods, we have experimented their GPU memory usage and processing time on a single GTX 1080 GPU with 8 GB memory. The sampling methods include Random Sampling (RS), Reinforcement Learning based Sampling (RLS) {{cite:8c3697c7585c195d89abc76bfe71985474976290}}, GSS {{cite:c0287eea58c368ef3897124bd3fb8ff4e1ee245d}}, IDS, Farthest Point Sampling (FPS), and Generative Network (GS) {{cite:56339ddcee57777ac04d08b0adc8be57e7dc93f4}} based Sampling. The point clouds are divided into batches consisting of {{formula:6c9cd647-9b67-4a02-ba8c-73d26fb00ad4}} and {{formula:033b611e-fd67-4597-a7b0-d7f388facd91}} points respectively, then the batches of points are down-sampled 5 times which imitates the down-sampling in our network shown in Fig. REF . The total time and memory consumption of sampling methods on different numbers of points are illustrated in Fig. REF . It can be demonstrated that RS has the fastest processing speed with the smallest memory consumption. However, RS will result in a stochastic loss in meaningful information, which will give unsatisfactory segmentation results. As shown in Table REF , mIOUs will drop significantly from {{formula:1060b9a2-7659-47e7-b26c-a3b2e50022e1}} to {{formula:331a08be-1ab1-4dda-81d0-56c13b92664c}} if RS is adopted. It should also be noted that GSS is not suitable for more than {{formula:9bd81d0a-8bc3-46f0-8f39-8daf53235212}} points because the GPU memory will increase greatly with the number of points. Hence, we only use GSS in the last layer of the network when the number of points is less than {{formula:4f44a3c3-fdda-4944-9867-9934966ba7b2}} . Leveraging IDS with adaptability to the local density of points, our IGSAM achieve the best performance among different sampling methods with only a marginal increase of computational cost compared with RS.
The segmentation mIOUs using different sampling methods are also shown in Table REF . It can be seen that our sampling methods give the best performance among all sampling methods on the S3DIS benchmark with mIOUs of 70.8%, which demonstrates the effectiveness of our proposed sampling strategy.
| m | 7069b275322f6dec642c4d4e14bd01d3 |
Using the experimental settings of sec:more-setup, we extend tab:cls and tab:adv of sec:class by comparing MultiMix and its variants with additional mixup methods in tab:more-cls and tab:more-adv. The additional methods are Input mixup {{cite:5157c8c6bebcc6e872c98acd012868b92aead743}}, Cutmix {{cite:416b08b88cfbfcf41510dce935a524bccd6030d4}}, SaliencyMix {{cite:121af16ebe0a19b0fcdc1ebd3ecf1d0bbfd200f9}}, StyleMix {{cite:020e32384baa3dfeb596793d1d8fb0b7077a4c42}}, StyleCutMix {{cite:020e32384baa3dfeb596793d1d8fb0b7077a4c42}} and SuperMix {{cite:3f5159912ff8e7ad3848c4c3ca0c4fc342075e49}}. We reproduce SuperMix using the official codehttps://github.com/alldbi/SuperMix, which first trains the teacher network using clean examples and then the student using mixed. For fair comparison, we use the same network as the teacher and student models.
In tab:more-cls and tab:more-adv, we observe that MultiMix and its variants outperform all the additional mixup methods on image classification. Furthermore, they are more robust to FGSM and PGD attacks as compared to these additional methods. The remaining observations in sec:class are still valid.
{{table:10b03225-3597-497d-9ef7-d4af3c688481}}{{table:3a70d52e-c306-4608-988a-5da012e34879}} | r | fb3db8ac87fc189b98447d167b34a117 |
A recent trend in the theoretical understanding of deep learning has focused on the
linearized regime, where the Neural Tangent Kernel (NTK) controls the learning
dynamics {{cite:c2a71195f5b7509be9dbae59780356f347436153}}, {{cite:151c2f630601dfe681108fb35c26647677d92e9a}}.
The NTK describes learning dynamics of all networks over short enough time horizons, and can
describe the dynamics of wide networks over large time horizons.
In the NTK regime, there is a function-space ODE which allows for explicit characterization of the
network outputs {{cite:c2a71195f5b7509be9dbae59780356f347436153}}, {{cite:151c2f630601dfe681108fb35c26647677d92e9a}}, {{cite:e1268e094c8cc4edc126d76eb23fe221302f8fe5}}. This approach has been
used across the board to gain insights into wide neural networks,
but it suffers a major limitation: the model is linear in the parameters, so it describes a regime
with relatively trivial dynamics that cannot capture feature learning and cannot accurately
represent the types of complex training phenomena often observed in practice.
| i | 0b33af5d5c588e4aa3109d4a6511da33 |
We summarize the overall algorithm in Algorithm REF . Our method is a special case of the constrained {{formula:f8084e76-cf27-4fc1-9b2f-92374b43bbfb}} -means {{cite:0f1204b98fede75635a8ee5fafdc52844c42fc21}} where channels recovered at each slot formulate couples of cannot-link constraints with each other. Same as the constrained {{formula:c73bd7d2-e9a0-4203-bf48-f981fafb6858}} -means, the proposed iterative clustering algorithm is guaranteed to converge. Note that even though the data assignment step and centroid update step are both optimal, the final solution often reaches a local optimum. Our method can also be treated as a revision of the balanced {{formula:cd09bd48-29e1-45e6-857b-34e133977378}} -means {{cite:665cbee5ea32dc097c31de1919d5b842a6938e0e}} to satisfy Constraint I. Dominated by the Hungarian algorithm computed in {{formula:9b4057af-2930-420b-842b-c6aa2cb2e530}} time, the algorithm complexity yields the order of {{formula:b3913af4-bb3c-469a-8d75-2251865e0d70}} , which vastly outperforms the constrained {{formula:8149ca81-6216-4be9-be58-2947aa5892c2}} -means of complexity {{formula:9084d83d-a8e3-4642-b39e-c92ae33fb96b}} .
| d | f4758bf06037ccd420c9dcf7bf7f049c |
Notably, conditional information such as labels can improve the performance of the generator {{cite:b335718bcc50d2776c944f79c2760d9a1fa36016}}, {{cite:002f91aceb7c0a8d7b79e29f16f6dbf91f857274}}, and the completed data vector can enhance its task prediction result. However, state-of-art imputation methods, e.g. GAIN, do not make use of the relationship between observations and outcome labels, which could provide additional information to help downstream classification tasks. Therefore, we propose Classifier-GAIN to bridge this gap. Figure REF depicts the overall architecture.
We explain each of the components and the training process of Classifier-GAIN in detail in Section REF {{formula:17ec1ee2-301c-4b24-a320-f281564ed19e}} REF .
{{figure:08f8b526-6d7a-4575-94b4-88b0d88b3470}} | m | 1fd4fda101ef0a6b22962ac95d2a371b |
Throughout this paper, particularly in Section REF , REF , and REF , we use a ConvNet named `compact-convnet'. As mentioned earlier, the proposed analysis is structure-agnostic, and we chose this network since it achieves a reasonable performance while being easy to understand and analyse due to its simple structure. Table REF summarises the hyperparameters which are similar to the network in {{cite:6a6a60fa3df3c87db14a97f26b33d9f11c50148a}}. The original audio files are encoded in mp3 format with a sampling rate of 22,050 Hz and 64 kbps constant bit-rate. They are decoded, down-mixed to monaural, re-sampled to 12 kHz, and converted into mel-spectrograms with 96 mel-bins through a windowed short-time Fourier transform using 512-point FFT with 50% overlap. The ConvNet consists of homogeneous 5-layer, {{formula:3e18ef22-18af-4f3d-a7ae-3505b1d3c20f}} convolutional kernels. On the input side, the mel-spectrogram magnitude is mapped using decibel scaling ({{formula:05e31339-82f0-47db-8d83-a9b68c381759}} ) and adjusted using track-wise zero-mean unit-variance standardisation.
We use 201,672/12,633/28,537 tracks as training/validation/test sets respectively, following the set splits provided by the MSD.
This networkThe trained network and split settings are provided online:
https://github.com/keunwoochoi/transfer_learning_music and
https://github.com/keunwoochoi/MSD_split_for_tagging
achieves an AUC of 0.845.
| d | 817261f4a843de2fff90ab4eda6b3f27 |
Based on this assessment, we propose in this work to keep the best of both worlds: use deep learning to process the image and discard unnecessary details, then use handcrafted methods to detect the line segments. We thus retain the benefits of deep learning, namely, to abstract the image and gain more robustness to illumination and noise, while at the same time retaining the accuracy of classical methods. We achieve this goal by following the tracks of two previous methods that used a dual representation of line segments with attraction fields {{cite:05f58d4c4a1b2778c3e11a4d830947d2587a5718}}, {{cite:04563ec4fa4933e42dda3d1eacdb7f29b0bbe4a8}}. The latter are continuous representations that are well-suited for deep learning, and we show how to leverage them as input to the traditional line detectors. Contrary to these two previous methods, we do not rely on ground truth lines to train our line attraction field, but propose instead to bootstrap existing methods to create a high-quality pseudo ground truth.
Thus, our network can be trained on any dataset and be specialized towards specific applications, which we show in our experiments.
| i | a5431e6b76ee6f423fc6176541713411 |
In addition, we compare UGCL with supervised methods (i.e., MLP and Supervised GCN) and self-supervised methods, including Node2vec, DGI, GRACE, and BGRL on ogbn-arxiv. The other GCL methods are not selected as they encounter out-of-memory issue during training. The experiment results are presented in Table REF , where we can observe UGCL has achieved on-par performance with the most competitive baselines (i.e., GRACE and BGRL). Except for UGCL, others results in the table are sourced from {{cite:530a8d3f8327ca6a9cf5f0f66e728382061c87d2}}
| r | 9b25a7c03c0ca3e9758d9b020d009bbe |
In this work, we have obtained constraints on {{formula:f59be0c2-86bb-4f0b-85c9-02cd82f284ce}} and {{formula:2dcee4b1-6b88-48b8-aa8c-7eb2dfb20ebd}} from the tomographic analysis of the two-dimensional slices of observed large-scale galaxy distribution. The amplitudes of the two-dimensional genus curves are measured in a series of concentric slices of density fields derived from the SDSS BOSS data. The amplitude at low-redshift is derived from the three-dimensional genus of the SDSS MGS data, and combined to find the cosmological parameters minimizing the redshift evolution of the genus. In doing so, we arrive at a constraint of {{formula:9929de3c-8589-4761-9f95-aeb1ec656c2b}} , or {{formula:c026f71d-0ca7-4bb0-b26e-61561f50b3b3}} , {{formula:4a738e21-e47f-4546-b39b-e14751a5493d}} if we combine our analysis with Planck temperature data {{cite:314047a2d1e61a93b9cf01b8215d77d506e58f10}}. The parameter constraints arising solely from the genus statistic are particularly weak; this is due to the strong degeneracy between parameters and also the limited statistical power that we are able to employ. The presence of shot noise fundamentally restricts our ability to reconstruct the density field from the galaxy point distribution, as we must smooth on scales of at least the mean galaxy separation {{cite:1d3f26024eb84873500907e7f36999d454d953fb}}, {{cite:8c6d26d84549726684ddc01a68c06cbb4d79ad8c}}, {{cite:77649118239cd63a5bd334f223e43c1ea9fb0ee6}}. In contrast, methods such as the Alcock-Paczynski (AP) test {{cite:dc9c8db6bff3f28991a5f4cd23f769cfae153d12}} (see also {{cite:2cd0634d797aec47223128e05fa4d6f53b56233b}}, {{cite:b9483271555b08746070311223c9607e8c56e417}}, {{cite:d4b0b0d0a9dddbbe7c7ac12f654d1ef0e81d4934}}, {{cite:fade62e056c32c0458b1c38cf2b5f1c6b2fa48f2}}, {{cite:850df79058df486f5cc078454ec3cb084c874278}}) employ information from very small scales, eliminating non-perturbative, non-linear systematics using simulations. In addition, the AP test does not require the application of mass cuts to generate uniform data samples with redshift, as we are forced to. As a result, {{cite:dc9c8db6bff3f28991a5f4cd23f769cfae153d12}} were able to obtain tight parameter constraints on {{formula:383b55bc-9232-433f-a5d5-aeaaf7200878}} and {{formula:f0c3ccbf-e786-4c83-8f6b-1e34e266feb8}} using the same BOSS data. For the genus to be competitive with other statistics, we must first learn how to model and remove observational systematics.
| d | 62f8d06fd20b152f82a602813ef08498 |
In what follows, we show that criticality, studied previously in literature, occurs when the norms of these Jacobians either remain finite, or vanish algebraically as {{formula:e29b6855-6325-4713-8211-849ce5061ad9}} becomes large. To prove this we derive the recurrence relation for {{formula:8784aa88-5d9c-4c74-a287-2ebbaf471f53}} in the limit {{formula:8a534f79-8c0d-423a-b43a-85f283623453}} ; and analyze it at large depth. Algebraic behaviour of partial Jacobians with depth is characterized by an architecture-dependent critical exponent, {{formula:0a0761ad-6f85-42b4-ba00-0ddf49ae8297}} , so that {{formula:5dd5c9e3-15a0-4adc-8a3c-13af633d07c5}} . Such behaviour is familiar from statistical mechanics when a system is tuned to a critical point {{cite:418cb97cbaf12d747bed030d2df645e05f7b122a}}.
Away from criticality, there are two phases: ordered and chaotic. In the ordered phase partial Jacobians exponentially vanish with depth, whereas in the chaotic phase partial Jacobians grow exponentially. This dichotomy of phases holds for both bounded and unbounded activation functions.
| r | 623252e41a682efd05e7ce82ab2beb1c |
The following formula {{cite:2f2e07e01abdd9a1a960b16448ea40cfe239dbf6}} can be used to compute the
adjacency matrix of the line graph {{formula:75145d8f-6bcc-4bb2-b430-276c253e74f2}} of a graph {{formula:9180c592-4140-4e5c-bd1d-cb3e298eedcf}} ,
{{formula:c171a0f4-0468-4a79-828e-bc3bb4427303}}
| i | 3f8a95a34599b40596f287175df3dc6d |
SLIM for Image Recognition. Fig. REF illustrates the Same-Layer Inception Module (dubbed as SLIM too). Similarly, we first split the input feature map into a number of groups (e.g., 4). For input group, the transformation consists of a standard convolution (with a {{formula:8ab40f62-c996-49f0-902c-7b1fdef76d91}} kernel), the channel attention (based on SE), and the spatial attention (which can be treated as a spatially-adaptvie variant of SE). The spatial-channel attention is the product between the channel attention and the spatial attention, resulting in a 3D attention matrix. Softmax is applied along the channel dimension of the 3D attention matrix. It is then used to re-calibrate the output of the convolution branch in an element-wise / spatially-adaptive way. It is used to replace all the 3x3 convolution in a feature backbone (e.g., ResNet-50). It achieves better accuracy with significantly smaller model complexity in ImageNet-1000 {{cite:b5b446c50d43d7a8cfb91371e5588d4deac015a8}}.
| m | 51d26ebdd866f6aa3d96b32e008852cf |
We recall the Arrow-Hurwicz (AH) method from {{cite:ac4cebfccbc7b7f1b022891a1017d6a5773afd6b}} for steady Navier-Stokes equations. The method is given in {{cite:d0179a36f6c5c7e13b996d18c6bbb929b8664c74}} with a slight change of parameter variables.
| m | 35328ae08bcc1629ca2dac5a5d821010 |
In this section, we present numerical results to illustrate the performance of the two proposed resource allocation strategies. For clarity, we denote the proposed resource allocation with ESB by PRA1 and the proposed resource allocation with ASB in a PACSR by PRA2. The numerical results are obtained by considering a rectangular indoor environment of size {{formula:411e589a-7aa4-4945-b65f-0ba2d06d06de}} . We consider that four APs are deployed symmetrically in the indoor environment in the same way as specified in the 3GPP standard {{cite:f42aed88119c54561a69efd21465605bd500a393}}.
Also, we consider that the 50 GHz spectrum that exists between {{formula:62baaeae-37c9-4122-b856-f01aaf9ba723}} and {{formula:b7d6fcf2-5006-4a70-b3fe-f14f684e4415}} in the first THz TW above 1 THz is used to serve the usersWe clarify that it is indeed possible to utilize PRA1 when the spectrum that exists anywhere within a THz TW is to be allocated. Despite this, since PRA2 can only be employed when the spectrum of interest that is to be allocated exists in a PACSR/NACSR of the THz TW, we present numerical results for PRA1 and PRA2 in a PACSR for fair comparison..
We use the absorption coefficient values that are calculated for the standard atmosphere with {{formula:4eee765a-de59-44b8-b9d9-543022ae00f4}} humidity {{cite:12c830d96d8a1fe79ce4e9aad4ecc909269b4711}}.
The values of the rest of the parameters used for numerical results are summarized in Table REF , unless specified otherwiseblackblackIt is noted we consider that the sub-bands exist only within TWs, where the variation of molecular absorption loss, as well as pulse broadening, is very small. Differently, a few previous studies, e.g., {{cite:c450da8928d6316c995e3bfc0302d7abc4ee1593}}, {{cite:2a686e1e5288568d3e0886320a356f20ae5f774c}}, considered that the sub-bands can also exist within ACPRs, where the variation of molecular absorption loss, as well as pulse broadening, is very high. Due to this, to avoid ISI, it is reasonable to consider {{formula:5204d4b6-7e91-4929-8292-4ce76a9de92f}} in this work, when {{cite:c450da8928d6316c995e3bfc0302d7abc4ee1593}}, {{cite:2a686e1e5288568d3e0886320a356f20ae5f774c}} considered {{formula:5f873be7-8e77-4c79-b240-15804af3d32c}} ..
| r | 649510d2fba486c534157950e09044d1 |
Table REF compares the performances of our NRR model to the state-of-the-art results reported by Paetzold and Specia paetzold2017a. We use precision of the simplest candidate (P@1) and Pearson correlation to measure performance. P@1 is equivalent to TRank {{cite:f6542c27ebf95720db45b41281ebb19a4f92202d}}, the official metric for the SemEval 2012 English Lexical Simplification task. While P@1 captures the practical utility of an approach, Pearson correlation indicates how well the system's rankings correlate with human judgment. We train our NRR model with all the features (NRR{{formula:b059bd3b-9fd6-4506-b2c8-4a9cd812d090}} ) mentioned in §REF except the word2vec embedding features to avoid overfitting on the small training set. Our full model (NRR{{formula:c35f3fda-524f-44ce-b59b-3cdffa43e29a}} ) exhibits a statistically significant improvement over the state-of-the-art for both measures. We use paired bootstrap test {{cite:5165a601e41ed3adbadc1eadcd56407d4c761d9c}}, {{cite:89260977fa6f920aa28fa609571f8a2254c81c6f}} as it can be applied to any performance metric. We also conducted ablation experiments to show the effectiveness of the Gaussian-based feature vectorization layer ({{formula:a442ddce-0824-4815-98e8-8abd0afc390c}} ) and the word-complexity lexicon ({{formula:8f98ec1b-9656-47ca-9b8a-1198c9bbbd3b}} ).
{{table:27a77558-e303-43c1-8eaa-d96ff6d43ee9}} | r | 8e6cf96a45ebb776d35287b628c483f3 |
Among these methods, GAN-based vocoders {{cite:b8cb4f191d46fd535c153807509ca27557d97417}} can generate high-fidelity raw audio conditioned on mel spectrogram, while synthesizing hundreds of times faster than real-time on a single GPU.
However, existing GAN vocoders are confined to the settings with a moderate number of voices recorded in clean environment due to the limited model capacity. The audio quality can heavily degrade when the models are conditioned on mel spectrogram from unseen speakers in different recording environments.
In practice, a universal vocoder, that can do zero-shot generation for out-of-distribution samples, is very valuable in many applications, including text-to-speech with numerous speakers {{cite:acdf08df03506f20249de54763874845940e38b4}}, neural voice cloning {{cite:453b0c302cd9c4e781aea15a629b468b3a42e8f7}}, {{cite:6b6422814f9ea33ea8bbdee30f394bf93c9533a2}}, voice conversion {{cite:a99787d4d1eebd5e06986fb832d39a8489b6d9ba}}, speech-to-speech translation {{cite:9512e7d9be8be2098f7bd36e84b04900f1eb1736}}, and neural audio codec {{cite:eb2ca190b026ffc34c19bfd3185013e27c6a39df}}, where the studio-quality recordings are often not available.
| i | 5b6e76fe96fb37263fdda048a558d461 |
Setup. We first invert the videos frame by frame using the Restyle encoder {{cite:dc624ae05e13fe778b6c360eeb1a5a26c9cdea5e}} (psp-based {{cite:dbeaefc883b0b1da730fd41c82c00b931812e0e0}}).
We then directly apply five different out-of-domain editing effects produced by StyleGAN-NADA {{cite:26acbeed3073a8ab1a2ed1fd539c90ec2aa72ffd}}.
We perform our two-phase optimization approach on the directly edited video using Adam optimizer {{cite:d83bf6b5a585293bbb62cde2cd06f72e68b93107}}.
For phase 1, we set the learning rate to {{formula:e5b65154-5972-467c-85f5-ec4ed79bc556}} , and update the latent codes for 5 epochs.
In Eqn. REF , we set {{formula:2106766b-0bec-4730-a395-70537ff7d2de}} for all the editing directions.
For phase 2, we set the learning rate to {{formula:9bf22a4a-4c59-4c8d-9b30-9ce2d7c4d35a}} , and finetune {{formula:b205cf90-f80d-40a3-81f9-e346f41e5897}} for 5 epochs. We set the regularization weight {{formula:794c3a92-d7c3-4396-8a45-c1054279e5b4}} to 200.
| r | 7c999f13ba47364d411ed03e79f61c53 |
The spin period of rotationally-powered pulsars range between {{formula:708d6c77-e504-4290-9167-b013203f0b46}} ms to {{formula:bf3fed8a-e17e-4356-a008-fb3dc2b90205}} s {{cite:d95bd654468d8e18ba02969787b18411e63eaacf}}See https://www.atnf.csiro.au/research/pulsar/psrcat/..
The spin period of galactic magnetars {{cite:2a1a4745048ed559bf28099668c1b0203845e746}} range between {{formula:d02df473-5958-4737-a349-6b2419057bdb}} s {{cite:4ad95e8602623f64b8447fab287f1bf627ebc510}}See http://www.physics.mcgill.ca/~pulsar/magnetar/main.html..
The {{formula:ad21f10c-9dc9-4131-acc3-9cb5232242fb}} ks period of the GLEAM-X J162759.5–523504.3 is unusual as the period of a pulsar or a magnetar with sufficient resources to exhibit the observed phenomena.
| i | 0fc9ee1a5a333c1125b0f0cc09452294 |
To improve the accuracy of the macroscopic approach, we could consider even more moments, since these would theoretically approximate the DSMC model to higher accuracy {{cite:4bda8bd039a097c95c72aad6513c34f73a604a44}}, {{cite:387f19685707c20a3adf3aabfe20dbb7c53ee6e0}}, {{cite:82c71e73d43f1e45e2bc90752e5b7033d0448563}}.
While work has been done to understand the number of moments required for accurate simulation of a given problem {{cite:cd2406225642a4371b7a1091b64b970cf15775a3}}, {{cite:05b2744de25a531930920c42dec9491d2f7a5c9c}}, the computational expense and modelling complexity added for an increased number of moments, particularly for two- and three-dimensional flows, makes this strategy hard to justify {{cite:4bda8bd039a097c95c72aad6513c34f73a604a44}}, {{cite:8bd0d701828b8f586b24f68db78b08569f8c384a}}. Notably, a promising new approach, based on using a different number of moments in different regions of the domain {{cite:ac4a2d0c38a58821ea96219dc1d56d48b7b09f7e}}, has the potential to overcome these limitations and should be the focus of future work in this field.
| d | 1822d7f16ccc33b516af09d9adbac039 |
OJ 287 is the first blazar for which periodicity in the optical light curve was detected, revealing prominent flares that occur approximately every 12 years {{cite:235949c11bbe9e914220ce8b24f04456922dd374}}.
At that time, the unified scheme of active galactic nuclei {{cite:be767dea801718320b2c32526bb0810a1dd259b6}} had not yet been proposed.
Therefore, early investigations of OJ 287 were predominantly focused on the interpretation of optical periodicity.
It was supposed that such a short variability period can be formed in a binary black hole system {{cite:235949c11bbe9e914220ce8b24f04456922dd374}}.
The secondary component moves along its elliptical orbit and passes the pericenter every 9 years (in the rest frame), invoking a tidal effect on the accretion disc of the primary black hole.
As a result, the matter of the accretion disc flows into the black holes, leading to the observed flare on the light curve {{cite:235949c11bbe9e914220ce8b24f04456922dd374}}.
This model does not take into account the structure of the 12-year flares, namely, that there are two peaks in each flare.
The interpretation of this fact given in {{cite:0ee9f00e18b35b17b7dbaa5e1297f6b7e7f7c2e3}} is that the secondary black hole passes through the accretion disc of the primary one twice during the orbital period.
This model also provided the explanation for some of the observed properties of optical polarization, but it was focused on orbital motion.
After the next 12-year flare occurred during 1995–1996, this model has been refined {{cite:44e7e08c59ff2230679ffac7122884929e9e31b4}}, {{cite:f25e6f3ac06e6f7becab33f57e544ecc287e8756}}, {{cite:2903f3021c1887801de93296c77d7e17cdc4be77}}.
The authors of {{cite:2903f3021c1887801de93296c77d7e17cdc4be77}} predicted future evolution of the VLBI jet position angle observed at 15 and 43 GHz, but it has not been confirmed by later observations , .
| d | 1930a66ab1d916ef6aacef1a8d54134f |
KITTI is a real-world dataset with street scenes from a driving car. This dataset provides sparse but accurate dense disparity maps as ground truth. Image size is H = 376 and W = 1240. For KITTI2012{{cite:6990a1653cbaf9f5cc5d710b44eadeba9cc07f09}}, it consists of 200 stereo images with ground-truth disparities for training and 200 image pairs without ground-truth disparities for testing. For KITTI2015{{cite:f5f7a23b79ea1415e0f423c4e456423b505bade7}}, there are 194 stereo images for training and 195 for testing. During training, we combine KITTI2012 and KITTI2015 and divide the whole training images into a training set with 354 image pairs and a validation set with 40 image pairs (20 from KITTI2012 and 20 from KITTI2015). We evaluate our method using official metrics. For KITTI2012, we use Out-Noc and Out-All as metrics. They denote the percentage of erroneous pixels in non-occluded areas (Out-Noc) and total areas (Out-All). For KITTI2015, we use D1-bg, D1-fg, D1-all as metrics. They compute the percentage of stereo disparity outliers with errors greater than 3 pixels for the background (D1-bg), foreground (D1-fg), and all (D1-all) pixels, respectively. After fine-tuning for 50k iterations, we report the official results along with running time in Table REF .
| r | 8e28876c76558fa0e3bdfadeb0352dfa |
In order to assess how different evolutionary algorithms perform on the generation of adversarial examples for deep neural networks in black-box settings, in this work we compare three different evolution strategies (ES), namely: (1+1)-ES {{cite:3fb4b0f7e7c130f7474933161cc0fc09a91a00f7}}, Natural Evolution Strategies {{cite:b52c4853f5381b548b5a74fae96fcd4877010292}} and the original version of CMA-ES {{cite:10c7735560310f60735c6c539a7041e0d1b502a2}}, {{cite:a6aa941be05d7ec429bfa45288c2f4797555f687}}. We decided to focus our investigation on these three variants of ES for three main reasons. First of all, as shown in {{cite:f2e72b6616ef859b0ffb732fd597640ac63e74c4}} and further discussed in {{cite:263f6c28e75b0e6b9842c36de7cc083f01b18931}}, ES can rival backpropagation-based algorithms in deep reinforcement learning (RL) problems and as such it has recently attracted research attention also in the deep learning community. Secondly, ES can be essentially considered a gradient-based algorithm, since it performs a stochastic gradient descent based on a finite-difference approximation of the gradient {{cite:263f6c28e75b0e6b9842c36de7cc083f01b18931}}. As such, it is worth investigating how ES can deal with a task such as the generation of adversarial examples that is typically tackled by (explicit) gradient-based methods. Lastly, we chose for our analysis two ES variants configured as population-less (i.e., handling one solution at a time), and CMA-ES, which is configured as a population-based algorithm and is considered nowadays the state-of-the-art in evolutionary optimization. Thus, we aim at finding if using a population rather than a single solution can provide a benefit on the task at hand.
| i | 48887d2f8efe66d07a105e66374dc020 |
Qualitative results of initially synthetically generated brain tumor images by different models are shown in Figure REF .
Using the best FID and KID of the pre-trained models, the brain MRI images generated by transfer learning are shown in Figure REF . By analyzing our results, we find that FFHQ gives the lowest
FID of 58.1097 and KID of 0.00862, and generates better quality images
when compared with other pre-trained models. Figure REF shows a comparison of the images generated using DCGAN {{cite:a3058973258c4252d2c68765c1d0cdd4835aa193}}, WGAN {{cite:97cf9668f4f1f12f3d8a5d25fcec68b8e72168ec}} and Ours (FFHQ) model using the brain tumor dataset. The results indicate Ours (FFHQ) generates better quality images when compared with the other GAN models.
{{table:b9fb0937-5014-4455-8c0b-336844c76c92}} | r | 31f7fdae0775055b61c364b55ba164d7 |
In e-commerce, recommender systems can provide personalized recommendation of products and services by discovering hidden user preference from data. Traditionally, the hidden user preference is discovered by techniques such as collaborative filtering and matrix factorization, which are based on users' past interaction with items (purchases or ratings) {{cite:5d0a2c868037c1eff3b52bfad2bce921171c7901}}, {{cite:f045ba64d92459ca3d518410c72b845a5cc122ca}}, {{cite:bb57e556aa8e284bfedd41b83f562d7d4e29cd33}}. A problem that attracts attention in recommender system researches in recent years is called cold-start recommendation {{cite:51bcc42bc14d39d1347f70e8d536104ec537b376}}. In this problem, there is no past record of user-item interaction, because, for example, the user or item is a new one in the system. To make recommendation in such cases, using information other than user-item interaction is necessary. A group of such information is called contextual information {{cite:fe1f7a31039218f6d386881326b644a47fcef8e6}}. Contextual information that has been shown useful in cold-start recommendation include user demographic data {{cite:7918e302109a52fb1ce17d3414cd9a06cd29df31}}, item attributes {{cite:a52eaa2cbb64a5a876a18e2c7741bfe9d3351bd6}} and item review texts {{cite:5b096edc397047e215d215a597dc4950e06fe666}}.
| i | 76b40f9bd648ab8bcc96ba7eea70cab8 |
Finally the concept of global normalization has also been visited with deep neural networks
{{cite:5e068cc35f671b8b2c492d82448d70f1d59860cd}}, {{cite:181a1116572ad9720c2e7844e759914d0162b5a3}}, {{cite:11fb0ba9ab78a3bedb76d888167ef1c476e5257b}}, {{cite:bd63ffd06d57c524a58fcded10a5deff891d1fb9}}.
These models can be seen as special cases of MMI thus all the differences between MMI and
GNAT model applies here as well.
Apart from their weaker modelling power as a result of using WFST composition cascades, all these models are non-streaming, where as
explained multiple times in our paper, global normalization and local normalization
are equally expressive.
| d | 7885b8c51feef85df3a0563baaa6439b |
Multitask Learning
Traditionally, the problem of disease normalization is tackled by first identifying the disease names (NER) and then normalizing them (EL). We attempt to learn from both types of supervision by having a NER and an EL model share parts of their architectures. This is known as multitask learning {{cite:8863d844f76243dbbed4f12e44473af1149b4a26}}. In particular, we share the encoder of the NER architecture, see Figure REF , and derive mention features for the EL model from there.
| m | 6ea8c9d4b872ab20c48b9ee494e0522b |
The policy is trained using a large-scale dataset collected via a VR-based teleoperation rig (see Figure REF , left) through a combination of direct demonstration
and human-in-the-loop shared autonomy. In the latter,
trained policies are deployed on the robot, and the human operator intervenes to provide corrections when the robot makes a mistake. This procedure resembles the human-gated DAgger (HG-DAgger) algorithm {{cite:8cc4d1262c6d66bb65c6c146ba2a2e5ae9f64c46}}, {{cite:5c939337a069f6d52cd5a96716e39cdaffe40a8a}}, and provides iterative improvement for the learned policy, as well as a continuous signal that can be used to track the policy's performance.
| m | 8adfe847d3ad00884a91100a6b93eeb5 |
The main contributions of this work can be summarized as the following. The application of acceleration techniques for fixed point iterations in this particular problem is new and have not been reported in literature. We have adopted a version of the Anderson acceleration {{cite:7d3fd224aa0042d11714dfd0bc2bb3fb037b447c}} (Section REF ) and also proposed a new way to define the Chebyshev sequence {{cite:1f5e5abe2e8fbd2363169854b3ec9254db7171e5}} (Section REF ). We have also tested two vector variable acceleration methods which are related to Aitken's method {{cite:cded70c99ce203671bea5a5a22b65e6774184436}}: Irons {{cite:a6ee0f00bea3847792c27326a36315cf38773e67}} and Epsilon {{cite:232e6c0f4207eeb90f0224a7d4b93068caea8526}} (Section REF ) which are less well known in the image processing community. Other contributions are as follows. (1) A re-development of T-, TDA- and P-method from fixed point iteration point of view, which leads to another version of the P-method which is called p-method for easy reference. (2) An extensive evaluation of the 4 fixed point acceleration techniques as well as 4 gradient descent acceleration techniques.
| i | 43bdc15f9d29741f1ea1812f1ebb85fc |
The whole network was trained on a Nvidia P100 Graphical Processing Unit (GPU) for around 250 epochs for each experimental run. 318 CT scan slices were split into a training set containing 268 images and a test set containg 50 images. The model was built and trained using pytorch-lightning {{cite:73b5df0d5c70c2d29932dd079cb416c721f0e7b6}}. Adam {{cite:8ae2995bdfe4774f3bb852232e93ee5ff2ed4eb3}} with a learning rate of {{formula:59bc701c-eff0-4180-8f45-bf27b81535c7}} was used for finding a local minimum in the loss landscape. Dropout probability was set at 0.6 throughout the network. The model was optimised using different objective functions described in the following sections.
| r | 1e278f23de28bfd4ca4ccfdf77b16360 |
The 17.7 d period proposed for the binary CSPN of M 3-38 is relatively long compared to the majority of binary CSPNe {{cite:23b65d5be647918c919fc503b68fcc8d9aec836a}}. In contrast, simulations of CE evolution result in relatively large separations of the order of 10–20 R{{formula:6063cd2d-49cd-46c2-84e0-618c40cc0bd2}} and periods larger than 3 d {{cite:61ff40f1b9620e985c0ee5a9f423f8d566951525}}, {{cite:bbc4726c1180d5311ed536643239e323bb6d7278}}, {{cite:6ff6f967fc829f282272c4282e0d60bc8e86429d}}, more alike that of M 3-38.
| d | b81daa799501f5116d32aa320acad2f2 |
Accuracy of overlapping region detection. Overlapping region detection is critical for our method to select the corresponding pixels and points, and the accurate overlapping region detection would increase the registration accuracy.
As visualized in Fig. REF , the overlapping region predicted by our method is the most accurate. Furthermore, we conducted experiments to quantitatively compare the accuracy of overlapping region detection on the KITTI dataset. As overlapping region detection on the image and point cloud can be regarded as pixel-wise and point-wise binary classification,
we used recall, precision, and F2-score as metrics to evaluate the performance of our overlapping region detection. We adopted random sampling on the image and point cloud as a baseline,
where 2048 pixels and 8192 points were sampled from the image and point cloud, respectively. Besides, we also used SIFT {{cite:42c9ebb9d7950861f691edc85cb2e57299f7a1d0}} and ISS {{cite:9cb6add3292908627a13f3da18fe50d75e6721a7}} to extract the keypoints in the image and point cloud and regarded them as overlapping regions, just like 2D3D-MatchNet {{cite:6a616fa795fed2788d25ab2d51fc3f814d1782ff}}. DeepI2P uses point-wise classification to select the points within the frustum, i.e., the overlapping region of the point cloud, so we used it as a comparison of the overlapping region detection on the point cloud.
| r | c1dba1a94f5acddd250df7e5cd496fdf |
Since our data is generated in an unsupervised way, we compare against other unsupervised methods in Table REF .
RAFT {{cite:3b0903b76e6c710498e32cda835fba6dae14bd33}} was originally published as a supervised method trained in stages on FlyingChairs {{cite:cd1d1beac3fbc1e5d81f8f38cadf2d612b7a3d60}}, FlyingThings {{cite:f95b1526bb883485fac7e86302395825784daa95}}, Sintel {{cite:33d4ac0d56f082554bd1e37c7e6ea6cd8edd7bee}} and KITTI {{cite:4cda4ada7d286b699010b67327c07ae74d99c27e}} in this order for 100k iterations per stage.
We retrain their model with our data following the same training schedules and augmentation settings and we evaluate after each stage.
The results are shown in Table REF .
We label our models evaluated after the FlyingChairs stage as “C” and the models evaluated at the FlyingThings stage with “C + T”.
The results show that RAFT trained with our Sintel raw data (Sraw) outperforms or is on par with prior unsupervised works when compared on the Sintel {{cite:33d4ac0d56f082554bd1e37c7e6ea6cd8edd7bee}} datasets.
When trained with KITTI raw data (Kraw), we are worse than the state of the art and compete with SelFlow {{cite:07d1f1e1390ff9c5463970743a0a948d537ed668}} and DDFlow {{cite:a5e2f0864b46dbc12fa63a785db3433e42bd5b21}}.
| m | 3e49228fe9d4f1c3c629ef8fb6d62b8d |
Random access memory (RAM) is a fundamental computing unit that allows on-demand storing and retrieving data. While a classical RAM addresses one memory cell in the database per operation, a quantum RAM permits querying a superposition of multiple memories {{cite:e54f4a0596dcfddd1ddab85a53ba9e11fd9dc126}}. Given a superposition of addresses {{formula:e4fc9498-82cc-4b02-8292-17e04ae55fad}} , the `qRAM' returns a correlated set of data {{formula:b480a3a2-6901-4278-a18e-96fc4940abe0}} :
{{formula:02f9b3cd-3aaf-4ae2-b922-6d74c7ccae59}}
| i | 68932915b4d5a42c614db06b251a59e0 |
The interpolation mapping in {{cite:b1c523ecd294eecb2eae08cd1291c0005242c447}} first assigns
a point {{formula:6757e87e-3eac-4395-8e6a-172139207b14}} to a Voronoi cell {{formula:89dc0b45-534b-4b03-bb10-4737fa4220a8}} ,
assuming that {{formula:6b81db5b-2b33-43d5-ae38-1a49b30a4b8c}} forms an {{formula:e20c3d69-f208-4955-b1c0-8add7781b4c9}} -net of {{formula:9ab28ab3-75da-4d48-8609-1e57b2e70cef}} to begin with (a non-probabilistic setting),
and this maps a vector {{formula:8d244dc2-554c-49b9-8bc6-2d69774ecdbe}} to a piece-wise constant function {{formula:e5de7ec9-32c6-471d-b4db-10d5958109f9}} on {{formula:b74ec7a3-3ccc-41a7-88cc-7887e7f92a1d}} ;
next, {{formula:f630312a-5c8b-4d67-8824-6fcd12fcff25}} is convolved with a kernel function which is compacted supported on a small geodesic ball,
and this produces “candidate” eigenfunctions,
whose manifold differential Dirichlet form is upper bounded by the graph Dirchlet form of {{formula:56a265fe-1826-4e1e-a4c1-933a78f93adc}} , up to an error,
through differential geometry calculations.
Under the probabilistic setting of i.i.d. samples,
{{cite:836a9a811d81b507213b99b474df2021883bf0c2}} constructed the mapping {{formula:c46b6662-5710-4639-b0b5-405dc8e5c4a4}} using a Wasserstein-{{formula:a26ab2e2-0ee6-448a-b01b-99631e645199}} optimal transport (OT) map,
where the {{formula:fcc45a08-49de-4d55-b524-f1f8d40f97af}} -OT distance between the empirical measure {{formula:a2da5c8d-ec5b-4e83-9a38-a131776a5b06}} and the population measure {{formula:517ec0f6-9321-4964-89d7-62b073ece0ea}} is bounded
by constructing a Voronoi tessellation of {{formula:01bca4b4-6c04-4166-ab7f-86039bbccaac}} when {{formula:d933f413-67d1-4dd7-b9b5-5a624b440060}} .
This led to an overall eigen-convergence rate of {{formula:a2ec3bcf-c21a-4d4f-8dbc-3f4083220a74}} in {{cite:836a9a811d81b507213b99b474df2021883bf0c2}}
when {{formula:d1d95ff1-c194-4516-9443-b654dbb328c3}} is compactly supported and satisfies certain regularity conditions and {{formula:f29b91c3-81c7-44d5-9647-14e517624965}} ,
the {{formula:7b956caf-0ab9-4ba3-8225-a2b321e7ae49}} indicating a possible a factor of certain power of {{formula:cc8d4bb6-3954-46f2-9873-5e8510a7f10e}} .
A typical example is when {{formula:518f5227-7e13-46d5-97eb-f6c16feabab4}} is an indicator function {{formula:a141add5-1f18-4242-a06b-2546b552a055}} ,
which is called “{{formula:a386fa07-4354-41b3-85bb-9e823630554c}} -graph” in computer science literature ({{formula:684f9ddb-e8a9-4a18-b68e-0b5caffe9cc9}} corresponds to {{formula:f539fd5d-7d63-4eac-9d78-4ead74be9c4f}} in our notation).
The approach was extended to {{formula:0c8b2bf6-9420-40e5-9190-7df9a64433f3}} NN graphs in {{cite:af767c29c06591a5438e9e0a7967e16ab5152377}},
where the rate of eigenvalue and 2-norm eigenvector convergence
was also improved to match the point-wise rate of the {{formula:ae61fb17-098f-440c-a927-ec28fd84eef1}} -graph or {{formula:b84d2869-f304-45d5-921e-db57c333c301}} NN graph Laplacians,
leading to a rate of {{formula:1148891d-1a2d-4947-96e8-098b9901cf47}} when
{{formula:6e3c676d-0011-4d55-83c4-144454301bac}} .
The same rate was shown for {{formula:1ff7edff-0202-4f37-8b8a-bdf21126db92}} -norm consistency of eigenvectors in {{cite:f56fa387bdbea5bbda9d36a7e787d6afda1ba780}},
combined with Lipschitz regularity analysis of empirical eigenvectors using advanced PDE tools.
| r | 005d4ed6dcab0c800f040a2e164bd4d1 |
In this work we perform an analysis of the backreaction on this region brought about solely by semiclassical sources, considering that all classical ones are part of the background. Our goal is to check the validity of the standard assumption that evaporation of the trapped region primarily occurs from the outside, and that the inner horizon is left only to its classical evolution. In other words, we want to analyse the dynamics of the inner horizon when sourced by the energy present in the quantum vacuum after a black hole is created through gravitational collapse. To this end, we first construct a toy model geometry in which a spherical black hole with an inner horizon forms by the collapse of a null thin shell. As a source of backreaction we use the renormalised stress-energy tensor (RSET) of a quantum scalar field in the Polyakov approximation {{cite:8043a82848067f6ecb21e834d2c08adc2ed113c8}}, which is known to capture the essential characteristics of evaporation when used at the outer horizon {{cite:1c563a83a18b32d65f9f95beda0d909da7f281ae}}, {{cite:8043a82848067f6ecb21e834d2c08adc2ed113c8}}. Whether this approximation gives the complete picture of semiclassical effects at the inner horizon is not clear, as no complete calculation of the RSET in 3+1 dimensions for this region is available, the closest being e.g. the asymptotic analysis in {{cite:71ea8df14f0e66947ee44197008a88ac81a49c12}}. Nevertheless, we believe a detailed calculation using the Polyakov approximation is worthwhile, at the very least in order to get a first glimpse of what backreaction at early times may look like in a tractable toy model.
| i | c18089108157173c5fca00d73850202b |
In light of these negative results, people have tried estimating {{formula:1646752f-8d30-42bb-96ba-ce3e358bde3c}} from the coordinates of {{formula:57602a99-06c9-46a6-8674-daab30543ad4}} .
When the entries of {{formula:b393b71a-11f0-42e7-ac06-979bfb9b9ac9}} are {{formula:0b4c195b-30e4-46ed-b792-874233b9a35f}} standard Cauchy random variables, the coordinates are distributed {{formula:28ead93f-a438-48ba-beeb-ea85c416fe7b}} like {{formula:1540fe14-393c-4cc4-a4b5-aafb1f94dc72}} with {{formula:f0666774-d9c9-49c2-9780-0b73d451c4d8}} .
The median of {{formula:a9f6b0b4-e4b7-4e18-a083-8a3ee79573a2}} is {{formula:02fb60a9-3f9f-4c95-92c0-37d67c3b25fc}} , so estimating the median
from the coordinates of {{formula:48f9f6ce-2c98-4ac1-b1cd-af9b497f1aad}} would estimate the distance this way.
Indyk {{cite:784f26bc177fa07f73c62e4b71060ee734768b5a}} considers the sample median as an estimator,
while Li, Hastie, and Church {{cite:34dc8e7351045d386860b19356cc61128637d5f4}} consider 1-homogeneous functions of these coordinates for estimators.
None of the estimators considered are metrics on {{formula:f77bd75b-67c5-4053-84bb-fc50a0edfd3d}} .
For {{formula:460f35fa-050f-4a60-88c4-51cf91d616a7}} -nearest neighbor methods, we should like to have a metric on the target space {{formula:9aba1892-86d1-478b-a015-5368eba6bed8}} and prefer a low number of coordinates for each point.
| i | ce608676f882225acfc6011aab7d3b62 |
The joint NICER and NuSTAR spectrum is well described by a broken power-law model with photon indices {{formula:d1b7942b-14cf-41bd-ae43-cb2a584c7da1}} = 2.10 {{formula:d616ce35-6426-486b-9501-68685b19c0c2}} 0.02 and {{formula:212eaa35-be68-4bce-91a3-7b3969edbb26}} = 1.60 {{formula:c32c571a-361b-4a9f-bf06-3f194620cf21}} 0.03 below and above an energy break {{formula:760c7249-980c-4e9f-b259-c86961a4423f}} = 2.67 {{formula:e9401630-3a9e-4b21-8252-719deb1b0e8e}} , respectively. There is a significant difference of the photon index estimated in the NICER and NuSTAR observations alone, in agreement with the results obtained for the joint spectrum applying a broken power-law model. This should be related to the presence of the high-frequency end of the synchrotron emission below a few keV, and the IC component dominating the emission at higher energies. The contemporaneous NuSTAR and Swift-XRT spectra of BL Lacertae collected on 2012 December 11–12, during another flaring activity, are well described by a broken power-law model with a photon index of 3.3{{formula:03b7cf2b-203e-4ef0-a089-3a6ee1028be1}} and 1.88 {{formula:49aa1f6e-3231-45e9-8e00-87fd9317787f}} 0.01 below and above an energy break of 1.0 {{formula:c724edf2-0bc8-44fa-8d70-aab8e108ff24}} 0.2 keV {{cite:2b56ce90c02c0cdc54c2930f7d2d25edd3932e6d}}. On the contrary, during the 2019 low activity state no statistically significant improvement has been obtained for a broken power-law model over a single power-law model {{cite:c385b2b310d4cd135e657ace5fe49d6859efa731}}. This source has been observed with several X-ray satellites in the past. Previous observations with ASCA {{cite:baf1397d3e1c0a87014b08c99b2f34a7d940e811}} and BeppoSAX {{cite:004201c9c650e19024439e3f9cf3b1dbf9afe269}} have shown that a broken power-law is statistically preferred over a single power-law model {{cite:baf1397d3e1c0a87014b08c99b2f34a7d940e811}}. In case of 3 XMM-Newton observations carried out in 2007–2008, a double power-law model represents better the 0.3–10 keV spectra with respect to a single power-law {{cite:d6964bccf5400c2eef32a613e11692b0ca81407e}}. In that case the photon indices of the two power-laws are {{formula:8c6f5185-5ec5-49a0-a309-50be95cf5661}} = 2.48–2.58 and {{formula:c49daad5-7ed9-443f-b05d-ff7d7ae06f1e}} = 1.51–1.72, in agreement with the two photon indices obtained below and above the energy break of the joint fitting of the NICER and NuSTAR spectra with a broken power-law model presented here.
| d | f61ed66582db4084ccdfb39fda9ec74f |
{{formula:956290a1-46e0-4c63-a14b-5b4d929fd1ee}} Quantum fluctuations and rate prefactor.
When the semiclassical approximation is valid, one can still worry about the impact of quantum fluctuations over the bounce {{cite:6c976803498699a7ad33b96ff9dc25b97caf3405}}
which give a subleading correction to the rate and amount to a calculation of the non-exponential prefactor {{formula:d486524d-480e-448d-9b87-6425f2d6d13e}} in {{formula:ac054311-604a-46fb-894c-afb97719368d}} . A one-loop calculation of this prefactor, summing over Gaussian fluctuations over the bounce configuration, gives the well-known formula
{{formula:1449a23b-a59c-4eb4-8f9d-306d142d946f}}
| d | 4a08f0d7621fe1d6b3c943d2d118fa3c |
Let us show (REF ). By the Law of Large Numbers, {{formula:7d7e4413-9e91-488d-a6ba-27a4e448fd07}} as {{formula:ad9fb470-5543-4ccb-abd3-8e4709df9cef}} in probability. Apply Slutsky's theorem: {{cite:f1efcffdb40456f1318bbab1caaa433ca129553e}}. From (REF ) and (REF ), we have convergence in law:
{{formula:557641c8-7eff-46c3-9979-2bb01e9a1b8c}}
From (REF ), we get: {{formula:132518c5-e21f-4c5c-b2d2-eafae6d4c492}} i.i.d. for {{formula:3ea734e1-ce31-4c6c-940f-92b482bb3424}} , with
{{formula:0572ab3f-ae90-4895-ac83-5975685a6b23}}
In the last line, we used (REF ). This completes the proof of (REF ).
| r | 194f33b2129a21245e5bd615fd99468c |
The algorithm's "division of labor" can be summarized as follows. The parametrized quantum part explores the search space. By exploiting quantum properties such as superposition and entanglement, the exploration is typically much faster than by classical approaches.
The classical part is concerned with finding parameters {{formula:64db3b33-eee6-4346-bced-b14866b495a4}} and {{formula:a4a441c3-3581-4839-953e-d52eb8c406e1}} that, fed to the quantum part, direct the exploration into promising regions of the search space.
With growing problem search space, the parameter search space grows as well {{cite:4612d329d706c0585ae125b1aebb41949c1d285b}}, {{cite:172a44478f5385c7610645872ef3bdd536dc61d6}}, making the classical optimization challenging.
| r | cffee0215c57d31822dcfcd2e08bcdcf |
In this paper, we visualize the internal spike behavior of
two representative and widely-used training methods: surrogate gradient training {{cite:de4c38d3abdf5642d1db1ad5f4729c75f5873f14}} and ANN-SNN conversion {{cite:dfd60914297e9c8c100de6c0baec178159dce37e}}.
Since ANNs can be trained with well-established optimization methods and frameworks, SNNs from ANN-SNN conversion shows reliable performance on very large-scale datasets (, ImageNet).
In contrast, most surrogate gradient training methods are limited to small datasets (, MNIST and CIFAR10) due to approximated backward gradients.
These simple datasets are too small to be analyzed by visualizing heatmap.
But, the authors in {{cite:de4c38d3abdf5642d1db1ad5f4729c75f5873f14}} recently proposed temporal adaptive batch normalization (BN) for surrogate gradient learning, enabling training on larger datasets such as CIFAR100 and Tiny-ImageNet.
We exploit this algorithm for the case study of surrogate gradient training to compare with ANN-SNN conversion on Tiny-ImageNet dataset.
| m | 86f391b60cc25e9c554f7194fbf41076 |
While there are a number of advanced outlier detection methods, it has been shown recently, that in many cases simple {{formula:15fc6ba2-e41f-4277-9c4a-d519d1fd1b27}} -NN queries do perform as well as the sophisticated approaches {{cite:30bbe446755d750fd50874f19ef57b8bf6fc369d}}. When using {{formula:11066cfc-217f-4ed6-85db-ee263cda8a63}} -NN, an observation's distance to its nearest neighbors is a measure of its outlierness. In fact, a number of the advanced methods based on density estimates, connectivity or angular distance make use of {{formula:58df1d0f-c5bc-49f3-af1d-a2954fb86518}} -NN queries, such as Local Outlier Factors (LOF) or Kernel Density Estimation Outlier Score (KDEOS) {{cite:b0183fd238a1b2b98c23db4f48d3818f666baf5a}}, {{cite:fb708b3eec1ec62be5cf7430356972ca909a006d}}, {{cite:dbd2fa7a624fb067057908543e988d37093840eb}}.
Being a simple and nonetheless very effective method, {{formula:c01b9205-b10a-498a-bee7-bdf956383ceb}} -NN is an ideal candidate for outlier detection under {{formula:2388b9a8-a82c-4e7c-8311-190af39bc762}} -DP. To the best of our knowledge, this is the first study which examines an approach of differentially private {{formula:5dd0a627-0a6a-468f-a6bc-6112ea034ac9}} -NN based outlier detection.
| i | 16ee7e928d5f14f41872e7704722ed6e |
{ mH1, M0} [103,104] GeV, mH2 [1.0, 1.1] M0, mH3 [1.1, 1.2] M0,
where {{formula:8a1df655-d2ec-4444-8933-33a43c2d6dec}} runs over the fundamental region.
Here we choose small {{formula:33040db5-6bc0-4cd1-b160-dc617d2ae0c7}} values that are required to realize Baryon assymmetry indicated by Eq. .
Then, we perform numerical analysis and discuss below.
In Fig. REF , we shows the allowed region between real part of {{formula:94994b3f-ab56-44c9-9f26-05a14884f579}} and imaginary part of {{formula:66497f4d-f1f2-4df6-9480-5f800284662c}} , where the blue points are allowed within 2, green ones within 3, and red one within 5 of {{formula:2632fa91-1c71-4dee-8f5c-d61aebc46363}}
for five accurately known observables {{formula:9f11453a-2017-46c9-9c20-fb6f4e57894d}} in Nufit 5.0 {{cite:7ca8e99d9a2f1bc889f61329e0256bb884a49b89}}, {{cite:11ea98102a8fe661da504c01df1bba0f61694149}}, {{cite:3d759bc83b8a2e4bae647130960fa738fbc31a9d}}.
The real part of {{formula:d4edadf4-4d08-425b-b226-e40d9cce782d}} runs whole the range in the fundamental region, while the imaginary one runs over the region of {{formula:9d9e6478-a068-4cb4-93cb-f2c45d2b7e75}} .
{{figure:fd31f5a6-39a9-42a2-b211-ccc15500e8f6}} | d | 323a2ee2f64f02fa9700fcab5f0c88d5 |
Table REF shows {{formula:74acb699-8c5f-4c1b-8ee4-7e26a216352d}} and {{formula:de6d4ae2-b7e6-4486-900f-81095e94ca24}} values of the models on the synthetic dataset. As seen, our pipeline outperforms {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}}, and {{cite:71311f097a38cb3a60617e6ce0bff13d23b173d2}} by a {{formula:64068da5-e582-42e9-b98f-f045c63d5443}} of 47.1% and 5.5% and {{formula:b0a135bd-f17d-4248-8cbc-4959af6beab1}} of 67.3% and 0.1% respectively. Also shown in Table REF , is a {{formula:96b05167-460c-4607-ae10-e5bcfbbec2b1}} improvement of 94.9% and 9.9% on {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}} and, {{cite:71311f097a38cb3a60617e6ce0bff13d23b173d2}} respectively which highlights that Y-Net continues to yield better {{formula:f25e56bb-4aac-4b06-8140-f8726726e272}} results even at higher IoU thresholds. Both our approach and {{cite:71311f097a38cb3a60617e6ce0bff13d23b173d2}} achieve an {{formula:20b47b75-525a-4e6a-83ad-bce078ed6bf3}} of 100% and outperform {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}} by 1%. For small area barcodes, Y-Net outperforms {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}} and {{cite:71311f097a38cb3a60617e6ce0bff13d23b173d2}} by a {{formula:eaea6fc8-bcd6-450e-95cd-5d32bcaa8511}} of 56.3% and 8.8% and for medium area barcodes, Y-Net displays a {{formula:dbefadf0-c8a3-4b3b-bd49-44bb19af431e}} increase of 45.6% and 4.8% on {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}} and {{cite:71311f097a38cb3a60617e6ce0bff13d23b173d2}} respectively. In addition, Table REF reveals that Y-Net a has much better semantic segmentation performance than {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}}. Table REF displays that Y-Net performs at least {{formula:9ffb9807-fdb6-46a1-8f3b-63727230bc4e}} faster than the fastest of models {{cite:0c2181219beb1a7f0689a3c59df9ab93cd25e27c}} and, {{cite:71311f097a38cb3a60617e6ce0bff13d23b173d2}} on LR images.
| r | dc0f83b07913ba548d16be4723e7733a |
The number of dictionary atoms {{formula:88b15de9-90b0-4a59-97e9-2d12f1392531}} is a central parameter of KDS. Because the dictionary is global, rather than local, it does not scale with the dimension of the data only. Indeed, {{formula:a240ddf2-5c18-4370-937a-547984ed0bce}} must be large enough to ensure that any observed data point is well-approximated by a sparse combination of the atoms. However, under the model that the data is sampled from a mixture of {{formula:3fee9b9d-dda5-4c5c-b4a4-7ebe99b0f65e}} probability measures supported on {{formula:a211f837-e6a0-4490-9d8b-4258392604e9}} -dimensional manifolds, {{formula:ab50ef93-affd-4113-a889-97bb49d6c5ac}} simply needs to be chosen large enough to provide an {{formula:76438630-3f40-4d96-a9df-c54cff96a9fc}} covering of the data. This can be done {{cite:5a1f6cc40b471b4e4e0262a6debfe6d81f32411d}} taking {{formula:67f019c7-575b-48da-9b7a-1893163060e4}} , where {{formula:f505e2d3-0182-47c1-92cb-0f32622bd48b}} is a constant depending on the geometric properties of the underlying manifolds (e.g. their curvatures). Importantly, {{formula:0cc6ddc3-c762-490f-96b2-eceae3c9311e}} can be taken independently from {{formula:3a982453-b52a-412b-9e15-b65c04d54c50}} and is “cursed" only by the intrinsic dimensionality of the data. This is most interesting in the case when {{formula:73840b27-6805-4204-9d0a-971ed56da609}} is large. Indeed, if {{formula:2f4805d2-1964-472e-a6b1-7d0051fa0f1b}} is small, then {{formula:649aed2e-9de2-46f0-95ea-fa3831877c64}} is computationally tractable and taking a dictionary consisting of all observed data points will be optimal; this essentially reduces to the SMCE formulation.
| d | fdbd3de27dfe53a8962cf0b3032986e3 |
The Tamagawa number conjecture of Bloch and Kato {{cite:bf6f13d8a50e0c9848dac6f94468dac52dfc369c}} expresses special values of motivic {{formula:b5c44b40-de3c-40be-90dd-6ccf33956e7e}} -functions in terms of arithmetic invariants. The following theorem is an instance of how one can tackle Bloch-Kato's conjecture via Iwasawa theory.
| r | 498d02d00ddf673be6f82ec93a4c451f |
Table REF shows the evaluation of Polar on the program from Figure REF and 14 benchmarks which are either
from the literature on probabilistic programming {{cite:20c7843f58b64f910af24aff700098e1a2ea81fd}}, {{cite:90623d71bb900bfbf6e8896571c4aadfd1ad3fdf}}, {{cite:d63e1c6a103ce5617840b2b6aa77853a06d3f859}}, {{cite:4118bd06309fcd1115ddddf6e9542aca83441d57}}, {{cite:c7d1c15aed2f0f49efd2d638de128a636cf83671}}, differential privacy schemes {{cite:58e1d2e4ca35839231096bbb77145c26ed2081e7}} (Randomized-Response),
Dynamic Bayesian Networks (DBN-Umbrella, DBN-Component-Health) or
well-known stochastic processes (Las-Vegas-Search, Pi-Approximation, Bimodal).
The benchmarks Retransmission-Protocol and Hawk-Dove-Symbolic were further generalized from their original definition by replacing concrete numbers with symbolic constants.
This makes these benchmarks only harder as solutions to the generalized versions are solutions for the concretizations.
Table REF illustrates that Polar can compute higher moments for various probabilistic programs exhibiting different features, like circular variable dependencies, if-statements, and symbolic constants with finite, infinite, continuous, and discrete state spaces.
Moreover, the table shows that the number of program variables is not the primary factor for the complexity of computing moments.
For instance, the benchmarks 50-Coin-Flips and Duelling-Cowboys have 101 and 4 program variables respectively.
Nevertheless, the runtimes for computing first moments for the two benchmarks only differ by 0.3s.
The complexity of computing moments lies in the complexity of the resulting systems of recurrences which depend on the concrete features present in the benchmarks like specific variable dependencies, symbolic constants, or degrees of polynomials.
| r | cdced787e97cb6b664c9ecc28abdb6c0 |
[Proof of lem:lemma3]
Recall that {{formula:d1113aea-0e4f-4a0a-8203-c7c67fd0a40e}} denotes the time-reversed walk of {{formula:e4c46652-66d9-45ba-8cf3-0ebbc3dcb9f6}} starting at 0 at time 1. Denote by {{formula:300f80d7-ab47-4283-b8ad-2b73bbbefc2a}} the family obtained from {{formula:ae4f46e3-45d5-4b7a-a87f-2122d7275217}} by reversing the time and changing the sign of each sequence, i.e. if {{formula:8caf52a0-d965-4dbf-a383-e7482c951735}} then {{formula:6ed9e584-9683-4eed-8ae5-f46558bf8982}} . Note that the increments {{formula:95bb7997-679c-44e9-bb62-56f1541f1203}} of the walk {{formula:f3e27c92-3931-404f-bb3d-ad5eed969376}} are supported on {{formula:592cd3f2-49bf-42fd-b8ce-4eefe84fbec3}} and so using the cycle lemma (see for instance {{cite:b260f4b3c74cdff7e2c0d1879c87eb50eb040318}}) we can cyclically shift the increments of the walk in order to
ensure that {{formula:91aa473c-cece-4b51-af36-75f5f21f67f3}} . We therefore obtain that
{{formula:e5365da7-99e5-4e16-a4e3-49df27eb1821}}
| r | 5d236fc1941ebdb1d33e33489816a8c6 |
One must note at this point that though there is a maximum in the
distribution of flux ratios near the value {{formula:53897cac-cb62-41a5-952a-d7a886f63f39}} , the histogram
and correlation of Fig. 3 have a finite width. Thus there are bursts
with {{formula:2c8622cc-7aaf-4abe-859c-b890faa2615a}} values as large as {{formula:63fec015-eadd-4c8d-a8c8-2891aac7b6a4}} and as low as {{formula:0ff3d451-f110-4055-a681-7f678ca6c016}} . Figure 2
shows a burst with a particularly large value of this ratio. As
argued earlier, one could assign to this burst a value smaller than
that given by our algorithm, given the peculiar form of its
afterglow. On the other hand, if one takes into account that the
apparent luminosity of a relativistically moving source can have a
dependence on its Lorentz factor {{formula:c36248d1-f100-42c6-b358-c1b41fe1de81}} as strong as {{formula:53a2a255-35ba-4fdb-abc2-fb7e73ffa0bf}} ,
even a small reduction in {{formula:ad492a21-3552-4081-894d-ee4e464b52a2}} could increase the pre-to-post
prompt emission fluxes to values larger than {{formula:2372f32e-abaf-420c-b7a5-4526bea75cdd}} . Values of
{{formula:8f86dc96-0f3b-4bcc-91cb-ffa1d970b841}} seem to be more problematic. One possibility,
put forward in SKM13, is that not all protons “are burnt" in prompt
phase, thus reducing the flux of this stage. A related possibility
is that besides the postshock Maxwellian proton distribution, of
characteristic energy {{formula:8e480bc2-0881-48b5-94a3-d733588bc6e3}} , there is an additional,
non-thermal, power law proton population; because this population
extends to energies much higher than {{formula:3ae7910b-faec-4322-88f6-a16f714823b7}} , these
protons continue to fulfill the pair production condition and convert
their energy into pairs, as discussed in {{cite:e975de7646bdc13cb2b7251f15c675491f810e13}}, leading to a
reduced value for {{formula:ef6f7fc2-1893-4e7d-a384-39453e1bca3a}} . The bright bursts GRB 110731A, GRB 130427A with
{{formula:f09171f4-bbad-41e5-9a68-59a845e844bb}}{{formula:b2257ac4-7374-4d76-8081-e7bb4aa49e92}} may in fact represent such cases (to keep the number
of free parameters to a minimum, our earlier treatments of the SPM
refrained from invoking non-thermal populations - a feature invoked
at will and expediently in all GRB models; this does not mean that
they are necessarily absent, however we prefer to invoke them only as
a last resort). Finally, it is possible that the angle between the
edge of the jet to the observer's line of sight, {{formula:00411481-9fc9-4199-8097-9d9280d95fb1}} , is
slightly larger than {{formula:5ad45954-a45b-4045-947a-306a9a082dbc}} , yielding a reduced relativistic
boosting for the prompt emission. After the RBW slow-down, the
smaller value of {{formula:2ee3c6ed-b045-460c-8f16-159ee0805483}} allows the observer's line of sight to
“peer" directly into the relativistic outflow, thereby reducing the
ratio of the pre-to-post prompt emission fluxes. Independent of the
details of reason for which {{formula:b77559a9-47e0-46fd-b1ac-e396e0123e50}} , the existence of
this characteristic value in the {{formula:1a49c9e0-b06c-4dcb-a140-6e8959152e82}} –distribution, provides a new
selection criterion by which we can distinguish the GRB properties
(e.g. Lags, {{formula:7ec60b60-49aa-4745-a3cb-9b6aecdc460c}} , {{formula:f0a11a24-34a8-48a9-8e9a-dee9ac3c8cab}} , {{formula:9a2678b2-f574-454b-82e4-da8d1ec1c0ed}} etc.) to get possibly
novel clues into the physics of GRB emission. We hope to return to
this issue in a future publication.
| d | ecc6e87ad89c5f62f544b90740aec10a |
With the aim of extending the global reach of Natural Language Processing (NLP) technology, much recent research has focused on the development of multilingual models and methods to efficiently transfer knowledge across languages. Among these advances are multilingual word vectors which aim to give word-translation pairs a similar encoding in some embedding space {{cite:1c7da0fe97e83d72b6c532437f92de621327e99d}}, {{cite:7df948dadb2d27a09a0ea54304afe0c35c351176}}. There has also been a lot of work on multilingual sentence and word encoders that either explicitly utilizes corpora of bi-texts {{cite:0337cc5e6bc321fc2bb1c5df967a955442aec68f}}, {{cite:b2b1778744650e06b75054c6f4c9e24c3666c6e5}} or jointly trains language models for many languages in one encoder {{cite:703c0bb48b6da81fc04915dbe28fc87e9bb0cd9d}}, {{cite:9d884f4e66b836cc913f449513204af0efa88ecb}}. Although great progress has been made in cross-lingual transfer learning, these methods either do not close the gap with performance in a single high-resource language {{cite:0337cc5e6bc321fc2bb1c5df967a955442aec68f}}, {{cite:9d884f4e66b836cc913f449513204af0efa88ecb}}, {{cite:094be214e75b6968ad77a3bd4bd179e3ebd0cdd5}}, e.g., because of cultural differences in languages which are not accounted for, or are impractically expensive {{cite:3a03c41b021c0bc453873547f387872945c2a780}}.
| i | 0f5f5227923ec73957ad757b437c6fbb |
In Table REF , we compare model complexity and symmetric-scale SR performance of our LTEW for both in-scale and out-of-scale to other warping methods: ArbSR {{cite:bf70bd9224ce50c5836cc5ced52ac7adcad1c4e6}} and SRWarp {{cite:57bb2a0ecab8b78273b294d5e652342f8cbe2898}}. Note that ArbSR {{cite:bf70bd9224ce50c5836cc5ced52ac7adcad1c4e6}} and SRWarp {{cite:57bb2a0ecab8b78273b294d5e652342f8cbe2898}} are learned to perform asymmetric-scale SR and homography transform. Following {{cite:fef9baa417c240a189e07ea91aeaedbe8f4ee66f}}, we use {{formula:4c6f3a3d-c3ee-49d2-92f7-3851125a1e25}} instead of {{formula:2fd3529a-3585-44b2-98a8-f3705e5c065e}} in Eq. (REF ) for phase estimation. We see that LTEW significantly outperforms exiting warping methods for out-of-scale, achieving competitive quality to {{cite:bf70bd9224ce50c5836cc5ced52ac7adcad1c4e6}}, {{cite:57bb2a0ecab8b78273b294d5e652342f8cbe2898}} for in-scale. A local ensemble {{cite:171c0f969dc64c9196d64b1a2f657959be5362b0}}, {{cite:68db252305d03241ab27bc3f290ea00e34416395}}, {{cite:fef9baa417c240a189e07ea91aeaedbe8f4ee66f}} in LTEW, preventing blocky artifacts, makes the model more complex than ArbSR {{cite:bf70bd9224ce50c5836cc5ced52ac7adcad1c4e6}}. SRWarp {{cite:57bb2a0ecab8b78273b294d5e652342f8cbe2898}} blends {{formula:37417899-406f-4dd9-bcbe-dc1356423763}} , {{formula:5ba130a9-ed3e-4555-99d0-96a16daea3fb}} , and {{formula:e79363de-b97e-4765-bb32-593c48591bf0}} features, leading to increased model complexity than LTEW, which uses only an {{formula:581cd44f-0857-43df-a0e5-7c31b45d464b}} feature map.
{{table:6119826f-5200-4f76-ac95-d0cfd643d593}} | d | 1c0031f2e141db60f2a4bccc7839babe |
On ESOL, we believe our CubeMol models struggle due to the limited data, the large size of molecules, and the lack of path and structure features used in Path MPNN. Even still, the ability for the CubeMol models to scale to molecules with more than 50 heavy atoms indicates the room for optimization. For example, a tree decomposition method used by the Junction Tree Variational Autoencoder {{cite:7f0d49694995aa04aff84a14726964b478ad2f61}} would be able to greatly reduce the number of elements in the graph by generating a new vocabulary of nodes that includes cycles and functional groups.
{{figure:3b31f2b0-39f4-4d76-ab22-1a96fa699675}} | d | 92b0dd9f05ed55bd63a2aa434aef90c3 |
The extent to which the degeneracy leads to diversity in the clusterings, depends of course on the optimization algorithm, as was also shown by {{cite:fc194197fc3e57c14ab55b44641edb87910c662f}}.
To calculate and use consistency in a sensible way, one could argue that a large diversity of clusterings is positive, as long as they are all close to the optimum. However, this is not what optimization algorithms are designed for and it is unclear to which extent different algorithms explore the modularity space.
We have observed that the Leiden algorithm, which we use in this paper, results in a more diverse set of outcomes than its predecessor, the Louvain algorithm.
In {{cite:3e1193b0990c9cf87e34300e5681f1d7ea9e5861}}, a generative model is used so that it is possible to sample from the posterior distribution over clusterings.
It would be interesting to combine this approach with our proposed consistency metric.
| d | ea4e2ce9d26c8846dae8be103d212388 |
Quantum computers are thought to enable calculations that cannot be carried out on classical computers {{cite:b0872dc54037986aa0f5098977e232c06f866036}}, {{cite:4da2c08e1b733392f5ff84c46e63a8cf9608f6cd}}. One challenging problem in many-body physics is to determine the zero-temperature phase diagram of finite systems that have level crossings in the ground state as parameters in the Hamiltonian are varied {{cite:1a5a2f90ef2917a2aa3f0c7df008cc6d638449e5}}. Such phase diagrams commonly occur when a system has competing order parameters {{cite:47d1d6fe3a403cb86619ec40ef13ad3090b44885}}. One possible approach to solving this problem is to simply create circuits for target wave functions that can have their parameters varied to allow for a variational determination of the approximate ground state. Then, one can determine the phase diagram by examining the quantum numbers and the symmetries of the variational wave function. But, such an approach is likely to fail or to be inaccurate; this is because there are low-lying states near the level crossings and the variational calculations need to be done with high accuracy to carry out such a program. This becomes especially complicated if the variational state ansatz does not belong to the subspace corresponding to ground state quantum numbers.
| i | 8ba7c3b20e9c7da9cf116ee471cc03a7 |
To compare the performance of LESS against other regression methods, we have selected 11 well-known approaches. Each method is tuned with the hyperparameter sets given in Table REF during cross validation. Linear Regression (LR) does not require hyperparameter tuning. All these methods except, Local Linear Regression (LocR), are available through scikit-learn package {{cite:547b0d08c91119ed7bfcaa94687189a9450df78a}}. Like LESS, we have also implemented LocR using main scikit-learn classes, and our implementation is based on Section 6.3 of {{cite:da7c884aa2c59bc1242b8558ea63322b195afe47}}.
| m | 51247faabf511093c0e24a3911b616a5 |
Language is creative, it is situated, and has to do with our
communicative competence:
its users can give new meanings to old
words {{cite:f7a15a0a6b9817952291947052846375066d5329}}, produce utterance
within a particular time and place
{{cite:f629b05273cdd1691fe655f755e039f3eb993086}}, and determine if they
are appropriate in specific contexts
{{cite:347821d5effa22918f778b3308f231f26e81fc1b}}. Hence, the variety of realizations in which
the same message can be shaped stems from many distinct factors. On
the one hand are variations related to personal differences between
speakers (e.g., a person's class, gender, social environment), on the
other are those occurring within the speech acts of a single speaker
{{cite:df270f268cfc267e05e10a9b4f8c44d6b0683fe5}}. We unified such insights into a
hierarchy of styles, which proposes how they relate to one another.
| d | 53993a50ebca7c3ae01c1778523de399 |
In this section, we consider the nonsmooth problem (REF ). From Assumption REF and the definition in (REF ), we know {{formula:0afffce1-28a9-4874-a8ae-12a969354b7f}} , and {{formula:5957a095-494a-43ce-880c-1acd1a1ef4d2}} is equivalent to {{formula:57078f7a-45fe-43f0-8c64-2739466a255f}} {{cite:83a2ad4d4bdb9f0d970d0e54d52d682a7cdc00cc}}. Thus, similar to (REF ), we can reformulate problem (REF ) as
{{formula:7ac102f8-83fe-41dd-bb0c-95b466f40cca}}
| m | 6995d90364b8c1cca532a381027314fd |
Recommender systems have shown great success in both academia and industries, and so become indispensable in our life by helping us filter millions of possible choices. Recommender systems provide a small set of items from the underlying pool of items based on users’ historical interactions and their side information. One of the well known recommendation frameworks is Collaborative Filtering (CF){{cite:75679fa994fa41761d07d5ce983f8dfa37477b10}}, {{cite:4cc5cf7003f4ed54af9543418bc78e3b7af63a3d}}, where the only available data is user-item historical interactive information. A key challenge in CF-based methods is to provide accurate recommendations from a large number of items with extremely sparse interactions{{cite:9605440b0c28143e3da9813139ae1b50b98473dc}}. Such recommender systems suffer from poor performance due to sparse interactive data or ratings and cannot even handle user cold-start and item cold-start issues brought by new users and new items {{cite:d8f55377e1441d0eae7075615269e472533f978e}}. So as a very critical problem in recommender systems, how to make accurate recommendation under sparse and cold-start scenarios attracts rising attention from a wide range of stakeholders in recent years.
| i | d6d8c793901473cde07bd38889631e83 |
Datasets.
We evaluate performance on ImageNet {{cite:a1790d21687338bf9cce3d715c0ec3fbdacb7edd}} and CIFAR-100 {{cite:ab61b8d3549583751c593627f127f6606300a1f1}}. ImageNet-Subset contains the first 100 classes in ImageNet in a fixed, random order. We resize ImageNet images to 256{{formula:0e6a307e-576c-4b65-a629-40c4dbb34f14}} 256, randomly sample 224{{formula:88910d18-c2bd-4343-a9c6-39280d785d6b}} 224 crops during training, and use the center crop during testing. CIFAR-100 images are padded with 4 pixels, from which 32{{formula:14e08db6-7622-4477-a78f-68f1c1d32717}} 32 crops are randomly sampled. The original center crop is used for testing. Random horizontal flipping is used as data augmentation for both datasets.
| r | a9e62c139e842b002576adf2e5df18c5 |
In Section REF , we detailed our model assumptions and
choices for training accurate and interpretable binarized
models using MIP and PBO. Similar to Rosenfeld et al. {{cite:6fd35953b3d85d87af1daebec43e595353acb8d4}},
we made the assumption on the existence of function {{formula:834ce456-2186-4ba0-80f4-d5a0fd000127}} which allowed
us to train linear regression models for the multiclass classification task.
In Section REF , we experimentally demonstrated that modeling
{{formula:8d2b7760-255f-4113-a22a-65154fc457eb}} instead of {{formula:71327dfa-30e9-4119-9d0e-4fc79e6d0953}} significantly improves the test
performance of our MIP model. Our results suggest that similar works
on training Binarized Neural Networks {{cite:5aa6359b0d8c7a06e6703427e73a2c03ba65e702}} using MIP
models {{cite:6b781e33baad0b5cd33fccb3899486f6725a8b24}} might also benefit from similar explicit
modeling of function {{formula:57b24b40-f3dc-417d-8c4c-a2c1a08444de}} .
| d | de324ca435b00a36612758e612607638 |
In this paper, we considered models with spatial connectivity patterns where each unit connects to all its neighbors within a radius {{formula:ceda0734-98cd-449c-9f05-a105cace57d8}} . In the future, it would be interesting to extend the current framework to study network models with random spatial connectivity. In this case, the connectivity patterns can be described by random band matrices. According to theories of random band matrices {{cite:5ebab68c74149e96e755ba9a7d5b43ae0ccc7662}}, the spatial correlation undergoes a transition from localization to delocalization phases, when the range of spatial connectivity exceeds certain thresholds. In addition, we focused here on the regime with a stable activity. Another future extension is to explore the spatiotemporal correlations in the dynamical regime where rate dynamics are chaotic {{cite:f209f71ff92cf2dff1d28381871fe7728fa4acb5}}, {{cite:94060ab9d9fcc029231e4ba9bd013ea266fa8142}}.
| d | 207e70ed2ced857e76c4754f53d50645 |
Any physical mechanism, which may be invoked to explain the emission up to TeV energies in PKS 1424+240 and TXS 0506+056 will have to be reconciled, however, with the low {{formula:33fe2ce4-efcc-437c-9f61-12cb25516fd5}} and {{formula:2c7463d2-95cb-4c86-9637-8b39f560919f}} factors observed on parsec scales. Most solutions to the so-called Doppler factor crisis have been proposed so far for the case of “classic” low-power HBLs. These include the near-core decelerating jet models {{cite:1f5dd4e9fb1c8295d83a0489412e56df970067b2}} and the shock-in-jet models, in which the low apparent speeds are proposed to reflect the formation of quasi-stationary shocks in the jet {{cite:672c82443970e683831c4c4bf0396e45e0cf60dd}}. It is a subject for future investigation whether such solutions are also applicable to the case of the high-power jets in PKS 1424+240 and TXS 0506+056.
| d | 639fa02e9d57ad0a8fbd1f5cd779a0db |
Our new representation opens doors to new mathematical and statistical methods to analyze brain connectomes; in particular, taking into account the tree structure of the data. Topological data analysis (TDA) uses notions of shapes and connectivity to find structure in data, and persistent homology is one of the most well-known TDA methods {{cite:6f145d8d5cc6041b97987bdedd2b20d418f05a1e}}. TDA has been used successfully in studying brain networks {{cite:51ada98b0f3d9f23709313862a9b6d6f7947998a}}, {{cite:d904ab4502e242834561bd2990a429658e5c274b}}, but we provide a fundamentally different approach.
Our analyses of the connectome trees in this paper are simplistic. We treat tree nodes as independent and non-interacting. Future work should consider the tree structure to enforce dependence between the nodes, and hence, between their effects on behavioral traits. The tree structure may also be exploited to model interactions between connectome structures across different scales. For instance, Bayesian treed models are flexible, nonparametric methods that have found widespread and successful applications in many domains {{cite:7e93d5dc20da696227d5084a4abdb29fe40eb9d9}}. Existing treed models might prove unwieldy to fit and interpret on AM-based brain networks but their modifications may fit the nature of our tree representation well.
| d | dbafa5f4bbc5d965d819bd1fc39e3f6a |
The jewel in the crown of the achievements of the LHC experiments to date is the Higgs boson discovery in July 2012 {{cite:56a619b73f9b35113b0a3eb892a1c69257fc282f}}, {{cite:e953b3cf8e1705d5e2696e490a41ba8de88ddb99}}. The discovery of a Higgs boson is, however, not just an end of a story - a quest that began with the theoretical predictions of Brout, Englert {{cite:7c4431b908d1082dca9f8846a79b1251c711ab79}} and Higgs {{cite:1fc58fa3a1e149061313355b9cf0f923fb31c2fd}} - but also a beginning of one.
While the presence of the Higgs boson provides a solution to the question of how fundamental particles can acquire mass, it does not actually explain the mass values themselves, and it also raises new questions. “The Higgs program" is a major research project at the LHC, and at all proposed future collider experiments. From the experimental side, the Higgs program refers to a large set of measurements aimed to learn the detailed properties of this unique particle. From the theoretical side, this is also a very exciting program, as it touches upon several open questions and puzzles in particle physics and particle cosmology.
| i | d0e329747213b800537870d784bb29ee |
Our data confirmed that O VI absorbing clouds are
ubiquitous throughout the Alpha and Beta quadrants of the Galaxy. The
O VI volume density {{formula:c9edd8d2-7a59-45f6-91e8-fcd28bf07aec}} falls off exponentially with height above the
Galactic plane, as had been shown from previous studies
{{cite:572723f4b11abc979e3372fd5cfa8df8491f38c4}}, {{cite:2148635fc264e7566f1c13a509b3b3d88ae8c162}}. With the FUSE data, however, we were able
to measure the mid-plane density to be precisely
{{formula:dec66eec-e215-4f25-ac63-5cd8661ac817}} cm{{formula:3e2763bb-5d3d-4d10-891d-d887e34c3cfb}} , with scale heights of 4.6 and 3.2 kpc for
sightlines in the southern and northern Galactic hemispheres,
respectively. However, even though the O VI density falls off with
height above the plane, the O VI absorbing material is not smooth, but
clumpy, with a range of cloud sizes. We were also able to settle a
long standing question as to how much O VI absorption towards a target
star actually comes from hot circumstellar material around the star
itself — only a small amount of {{formula:68ab86ec-3dab-4f3a-88c4-7436cf2e1ece}} (O VI) arises in such regions. We
found that {{formula:88606d2e-bd07-4fc9-80bf-2ebd3d894782}} (O VI) correlates with {{formula:1f34470e-127c-4704-9dfe-cf2744843c92}} , demonstrating that O VI
absorbing clouds are truly interstellar, and composed of many
individual, overlapping, components. The dispersion of {{formula:ea261b88-d5b8-424e-a1d1-908a7c3b46ff}} (O VI)
with {{formula:87470ca1-3a6f-4864-b0a4-131e1975fcdc}} is large though, and very different from what would be
expected from absorption by an ensemble of identical clouds. The
velocity extent of O VI lines follow those of lower ionization
lines observed along the same sightlines, showing that hot and cold
gas are coupled.
| r | 9e6613a902cd9e1627530a0acfdeecc3 |
In this article we derived the integrals of hyperbolic and logarithmic functions in terms of the Lerch function. Then we used these integral formula to derive known and new results. We were able to produce a formal derivation for equation (27) Table 27 in Bierens de Haan {{cite:e236f1746b8ecedb73878258fd5d85f74cc56310}} and equation (3.514.4) in {{cite:e5a59a0532fcc7f3121662f58939b770f04af1fc}} not previously published. The results presented were numerically verified for both real and imaginary values of the parameters in the integrals using Mathematica by Wolfram. In this work we used Mathematica software to numerically evaluate both the definite integral and associated Special function for complex values of the parameters {{formula:14e68e62-3096-4608-815a-6bf1d96e75d4}} , {{formula:4f4db951-3576-4b89-a8f6-91076ff2e84f}} , {{formula:4f2f6dcc-af57-49d6-af22-cc5881c48fb4}} , {{formula:5e25809a-b63d-4415-b6b5-f9b3cd953941}} and {{formula:038f3dcf-90da-4dd5-aee1-fd16bf5742af}} . We considered various ranges of these parameters for real, integer, negative and positive values. We compared the evaluation of the definite integral to the evaluated Special function and ensured agreement.
| d | 6b96b2b42853fc286a21453e6a74c04c |
It is common for {{formula:0e7cd02d-16af-4b85-8570-fceacc6747b4}} to be large, {{formula:dae874d9-b842-413b-bb31-fba121c6b219}} . Optimization in such a high-dimensional design space is difficult, especially when {{formula:205644c9-a577-4319-a144-9a2736f67be0}} is the output of a high fidelity numerical simulator
that can only be run a restricted number of times {{cite:00f6dfdcade368731f28361e49314ccf65997e47}}. In computational fluid dynamics for example, simulations easily take 12 to 24 hours and evaluation budgets range between 100 and 200 calls.
Surrogate-based approaches {{cite:8da66c3052c74e2b47a6c39fdc4975ae4b2e1eed}}, {{cite:baaa6a1919854f637cbc8a5a7a370a94adb6e5d1}} have proven their effectiveness to tackle optimization problems in a few calls to {{formula:10b0bdbd-4646-4a5b-90e1-5a3b9a7c21a4}} .
They rely on a surrogate model (or metamodel, e.g., Gaussian Processes {{cite:3ab03b5d1cdb860eea2160d000faee6734a325b6}}, {{cite:845ae61ff4e3fad02d32179bb117b6fc9fa257d1}}, {{cite:ff0b307f6835996a93d344746475e3454078dc64}}) built upon {{formula:cb0fbd60-b2f4-4d4f-b0c6-54357ccb54ac}} past observations of {{formula:4c5386f2-b7a9-429e-b33b-4dad1e2b6f3e}} .
For a Gaussian Process (GP, {{cite:3ab03b5d1cdb860eea2160d000faee6734a325b6}}, {{cite:845ae61ff4e3fad02d32179bb117b6fc9fa257d1}}, {{cite:ff0b307f6835996a93d344746475e3454078dc64}}), given {{formula:8f658a0c-9999-465c-bebd-a3f9573969f4}} , {{formula:07ad0cd6-806d-47e2-a060-9f294eac0fb1}} can be predicted in closed-form at any untested point {{formula:e13a6662-0b55-45b9-8c0c-fbd89c5b1b28}} via the kriging mean predictor, {{formula:1468f776-005f-44d5-aef9-a062ff35fb78}} . The probabilistic framework of GPs additionally provides the uncertainty associated to the prediction, known as the kriging variance, {{formula:b8271bd2-581d-4f0c-ba8d-5a5de13e38d2}} , also computable in closed-form {{cite:ff0b307f6835996a93d344746475e3454078dc64}}.
For the optimization, the metamodel's prediction and uncertainty are mixed by an acquisition function such as the Expected Improvement {{cite:ba566f7e8f0a91899d6e32127e25c4ea5364cdd9}} to decide which design {{formula:01340972-3d75-45f2-8358-6ef87ec7e7ac}} should be evaluated next.
However, such techniques suffer from the curse of dimensionality {{cite:3fa42e7ca3e6bd9e8787067184085fb0dd3a536e}} when {{formula:4e6e425a-328d-4127-b910-35f65e46f42d}} is large. The budget is also typically too narrow to perform sensitivity analysis {{cite:8c6246091552c60c2f750a92b930c1fbb0abbc31}} and select variables prior to optimizing.
A further issue is that the CAD parameters {{formula:e60ac638-f626-4364-a805-fddce6138a7d}} commonly have heterogeneous impacts on the shapes {{formula:c08133c7-3943-4974-a0a6-7a812cf244da}} : many of them are intended to refine the shape locally whereas others have a global influence so that shapes of practical interest involve interactions between all the parameters.
| i | e9de6a907b34947e7e9574af6612388e |
Consider the following setup. At each {{formula:6c7c229f-1d00-4316-bbd1-b858c97ab1c9}} , a forecaster {{formula:038388cb-019c-419d-b183-78aec3d02e27}}
outputs a density forecast {{formula:ea44bfbb-04b6-46ea-b28a-f2f36eec085c}} given observations {{formula:a5a7caf2-6382-4e50-a166-606c9b0561d4}} for a continuously
distributed scalar random variable {{formula:13596acc-bf47-4847-af0c-500abde4e1bb}} whose true distribution is {{formula:504f00ea-dbc5-43b3-bb09-9e792c94b8f6}} . We
assume that the corresponding cumulative distribution functions (CDFs)
{{formula:8cc11bf8-020d-46d2-bdc4-3dfcef22fc60}} and {{formula:e79a6a48-3e25-4965-ac8d-a4d813c677f1}} are continuous and strictly increasing (for simplicity). The
forecaster {{formula:08e219a4-58cd-43ec-b564-0b38e88320d9}} is evaluated according to a proper scoring rule, such as the
Brier score {{cite:0bad2934e4d2e2d585c5649447f8de9fa2238d8f}} or the logarithmic score {{cite:acc92d97916c240a3c98713366ec3200db07bdf3}}.
| m | f7e97c7833599f80a780d6a77f72ff24 |
We summarize our key contributions as follows. 1) We propose to harness the complementary features from both modalities in forming enriched feature embeddings, that are consistent with semantics of identity, thereby allowing improved identity recognition. 2) We propose to impose orthogonality constraints on the fused embeddings. They are not only coherent with the angular characteristic of the commonly employed classification loss but are very efficient as they operate directly on mini-batches. 3) Experimental results on large-scale VoxCeleb1 {{cite:561e990cdbe917ba94c5760f814faf5cc40cce2e}} show the effectiveness of our method on both face-voice verification and matching tasks. Further, we note that our method performs favourably against the existing state-of-the-art methods. 4) We perform a thorough ablation study to analyze the impact of different components and empirically show that the proposed supervision formulation for face-voice retrieval is more effective and efficient than the ones employed by the contemporary works.
| i | 3654873bce56da9079c8de06b73ba1a8 |
Tables REF -REF show the ImageNet test performance with 8-bit floating-point quantization of the activations, weights and gradients for different EfficientNet models {{cite:ecd34da972a4a02678a7cd7d1e4b8d3cfd9f24fe}}. Following {{cite:ecd34da972a4a02678a7cd7d1e4b8d3cfd9f24fe}}, we train on ImageNet for 350 epochs with RMSProp optimization {{cite:bbd6096917df2ad8b0e18f5c81d095cb661513ab}} and decay the learning rate exponentially by a factor 0.97 every 2.4 epochs. We use a weight decay parameter {{formula:c8cb7808-36f6-48a4-b3a7-6776bb488692}} on the convolutional weights, and a label smoothing factor of 0.1. We use a slightly smaller global batch size {{formula:3a66d9b5-054b-42c0-be17-e407956c365e}} across all training cases and scale the original learning rate and RMSProp decay factor. For the RMSprop optimizer we use learning rate {{formula:41dec665-a984-40b5-826d-4820864631f6}} , momentum coefficient {{formula:e408f0b4-1e98-49bb-a20c-e9a2a630c3b6}} and learning rate decay {{formula:ad108443-aff2-45f8-86e1-2fea236db179}} . Our final weights are obtained by using an exponentially weighted average over checkpoints from each training epoch, with decay factor {{formula:5c63a12b-f874-4421-be42-2e25e6e3b847}} . All the accuracy results derive from an averaging over five independent runs. In addition, as presented by {{cite:d999ddd5c370b03a8835e763fd615046f7bdfce5}}, the augmentation strategy uses a combination of Mixup {{cite:e998a2d5a0312bf7704d3a65f20d9710a1f8e0fa}} and CutMix {{cite:1439d9800accda2b16700ccf585f7c65956c9724}}.
Also in this case, the accuracy obtained using the 1.4.3 format for quantization of activations and weights and the 1.5.2 format for quantization of gradients fully matches the baseline accuracy.
| r | 1c817b4910a3d70614098cb0e956090d |
We investigated the footprints of the planet in RVs by searching for periodic signals. To do so we used the Data and Analysis Center for Exoplanets {{cite:d0ad72ee60902a714a62f05262b47a0d0d1ec37b}} web platformAvailable at https://dace.unige.ch
and computed periodograms for the RVs (Fig: REF ).
| r | cb03251c37e90138ec84fd0f6e5555d0 |
Machine learning (ML) mechanisms were typically designed without considering security risks, as recognized by a plethora of studies {{cite:cebd266a25a60a256847dcd05a85b6669f20b862}}. Attacks on learners were introduced, many of which corrupt training data. The latter, referred to as data poisoning attacks {{cite:ccb726022b5d8ff07432d9018d1d4a7c06c100f9}}, modify training data to manipulate model behavior at test time.
Many poisoning attacks aim to manipulate the model and impact performance and accuracy. Their aim is that some data samples, not necessarily specific ones, be erroneously classified. Targeted poisoning attacks, e.g., {{cite:12dbfeee58d5ade4e7a416cd268de0f1036c7517}} ,{{cite:148096b7bd675e41303a38cea2374084a60f6ea8}}, aim to misclassify a specific targeted data sample, and only that sample (or sample set), with a negligible change in model accuracy.
| i | 116b7c8b723a7f00a82d3a1f8254ae2e |
The condition number of the cross-correlation matrix has been pointed out in several studies as a key quantity in determining performance {{cite:7f6ee32db1d6946ae91a4a9734a4c3c8c52d49f1}}, {{cite:3d3faa0a7209821048524af967594f8858163b5c}}.
Our work analytically quantifies those empirical observations in the framework of networks trained on a simple task via common LS-based algorithms.
We have shown, however, that performance might depend on other features, such as closed-loop stability, for other non-standard algorithms (see Fig. REF ).
| d | 17cce215648ba67b439590be7dc6b7d0 |
We see in Fig.REF that the binary separation is
correlated with the mass of the parent gas structure.
It seems that no correlation exists in the case of the
fragment mass, as can be see in Fig.REF .
This missing correlation is expected on physical grounds, in fact, for the Taurus
dark cloud, {{cite:18232d3d748882166f35480e2791ba189998eb25}} reported a correlation between the mass of the newly
formed stars and the mass of the associated dense proto-stellar
cores. More recently, large proto-stellar masses were observed by
{{cite:86643848282e7598968bbd61412859b57d8ec762}}.
| d | 017f8f94cb4b861dd8afb3e7aaeaa368 |
The starting point of our training pipeline follows the proposed methodology in {{cite:dc1a11df373a009e8ef9022accc36a91c0d389b9}}, difference being we utilize batch-norm (bn) during ANN training and subsequently the bn parameters are fused with the layerwise weights as done in {{cite:bc7a84c04a2051d5e82260bf9dd8346c9502c98b}}. With this pretrained ANN, the weights are copied to an iso-architecture SNN and we select the 90.0 percentile of the pre-activation distribution at each layer as its threshold. Then the SNN is trained for 5 timesteps using bp which serves as our baseline; training steps are detailed in Algorithm REF . Our starting point is chosen as a 5 timesteps trained network, since it is lowest latency that previous works have reported for SNN ImageNet training {{cite:dc1a11df373a009e8ef9022accc36a91c0d389b9}}, {{cite:38a774de214c4dd03cf80e357a15558f049b4a88}} with high performance. Going below 5 results in convergence failure due to spike vanishing at deeper layers.
| m | fed0accda1840b013c294ff10d12f56b |
Since our data is collected with the old policy and value estimation (off-policy), we keep introducing more bias as we train the network off-policy using batch data (i.e. {{formula:ddfca3bf-a49e-48fd-a5bb-c968b05af591}} ). This is because when the difference between the old and new policy ({{formula:c216cacc-41bd-4610-9f80-0f58f2257aef}} ) increases, so does the inaccuracy of value estimation. The bias usually causes the training process to be less stable. To solve this, we use proximal policy optimization (PPO) proposed by Schulman et al. {{cite:e727f18119875ef227980e77a3de0c929d9d1a94}}. PPO sets a restriction for the induced bias by restricting the policy change in a single training episode. The objective function of PPO is
{{formula:99906be3-c547-4fbc-8e06-f0e1e02489fc}}
| m | 94a7fcf3965e2d260af408cff779bbd0 |
Obviously, given the significance of the above result it is highly convenient to compare it with previous analyses of the XCDM reported by the Planck and BOSS collaborations. The Planck 2015 value for the EoS parameter of the XCDM reads {{formula:d3876d48-04b9-4acb-abc9-a532b35b015d}} {{cite:1e0a05971d4affd43d8a0aa8511855833d334be1}} and the BOSS one is {{formula:342da290-74c3-41db-ae8d-cc8a9e0f2bfd}} {{cite:1af10036d3cd3969dc0097c409eabe1cdcb38a8c}}. These results are perfectly compatible with our own result for {{formula:4aaad47e-2a70-49a9-9fb0-db605b44dc73}} shown in Table 1 for the XCDM, but in stark contrast to our result their errors are big enough as to be also fully compatible with the {{formula:c5c313f0-ae6c-42bd-bff3-5462e0920779}} CDM value {{formula:55bf9a49-d4ec-4346-be80-d57aa2594657}} . This is, however, not too surprising if we take into account that none of these analyses included LSS data in their fits, as explicitly indicated in their papers Furthermore, at the time these analyses appeared they could not have used the important LSS and BAO results from {{cite:4182c8ecda16f1712a6d9c34c9ac8484be020405}}, i.e. those that we have incorporated as part of our current data set, not even the previous ones from {{cite:4182c8ecda16f1712a6d9c34c9ac8484be020405}}. The latter also carry a significant part of the dynamical DE signature we have found here, as we have checked.. In the absence of LSS data we would find a similar situation. In fact, as our Table 6 clearly shows, the removal of the LSS data set in our fit induces a significant increase in the magnitude of the central value of the EoS parameter, as well as the corresponding error. This happens because the higher is {{formula:328c9e8f-16cc-49a0-90ab-297a3abffbec}} the higher is the structure formation power predicted by the XCDM, and therefore the closer is such prediction with that of the {{formula:9eb38593-8e1a-46c3-ad36-c72fe4db0a88}} CDM (which is seen to predict too much power as compared to the data, see Fig. 4). In these conditions our analysis renders {{formula:c354fcf7-6230-4563-918f-2ccc23949ad8}} , which is definitely closer to (and therefore compatible with) the central values obtained by Planck and BOSS teams. In addition, this result is now fully compatible with the {{formula:183ac92f-108c-4733-92f9-9ec8a65b6081}} CDM, as in the Planck 2015 and BOSS cases, and all of them are unfavored by the LSS observations. This is consistent with the fact that both information criteria, {{formula:9cc64f96-c60d-44b0-bef5-1e1f719d97b9}} AIC and {{formula:3b90cfc1-59e3-42b6-a6c8-b305bbc50411}} BIC, become now slightly negative in Table 6, which reconfirms that if the LSS data are not used the {{formula:28eb52c2-3555-4ce2-aa31-ea826078428a}} CDM performance is comparable or even better than the other models. So in order to fit the observed values of {{formula:b7600127-e8f7-457c-b5d4-b180371e4024}} , which are generally lower than the predicted ones by the {{formula:fe5ef558-d3ab-48df-941f-f146d3ba490e}} CDM, {{formula:983fb268-2df9-4aa5-a14c-3ceef0e5595a}} should decrease. This is exactly what happens for the XCDM, as well as for the RVM's, when the LSS data are included in our analysis (in combination with the other data, particularly with BAO and CMB data). It is apparent from Fig. 4 that the curves for these models are then shifted below and hence adapt significantly better to the data points. Correspondingly, the quality of the fits increases dramatically, and this is also borne out by the large and positive values of {{formula:f8b7aa5e-ffff-4f7f-abc3-0a31b85cf381}} AIC and {{formula:5bf2581e-db0b-4573-80b2-7eb360a8916a}} BIC, both above 10 (cf. Table 1).
| d | 40d81e9fd148b89ee6fed1b187112d8e |
However, in most publications the research focus so far is mainly on a weak coupling as pointed out in {{cite:1e2a228a546a3af817933bb2ad4c16116068f0bd}}.
Works considering strong coupling especially in the 3D case are rare. In this direction, for several reasons, port-Hamiltonian systems provide a good framework to solve this kind of coupled multi-physics systems, see {{cite:430af7e2ad9c170cd532655969af0c7df480355c}}, {{cite:6e5804994ca78e3c6c8ac1ba1d1df7dcb489dcaa}}, {{cite:62f866c4cbb3a62c044539a21bafc95f1f890ece}}, {{cite:9921a8f5125af921d2119fd1a1ef994a7cf5c691}} and the references therein.
Since energy (or power) is a common quantity in all physical domains, one can model all the subsystems using energy as the common quantity. and couple the systems via energy exchange.
Furthermore, the power-conserving interconnection of port-Hamiltonian systems results in another port-Hamiltonian system.
This means that one can model the subsystems independently and then interconnect them and solve for the overall system. Since pH systems are stable and passive by construction, the interconnection in the pH way will preserve these properties.
| d | 490c81b6a4cbac0f367d4f95ea724635 |
Conv-KNRM uses 21 kernels, one exact match and the rest soft match {{cite:f9b6048fc5b85bbf3bd1898155053359d17d0ffe}}; the uni-gram, bi-gram, and tri-gram of query and document texts are considered, the same as the previous work {{cite:ed006a971c184519a4dbfd1eaeaed3ffbdcec5a1}}, {{cite:b5ae2981ed15142a2a46ab5387e6f090b23db3ab}}. The word embedding dimension is 300 and initialed with Glove {{cite:d0eca5e876fbb5314d19e9d9432dfa624c23a4e3}}; the learning rate is {{formula:6e213a2d-c225-48dc-aac4-d37ab44d01dd}} . The BERT models inherit pytorch-transformershttps://github.com/huggingface/pytorch-transformers. The max sequence length is 384. Adam with learning rate {{formula:8e72af92-6037-4d02-89cb-19e170f7dd04}} and warm up proportion 0.1 is used.
| m | 443aca44316160c3366cf094c8a8ded4 |
In all these settings two key questions are speed of convergence and error of computed versus true values. For the latter, the algorithm converges to the exact average {{cite:4d1077cffb46677f6499fe7fe5c8cf7f776a191f}} in a rather general setting {{cite:e8cb79721102821319b1e153f3b673caad241454}}, assuming no packet loss in the communication, but possibly with bounded communication delays {{cite:850a1110d998b3f3e97b32de1eb05c3ae94615c2}}.
Thus for the current paper the focus is solely on the first question, estimating the speed towards the average.
| i | 35e4203062bb03c9f9f9e60836cbd4ae |
Many classical algorithms {{cite:dbf03dd7f5970e141668ff9664e879b26eee348d}}, {{cite:bab0f9263de017420a82e7465df9816398f0b610}}, {{cite:4c3c0397d7f3a06b14484072c223bd9a1975a5ca}}, {{cite:d4ba4a445d0e699f010555fdbbf63ebac8737d63}}, {{cite:ac6f190d94604bdfea0154da7f63b4463bd7b31e}} heuristically search similar patches for the reconstruction of missing image regions, while it is still very non-trivial for these methods to preserve good textures and holistic structures of the corrupted image.
Benefiting from the excellent capacities of CNNs {{cite:e5b017cd89a4dbd5dc168b3246a77898318a917a}} and Generative Adversarial Networks (GANs) {{cite:ddad47180a045cbf3ed6470d197e917542ebb0de}}, existing deep learning methods {{cite:ab8f758bce87f5e6600e934bc9d8ea2000de398e}}, {{cite:dbbfb469b52901ac53a9cd80addc01aed015630d}}, {{cite:c86a089c620d24b30c377ee965a57a666b5947ff}}, {{cite:de13b25b30827034ac3b2705e0a737caced87378}}, {{cite:0139ce4a05d84bdfb7af5f6ce12ef4e2ea6671f1}}
could conduct the image inpainting tasks in some common cases. However, the capability to inpaint realistic image content is often limited in practice by the underlying challenges as follows.
| i | d9821d77d43b9672f4e02da1029b28d3 |
Dynamical dark energy models in which the EoS of it varies with time have been proposed as alternatives to the cosmological constant. A wide variety of such dynamical dark energy models are abundant in the literature, a few of them are quintessence, k-essence, phantom, chaplygin gas, tachyon models, holographic DE models and so on {{cite:61c107db9a57368566c89b7fafc03d9f99ced2c3}}, {{cite:164397a9b684d974a23311ea4a56d1afa478fb1e}}, {{cite:b40efc37d149ffec6a5e3821ed77825825f4eabd}}, {{cite:9286268e61c32badf6efc6be4ea0fc3101e93bc2}}, {{cite:4ee3320150d4588cba8c765cb73307dc3e224bbe}}, {{cite:595c73345c9f1f7ca932fcfc9808a967d77faee1}}, {{cite:309f7406e28172d725a8918dede7ac0108b38ba1}}, {{cite:fee194dc07bae3c6c924a521e5ce1b73e1a087cc}}, {{cite:fd95ccfd562e1d3264cb03ac19f39bdc699f306a}}, {{cite:095d09ad444d6b74848863aee2552122262344b5}}. But there is no consensus on a particular model as each model has its benefits and drawbacks.
| i | 6280e353bcac2d3ec79ae94e3337c286 |
Setting aside the large influence from the local dynamics, we propose that the topological features which play major roles in shaping the interaction between two nodes are: ({{formula:4eee07c1-9e89-417d-98bd-378b0e1bb2e0}} ) the strength of the links, ({{formula:097b5085-ead6-4365-8cbf-8e80979d915a}} ) the length of the path between the nodes, and ({{formula:dd62ffe0-1d22-43ec-99ff-1ecca8fcf99b}} ) the routing of information along multiple and redundant paths. A strong direct connection between two nodes is usually a reliable indicator of the strength of their functional interaction. In fact, in general direct links lead to more effective communications since the content of information (e.g., the amplitude of the perturbations) tends to decay over longer paths {{cite:98b838bd03658de7f2bf04829c14290fb5875ae2}}. However, the flow of information from one node to another does not follow a unique path, but rather spreads along several. Therefore, the total influence that one node exerts over another is accumulated over all possible paths, of all lengths {{cite:cd26724f28090dc626a44bef8e75e3a2e1e494a7}}, {{cite:e4ca3e3de9bbe44243e99b41a0e90884ba3457ac}}, {{cite:538b071e27d4ba8239c167cf05425c7a5f7834c4}}.
| d | 6eaeff171c6674c40f6b387f8816b95c |
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