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Critic baseline
Figure REF illustrates that, for identical models, the critic baseline {{cite:40d21ad23dc11790941a05e3ee685ff32bc1bd1a}}, {{cite:0a15004e74b45fd9515552faa939db607d29b349}} is unable to match the performance of the rollout baseline {{cite:cbb2aade89e8d9eed655769f7948340b8019258a}} under both greedy and beam search settings.
We did not explore separately tuning learning rates and hyperparameters for the critic network, opting to use the same settings as those for the actor.
In general, getting actor-critic methods to work seems to require more parameter tuning than the rollout baseline.
| r | 76f3d38806228de8127ae2703b4e7918 |
GNNExplainer {{cite:42afe5eeb9fe5f6bc88904289d148237f94bd2d2}} is the first general, model-agnostic approach for GNN-based models on any graph-based tasks.
Given a graph {{formula:2cb1b51d-baf1-4068-8c18-da76fa5e91a1}} with node features {{formula:f51b3192-2297-4516-b695-f6855910c0f8}} and a trained GNN {{formula:3fe93505-4ae5-4d3f-a7c3-b0c3e8e70677}} , GNNExplainer can provide explanations for any node {{formula:2b4a7852-1b1e-4439-8332-7b783a0e0ab6}} .
It aims to identify a subgraph {{formula:7e48b5bd-081b-4c9b-a703-ca4c083e09ce}} and the associated subset of features {{formula:dbf1da14-da7f-4d85-9e79-d1cf31c0eca0}} that are important for {{formula:b09bfd9e-56f8-4d98-9c14-d4db3c673009}} 's prediction.
Here {{formula:a3192331-be9b-407f-956a-2049fc80f057}} is a binary feature selector which is a feature mask, and {{formula:fd8fd847-6cc8-4823-ae19-e806a8e74960}} .
The objective is to maximize the mutual information between the explanations and the original model.
Mathematically, it follows the optimization framework:
{{formula:55c52175-a0da-46fb-87dc-679ef7641c9f}}
| m | a72177c1fd611099b8014c6e803b0985 |
In the second set of numerical results we quantify the probabilistic performance of APLF in comparison with QR {{cite:869356b3df9550cb40d14a9c011f9391763f6aa0}} and GP {{cite:a2828500e93b7684ee11aa42e6e80a4488047b0c}} and we study the relationship between training size and prediction error. Pinball loss and ECE assessing probabilistic forecasts are given in Table REF . Such table shows that APLF achieves high performance in terms of both pinball loss and ECE, while GP sometimes achieves poor results in terms of ECE and QR achieves poor results in terms of pinball loss. Figures REF and REF provide more detailled quantification of the probabilistic performance of different methods. Figure REF shows the empirical CDFs of pinball losses of APLF method, QR, GP , and the benchmark for the GEFCom2014 dataset {{cite:3a93a9fbb5e9febd349b4a5a6436c9a96c7d84d0}}. These CDFs show that the probability of high pinball losses is significantly lower for APLF method. In particular, the CDFs in Figure REF show that APLF and GP have a similar median pinball loss of around {{formula:8b0c3518-2930-4cd6-b815-0b18661ab100}} MW. However, APLF has pinball losses less than {{formula:3aabea7d-ebe2-4b79-b981-d22ee49bc2b8}} MW with probability {{formula:eb91d3bd-5e36-4bee-87e8-bf2f74f66e3b}} , while GP reaches pinball losses of {{formula:9f4f209d-6e2a-4c51-98f3-f58623eb7827}} MW with probability {{formula:c387326a-e32e-402b-a224-88179630002b}} . Figure REF shows the correspondence between the calibration {{formula:4dfba033-1220-469f-a762-40dde652b129}} of probabilistic forecasts and the quantile {{formula:a1178513-a519-48ce-8762-f89f66c8b629}} for the datasets used in Figures REF and REF . These calibration plots show that GP and QR tend to obtain forecast quantiles higher than the true quantiles, while APLF obtains more unbiased probabilistic forecasts. In particular, the true load is higher than the 50 quantile forecast load with probability very near 50 {{formula:eec88e32-4b36-42d0-9c60-c19b7ebafe8c}} for APLF. Figure REF shows that APLF obtains improved calibrations especially in the lower quantiles.
| r | 2c805d6bcfe3f019a19dae935a58199e |
One challenge is that it is not practically possible to learn {{formula:5fb02d0d-4570-47c0-9115-0707e25cefff}} -SNICA by exact maximum-likelihood methods. However, by framing the model within conjugate exponential families we are able to perform learning and inference using Structured VAEs {{cite:2d9199427ec50875f8623c3d5264873af83c9d2a}} – the current state-of-art in variational inference for structured data. Despite lacking consistency guarantees (but see {{cite:1f865faff354d185e8a19b2a55b8b158e4f92ece}}), we find that our model performs very well. A detailed treatment of estimation and inference of {{formula:4b3e9e4e-0c63-4453-8a05-551fd5bf7d78}} -SNICA is given in Supplementary Material. Our code will be openly available at https://github.com/HHalva/snica.
| m | f98fcadf1bb4e6774c7a1bdb71051d24 |
Neural Rating and Tips generation (NRT) {{cite:c1994a05d73d3055468a9b53ed8d320c3a174f7f}} can predict a rating and generate a tip simultaneously based on user and item IDs.
The generation component is a GRU {{cite:3ff56cfcb9363aed4c62d7f1a76c89db1079e09b}}.
We take the explanations in the datasets as tips.
Moreover, we find that the model's problem of generating identical sentences (as reported in {{cite:660c5217cc0a1aafccc3204626c432c536b060c2}}) is caused by the L2 regularization in its original design.
For fair comparison, we remove it.
Attribute-to-Sequence (Att2Seq) {{cite:b819d7d1bb3c2ed10c6214111ff4138695189851}} is a review generation approach with a two-layer LSTM {{cite:8e80d294657c167125b1b663523ab5407701547d}}.
We take the explanations as reviews.
This model has an attention module, but we find that it makes the generated content unreadable.
To be fair, we remove it as well.
PErsonalized Transformer for Explainable Recommendation (PETER) {{cite:697f58b5fe2bbfcadc7ae8d1cd3fea5ff2284093}} is a small unpretrained Transformer {{cite:200f3d03589ca799b2e2dba2f70c55c21c4d79e3}} particularly designed for explanation generation.
To bridge the gap between IDs and words, an additional task named “context prediction” is introduced.
This model can also make recommendations.
| m | d41c3fe19783b05bfa5379ee6a4e021a |
We compare our model against three baselines: L2X {{cite:d841e07ba2734e4da37289a561f2803d3b0ef055}}, LIME {{cite:3a004b4d85813229de9001a1a0d0da9a44a38989}} and VIBI {{cite:0c95eb9fb9b550f851e78a4a374b7be5b464d38a}}. The experiments for the baselines are run on the authors' published codes. All the baselines are trained at {{formula:29ae0b69-09fd-4183-9b2b-b8c1a66f85b2}} and we use the default architectures reported by the authors for all datasets. VIBI further offers multiple options for the approximator. In our experiments, LSTM approximator gives the highest accuracies for both IMDB and AG News, while CNN works best on HateXplain. For training LIME, we have 2000 perturbations generated around per instance, and though LIME can explain a single target class, we use the multi-class setup to keep it consistent with the other baselines. It is worth noting that our black-box architecture for IMDB dataset is different from ones reported in {{cite:d841e07ba2734e4da37289a561f2803d3b0ef055}} and {{cite:0c95eb9fb9b550f851e78a4a374b7be5b464d38a}}. In their experiments, {{cite:d841e07ba2734e4da37289a561f2803d3b0ef055}} adopts a CNN {{cite:acbd29e112a562b8ee154b04aa7a3d948422780d}} while {{cite:0c95eb9fb9b550f851e78a4a374b7be5b464d38a}} chooses a hierarchical LSTM. These architectures are similar to those of their own explainers, which we suspect might have some influence on the explainers' performance. Since our explainer is not GRU-based either, we intentionally opt for a bidirectional GRU in order to examine whether these models can explain different kinds of black-box architectures. Apart from LIME that runs on a single CPU, the other models including AIM are trained on 4 NVIDIA Tesla V100 GPUs.
| m | 52304ad9cf8419c3eeccdd57d2145766 |
Recently, the spin-averaged amplitudes for the two processes (REF ) were calculated in ref. {{cite:f61024cd4ca2e82789be147328e18c56a0fd2d52}}. We have found complete agreement for all terms except for those containing {{formula:05949b09-8c4c-4dab-af6f-b4f95689ca8b}} . We have investigated the origin of this discrepancy. In the process of doing this we observed that we could reproduce the results of that reference if we do not flip the sign of {{formula:310eeabb-6f11-4eca-9cae-699301573a47}} under permutations during the mapping of masters to pentagon functions as well as during the numerical crossing of momenta in order to obtain all other helicities. As explained above such a treatment of {{formula:9970a3ca-897b-489b-a19e-74595db7dca8}} is inconsistent. In order to verify this, we have calculated the terms of order {{formula:025653e6-5e6e-4c6f-b16d-b18fbfa54129}} and {{formula:49a9558e-820c-4357-9fe8-5875968e4409}} of the one-loop pentagon integral which are sensitive to the treatment of the parity-odd invariant and functions. We have verified that the calculation in terms of pentagon functions as described above agrees with a direct numerical calculation of this integral with the program pySecDec {{cite:295778a788a71645a2ca6373cdf23c71271c1c70}}. Our interpretation of the above result is that the disagreement between our calculation and ref. {{cite:f61024cd4ca2e82789be147328e18c56a0fd2d52}} is due to an inconsistent treatment in ref. {{cite:f61024cd4ca2e82789be147328e18c56a0fd2d52}} of {{formula:688b23f3-bc48-4695-a351-e1813fb582d9}} under permutations.
| r | b0c8264e8499615081b1d09e9b43141c |
Regarding the quantity {{formula:6faa5fae-ff8e-44d4-be7f-4151ea68f4a5}} itself, it can be nicely related to the Fourier coefficients of {{formula:b7ba9add-3b75-4d73-994f-1eefc50a2c58}} (see Theorem REF in the next section). We briefly mention the noise stability for a few functions. For Parity ({{formula:7b6b45a7-638f-4f1a-85e6-56c48848b143}} ), {{formula:a6b78de3-3dba-45b3-81e9-2108b87e05f7}} , and, more generally, for any function {{formula:efa0fa26-2a2f-4108-9122-296697223b73}} , {{formula:fff016d5-629b-4214-8bbc-0c76798f9ba2}} . As for the Majority function ({{formula:c79582a4-acdd-4d04-8547-da533b4ce899}} ), one can show that {{cite:6222cd11c12fe4474fceafb504df474ee384e2c2}} {{formula:a2256ff5-90ac-4146-8af8-ac630d007f0f}} . Other examples can be found in {{cite:60da09436e38c3f391f0effaf2f10a36134e5170}}. Moreover, a randomized algorithm for approximating the noise stability of monotone Boolean functions up to relative error was proposed in {{cite:a49f5dfc0143a6f7949bc94ec77eeea7d4232f07}}.
| r | b236a05aa2d67891bbd3eea93a1fe2a2 |
In addition to one-vs-rest, other methods are applicable
for our scenario {{cite:49e16c029b71e97f3868d9b98bcd789f83651f19}}, {{cite:02ee1094e8e62be923c336c9fcdba4c1b5803b63}}, {{cite:ca50c811864f491f9655fb49b6d84c03594314e8}}, {{cite:9b8b7000d6a6d34ae8a619bcd5e66167c53288f7}}.
Because one-vs-rest does not consider label correlation,
this aspect is the focus of some methods.
For simplicity we
stick with the one-vs-rest setting here
and prioritize achieving good Macro-F1.
Macro-F1 in (REF )
is the average of F1 results over labels,
so under the one-vs-rest framework,
all we need is to design a method that can
give satisfactory F1 on each single label.
In contrast, optimizing Micro-F1 is more
difficult because it couples
all labels and all instances together;
see the definition in (REF ).See, for example, “... is the most challenging measure,
since it does not decompose over instances nor over labels.”
in {{cite:b2fac5dadc3a684e31894e7ff08db46383336a0a}}
Therefore, we mainly focus on techniques to optimize Macro-F1
in the following sections.
| m | b7841c3018a034a2547f1fee29886e21 |
The discovery of these potential laws begins with a formalization of the dynamics of information content utilizing the combination of network dynamics and information theory. The presented network dynamics offers a general description of the information-related interactions between individuals rather than constrained by specific information propagation models. It concentrates on the process during which each individual attempts to learn about the factual information based on the received information. Although individuals try to maintain the ground truth content while passing on the information, random distortion still originates from the confusion relations between contents {{cite:b4ec6002063606b6575c98f70fbb3e4ad35e717c}}. Building on Shannon's theory {{cite:b4ec6002063606b6575c98f70fbb3e4ad35e717c}}, we have demonstrated that the distortion and dissipation processes will inevitably emerge if the information content consists of not only information invariants. The maximum information rates of these invariants are limited by the upper bound, which has been mathematically and computationally validated as optimal. Throughout the analysis, we have distinguished these properties from the effects of noise during information diffusion, proving that the existence of information distortion and dissipation is inherently determined by the information selectivity patterns in complex networks. The speeds of information distortion and dissipation are shaped by the diversity of information selectivity in networks and might be accelerated by noises. Taken together, the theoretical framework depicted here offers a natural interpretation for the characteristics of information evolution during diffusion.
| d | e404d6e260533446cef8d6ada589f4e6 |
We further evaluated the baseline Places365-CNNs on the validation set and test set of Places365 shown in Fig.REF . Places365-VGG and Places365-ResNet have similar top performances compared with the other two CNNsThe performance of the ResNet might result from fine-tuning or under-training, as the ResNet is not trained from scratch..
Even if Places365 has 160 more categories than Places205, the Top-5 accuracy of the Places205-CNNs (trained on the previous version of Places {{cite:0814ae654a2abbe76ad9ee31a75ed33c20abfb9e}}) on the test set only drops by 2.5%.
| r | 4b086133e10e296e4008c860cb0ca8c2 |
The other approach takes advantage of the practically null average voltage drop across the junction produced by breathers. Given the structure of the second Josephson relation {{cite:0d1e5dddd27e9eb139b1591b1fd06c4440ad0121}}, it is possible to define the (normalized) time-averaged voltage
{{formula:fba0b41b-b667-4c9d-87d5-a4852e78ee36}}
| r | 5c811fb79e2c86602230956042334273 |
Suppose we are interested to obtain a batch of {{formula:9135da98-7c48-4bc3-b91e-b3398086136c}} samples drawn from the posterior distribution {{formula:f133902f-4c2e-49db-8d7f-0b6c7bf22b23}} .
Suppose further that we have a method which, relying on the evaluation of the potential {{formula:e11126ec-8fa4-44af-8548-82d1823d3293}} or its gradient {{formula:aa5363bb-db38-444b-bb0e-cb8b6c65d682}} , maps {{formula:db4ef79d-fda4-4711-b879-36a16d4a0b48}} particles/samples drawn from some initial measure {{formula:633b9570-e367-475b-b42c-5a247509e311}}
to particles approximately being distributed according to {{formula:5a2313bc-1612-4929-b062-0a00b5307e96}} in {{formula:3e181180-0fb9-4fb9-8da9-6eea6b61df5d}} iterations. We will refer to this method as the particle propagator. One such particle propagator is given by Langevin dynamics based particle systems {{cite:21b73df653ef0fe2ad0cc59d9ba30c902102a2e1}}, {{cite:70057aeeb2289774a6e01ef77f901d2c9afa066a}}, {{cite:dea693fe36f508b789f7c2fc92e3aa5373dda7db}}, {{cite:77b6de3560aedea51f45768955fea364f2abd9e4}}.
Here, {{formula:d6132eca-2a3c-433a-a544-ec1b13f414fa}} depends on the distance {{formula:6e79a080-c0ed-46b7-af35-23047f06e9c1}} between {{formula:04273ced-ee3c-4f14-aec9-eecbdc9af2ed}} and {{formula:b26b1a22-d20e-4fef-887f-6b6335588460}} , where {{formula:784de801-6e50-40a2-8439-1284fac91cf3}}
is a suitable metric on the set of probability measures. Note that we do not require the initial measure {{formula:467d6d0c-11cb-4811-8708-96dc9b33a671}} to be identical to the prior {{formula:496015cd-6c6c-4e40-89b3-9f2226ae26f7}} although this is a natural choice in the setup of Bayesian inference.
We assume one iteration step of {{formula:09995ee6-7a78-428e-bd84-28217118dbbf}} particles to require {{formula:10770607-dcd2-45e4-bae3-3701c429a915}} forward calls (as is the case e.g. for ALDI {{cite:dea693fe36f508b789f7c2fc92e3aa5373dda7db}}, {{cite:77b6de3560aedea51f45768955fea364f2abd9e4}}), leading to a total workload of
{{formula:7ce8e1c9-abb6-422b-a2a2-55ce3f24ef71}}
| m | f94426651e62e321a0de885a218fe8ca |
Logistic regression on pre-trained Imagenet features: We found this performed noticeably worse than ERM across the board, with a slight improvement in loss on hard positives (but worse than most other methods).
ERM trained from scratch: We found this to perform slightly worse across the board than ERM from a pre-trained model.
ERM with learning rate decay: We explored several learning rate decays and found, with tuning, minor improvements in overall performance from ERM.
Due to the level of tuning required, we chose not to include these results and just used a constant learning rate.
ERM with data augmentation: We explored using data augmentations such as random affine transformations, cropping, and horizontal flips, but found they did not improve performance in ERM.
Adaptive parameters {{cite:549874fefcfa5551e14a2bf64994b2aab09ac662}}, {{cite:4eca98502fee2b64b3e1c7accd30ae6dad3fd219}}: We explored the possibility of learning affine transformations after each ResNet block.
With tuning, we found this improved performance on hard examples over ERM but not close to the level of the other robust methods shown.
Auxiliary prediction: We explored adding a second readout head to the final layer and predicting the highest {{formula:6f0fe386-3c6a-470a-8772-61874f0d6e47}} -context variable as an auxiliary loss.
We found this to perform nearly identically to ERM in all metrics, and occasionally slightly worse.
| m | 418e0fe1a4e2486a6f4167fe54303ee1 |
Another class utilizes additional noise or speaker information to guide the SE adaptation to certain types of noise {{cite:6bc95dcebd69662f7983e89175cbf4cd43c48961}}, {{cite:a671399e80c88267edcd7e3a3a424a18072c5cd5}}, {{cite:78c7d473c72ad6d096572a71b9fef2c1a3078dca}}, {{cite:7ee736e3d9a68b24b5ccc13f5930c97fe1a62d72}} or speaker {{cite:f7d5feb440907adab28fc94ee4640df295ffd2ab}} conditions. In this study, we go one step further to simultaneously adapt both the model inputs and model weights through embedding vector and meta-learning, respectively. Specifically, we propose a novel one-shot speaker-adaptive SE approach using meta-learning (OSSEM), in which the SE model can be effectively and efficiently adapted to a particular speaker with only one adaptation sample. OSSEM consists of two networks: a modified transformer SE network that aims to achieve an SE and a speaker-specific masking (SSM) network that generates speaker-specific masks for adapting the SE model. For the SSM network, we adopted ECAPA-TDNN {{cite:f2fbab5d6432934cbda86b77cdd08c047f58900a}} through the SpeechBrain toolkit {{cite:4393760956d266ce10b9aa967ff8440a0742e10a}} to extract speaker embeddings as the input features. The two networks were trained in a meta-learning manner, which has been shown to be effective for one/few-shot learning on several tasks {{cite:8350a01f7e6d590b369f6905fcf5417a58259d76}}, {{cite:4c4cb2604b95ad287af4f6c2aadfd06740b7bba7}}. In contrast to previous studies that adapt the overall SE model {{cite:550356d47c208e013f5198f4cd8a60d08fc50cb5}}, OSSEM can reach a fast adaptation because only the parameters in the SSM network are adjusted instead of the entire OSSEM system. In addition, we propose several training techniques for OSSEM to further improve its stability and performance.
| i | 4f3a2d5208caad64ef2cbcc12c4e21e8 |
Thanks to their ability to extract abstract information from raw data acquisitions, Machine Learning (ML) algorithms such as Convolutional Neural Networks (CNNs) are fostering a revolution in multiple and diverse fields, ranging from personal mobility to health-care. Nevertheless, the increased accuracy of recent CNN models comes at the cost of massive memory requirements and intense workloads {{cite:05a3f7fb78c9b85e04a027b4cfe3168400565593}}.
| i | 27c4dabc0eeb7737f6b0e15a7535bc7d |
Domain-specific training of BatchNorm
on a mixture of multi-domain data has been proposed frequently
in previous works, under the name of
“Domain-Specific BN” {{cite:4c7a2aed4397e9b4b2af53145ed758e1ea47a789}},
“Split BN” {{cite:f9d725080738ad54d65172abdd5dd55b9b8bbce9}},
“Mixture BN” {{cite:062980034254816f6f069f089a7d62c5a85ae465}},
“Auxiliary BN” {{cite:5c63d1aa2ba5196b0c9d2fddcdf12c432dcdaee4}},
“Transferable Norm”{{cite:2efa1de2903f4c3c9d0be112e74f44cb0aba1a57}}.
Domain-specific population statistics in RetinaNet
has been used in {{cite:60153e4ca9074727fe4a85c3e7477fba3c0fa9fd}}.
These methods all contain some of the following three choices.
| d | 3fe0ccdb5691774b19061a8f3081f4f0 |
By combining {{cite:743a9cf2865cb3ed20dd93f7a053a200db15635a}} and {{cite:cc9243111e19a8d7f8d35f0c846d0c41bf7e1123}}, the following bound on the Rademacher complexity function is achieved.
| r | 99e84d1d784b556e2925cb1719489a79 |
Here, we consider the goal of finding a sparse
solution to this representation learning problem, one where each feature depends on a subset of the latent factors {{cite:b0eba22ae98b36cc53e7c04004d4e9080dcb0474}}. Sparsity is an assumption that often reflects underlying patterns in data. In genomics, each gene is associated with a few biological processes; in text, each term is applicable to a few underlying topics; in movie ratings, each movie is associated with a few genres.
| i | defcc4c7905e35b17122c63be2705781 |
Rather than applying 2D CNN on variant hand-crafted spectrograms, some researchers try to directly apply 1D CNN on the waveforms of speech/music signal to learn acoustic features {{cite:3257527eee3cb417ef2be094c2e7dfea1164b574}}, {{cite:19e2ac4d8da2d56443b8d6d8aaa31d918bfa51f4}}.
In these standard 1D CNN architectures, the learnable parameters are the kernel/filter coefficients.
Typically, kernels with a large number of coefficients are needed in order to effectively characterize the timbral/rhythmic properties of the music signal, which often takes a large amount of computational cost during the training process.
To reduce the number of learnable parameters, Ravanelli et al. proposed a new architecture, called SincNet, in which a set of SincNet filters is appended to the CNN structure as the first convolutional layer {{cite:19a625a334f2a3767af65c8f04f0f30857b18ff9}}.
In fact, the SincNet filters are the inverse Fourier transform of some rectangular (ideal) band-pass filters parameterized with the cut-off frequencies of Mel-scale band-pass filters.
That is, these SincNet filters, can be viewed as 1D kernels used for performing 1D convolutions on the raw waveform.
Their experiments have shown that the learned SincNet filters can extract features like customized band-pass filters with faster convergence, fewer parameters, and interpretable kernels.
| i | 4611673ef26f68eff8647c90b8ea6e41 |
The first term accumulates a large penalty if it takes long for the agent to reach the end point, while the second and third terms describe the change in free-flight time to the target, i.e. the difference in time it would take, if the flow is neglected, to reach the target from the locations at this and the previous state change. {{cite:3cdee48bf586971ec869c3be6bac0b73f954688a}}. It follows the the total reward is proportional to minus the actual time taken by the trajectory to reach the target,
{{formula:dda094c6-ca28-433f-8290-d1fd16c25818}}
| m | db10a68ba9a8d64d1e46b5972c623b09 |
Figure REF provides a global trend in terms of types of machine learning approaches employed in our identified records. Among the ML approaches, we distinguish supervised, semi-supervised, and unsupervised like approaches. The analysis revealed that most of the works adopted supervised methods (73%). From Tables REF and REF , we can observe that any of these three methods can achieve high-performance accuracy, and there is no substantial evidence to favor one over another one, whereas only the context of data (e.g., availability and quality of training samples) can play a role in deciding about the suitability of one category over another one. For example, {{cite:f2db771015f4901be513f97a9b8fc46b872fb056}} used an unsupervised method and lexical & syntactic features to achieve 98% accuracy. Similarly, several works were based on supervised and semi-supervised methods that have shown close or better performance {{cite:8af20ea3486d76462ba9156794eba2e63d063e2d}} {{cite:4a812b45a5cea6fb26ed7da2d181925620be40bc}}. Nevertheless, it is worth mentioning the popularity of the supervised like approach over other ML approaches, possibility due to the multiplication of benchmarking dataset and machine learning / deep learning platforms that promote supervised approach.
{{figure:0a22d60d-ef3c-4f09-8b60-e1c6572ca4f9}} | r | 0be99ae95cff1b729414fa744cbe20a4 |
Discussion on TUBerlin-Extended: As stated in Section , the results could be heavily affected by the chosen classes for experiments. Since {{cite:d4808f8b8793c4510f2e664d1ab34fb4a498a049}} did not report specific details on their train and test split, we can not offer a fair comparison on TUBerlin-Extended. Instead, for both {{cite:f4f7946e9de8522d692b4435cb1bf00f3080c83c}} and ours, we resort to the commonly accepted median over random splits setting. And it shows our method favourably beats {{cite:f4f7946e9de8522d692b4435cb1bf00f3080c83c}} by a clear margin. We did however observe a high degree of fluctuation over the different splits on TUBerlin-Extended, which re-affirms our speculation on how the categories included in TUBerlin-Extended might not be optimal for the zero-shot setting (see Section ). This could explain the superior performance of {{cite:d4808f8b8793c4510f2e664d1ab34fb4a498a049}}, yet more experiments are needed to confirm such suspicion. Unfortunately, again such experiments would not be possible without details on their train and test split.
| d | 27bf097c720b9501459b7764bbf14101 |
The inequality (REF ) still works when {{formula:19c1ff94-b429-4cec-9af4-6c0ac9b38019}} is a nondecreasing convex
function and {{formula:49d05bb2-09fe-40c8-a027-2b207dc9132d}} This important remark, due
independently to Tomić and Weyl, can be derived directly from Theorem
REF . See {{cite:03bc50f228705f0fabbd114da4320959772671e6}} and {{cite:d55cdacc1a363f80dbacfa0f33f66e4abc670b60}}.
| i | b10847b01c14452dc5acd4781e7fb7c7 |
The fast multipole method (FMM) was described as one of the top-10 most important algorithms of the 20th century {{cite:fbcbc0e514e4fce497435177dc677c1be5dd10b8}}. It is a numerical technique that was developed to speed up calculations of long-range forces in the {{formula:ea662248-8262-462e-86a5-4cbe23b0a8c9}} -body problem in physics. In 1987, FMM was first introduced by Greengard and Rokhlin {{cite:c6285d714aec513567c02db20950a0dc77cabe81}}, based on the multipole expansion of the vector Helmholtz equation. By treating the interactions between far-away basis functions using the FMM, the corresponding matrix elements do not need to be explicitly computed or stored. This is technique allows us to improve the naive {{formula:ee242239-c204-4fc5-b644-0e4294dbed22}} matrix-vector multiplication time to {{formula:fccf0c80-48d7-409a-8e2d-8b75a64016dd}} .
| m | c5d824908c285c056c79518e8a197d1f |
In the complexity theory, it is a well-known fact that the deterministic polynomial time (P) complexity classes are not equal to the non-deterministic polynomial-time (NP) {{cite:a27f7435eeef75e12c90adc471d6bb5b3852b176}}, {{cite:ebd8f31f8f15cda1d71728359b2df207cc5bda69}} complexity classes. The existence of the one-way bijection {{cite:9ba83f51d13bab70c15688626e227675c4049a7d}}, {{cite:98af590c40cf31d27ec69bca976f89d6b09ada37}} proves this statement. The existence of such bijection arises due to the self-referential character of P {{formula:0ea95301-6a1d-4016-a2be-dea69f9978a9}} NP {{cite:ad9b17835ddbdabcda230da1144169992e2382c1}}. Different approaches to prove the existence of one-way bijection mathematically have resulted in a debacle. The existence of one-way-ness has a great impact on the complexity class problems, as one can link this to the physical constraints rather than its mathematical limitations {{cite:3a1dcaa2f6471951e2e518fb719d458bb4da3206}}, {{cite:d2c381388f510e0e2d6f862393c0aca498e0248e}}, {{cite:e37acf206cc7ca74729a5ab870bd2ba4170bccd9}}. In the seminal work {{cite:9b96dcdf8efb3b742fd664d9e726ffbba4951038}}, they have proposed an approach to bridge a connection between the one-way permutation to thermodynamic computation. They have shown that a quantum circuit maps a target bit to itself {{cite:9f34a370ae2a4f78ac77c303c7f9bd30ec2e99c4}}. During the execution of this process, it encounters entropy constraints which can be easily inverted when the system is immersed in an adiabatic heat bath.
| i | e128355cec5e3679ac1e91d8c20408ee |
We use the following objective metrics to evaluate speech enhancement performance: the perceptual evaluation of speech quality (PESQ) {{cite:4684694e5e58ab139217bcf22ba24000666ae7d3}}, short-time objective intelligibility (STOI) {{cite:92baeb9defee084444e725f63f45de51b76190d3}}, segmental signal-to-noise ratio (SSNR), the mean opinion score (MOS) prediction of the speech signal distortion (CSIG) {{cite:1c7e957ff306a6aceca74712ab008c9947cafea4}}, the MOS prediction of the intrusiveness of background noise (CBAK) and the MOS prediction of the overall effect (COVL) {{cite:1c7e957ff306a6aceca74712ab008c9947cafea4}}. In addition, we evaluate the subjective quality by DNSMOS {{cite:9a67f6e35e11bd520f67ce4cc8772b20434b6b94}}, which is a robust non-intrusive perceptual speech quality metric designed to evaluate noise suppressors. Higher values of all metrics indicate better performance.
| r | d77207aba49b6dc6a44f374552f9318b |
SmoothGrad and VarGrad. SmoothGrad {{cite:0e15c1eae6f17c3e8967a2fd4564f6acfc85cb85}} and VarGrad {{cite:49e37cae36029af2e243db802a129cf188cce8ee}} are proposed to relieve the situation where the attribution graph is full of noise.
The SmoothGrad is defined as:
{{formula:d7b2f424-5ea8-4e99-ae93-798e0fc9814f}}
| m | cf624b93bbcef845998965a6e0e63766 |
In addition, {{cite:8b55802a73def4276b37d05269138e41a9afdc5e}} states that the radiative efficiency of accretion flow increases with increasing accretion rate, which gets intensified by viscous interactions. However, since the viscosity parameter of the disc is not related to mass of BH, it could suggest that viscosity plays no critical role in explaining the dual radio/X-ray correlations, if the mass dependence reported here holds.
| r | 41641b050712063b9340d5c4f2f6db6d |
The differences created by WaveBlocks and enlarged by attention mechanism are quantified in this part. We adopt the strategy of Post-A with Non-local. The difference is quantified by calculating the Frobenius norm between two gradient-weighted class activation maps {{cite:3d5db8e38fe20bf68be3b2c8856b0b395bbf6c9b}} of the same input after Stage 3 or the proposed modules, as illustrated in the introduction section. Further, the differences in Frobenius norm for all images are averaged to obtain final quantified differences. As shown in Table REF , the quantified difference of WaveBlock is larger than MMT's. The quantified difference is further enlarged by integrating attention mechanism with WaveBlock.
| d | 4235cf98ac0cdbb654c526fb1bf0e89c |
Continual learning is an active research field within the machine learning community {{cite:36000488fbbb263fb39cfb251975286680d752fe}}. To tackle catastrophic forgetting, CL-based methods can be divided into three categories based on how task information is stored and used throughout the sequential learning process (see {{cite:05124b60133dffa2c8af807d9e0ccd8ea107fc79}} for a comprehensive review):
| m | a07d158f072fcc4564c0f7b4aaa7c8b9 |
In Fig. REF , we display the effective potential (REF ) of the {{formula:9fb62116-fb3e-4811-a682-d6fc15f393c0}} Cr condensate in the absence of the temporal modulation of both nonlinearities. One may infer from Fig. REF (a) that the potential energy curves do not show any minimum for both repulsive (dotted and solid curves) and attractive (the dashed curvraction ({{formula:0da715f3-3757-45fa-b15a-e1ad124d6778}} ) strengths. In the repulsive case, this indicates that the condensate leads to expansion due to the repulsive two-body interaction and the kinetic pressure. On the other hand, no stable counter balance point (i.e., potential minimum) exists for the attractive case either, which indicates at the attractive constant two-body interaction overcomes the kinetic pressure, leading to the collapse of the condensates. These conclusions are commonly known for the cubic GP/nonlinear-Schrödinger equation in 2D {{cite:fbc1e559effba1e9885d8bbdbb4865818583f12e}}
| m | aba3849c6abb85d45d120bb8febdf14e |
Mechanical model for cell shape and growth. There are many details of cell growth and shape that require interpretation. For example, it is not obvious a priori that growth should be almost exclusively longitudinal. Therefore, we have developed a minimal mechanical model that can explain these observations. We parametrize the geometry of the cell wall by a collection of shape variables {{formula:53de5c45-e19f-4cb1-a943-0b3ef7c86eaf}} , where {{formula:a21237a5-e576-4247-ab72-bc0089cef9c8}} , {{formula:4207c31b-2b92-48ca-8a2e-f858f671ddc0}} , and {{formula:7932b4e7-6b57-4d70-bc47-4dc25abd70f3}} are the parameters introduced above (Fig. 1c). As the cell grows in overall size, we postulate that the rate of growth in the shape parameter {{formula:62636339-874d-47d2-af4c-a4139edcaf47}} is proportional to the net decrease in cell wall energy, {{formula:07f9b59c-aded-442a-b2f6-682443ff8533}} , per unit change in {{formula:0ac78cf9-72a5-4d19-8e5a-d28f7f4d4681}} {{cite:6488f70bc74e8c50bb1cbe688492715b51110a3d}}, {{cite:682e5d0ae2e70960de1cd17100b9c0d316a81292}}. Assuming linear response, the configurational rate of strain, {{formula:ec001b88-09ca-4517-981b-1c7f149a51b0}} , is proportional to the corresponding driving force {{formula:0254095b-40b0-42cf-bb18-175797d4ea82}} , in analogy with the constitutive law of Newtonian flow {{cite:1b8abe1d416d081db540989eab166737846a685b}}:
{{formula:564c46e3-9d7e-48a6-ae08-e48ec0b7e990}}
| r | abf623cc583a5fc038a9f8f69e82efec |
Various independent cosmological observational data like the Type Ia Supernovae (SNe Ia) measurements {{cite:e8bcea102540836cf71e85be9ff41ce70b37a216}}, {{cite:12abb410802b68a1ef839863d784a6245a0ca3b1}}, {{cite:5fb01755004f1cb6da13ab2032b346ab31a10e08}}, {{cite:384227e3fe8012a06d2ec650b9b13ccebeb22c92}}, cosmic microwave background (CMB) {{cite:ee0c6286d1ba294765cab8442756a2254699ec0a}}, {{cite:033be61bbbe712c4825bc45146939764a34b14dd}}, {{cite:0ff70fb6a1eba3fa97c1020fec5827ac192c74de}}, Particle Data Group {{cite:71df2b9f0c7d40ab301b2f63b1249f8e56159f05}}, large scale structure (LSS) {{cite:cc63001028d17e8362dde048130527933ec75a33}}, {{cite:30eee8160d3e04199133a83616bc215e6c327db0}}, {{cite:554556af4f99bd6e569e8032e7a502e99855dc6b}}, {{cite:d8f23494cdadfe33161d3c8cea506c0239707dcf}} has consolidated the fact that the Universe is expanding with an acceleration and {{formula:e5af3a99-c760-4c4a-bfe0-d8fe4553a29f}} of the energy content of the Universe of unknown nature is the reason for this acceleration. The cosmological constant {{formula:3924bab0-ae68-49b5-a0a5-927fcbd388e3}} as dominant component, named dark energy, though observationally most favoured, is riddled with problems like cosmological constant and coincidence problem. Hence, other candidates as dark energy have been looked for, and no one of them seems to be a clear winner. Density perturbations may provide a way to distinguish between dark energy models. The motivation of the present thesis is to study linear density perturbations in different DE models. After a brief description of the perturbation equations in chapter , the next four chapters contain the perturbation evolution in different dark energy models.
| d | 1f9bde5b8d8df691dc7ab8817b70404d |
DLPNO-CCSD(T){{cite:78ca539a40ee8dc768331eb4a631dc9a9d839a6d}} single-point
calculations were also performed with the ORCA 4.2.1 software.{{cite:7ff002f642007b3abc3c4f03b3d9e5598e254bc1}}
The Ahlrichs's def2-SVP basis set{{cite:78234e7ac792c47f144d49429f6589e1381b290c}} was
used for all the calculations with the corresponding auxiliary bases of Weigend for RI-J{{cite:cfa25cb45631b4896b0f24ea52c4d84a73647eca}}
and RIJCOSX approximations.{{cite:da2201aa76430574b83971872b06ca2a29612103}}
| m | 4b9cc11d41ff6c3f29c7dad8b42d52fc |
Tuning of free parameters: There are three set of parameters to tune in Algorithm 1, namely: i) the step-size {{formula:953309d9-bc64-49d0-9a12-db42f27b4569}} ; ii) the proximal coefficients {{formula:1467872e-c1d3-4d3a-87b2-164f96a573c4}} and {{formula:24fdb023-9fad-43bf-bc98-1b8b33ad9c25}} ; and iii) the weights {{formula:99242184-57f5-485b-8572-3486083c2c70}} . Theorem REF offers some flexibility in the choice of these parameters (cf. Assumptions B and C). For instance, the condition on the step-size–Assumption C1–ensures that the sequence decays to zero, but not too fast. There are many diminishing step-size rules in the literature satisfying this condition; see, e.g., {{cite:90a5a3332c37fa21311418fdbc9028dd072fc58b}}. An effective step-size rule that we used in our experiments (see {{cite:079af5c27d1e6da5cadd6f1e81b9e9dc2e129cbf}}, {{cite:41f52d5f3ded7b09c3b7298d15fe7c765913808d}}) is {{formula:431372a7-1375-422b-bf78-4e2c6028ef0d}} with {{formula:5d137cf2-39fe-42bd-8152-d460853eb6af}} and {{formula:9df505e8-2736-4fb5-9228-e607325a75ce}} .
The proximal coefficients can be set as {{formula:1a2d2787-991a-4160-bdd2-d13ac90cfec1}} , for all {{formula:2728b100-1a72-4e84-8f13-fbb72d304b05}} and {{formula:a6170aa7-3f5b-462f-822c-299d1d72f8d4}} , where {{formula:173a77c7-5c90-4020-89c2-b8bbf681f78f}} ; and the explicit expression for {{formula:1ddda751-adde-4ef5-9f83-0bdabe7d340e}} is given in Assumption C2.
Note that the above choices of step-size and proximal coefficients do not require any form of centralized coordination among the agents, which is a key feature in our
distributed environment.
Finally, referring to the weights {{formula:5ba4cac7-4606-4dc5-af61-cdb99e8f50de}} , several choices satisfying Assumption B are available, see {{cite:3499f0717179d5470fb23523ce4340d2b4143ad5}} and references therein for some examples.
| d | d3f150ae0e619e2747b5cc5f89560c5c |
We formulate the disease progression as an Initial Value Problem comprising an ordinary differential equation with an initial condition which specifies the value of the unknown function at baseline. The initial conditions take the form of the embedding vectors which are generated for each pixel of the baseline image using any segmentation architecture such as UNet{{cite:557bd135d576b7cbbcbe80d9dd392baa9b28ebae}}.
The ODE system defined on the embedding and logit space is numerically solved for the given time points in the future. The obtained logits corresponding to the future time point are then converted to the segmentation maps (Fig. REF ) of the target anatomy. We utilize the method introduced in {{cite:db54970b5f3af05ab64effa86a02654afb567a38}} for training which requires a constant amount of memory independent of the solver's step size and integration time.
{{figure:36d60b53-df19-47bc-ab2b-00863e2cbd88}} | m | 4789eb939a818371c4dc12154ed8bf43 |
Tasks like open-domain question answering have been popular in recent times in the field of natural language processing. We know that only using unstructured text cannot be fruitful sometimes as this technique uses shallow methods. Using only a knowledge graph is also not practical because of noisy data and missing information. Combining both processes, following the "early fusion" technique the performance can be much improved. Such work has been done by the GRAFT-Net framework in {{cite:4ed74c85162a1bed277457c25dafc700ca17a343}}. But the sub-graph retrieval process still remains too complicated at times. A significant improvement can be done with early fusion to make the model easier in integrating knowledge.
| d | c0782fdff866984847e45fe8846bb89f |
Tensor decomposition methods are able to provide a lowparametric representation of specific {{formula:6d0d5f5a-05e9-474e-9f79-7ca56c578a6d}} dimensional arrays that possess lowrank properties. Available methods include the canonical polyadic model {{cite:7a10c506043ebbf44af03a18fe7155a935d93f20}}, {{cite:befb1ae5c616b0c709518047722e49bbc50b9bf9}}, the Tucker decomposition {{cite:31fe5de23aa03e850c27a0a5e6f6983c5d43bc34}}, {{cite:0f4c9f366adee7e312421d8843177027b3537438}}, the tensor train {{cite:c466ea5e9c1e8f099a2b91df0fcbd6f99cbaa198}}, {{cite:3edfd43fa7e07b5e39edcac7c84463ff74c6e2dc}}, the hierarchical Tucker decomposition {{cite:65dc55f695b780a55f1fa8540a3f1ecff4d6dfac}}, and the tensor ring decomposition {{cite:272518ce28aa6765b3c7c2f9d53307a33e2b87d0}}, with various applications in electrodynamics {{cite:1a77eb56febe6ef597ee64d81908c61293878d5a}}, {{cite:7693e29b43606784d9add1f3487c74c0bbd1cde6}}, {{cite:c1244117ed9620203de49f64a7c5419ceb9b4813}} and MRI {{cite:178296798db13c82a8722f3d2496f868de4ea446}}, {{cite:ec35578a09791610a28799c8c658ef907d897d9c}}. Next we briefly review TT and Tucker decomposition since they are used in this work.
| m | f9bf83c15de2cb825ab5fce067f98d86 |
Efforts have been made by the community that researches Explainable Artificial Intelligence - XAI in developing different measures to explain black box models. Many of these efforts are defined in XAI measures that use the well-trained machine learning model, its input data, and its outputs in order to explain the model. This type of measurement is called Analysis Post-hoc {{cite:3eefb3337cdbb9227a5873d848037acb9e3ad7ca}}.
| i | afbddef282391d7af594b760708b14bc |
As illustrated in Figure REF , inspired by VITS {{cite:26e08a4b981a78bed73ee15dbf7011c5fc72b915}}, we formulate the proposed model as a conditional variational autoencoder (CVAE), which mainly includes three parts: a posterior encoder, a prior encoder and a decoder.
The posterior encoder extracts the latent representation {{formula:2ab7e6cf-5761-42be-ad76-b4b5457beb2c}} from the waveform {{formula:0c9f0f99-3d00-492e-a7d8-1a05487b0878}} , and the decoder reconstructs the waveform {{formula:e184acfe-f125-4862-8b83-9df0658631e1}} according to {{formula:b1216412-74c7-47c0-bce9-6550d1cddbbb}} :
{{formula:3c2f3363-f7b4-4441-8e6a-d07dd7ff3e0f}}
{{formula:37ff47df-e2de-4285-9a8b-5924d750c9c3}}
| m | 6a6277512ffa50749c3c2955100c8f3e |
To derive the data in the MPA-JHU catalogue, the continua of the spectra were corrected for the foreground extinction following the {{cite:2779af5687cb52d24e1205d928afa838bbe358a5}} dust maps and were then fitted in the wavelength range between 3200 and 9300 Å following the models by {{cite:ad34a5ee974f46615d560304ee108c5937834aa6}} with ten ages (between 5 Myr and 10 Gyr) and three metallicities (1/5, 1 and 2.5 Z{{formula:012f46b7-6f9e-4c57-9202-e67f151c70de}} ). A {{cite:52b36c9a10fa0c779d90fc46d2c53aa8a3e79680}} IMF, Padova 1994 evolutionary tracks {{cite:e03b431c3070b66ef4c3f33f3d6ec76f3f4f93c1}}, {{cite:2213ca01e4e6780e89315c2092f13e87a6017572}}, {{cite:a96c90087e728b451d558127e1a7b1af7f87ba7c}}, {{cite:ee6bd2b19e29d7233370630558a80f2ac03a4e55}}, {{cite:720036b30706e3d2b0781b2eef8818de72dab0d0}}, and the {{cite:c190bab3061e6d742601d7476d31c836ed2fc7bc}} extinction law were used.
| m | ab5f468c3f4166fa59ee08e2b69989bd |
Theorem 6.2 ({{cite:ec773204f2dd59eee4c4df474dd4dc684ac6976c}})
In the conditions of the previous theorem, {{formula:402306f2-18d3-421f-991e-34122032d49c}} converges to holomorphic functions on {{formula:01000b40-38ea-4a7f-9b9a-943ad1168b14}} and the space, spanned by
{{formula:4d0fd35b-ddc4-41c1-ac15-f1739844d299}} , {{formula:7d1f3a95-90d3-4c3a-8749-451d822eb783}} , is invariant under the action
of {{formula:552dda48-e6a7-4810-ab1d-3f6e83670c79}} .
| r | 9498aa4cec828b41389a1fe85f2871d5 |
The nonlinear hydrodynamical radial-pulsation instrument called RSP in
the recently released MESA version {{cite:0525caefe29635b0cc293c98e28201e463d68c30}} allows to study in
detail fundamental and first overtone pulsations in RR Lyrae and Cepheid model
envelopes. Light curves of both pulsation modes could be reproduced satisfactorily.
| d | a49ef4dd8220d10b7e8f1726b236328d |
Comparing the range of trajectories for each UFD, it is apparent that most have
substantially different orbits for the different values of {{formula:6bb968ee-fa99-4d7e-9f00-787d6daaf46b}} . Since these are just the limits
from {{cite:54c0724d3b3bd23bc1eb0524db29e2ae77fa1e31}}, any similar orbit between these two extremes is plausible.
The first pericentre for Tri II, Hyi I, Horo I, and Tuc II could reasonably be anywhere from {{formula:a272e3e4-f9c8-46e3-b037-3f5262476c84}}
Gyr ago and beyond, and Car II, Car III, UMa I, and Boö II could be as recent as 6 Gyr.
By comparison, the difference between the evolving and static models is more subdued.
The models start to noticeably diverge after {{formula:5ddd4a6f-f3e5-4b4f-a9ac-67448bbc116b}} Gyr, but this is mostly restricted to the
low-mass cases where the UFDs are on very long orbits. These orbits can see a significant change
in the timing of the first pericentre approach (e.g. UMa I), but this is certainly not guaranteed.
At the high-mass end, the difference is minimal until the final Gyrs, and even then only in some cases.
The first pericentre approach happens at more or less the same time across the board.
In roughly one third of the cases (Seg 2, Ret II, Seg 1, Wil I, Boö I, & Tuc III),
the orbit is bound tightly enough that neither changing the mass nor evolving the potential
greatly affects the trajectories. Because of their proximity and relatively stable orbits,
most GCs also fall into this category, so we do not provide the same plots for the 154 Galactic
GCs studied in this work.
| r | 9105648f8e0a5ce368629a43779008e0 |
In fact, our results imply that we can distinguish between slowly rotating Kerr-Newmann black holes
and the Ellis wormholes with their Einstein-ring systems. This is because the leading
term of the deflection angle for the lensing by the Kerr-Newmann black holes in the weak-field regime
is equal to the one for the lensing by the Schwarzschild black holes, while the black hole charge and
small spin only slightly change the radii of the relativistic Einstein rings {{cite:acbceb1e6e6e7de274f068ad28229542cca881ef}}, {{cite:a1d356b2b340edbf30a9d3cc8a9fd663599a469b}}, {{cite:a676cb71c619a0f184ada9e0721450440601f826}}, {{cite:6f5ab02f03d2e643ffac14520b0c78dbaa7f0469}}, {{cite:f153e0be3e707d4735faac07268d598d0471be55}}.
Moreover, this also suggests that it is much more challenging to determine the charge and/or small
spin of black holes than to distinguish between black holes and the Ellis wormholes.
| d | 4ff5f7c568909c62f847e5bdc48f7403 |
The investigation of null geodesic motion can
reveal significant features of a curved spacetime. Especially, there are unstable and stable photon
orbits around the compact objects. The unstable photon
orbits define the boundary between
capture and non-capture of across-section of light rays of black hole such as the shadow in lensing images{{cite:020836cd9fe2c7e31edbe1fe35b76e463bb74c42}}, {{cite:20ddce5540da3a13d6a2ce19e0905987f359ef09}}, {{cite:75cdc92a860b58f87dfba946d9db3c3784603356}}, on the other
hand, the stable photon have directly link with the optical appearance{{cite:b6499ddfaadcdfb23766c2e4082bb579a6ac6be9}} of the thin accretion disk{{cite:d880ca2580533f5f56f38b9fd2f5d7d8f0928567}} and chaotic scattering in lensing around of hairy black holes and spacetime instabilities{{cite:ae57bfa6b370763b8e61b12467d4d0e9356768f9}}, {{cite:ab6fbca62d63befb086ec7cc8d510ef3739acd98}}, {{cite:894b009c8d7a7beeac30e92ad20c3f6410d224b8}}. These fundamental photon orbits have an interested invariant structures around dynamical
systems and compact objects{{cite:259f6224e5df565502bb2a28c64f73c7ee4329a3}}, {{cite:ff666c9e7cd2cb9fafa2d42d4937e9b84d5d9909}}. In more specifically, the so-called spherical photon orbits{{cite:d18976e9b1ac0d475029205b917111f26c9aa2b4}}, {{cite:1d172ade160f3d7084cf6805985f4cd0fc7b406b}}–orbits with constant coordinate radii that are not confined to the equatorial plane, have rich orbital structure, i.e. periodic orbit of the longitudinal motion of particles. This orbits can further reveal the feature of black holes.
| i | c71f788eb0c07a4d0eac5fdbc811ad07 |
where {{formula:b1101042-e485-45ea-9e30-d08e94f61328}} dB represents the path loss at the reference distance {{formula:0af0f50e-75eb-4990-bd16-a97664929885}} m, {{formula:46ab1239-c4ad-4c8b-8b76-92ed6d276b89}} denotes the path loss exponent determined by the environment between the links, and {{formula:480f1b52-1d61-4521-a71f-a1f503d07f2f}} is the distance between the transmitter and the receiver {{cite:4a515282b00e86f911f02fee773694299b51b802}}. We assume {{formula:0b4d9605-0462-4ac4-9c9a-85b96b76bfd0}} for the BS-IRS link and {{formula:546e8784-f3d2-4411-92ab-1d2b9397eae4}} for the links between the IRS and the users. As for the direct links, we set {{formula:b2a52cea-df3c-48e7-9549-6f095375665e}} due to the rich scattering environment. Additionally, we set the noise power {{formula:5e5c61dc-94f2-44d1-9566-4852203a4d7a}} dBm for all {{formula:7f1026a4-1ef3-409e-84e4-d9870d1b0f1e}} .
{{figure:3df5478c-a95f-4f81-8211-7e47980acdaa}} | r | 53fd59def2d0108c0b2295864fd160b6 |
Finally, a rather interesting avenue to explore is to find more general examples of non-local CFTs, along the lines of our discussion in section . Possibly the simplest such generalizations are the single-trace analogues of the {{formula:53f4d306-792b-4e15-90a7-bfbfb8bea7df}} and {{formula:a4496605-5c32-47b5-935a-5ae34877046b}} deformations that we have already mentioned, whose advantage is to have a rather concrete definition. In this setting, it appears worthwhile to better understand the effects of these single trace deformations on the twisted sectors. By doing so, one would not only be able to test the holographic duality proposed in {{cite:5058fad89c291f890dc8337badccd25f83b1fcd1}} at a more refined level, but also make new field-theoretical predictions that should be reproduced by the gravitational side of the correspondence. One can also consider deformations of this duality and understand what is the most general structure of the deformed CFT that still allows for the existence of a Virasoro symmetry, as well as whether, in the holographic duals to the string backgrounds discussed in the introduction, this symmetry is exact or, rather, emergent in the large {{formula:8f037e16-d0ea-49d4-80d6-e652b3b08d38}} , large gap limit.
| d | b09cbc2928387d9985ce9e8fc3301984 |
The key challenge underlying DA is to reduce the discrepancy between the source and target domain distributions, which has been tackled using a number of approaches. One main approach is instance weighting in which the source sample instances are re-weighted to minimize the distribution mismatch while learning a decision function {{cite:f620c2cbc4ef7bb7e0dcee706dcc2ef82bbab6e3}}, {{cite:7d2d2748e2e9b7a3ac009221c29742bff13ae286}}, {{cite:8c4bc096869dee19ce495aaa91f617de1dcc1fa0}}. An alternative strategy is to find across-domain feature representations that simultaneously minimize the discrepancy between distributions and preserve intrinsic statistical and structural properties of the data {{cite:3000b21c98883016ca9ffb8328a07457a7e9558a}}, {{cite:282ebd99d218042de17d56864f3e6d86507f4e3f}}, {{cite:c8f1d221871b950422fb746230041296acd4b559}}. The main shortcoming of the foregoing approaches is that the decision function they learn is often insufficiently robust to generalize to unseen samples from the target domain. This is largely because they minimize the discrepancy between the empirical distributions associated with the given source and target samples rather than the true population distributions.
In turn, the learned decision function has propensity for unpredictable performance
in the presence of noise or with out-of-sample data. This could have drastic impact on AI systems for autonomous driving, automation, and surveillance which, in addition to knowledge transfer across disparate (but related) domains, prioritize the safety and robustness to perturbations that disrupt normal operation. This motivates our work on developing robust versions of DA methods with out-of-sample performance guarantees.
| i | 6358664eff1b85557a202ec0e756408b |
CAP12 significantly outperforms previous single-model SoTA on ASVSpoof2019: Linear models on averaged CAP12 would've been the best single-model entry in the ASVSpoof2019 competition, and would've ranked 3rd overall {{cite:8f6c6d9abec33aa816290e4da1c41ff5349ab135}}.
{{figure:971d44a6-015d-467f-b794-a0472b82b6c7}}{{figure:aca6f53d-144b-4347-9d21-a71c4f0e9f97}} | r | 25a536c1fbe0a1aaefd603374b87042c |
Experiments on a number of target distributions have highlighted that the Restore process is particularly effective at simulating from heavy-tailed distributions, a class of distributions that other samplers can struggle with {{cite:ddfcd1adf3c7bd8b843aa9a53d7b88cb5616d2a9}}, {{cite:1861d9dc40d4c95f4a20e79d6689e616b17ad86d}}, {{cite:a4e4505df713bb449d9ea1207deff54377a5cec9}}. A heuristic explanation for this behaviour is that regeneration is a useful mechanism for allowing the sampler to escape the tails of the distribution and move back to the centre of the space.
| d | 81a8d6238dc129371858cc4826cf5aef |
of the {{formula:6c3726e9-e9c5-4496-ac6f-c4bb3294d613}} -learning algorithm (REF ) is GAS. We next briefly compare our condition to those proposed in {{cite:8dadd371aa32148e7a24878287c33eb47ea265f6}} and {{cite:80b1cf05a31f7870d1325be46903cd10925bd6ac}}. The condition in {{cite:8dadd371aa32148e7a24878287c33eb47ea265f6}} (their Eq. (7)) implies
{{formula:25da37d3-6739-4ef4-994a-72c89697c105}}
| d | 9c01d122d0af7b7250153dbb03365875 |
Let {{formula:eae648c8-6999-4fd1-b77e-5c22e3df7c51}} be the smallest prime with {{formula:422ed4b4-73c8-4a99-b554-d3458d8abcfe}} and similarly, {{formula:e4bf56af-8476-4bc1-b12c-a3a1a3722f36}} be the smallest prime with {{formula:aac44a88-901e-441f-88b8-05a1007ae683}} .
Now, {{formula:bb9bb191-4cab-438d-8b65-85aef3edf57d}} . Now using Lemma REF , and taking
{{formula:fc85c2ac-4435-4d12-850a-8497a8e189bf}} , we get,
{{formula:3cedfcbd-618b-4cf4-9c39-18f538f87fbd}}
We know from the prime number theorem that the average gap between the consecutive primes upto {{formula:ff4604de-e1a2-462a-a19b-268c42146ac6}} is {{formula:3544d712-1fb4-404f-96d9-bae2d86cc36a}} . Therefore, while taking the limit
{{formula:bc31bccb-78da-4c8c-86d8-869437f0849b}} , one should be able to choose {{formula:f4ed0865-05c8-4f9e-80c0-deb51067f484}} in such a way that {{formula:c1894bad-1719-4ec2-82a5-ac5e4b4f89fe}} and {{formula:273daedf-a152-43b9-8aaa-2b0ae8f42f0e}} . In fact it is conjectured,
by Cramér {{cite:6e62849011aa0a93cb78755d6c1a81896fd48bc6}} and later with some refinement by Granville {{cite:91b37347630f4521991977b3cddd2e98115cf2ed}}, that, if {{formula:60f48493-1478-4cb9-ba78-75dbeaf1623d}} is the largest gap between two consecutive primes
upto {{formula:4259b0a1-b4b9-4734-acce-b4dd7ac3d5be}} , then {{formula:058f8393-a7bc-4ff1-9f6d-6a2f193ce52d}} . In this regard,
currently the best unconditional result is due to Baker, Harman and Pintz {{cite:e2e1134056cd0e729bad1d5f94f23bbea029a98e}}. They showed that {{formula:d3a03372-b50e-4270-9893-092ba5d9bd93}} , where {{formula:15316ea3-b9d4-45f9-a65a-e34b2ea22d39}} .
This result is sufficient to prove the lemma. Taking {{formula:c5890b2a-86a8-4779-b4ee-fd13d2a222b0}} and {{formula:05373ba7-49f9-4fc4-b5aa-4130d855c73f}} in Equation REF , we get,
{{formula:8bd62f30-2d8c-4cfc-b445-4230851e35de}}
| r | 92fbd609a77b1d386810223986c4eb01 |
Analysis of keypoint representations.
We analyze the learned keypoint representation with t-SNE {{cite:cbe043e591a47659342b0980099af3807f8817b2}}.
The t-SNE algorithm maps a high dimensional space (64 dimensions in our case) into a two-dimensional while preserving the similarity between points.
The t-SNE plot for the keypoint representations of LSP test set (Figure REF ) shows that representations for the same keypoints are clustered together.
{{figure:3e0318c0-a737-4704-a9ed-6307a66a0f5b}} | r | 023d6453c93e3e5c517ea602d8b0a365 |
The continuous {{formula:29070540-9052-4e62-9f7a-ef9f32c3a887}} -means and median problems have been investigated quite a bit in the specific setting when {{formula:fec384c1-2286-4626-bbeb-b2f53e11d650}} and when {{formula:6eab5a92-18a2-4e2a-9ddd-23b8489e8676}} is the {{formula:363cad84-b21c-4cd9-a6e0-26ffb4a886ef}} distance.
The paper {{cite:714225636a177f1ebfa48ccab675563fa1141d33}} by Matoušek describes an {{formula:4c81d44d-7f70-40da-a48e-8f0527c7bf77}} -approximation (PTAS) that runs in time {{formula:d5c43b2f-e4b5-4959-b1dc-f23629198d6b}} . This led to a flurry of results {{cite:089dabaad1d5e52904a1aa8c01adc4d7f0cbcef5}}, {{cite:c97d15aeee17904231fbbeaa7cb74c5892e247fa}}, {{cite:bbfa272b2c7be5638ac841db332f902942fbee74}}, {{cite:66edf6e6965c0710553a16ab2f686e3c4ea09089}}, {{cite:e2aa6ba888e9554625d80be99c87394edc840cc7}} on obtaining PTASes with better dependencies on {{formula:e9e84257-1c2e-40b4-a6e7-83ec2e3a18f1}} and {{formula:70a621a5-a3c0-448a-ae2b-b101ea8a440b}} via the applications of coresets. There is a huge and growing literature on coresets, and we refer the interested reader to the paper {{cite:8ed8c4c55ebd3b47a840bcce4edd86aef3f7bbc4}} by Cohen-Addad, Saulpic, and Schwiegelshohn, and the references within, for more information.
Another approach to the continuous {{formula:4685d858-63f0-4b7c-b439-4ddc3f33b580}} -means problem has been local search.
The paper {{cite:e266c5e6f9fb248d8903c2df7b5106e73b6b305a}} which describes a {{formula:cd5f62e0-b409-4a0c-959f-ae49fe32ab4d}} -approximation was first stated for the geometric setting, however it also went via the discretization due to Matoušek {{cite:714225636a177f1ebfa48ccab675563fa1141d33}} and suffered a running time of exponential dependency on the dimension. More recent papers {{cite:dff0a62c4296fcc4c0e67c680b81100ab261f88e}}, {{cite:58d3a9a2efb0624f8c081b1209cf2cca591213d0}} described local-search based PTASes for metrics with doubling dimension {{formula:9cae974f-9d33-43ac-9de4-47f7165a9a52}} , with running time exponentially depending on {{formula:59793a49-71b9-4ab8-b2f1-ebb5ad48379f}} . These doubling metrics generalize {{formula:ed7b3a5a-9e72-44ce-8e28-2470210b9553}} -metrics.
However, none of the above ideas seem to suggest better constant factor approximations for the continuous {{formula:450cbfcc-bb41-4e92-bd96-ff92368e06b9}} -median/means problem in the general case, and indeed even when {{formula:dbea54dd-17b1-43bd-bf4f-bf4299abfe68}} but {{formula:ecac0921-dbef-4143-b711-1262c4a3d641}} is part of the input.
| d | 1e7f65c2e423df3273de8aa58db3977b |
It can be seen that the proposed unsupervised feature learning method can achieve competitive results on the bearing fault detection dataset, combiming the hybrid model introduced in {{cite:7a2e93c82263a39b9c129dd48dfc600fff4d7058}}.
| r | 09e89722059affc519d424a6fb285d1d |
In conclusion it should be underlined that our analytical expressions for Tan's contact of spin gapped
compounds are expressed in terms of magnetizations which are directly observable.
For example, at very low temperatures, {{formula:e72fd763-2243-4dfd-b190-f098a948fe1f}} , one evaluates {{formula:442a7800-f45f-40fd-a1d6-de64d76fe803}} simply from the expression
{{formula:0e83491c-4f11-4042-b7ac-b1093aa5891f}} , where the only parameter, effective mass should be estimated.
Note that, in this region contact of a {{formula:47faab37-9be7-41ca-948a-b12051dfb369}} ensemble is almost not sensitive to the strength of
the boson-boson interaction {{formula:474071d8-56a8-4176-a410-1da5ba2fbe08}} , while the dependence on {{formula:6fa4f10d-b323-4a7d-b88a-937c8aed30d1}} of the contact of an {{formula:206f19ff-90ec-4337-9d28-c03a84fea003}} ensemble
is rather strong even in the classical approximation, when {{formula:5b1aaf46-592b-4673-b3f4-b7b4faac00af}} is given by
{{formula:cdd731c4-9557-4254-ab56-009dabd05d62}} {{cite:1a4c3df18c1ce8a07d675cba2a1d0bf95b634da0}}, {{cite:1cd94bf182dc3457b1677affbbd2e1e3bff2d00a}}.
| d | 92872108cf2839d8968416b578d27525 |
Using the above cosmological observations, we adopt the Markov Chain Monte Carlo (MCMC) method to explore the parameter spaces of our three VDE models. We modifies the public package CosmoMC {{cite:9a64bc6ae9a464122d8360449cf970f3b1692cd4}} and Boltzmann code CAMB {{cite:065a2e69e1db731895ad77d05f36c1972ed350a1}} to infer the posterior probability distributions of different parameters. To perform the Bayesian analysis, we choose uniform priors for different parameters as shown in Tab. REF . In succession, as studying the effects of different data combinations on the parameter estimations is beyond the scope of this study, we shall implement the tightest constraint on these VDE models using the data combination CMB + SNIa + BAO + CC + L, which is abbreviated as “ CSBCL ” in the following analysis.
{{table:039646c3-1ed0-42cb-bd9c-610a3d9a898c}} | m | 05979b6586cebdbc8835600a6b398108 |
It is vital to note that the system proposed in this work can be extended using additional components with few adaptations to the code. Some additional interesting components to explore are lexicons (both generalist, such as Vader {{cite:4f5ba3865d7fcf79fd38b3992f3c787768874e90}} and domain-specific, such as Hurtlex {{cite:b18c32eec704e85bf43d2922d4d07a92aadb62d9}}), word embeddings, and transfer learning (via training on multiple datasets). Additional models could also be implemented to improve feature engineering (such as unsupervised learning models) or improve prediction quality (such as different weak models used in an ensemble strategy).
| d | 33b3f313186e5ca9756e2ea9efc21b9c |
Multichannel nonnegative matrix factorization (MNMF) {{cite:25deda6487de09fde609d40b8eb34b7d02bf5b38}}, {{cite:c9704127b1147fd963757d4bba7aa07d0948e9c9}}
is an extension of nonnegative matrix factorization (NMF) {{cite:58e5c22fbabb72f2087e723ec0707513966eb41f}} to multichannel cases, which estimates the spatial covariance matrices of each source.
MNMF employs full-rank spatial covariance matrices {{cite:442e9b6bf909c1c16ca4ff6963a9c3d487fd48f7}}, and this model can
simulate situations where, e.g., the reverberation is longer than the length of time-frequency analysis.
However, it has been reported that MNMF has a huge computational cost
and its performance strongly depends on the initial values of parameters {{cite:8292bf369869b4c32bf2deceef8c6e90997f5cc7}}.
| i | 26d543a8a879fd4e35b05b1f7d8cdaac |
Finally, we can easily recover a very recent result {{cite:98968b65f508bae670d2995c631ffc6870e9a7c3}} concerning light rings in extremal, static and spherically symmetric black holes within the framework of General Relativity under the dominant energy condition. Specifically, if the dominant energy condition holds, then {{formula:7a921f42-e241-45eb-9b86-0ec661426b94}} . Then, if the Einstein equations are assumed, {{formula:08d83554-13b5-4071-9dfa-6664b0212311}} implies {{formula:b510138c-67b6-4309-be1f-96fa7f8b8339}} . Note that {{formula:492dbf49-f510-447f-b959-9cba84ca617d}} implies, by Einstein's equations, {{formula:3809e7f8-a26f-4313-90b2-7621c7b81682}} and, therefore, we get {{formula:16344c26-55ab-4f58-afdf-d285a15e1a58}} . But, as shown in Ref. {{cite:3eee5e83f5dbec3c7e801a96b0921a050e006b0b}}, {{formula:05311584-4054-423e-a031-c1935ccb640c}} for an extremal black hole. Then, {{formula:ff9646a0-0962-4dc7-825c-4ae9436c592d}} implies {{formula:e5ef650d-bce2-44af-991b-b418c9045954}} , which coincides with the main result of Ref. {{cite:98968b65f508bae670d2995c631ffc6870e9a7c3}} when our mostly minus signature is switched to the mostly plus choice of {{cite:98968b65f508bae670d2995c631ffc6870e9a7c3}}.
| d | 94f38734ca0d6d526392afccb59c3d96 |
Finally, we also tested the fgsm {{cite:a170eaa880f165d3c08c7db76158b5007010d1ad}}, which is the first method for generating adversarial samples. FGSM can be considered a single pass of pgd on the loss function with an equality constraint on the {{formula:66ebabcb-afab-4a87-b4e8-75459d06b6fc}} distance, i.e. the adversarial sample is found as
{{formula:49457a12-5969-46d2-9a9b-29f955de3fe2}}
| m | e71151e5efcb9a4606cb4cef712dec0e |
In case of normal-inverse Wishart prior the posterior density with parameter {{formula:0f0cf353-47ae-4683-aa85-bbba2ff7bd82}} is the following:
{{formula:c549d7d4-960a-4047-a752-8ce1ed16fbb9}}
After taking logarithm and differentiating we get :
{{formula:529a6e58-3979-4952-bb25-b874ee1a14b8}}
By applying Theorem 4.2.1 of {{cite:42a68b2826a8017ef282d4f6f1ad43309e6fa8f3}} we can say that this is indeed the MAP estimator.
Let {{formula:12931f38-2fde-427f-8298-dd63ccff2cb9}} and the prior on {{formula:e7994032-c040-4157-8306-df5fe07b3d07}} is normal-shrinkage inverse Wishart prior i.e. {{formula:a76f817a-08a4-4b56-b656-fb91fe1287dd}} and {{formula:f539aae5-9d60-48ec-a6f4-76cc855996c8}} . Here w are interested with {{formula:9fe9f0b4-f96d-431c-b5fc-6db23c7d8ca6}} as stated earlier. The posterior distribution is calculated as follows:
{{formula:a4a2d1e9-d47d-4af9-aea6-233597d8beb0}}
This is because shrinkage-inverse-Wishart can be obtained from inverse-Wishart density by dividing it with {{formula:c977602b-7e91-4887-adc2-3283fc68986a}} . We know that the normal-inverse Wishart prior is conjugate with posterior parameters described in (REF ), {{formula:9d6ac445-2339-46d7-906b-e1d117dbba93}} and {{formula:2099532f-5a9a-4f64-b70b-8a66a7c7de9d}} respectively. The numerator is the posterior distribution corresponding to the normal-inverse Wishart prior and gives us the following:
{{formula:d38c72f5-96fe-4af0-aa86-4f1c4c31f9f0}}
From the above calculation we can see that the posterior is normal-shrinkage inverse Wishart with the same parameters as in normal-inverse Wishart proving our hypothesis.
Calculation of the Posterior Distribution:
{{formula:21080f02-3b8c-439d-81c1-295c9f608d97}}
where {{formula:0545962a-aae4-42e9-be39-f2c11de9cba5}} .
| r | 84f9bba1fb3d079643304267021c1536 |
A single-photon emitter is a crucial component in building quantum information technologies, such as linear-optic quantum information processing {{cite:a9d3be479787d7c80d834b3748af32bb8bb553e4}}, quantum simulation {{cite:f62189d31187308ef2dc1c944db2c5a35f534980}} and quantum communication {{cite:bee5423d595d8f7cf69933ad129d28e7dabd5ef0}}. Hexagonal boron nitride (hBN) is a two-dimensional (2D) material with a wide bandgap ({{formula:030b2f42-70cb-4022-89c3-4bfc4d6eacdd}} 6 eV) {{cite:25d60ae3d2597ace8b88e32d623a45482ccfb897}}, {{cite:37067479670b6b218e2064e452df7f50de6bd076}}, and can host stable and bright color centers which possess single-photon emission {{cite:f0afee901d619eb6f6b361c33348eaff419a02cd}}. Meanwhile, the manipulation of the optoelectronic properties of singe-photon emitters has garnered special interest {{cite:2afba2c29f6e953140636f334b45ec553d4a87d6}}, {{cite:93062eb36ecef98ba1f14142cadd7127778f7cc4}}. These properties imply a great potential of hBN in developing quantum applications. Being able to select and purify single-photon emitters is critical for generating
controllable and narrow line width single-photon emission. Hence, the identification of the atomic origin of the single-photon emitters is crucial to the development of this field.
| i | 5dbc6e8831c53d83bfd50a681b211a08 |
Table REF (part 1) shows the ASR results on WSJ. Rep-Phonestream augmentation improved the baseline WER by a margin of 2%, while none of the other augmentations helped.
This corroborates our intuition that data augmentation works better when synthetic inputs are similar to the real training data.
Furthermore, we continued to observe gains in WER when an RNNLM was incorporated in the decoding process {{cite:dab4cbf1a8d561539777238b21ded6e2b84fea63}}.
This suggests that while MMDA and LM have a similar effect, they can still be used in conjunction to extract further improvement.
| r | 318ed5db8be2e835c2dacf8483ec4146 |
Therefore, we obtain the heat current from electron part as {{cite:3d9673ba08b96b9300428d26ce95bcb70ee66f09}}, {{cite:71a3eba588734738359f1f171eb2e9ffe976d6fd}}, {{cite:f5d75fe9b87e5b184733af904bd9e8374475465d}}
{{formula:b9770ac3-8f63-48b5-a6a3-d95d0dd7ca8a}}
| m | 248ff014196fe285c03aeb43d7a2d8c3 |
Another major implication from the asymptotic posterior normality is the ability to facilitate the derivation of the reference prior suggested by {{cite:4c61b8d765e56282b5880e67afec7f776c962d2e}}. This class of rule-based priors attempts to maximize the information from the sample so that in a formal sense the prior has a minimal effect on posterior inference, compared to other candidate priors. blackThe reference prior formulation is attractive in part because it overcomes the paradoxes of {{cite:f0d620356657fd0e7603580e8098322e86e478b3}} and {{cite:187c48f4bcca428ed47730c499ef69671ad5a1ae}}, which may occur with flat priors and Jeffreys priors. In the general univariate case, computing the reference prior requires solving a sequence of integrals, which can be prohibitive for many distributional models. Under posterior asymptotic normality, however, for models with one continuous parameter, the reference prior blackis easily obtained, as it coincides withthe Jeffreys prior {{cite:aa5f6fba687fc53074ab13c37b8be8d5af140364}}. For models with multiple parameters, {{cite:4c61b8d765e56282b5880e67afec7f776c962d2e}} organizes the parameters by the order of preference, and derives the reference priors sequentially via a conditioning argument. blackWithout posterior asymptotic normality, this conditioning procedure requires multiple applications of the difficult univariate sequence of integrals. Under posterior asymptotic normality, however, the procedure can be streamlined into a rote algorithm {{cite:aa5f6fba687fc53074ab13c37b8be8d5af140364}} blackrequiring only the Fisher information matrix.
| d | 2c5cf4d3b2051600a5bef20d940af173 |
If one seeks to reduce the complexity of a model or the size of a data set, it is a common approach to project it to a lower-dimensional linear subspace of the state space, which is believed to contain the most important interactions of the model or the data set. The hope is that the parts which are lost during this truncation procedure are not essential and that they can be neglected without losing any meaningful information. Such techniques can be very useful in many different situations: Galerkin approximations can be used to derive well-posedness of partial differential equations on an abstract level {{cite:76c42503e83f12374ee4f29698f1d4626b06b5a4}}, finite element methods are a standard tool in numerical applications {{cite:7b182b583083369eaa25bb0c3304bfefe443ab5e}}, and a principal component analysis is a well established procedure to structure a given data set {{cite:5dce22516295ef94292930accc4232b266d079f4}}. There are many different ways to construct the linear subspace on which the model or data set should be projected and it would be beyond the scope of this paper to discuss all of them. Instead, we just treat three of these methods: First, we study a Fourier-Galerkin approach which can be used to reduce a partial differential equation to an ordinary differential equation. It can also be used to establish a splitting like (REF ) in a fast and a slow variable. After that, we discuss empirical orthogonal functions (EOFs) which is a standard technique to reduce the dimensionality of a data set. However, when applied to a dynamical system, it usually only preserves the statistical and not the dynamical properties of the system. There are methods which try to address this issue, one of them being the use of principal interaction patterns (PIPs), which are the last method we study in this section.
| m | 31610710408b90615a4f06d339ca62b1 |
The virtue of the real-space approach lies in its elementaryFollowing the definition by Richard Feynman, elementary does not mean easy to understand. Elementary means that very little knowledge is required ahead of the time to understand something except to have an infinite amount of intelligence. nature. In developing the formalism in this work, we just had to find the energy eigenbasis, use the spectral theorem to construct the time evolution operator, and apply the Born rule to find observable quantities. We did not introduce any approximations beyond those already established in the literature. This is precisely the abstraction level taught in elementary quantum theory {{cite:dd2216992ce2b91acc2412f971d0eddcfbb27470}}.
| d | 98963bf2e6abacf19215827ce6468657 |
We test our comprehensive search method on widely-used face verification benchmarks including LFW, SLLFW, CALFW, CPLFW, IJB-B, and IJB-C. The results are shown in Table REF . The bold numbers in each column represent the best results. In Table REF , the last line represents the baseline results without any search-based design component. For the baseline, the training dataset is semi-automatically cleaned by {{cite:2e2de6985144dee4335c8ca79882fef8ec705dbb}}, the loss function is finely designed margin-based loss function ArcFace {{cite:2e2de6985144dee4335c8ca79882fef8ec705dbb}}, and the backbone architecture is modified MobileNet {{cite:b9de58b7011536621f69576925035cd64cc31e5a}} that is specially designed for face recognition.
From the results, we can see that our comprehensive search outperforms the baseline by a large margin on all test benchmarks, i.e. 0.97% performance gain for IJB-C at 1e-4 and 3.16% at 1e-5. The huge improvement demonstrates the great potential of comprehensive search compared to manually design components separately. What's more, the search for each component also boosts the performance greatly, which shows the excellent and flexible design of our newly-designed search space for each component and the limitation of hand-crafted design. From the result of row 1 and rows 3-5 in Table REF , we can also observe that searching for each component separately may not achieve the best performance. If we comprehensively search for all three aspects jointly, we can further boost the performance significantly. Comparing rows 1 and 2 in Table REF , the addition of search for data cleaning strategy improves the search result dramatically, which has been ignored in previous searching methods {{cite:25d710d25046eccec3e5dfddd06a09daca40fc9c}}, {{cite:e2d2a2b689369205cd7a0efd8334f12729612b0f}}.
We show some combinations of top verification accuracy we searched on MS1MV2 in Table REF . The results show a very different design preference of searching from the previous manual design for each component separately.
{{figure:2d78e275-e469-4813-bb07-55101e285037}} | r | 1ce570f4275f7f54ced786df444b4235 |
The QSCMF theory is a kind of mean-field approximation based on the nonequilibrium Green's function, which is similar as the mean field approach in the literatures {{cite:5769172bf0b523cc389b146cfb3eaa1118f9d6c8}}, {{cite:6c34776634251891bf2fbbd85dfbcaa7328d7a00}}. The QSCMF is a good candidate to solve the nonlinear problem with arbitrary nonlinearity and arbitrary system-bath coupling. By comparing to the quantum master equation which is limited by weak-system-bath coupling, we find the QSCMF is a quite accurate method while it can be applied to strong system-bath coupling. For the interface problem with two-layer atoms, the QSCMF has a very high accuracy in the wide range of temperature and nonlinearity. However, if more layer-atoms includes, the accuracy decreases. If the QSCMF is generalized to two or three dimensional interface with more atoms in the interface, the self-consistent process is time consuming, and we also need to pay more attention to its convergency. The QSCMF is quite good for two-layer-atoms interface which is a reasonable approximation for short-range inter-atom coupling; however for long-range interaction, more layers need to be considered at the interface and the numerical calculation on the nonlinear thermal transport is challenging.
| d | 3db614b5b9c2ad79f51a01c9eb048f0d |
Analogous results arise from considering a fully classical damped harmonic oscillator with complex position {{formula:1aa0558c-704e-4871-ab1c-bb54fb3655ef}} , driven by the force {{formula:71996a22-3bd1-464e-9947-a8dae43fa334}} , with a slowly-varying amplitude {{formula:50d14adb-bc2f-4944-a413-a2d8e90ad636}} , where {{formula:96982b85-0f43-41c6-8a83-f10b8cefec49}} is the oscillator dissipation rate.
We then have from Newtonian dynamics that {{formula:9e0ce1a3-62cf-4dd0-81f6-812a8bd77943}} , so the classical work reads
{{formula:cb0d8a3a-73e7-4b16-807d-df002debdd20}} ,
where {{formula:2c35fdba-3bf0-4ac1-867f-0be08777b068}} is the reactive (dispersive) part, and {{formula:ef13978f-4f14-42ef-a345-ba3ceccd4502}} is the absorptive part (see ref.{{cite:96a8f06f90d73c32665581190b6247d5e0163050}}).
| r | 48ce6ed5f31cebdb96fb9978e399f7a7 |
where {{formula:2fccddc9-fc91-4710-a7fa-4d0025b74c74}}
are respectively the susceptibles and infected,
{{formula:c26954d5-f852-48d0-927c-8eb720006702}} are respectively the infection and recovery ratios,
{{formula:c3db2626-a6db-4f18-beb6-9aa7be61b092}} is the graph Laplacian
matrix {{cite:6851abfd06c3198d27b7f86cb8cb207657a5831e}}, and where we denote by {{formula:21afb753-8c2f-4e89-aad3-c504e501e464}} the vector
| m | f8235c8a5ae0acecd4d62d10638c7d96 |
Several studies have demonstrated the
inaccuracy of
linear approximation spaces to deal with parameter-dependent hyperbolic partial differential equations (PDEs) with parameter-dependent shocks:
this challenge hinders the application of
parameterized model order reduction (pMOR) techniques to this class of problems.
To address the slow decay of the Kolmogorov {{formula:ccd9dd09-7c8a-4343-88f6-4bf35490653c}} -width
of the solution manifold
associated with the problem of interest {{cite:1773e438413796f95cf2f30ebc8afaddab374e99}},
several authors have proposed to resort to nonlinear approximations.
The goal of this paper is to develop
a Lagrangian nonlinear compression method, and associated reduced-order model (ROM) for
one-dimensional (systems of) conservation laws: the key element of the approach is
a space-time registration procedure to improve the linear reducibility of the solution manifold.
In computer vision and pattern recognition, registration refers to the process of finding a transformation that aligns two datasets; in this paper, registration refers to the process of finding a parametric spatio-temporal transformation that improves the linear compressibility of the solution manifold.
| i | f061d93f62b7e2504cee46918038558c |
The X-ray Quantum Calorimeter (XQC) is an instrument flown on a sounding rocket that provided high-resolution X-ray data for the diffuse X-ray background, including the CGM {{cite:fb9a020ee51a7fa50cbed656e9527c02862076ef}}. It has been flown multiple times, including observations during 1999 and 2008 targeting l = {{formula:c9cc33f9-2ff6-45b1-a596-d81335b5dc05}} and b = {{formula:363cebea-caba-4f21-8bdb-62903fe6ea30}} , which aligns with our data set. The XQC field-of-view is 1 steradian, so it includes quite a few HaloSat fields. However, the XQC field does include a few HaloSat fields near the ecliptic pole that are removed by our sun angle cut in order to reduce the contributions from SWCX. {{cite:2a7468024d38888bc098d7b1295c0e8bbe5bfc46}} reanalyzes the XQC fields and report line strengths for the strong O vii and O viii lines that contribute to the LHB, SWCX, and CGM. We can compare line strengths for the CGM derived from HaloSat to those from XQC to check for consistency. {{cite:2a7468024d38888bc098d7b1295c0e8bbe5bfc46}} estimates that 37% of the oxygen line contribution is from the CGM. This makes the estimated 1999 CGM line strengths for O vii and O viii {{formula:d58a3d6d-5205-44e5-88e4-438724280fb4}} line units and {{formula:9fbaebed-f782-42e2-833f-618f49fc6bb8}} line units, respectively. The 2008 observation (with the individual O vii lines summed) is similarly {{formula:22cc1160-0602-4f80-b587-ee96783334f1}} line units for O vii and {{formula:28faa617-1546-4f52-a86e-6528d3acb0ff}} line units for O viii. The HaloSat O vii and O viii line strengths (averaged across all of our included fields within the XQC field-of-view) are {{formula:767348fa-ace0-4a5a-9ec5-69c977bffa61}} line units and {{formula:858e9ba7-3ecd-45ee-9755-6698af0705e9}} line units respectively. These lines are consistent with the values reported in {{cite:2a7468024d38888bc098d7b1295c0e8bbe5bfc46}} for 1999 and 2008, with the exception of the 2008 O viii lines. The 2008 O viii lines are still close and the difference could come down to the estimate for the CGM contribution.
| d | 0f177783a4ff01b48719635948dafec9 |
We propose a multi-objective optimization based solution to mitigate both directThough not done explicitly, reducing direct bias also reduces indirect bias as stated by {{cite:775d42ab0c289f95e683b50828d539eca5ca8817}}. and gender-based proximity bias while adding minimal impact to the semantic and analogical properties of the word embedding. For each word {{formula:82ba0db9-0f1e-49bb-a2aa-39d869d6ba0c}} and its vector {{formula:3ef6c719-5944-49fa-b738-ddb40daced1a}} , where {{formula:70a050ca-bd16-4f99-ba73-c0535db26e0b}} is the embedding dimension, we find its debiased counterpart {{formula:a1612a07-6d76-4686-9dbf-e0ad2e9936de}} by solving the following multi-objective optimization problem:
{{formula:e9990113-8938-463c-9225-0e40eff9bfa1}}
| m | 15c272e121381522e5fbd6ce0a627925 |
The data size requirements of the GLM point process model are reasonable for our purposes,
as indicated by our ability to recover stable repeatable influence kernels with 15, 60, or 180 minutes of data.
(See also the SI for a simulation test on data size requirements).
The approach requires the same amount of data as does cross-correlation.
We note that dividing the calls down by call type as well as by individual
can lead quite quickly to data sparsity issues.
This is seen in the slightly rough nature of the median kernels and higher variance in Fig. REF
versus Fig. REF .
This is of course true for other analysis methods as well.
The GLM analysis has been applied to data sets having hundreds of neurons,
and so it has the ability to scale to larger groups than we have studied {{cite:a8b8de0f7284cdffe8952dfec414bb6ec53edac0}}.
| m | 54091903e52958e9c40f6e4b22198b65 |
Networks.
Erdös-Rényi networks were constructed by taking a large number {{formula:ba6ea611-a124-4c93-96af-3d0a6d78dcb3}} of nodes and randomly connecting any two nodes with some probability {{formula:2e5dce9c-8418-4ae5-b601-235f347eeee5}} . This construction algorithm yields a Poisson degree distribution with the mean degree {{formula:5a11ba56-e927-421f-8265-493b90f0f81c}} {{cite:358b1a084a48319e16a3128c5055533a711bebaa}}. In our study we have considered the largest connected component network, namely, we have removed the nodes with the degree {{formula:ad4f6e3c-5ac3-40b9-9001-8e8f578a0a91}} .
| m | ff26fdd0b937b4b8afc6f4714042d1c7 |
Another source that deserves spectroscopic follow-up is N5486-2-1. Although this was located within {{formula:9708ebff-043c-4305-b1d7-7d11fa124003}} of NGC 5486 and does not satisfy the classical definition of an outlying H2 region, assuming it is physically near NGC 5486, it displays many properties similar to local dwarf galaxies. The knot of star formation our survey targeted could be powered by {{formula:38ac9284-cf89-4465-8400-1f5caccbd194}} 80 O9V stars {{cite:ef53f61a733f3685b75d1da4e4f937c31ca74dc9}}, consistent with dwarf galaxies {{cite:43eee306b59affb2fc4b25ad5d5d1f72dfc65639}}. Additionally, this source has a similar {{formula:5384afb8-0dd4-4d45-b9ab-ca0c7737aac2}} -band and H{{formula:4b4b0fff-e5b4-4fe5-8355-964f8f2b510c}} luminosity to the dwarf irregular galaxy NGC 4163 as mentioned above. Another striking resemblance is the asymmetry in the broadband images. The source appears to consist of a bright compact region with a more diffuse extension to the west, structure which is also evident in the shallower {{formula:28e78bf8-03f1-412c-9d82-72e705410eff}} composite from SDSS. Similarly NGC 4163 is itself asymmetric in nature, with a burst of star formation occurring in the central portion of the galaxy, but not the outer regions {{cite:90c0316489e026c4b47369939e558059c9ad9cb7}}. It also has a peculiar H1 distribution, with an H1 tail to the west and possibly the south {{cite:d457f51311db9d2a058e4187bf6504eb828e7e93}}, {{cite:b02905b3bb619e9796a56b65945918d43d60ea88}}. Although it is not clear what could be causing the behavior in NGC 4163, perhaps some large-scale interaction with NGC 5486 has caused this asymmetry in our source.
| d | d7e0c44258238ad8b604bdc293ea03e6 |
CLEAR is based on the view that a satisfactory explanation of a single prediction needs to both explain the value of that prediction and answer 'what-if-things-had-been-different' questions. In doing this it needs to state the relative importance of the input features and show how they interact. A satisfactory explanation must also be measurable and state how well it can explain a model. It must know when it does not know {{cite:4dea21abcb5fece70bd8829e604ccc5091141644}}.
| m | facefc298ff510b0811cf345b5aac322 |
Extending recent work on stress fluctuations
{{cite:c8c2ebcafe1e63df55f61705324a115f91c9a06a}}, {{cite:d656087ae93d5b0e55b37af690e1a9f007479657}}, {{cite:a30350ff511c2c672a1a47064ae1d55d78236d17}}, {{cite:c4412ed71d0e042f68d04b006eedc31e5de591fc}}, {{cite:feea8315b6e21038d7ceaf5e0baac4a5d822d982}}, {{cite:2635f0ec9c0859954245032dc00bbc1bf6017dde}}, {{cite:6b8f7a3ff631758fe0e3abf2729961d75b6253d9}}, {{cite:455cfb2d46ff8bc6715c2ff2f4423b58b8d9ba17}}, {{cite:26928505e122664e8babe4b3758cba6b83191fbb}}, {{cite:fb65ffbe6ddccda111a3f2658a6ec0f4abe25db5}}, {{cite:a1af3cf14f30f8d040de860cc42ac2f55d1c4240}}, {{cite:b3ba08e199a48c2e84abb198276fa811b1e70003}}, {{cite:39d456121cf068a2fc84c6bd0277b45871cd9806}}, {{cite:655160454fb968604133962e177cf7c3e1e93898}}
we want to give a systematic and uncluttered overview of three general points
of relevance for a large variety of problems in condensed matter
{{cite:c10f17792f2ee8b40ea42832857d0d4710c8d31a}}, {{cite:7e96c2c3ce673b83f4be395f807951cb7c3c9ce7}}, {{cite:9be569ab7efd56ad08c8d31f5f43bebc8609f8f7}}, {{cite:3b3cda4ea7484653432f8eeb5951403d92be8e29}}, {{cite:0fb16bb4520ae5b27e9681712e2c6e30e85c8b79}}, {{cite:f918eb8c9a39fbd7100428184aef5b22f8b399d9}}, {{cite:98c691ac026cfb8d2ee466c2e3e10c11e3c2b641}},
material modeling {{cite:edac0e39eca9bcc872f61e56caf7d3634a1d02db}}, {{cite:54fe772c5f46037c28a4cc4a73e60c95f7279fc4}}
and in computational physics {{cite:c2e2c5f218640f88b44334a2f15074243004fa53}}, {{cite:0e353cdc475734a8c915bf6b4ee457562326632e}}.
One important motivation is that many physical quantities can be obtained by
equilibrium molecular dynamics (MD) or Monte Carlo (MC) simulations {{cite:c2e2c5f218640f88b44334a2f15074243004fa53}}, {{cite:0e353cdc475734a8c915bf6b4ee457562326632e}}
using fluctuation relations {{cite:e61376a42a1ed02d4b36f48ce95ec2dccfadfe6e}}. Studying how the respective variances {{formula:484a25a4-73ee-4db7-83b1-aff1ea3662d0}} and their
standard deviations {{formula:cfef393f-978c-4ccb-aefa-21b9067abdf6}} evolve with the computational feasible length {{formula:b88e1a53-da57-43ea-8d75-c84b20a2fc79}} of the production runs of the simulations
is thus of particular interest.
| i | 93a751f8628ba9938a99f13569a99fa2 |
We adopt average accuracy (Acc), sensitivity (Sen), specificity (Sp) and F1-score (F1) for quantitative evaluation.
Besides, following {{cite:8d0c79821e41572efdde48fd0762b94237079dd1}}, we evaluate A/V classification
on the ground truth vessel pixels rather than the segmented vessels, which is more strict since some capillary vessels may not be well segmented.
We report the results of the proposed method on four cross-database experiments in Tab. REF . Also, we compare with several UDA-segmentation methods, AdvNet {{cite:e158d53704c838a8cbd0129ecc9601c5e4d3bb49}}, PnP-AdaNet {{cite:31fcfc3a708a690b5c32b6c10c1d0aeb8a83fae3}} and ST-CR {{cite:331d85d0e59bb336d98f1d733e914118db4c2264}}. We use the publicized codes provided by their authors.
Among them, the first two are the recently proposed domain-align based methods. ST-CR and VM-CR stand for the spatial transformation based consistency regularization and the proposed vessel-mixing consistency regularization, respectively, and the main difference is the utilized perturbation. Besides, UA-AV {{cite:fe59f93a350651cefa95f23e388e5ee83e056c18}} is a recent work specifically for cross-domain retinal A/V classification and trained on only AV-DRIVE.
| r | 62119cd293c2cda186e4dc05f854eb27 |
The space {{formula:5c67d003-b8b8-464d-bd02-1f6a23f2d035}} is endowed with the norm
{{formula:370aac48-0b07-488b-9629-4ac3631ebd77}} and it holds {{formula:b4f30b82-d42c-4a5e-920d-6d3ce912dd18}} . Our main reference for functions of bounded variation is {{cite:290108fa2e1ef1f9bd7157d1b4cac5e8cd8028ab}}.
| i | e37bad8e61470d16b0a27f6d39898ee7 |
This work can be extended in a number of ways. One potential direction is to use different ways of creating model ensembles, for example, by using Dropout {{cite:b792321251ece700c27393e8902aa4faf028cb28}} or pseudo-ensembles {{cite:74de560682814fc58c922d4c017d54a326e387bc}}. It is interesting to investigate how the proposed algorithm can be combined with other tricks from the PINN literature, for example, adaptive balancing of the loss terms {{cite:b755f176cf0e64382368b6ed4161ea2a02df3829}}. Another direction is to find alternative ways of the solution interval expansion (e.g., update sets {{formula:042aa021-53ef-42d6-979a-72b090671591}} , {{formula:fd9fdfba-315b-43a1-be28-84c00a7e2cf4}} more frequently), which may increase the convergence speed.
It would also be useful to improve the PINN architecture such that the knowledge of a found (local) solution in one area could be used in finding the solution in another area. Using neural networks with the right inductive bias (see, e.g., {{cite:b3fb890e461b2f13cdc320ed728f952ada8889aa}}, {{cite:e9163d4d67b870a93dfafb56406e470f3d335b2d}}) might provide a solution for that.
| d | b7604c1a91bc1f697a5614689faa7a19 |
The convexification method.
The main idea of the convexification method to solve (REF ) is to minimize the Carleman weighted functional
{{formula:0d5fd6b2-5369-4fd7-b07d-e21d316e9b88}}
subject to the given boundary conditions for some
Carleman weight function {{formula:dafdc342-ab32-47e5-8b70-da8920dbcda3}} .
With suitable choice of {{formula:622bbba8-1c6d-4be3-ad4d-666b12b9166e}} and the regularization term, one can prove that the functional in (REF ) is strictly convex in any bounded set of {{formula:2d000612-3d06-4c56-a924-0be129d0b219}} where {{formula:601531ad-463a-4d88-b5ca-e8a7fdb3b887}} The strict convexity implies that the minimizer is unique. Two other important theoretical results for the convexification method are (1) the minimizer can be obtained by using the conventional gradient descent method and the (2) the minimizer is an approximation of the desired solution to (REF ). The original idea about the convexification method is introduced in {{cite:cc6d40246d1acaf6b35496f9ba10bc7f3b49278e}}.
See {{cite:862fdd647290068ea3257b13f911a4e2b157bef0}}, {{cite:f8bc8eb3e652872451e4f712a661abcd74ce34e4}}, {{cite:0d418daefd7d4a7bd5fa40c5d5d26dee5ef4b67d}}, {{cite:932652c9d1ae17d9209d2d67b0c1847286f0fbf3}} for follow-up results.
Although effective in delivering good numerical solutions, the convexification method has a drawback. It is time consuming.
We therefore do not employ the convexification method in this paper.
The Carleman contraction method.
The main idea of the contraction method to solve (REF ) is that we take an arbitrary function {{formula:672e0a61-d3ac-4856-b355-084aa74a4c3e}} .
Assume that {{formula:923297f4-4d30-4120-96e3-e600ae2ed6d0}} is known, we compute {{formula:a9ed0a3a-e12f-4f8e-ba8d-7c39e22b29db}} by solving
{{formula:52639d92-8e52-4706-97f0-6825f8dcceee}}
by using the quasi-reversibility method {{cite:bb8f4902f3ab07b73c39ef9e501a6b4345c8843f}} combining with a suitable Carleman weight function as in {{cite:b4f6ed9cedcd556dae9cbaa283fe321d27646d7a}}.
One can follow the arguments in {{cite:b4f6ed9cedcd556dae9cbaa283fe321d27646d7a}}, {{cite:99a05566cf1ced7ff6ea4ff906967ef8bf69a6e1}} to prove the convergence of the constructed sequence {{formula:765f8b21-c549-462a-bfc0-d8811ca4a6a6}} to the true solution to (REF ). For more details, see the following papers {{cite:7d3d630f7bef176877b016262f0e0e4f08a72632}}, {{cite:b4f6ed9cedcd556dae9cbaa283fe321d27646d7a}}, {{cite:99a05566cf1ced7ff6ea4ff906967ef8bf69a6e1}}, {{cite:dc918e68c5a1402b1712cab0acdcea5cd3c1f2e8}}.
This method was used to solve a similar inverse problem to Problem REF . We therefore do not repeat it in this paper.
The Carleman method combining with linearization {{cite:4be1068ddf4de4588d2d7b3256ffcd7350136d56}}. We name this method Carleman-Newton method. Details of this method will be given in this section.
| m | 93e903c37e13b9a27dec49c2dab1a7fe |
GSD vs. Single Pass Models
The current state-of-the-art single pass models for inference on OOD data, without training on OOD data, are SNGP {{cite:2776ffcf767ba29c1aef427aeb45efac2f570546}} and DUQ {{cite:7795c883a1f36a9e80e66970ed408bf4c08839f3}}. The primary disadvantages of these models is:
1) Hyperparameter Combinatorics: Both DUQ and SNGP require many hyperparameters as shown in Tab. REF . SNGP requires the most hyperparameters out of all the single pass models. The large combinatoric scale, in addition to the fact that these hyperparameters must be tuned via pre-training grid search, make these methods costly as a full training procedure with multiple epochs are required before evaluating calibration. Our model only has one hyperparameter that is tuned post-training with 1 epoch on validation set. 2) Extended Training Time: DUQ requires a centroid embedding update every epoch, while SNGP requires sampling potentially high dimensional embeddings of training points for generating the covariance matrix as well as updates to the bounded spectral norm on each training step, thus increasing training time while our model trains in the same amount of time as the model it is applied to.
| d | e1e0a1e8130edfb032de4157980db18d |
The numerical algorithm considered in this paper is based on the ideas proposed in the works {{cite:e1414e92c2165858ee53f230aa9aafe136a33094}}, {{cite:e22502d26cc953fca716d361472d8cbd59e7ec6e}}, {{cite:778db4c5c2ced87a4fec3486088fca10cee463aa}}, {{cite:9f2ace524b549cd63612229494fe43e106d4f1cb}} and modified for application to the problems of epidemiology. The algorithm gives a direct and simply rule for minimizing the cost functional, ensures the fulfillment of the law of conservation of the entire mass of agents, and allows to take into account more complex functions {{formula:d404d18a-ddfd-44f8-9bdf-9f4c0e511215}} responsible for control, instead of the traditionally used quadratically dependent on {{formula:bbedc66e-c3a0-455b-8317-1b4dacf2f04e}} {{cite:773dd025cbdd7e6d496566c2e6a90bc58464d314}}.
| d | e0a4dcca6794c6c5b6dcc55f1a128497 |
We will label solutions as usual by the integerThis restricts the generality of the method but getting non-integer {{formula:741b4ada-8c53-4258-ac4a-f97e87685a93}} solutions to work is highly non-trivial due to the complexity of the EM which only contain explicit integer powers of {{formula:b7720053-a053-42d8-bd98-163f52bb9f9e}} . indices {{formula:d78054a4-a1c7-4f16-8854-8b266bd409a1}} .
We shall see in particular that the (2,2) solution first found by Stelle {{cite:513a598edb0f0822be9db64c14bdaa990c14023c}} in quadratic gravity and discussed by Holdom {{cite:c992ce66d37c17c440f86340861121e5c0b0416e}}, is still a solution when the Weyl cube term is incorporated. Also there is a {{formula:cec15398-da48-4dc8-a300-cb522dd97398}} family containing de Sitter and Anti de Sitter spacetimes.
| r | 7e48acbc63cc771e9257c7ec16ab7009 |
Denote {{formula:d1141c3c-1305-4afe-9620-d2aed503f747}} and fix a bounded infinitely differentiable function {{formula:fb4c2cca-0483-4d40-bc00-e9d6766a057a}} defined
in {{formula:11cef833-c921-4b6c-a8e8-a4842ed4b8e1}} such that (see e.g. Lemma 4.13 in {{cite:b79b69f6c83fadece5daaf28ad6bb0a97452c17e}} or formula (2.6) in {{cite:a16ce41a184a36c4100d4c571b404e8ee0ba5aa1}})
{{formula:b7c0d48f-3e7b-40fe-915b-b3e0b7e0ac70}}
| r | 19116e5456b389746eb0dd0682ef36d1 |
Table REF represents the challenge benchmark {{cite:1e740c1470c23b1965731160a3c559cc47e796c9}}. The best 3 approaches achieve above 30dB PSNR, which denotes a great reconstruction of the original RAW readings captured by the camera sensor. Attending to “Test2", the proposed methods can generalize and produce realistic RAW data for unseen similar sensors. For instance, models trained using S7 {{cite:004318928eb4ccae421fb1053c7dbc472925b639}} data, can produce realistic RAWs for S9 {{cite:ee9fa2143a7e728dc524e3620dc0a5b982e171b6}} and S6 {{cite:28b9fbf59ce4f951f7116d5ea544812f79257f04}} (previous and next-generation sensors).
| r | 8da553157a095d78348d956b993962c0 |
In Fig. REF , we present the results for the condensate of {{formula:49883dde-53e8-49f3-8155-d2b3d6f845bc}} Cr atoms which have a moderate dipole moment corresponding to {{formula:dacae44d-2283-4477-b5df-7650d0fce3cc}} {{cite:ffa295650969d53329e2d37c01d47bc5838ad5be}}, {{cite:9aaded3dc61c5eb4f82e1badc709eea043d1ffdf}}. The figure demonstrates how one can stabilize the condensate with {{formula:5405b51e-a6bc-4aa5-967b-e12e4f738569}} {{formula:62d0c69a-b587-44ad-aaab-cfd08bf28a56}} by varying the strengths of the repulsive three-body interactions (without the contribution of the oscillatory part of the interactions). In panel (1,1) the condensates are found to be stable up to {{formula:0e60d26c-8be1-45a7-9251-5a4270153bd0}} for {{formula:e0f3be15-2eab-422d-96bd-1088f341c758}} -0.013{{formula:6d04ad60-97eb-443c-9783-a36ddd802756}} . Similarly, in panels (1,2), (2,1) and (2,2), the condensates are stable up to {{formula:b3749fc1-f374-41da-a3e2-2badad00c4dc}} , {{formula:891da860-0e7e-4c04-a2fc-3379ac27f7cf}} and {{formula:62eba1e2-0ad2-469d-abbe-346218c5f20c}} for {{formula:7c29660b-1a15-46ac-877c-57329735232e}} -0.012{{formula:009c2adc-0d59-46c8-a381-b87c278021e8}} , -0.011{{formula:d39b835c-0d86-4140-aacd-4efbdbd80f11}} and -0.01085{{formula:19928b7f-d317-4df2-808e-0171e91d85fb}} , respectively. Further evolution of the condensates may perhaps lead to their collapse or expansion.
| r | d1baeee8ad390fb0b4d1887a5a944910 |
For the first automatic speaker verification spoofing and counter-measures challenge (ASVspoof 2015 {{cite:ffa9e2291d17390d8e8fcbfae32b7bd1de72a5fb}}) even though the best results showed an overall average detection EER of less than 1.5%, the EER of unknown attacks is five times higher than that of known attacks. In addition, while some attacks were easily and consistently detected, others provoked extremely high error rates nearing 50%.
| i | a0418111805f57321fc30783c5a29ce6 |
Limitations of state-of-the-art KGE Models:
KGs are openly available, and in addition they are largely explainable because of the explicit semantics and structure (e.g., direct and labeled relationships between neighboring entities).
In contrast, KG embeddings are often referred to as sub-symbolic representation since they illustrate elements in the vector space, losing the original interpretability deduced from logic or geometric interpretations {{cite:40aecbae7d98cd4bad9e776b8b7e5f16b6ea850d}}. Similar issue has been observed in a few initial KGE methods {{cite:27b79f5ae4f29727e817db6b0bd52d9364e4558a}}, {{cite:42f520666bf6e5112ca120364e899077198e2b9d}}, {{cite:91a3fa37cf7ec8ef83cb0099544719de684e441e}} that lack interpretability, i.e., these models fail to link the connectivity patterns to a geometric interpretation such as rotation {{cite:906156a6719e66a5b7e54735f97d56f55766aa42}}. For example, in inverse relations, the angle of rotation is negative; in composition, the rotation angle is an addition ({{formula:ec7968bb-c24d-471e-97ec-a9c0e719d39c}} ), etc. Other KGE approaches such as RotatE {{cite:906156a6719e66a5b7e54735f97d56f55766aa42}} and NagE {{cite:40f839cccaa15c68865e2764753ec40e11b10220}} provide interpretability by introducing rotations in two-dimensional (2D) and three-dimensional (3D) spaces respectively, to preserve the connectivity patterns. Conversely, QuatE {{cite:320b9312265b00f44b7969728257bac55da34cd6}} imposes a transformation on the entity representations by quaternion multiplication with the relation representation.
QuatE aims for higher dimensional expressiveness by performing entity and relational transformation in hypercomplex space (4D in this case) {{cite:320b9312265b00f44b7969728257bac55da34cd6}}. Quaternions enable expressive modeling in four-dimensional space and have more degree of freedom
than transformation in complex plane {{cite:320b9312265b00f44b7969728257bac55da34cd6}}, {{cite:53e40327617b6764ed068f5ab97874f2cac18292}}, {{cite:fadfb19fad7870ddd143d33e7f50254646ce4ab4}}.
Albeit expressive and empirically powerful, QuatE fails to provide explicit and understandable geometric interpretations due to its dependency on unit quaternion-based transformation {{cite:40f839cccaa15c68865e2764753ec40e11b10220}}, {{cite:75171f072903206f5eeff3dfe1908a9bae69d134}}. Hence, it is an open research question as to how can a KGE approach maintain the geometric interpretability and simultaneously achieves the model's expressiveness in four-dimensional space?
| i | 2d5fa3ef0a32af72c10e9b43e71abb20 |
We first give the necessary notation used in this paper. Let us assume we have {{formula:ee848c24-521c-4db6-84bf-de00f1f9e4dd}} i.i.d subjects, where we observe functions {({{formula:c306488b-95ab-4306-96f9-b2cdf7376712}} , {{formula:0a5101d5-8572-4bb4-a7ce-fccb7a588213}} , over a compact time interval {{formula:0cb11fc5-8c52-421a-bd45-d0c6bc551b96}} . These functions
could be observed on other intervals, but as long as they are closed and bounded, then they can always be rescaled to be on the unit interval [0,1]. For the {{formula:474b5964-65fc-4113-b854-236e1d9a23ea}} subject, the functional inputs are {{formula:ee74f51c-8a62-4ea7-8a6a-fad663b861d3}} random curves that can be denoted as {{formula:0c8bd226-828b-491e-92dc-29e47321bfe0}} and the functional output is {{formula:f173361a-a4ad-4ff6-8a5d-48860ca4704b}} for {{formula:1e537317-4fbe-4548-9bf6-3ab2998b605e}} and {{formula:a73f583e-8816-4e30-9325-4de54f4360ad}} .
We assume that all the functions are completely observed. This is known as dense functional data analysis {{cite:ebf7594d427c24d1cedc1fa22bc92a657ea213ba}}. Our main objective is to learn the mapping, {{formula:da94e695-2456-4cd2-b752-4809d32ddd1a}} from the functional inputs {{{formula:ce859fdf-dbe9-40a5-ada5-73223c912a95}} to the functional output {{formula:f40e6dc7-5495-4072-b831-d97760bb8d48}} :
{{formula:052bff2f-05fe-47be-99d7-e50e2919a978}}
| m | f32c01ba18e0aeba43fb65fe338f635f |
The algorithm below-{{formula:8adb1ecc-999e-457d-aa97-e951ea0ac9e8}} is just modification of the algorithm {{cite:ed84a86370a5bb7b9f10edccbc7d862559cb05a6}} or {{cite:a0fdb2871185f0d52add30be60c4eb06bfa5ec8d}} in the input phase.
We show observing just {{formula:d93c61f8-26e5-4ea5-b9c3-adf99c057c58}} many entries in each column is enough te decide whether partially observed column is contained in the subspace or not.
| r | 0f322729961c6bd3fa259864360103aa |
To this end, we introduce RONELDv2, which incorporates the use of lane point variance, lane merging, and an exponentially weighted moving average method to compute weights in order to strive for a more robust and lightweight solution which further improves on the RONELD method and increases its suitability for real-time use on autonomous vehicles and ADAS. To verify the usefulness of our proposed changes to the method, we test the proposed changes on the TuSimple {{cite:5159d8a9308f8e584a7ee082459db6438e1f7429}} and CULane {{cite:fe8d06bd40547af45473b009d5c9b6f9b9695964}} datasets and compare accuracy results with those achieved in {{cite:eb12596a0196884c5a8df57cf9999220168354c2}} as well as the two state-of-the-art models used in the RONELD paper, namely SCNN {{cite:fe8d06bd40547af45473b009d5c9b6f9b9695964}} and ENet-SAD {{cite:ac08621fe55ba5bd7d1f5b04e611b0f11261f677}}. Our experiments demonstrate the effectiveness of the changes, with increased accuracy results above those achieved by RONELD and an up to two-fold decrease in the runtime compared to an optimized version of RONELD. We present two simple before and after comparisons of applying RONELDv2 onto the CULane and TuSimple test set images in Fig. REF .
{{figure:0b180002-b84f-40b0-aaa9-8f814da1453e}} | i | 95cd3d04618a050ef943e0bc48ee40f8 |
The procedure for computing a diffeomorphic deformation can be modeled by an ordinary differential equation (ODE) parameterized with a stationary velocity field {{formula:bd41b74d-9195-4ebd-af66-5e18f905d215}} {{cite:121da4de531d3c135ce5148facc5246da5f0e82c}}:
{{formula:0684be4c-640e-419e-a51f-52576e22c41a}}
| m | ffed158f4cbf4bf09fef0a71382a69ba |
First we introduce notation. Let {{formula:a8b904de-168b-4d4a-a91f-4c5991619175}} be a non-negative matrix containing the imaging data, with {{formula:7a58f39b-1b25-4c9d-8013-ca6770a6575c}} frames of {{formula:b51c0d22-a048-4d57-80cd-d345cf713abb}} pixels or voxels each.
The goal of non-negative matrix factorization (NMF) is to represent {{formula:30848168-507f-495d-8f48-a2a4ca71eaba}} as a product of two non-negative matrices {{formula:ed60ec0c-db4b-4e07-afb2-06c1d75c8984}} and {{formula:9a5da164-3ec0-4b4f-8c7d-e377e145cc76}} , where {{formula:c50b5eb5-0079-46ab-bbf9-09782c724aab}} , effectively compressing {{formula:5e55db63-64ee-4f2d-beab-35dec66a0c1c}} to a lower-dimensional latent space. Each column of {{formula:d3255bcb-3a44-4bdf-b9bf-137181671c76}} represents the spatial footprint of one of the {{formula:96aba3f9-0e90-4a83-b375-4a89a3f3526a}} latent components, and each row of {{formula:6477d5c7-64ec-4690-a5b7-9d641e008db9}} represents its activity across time. To compute {{formula:23ab59d4-7f5a-46a2-b59e-3a5830134a82}} and {{formula:4ba80029-1da1-4609-98c9-cbb477392d63}} for a given {{formula:f9017075-e5df-409f-80c9-f2c8292c5cf2}} , we minimize the cost function {{formula:d76d9672-e2a5-4a98-a1d8-0a6f3eeef574}} , subject to the constraint that {{formula:495a51e4-7be6-49ce-8ba0-f4337ec22fbf}} and {{formula:bd1f7ebf-a32c-4b5e-8053-73aed6a16122}} are non-negative. This can be done efficiently using a simple iterative procedure {{cite:8715f5ada2fbbe4b8a39216119ce1f470d08f0cf}}. If the signal-to-noise ratio in our data is sufficiently large, the components we recover correspond to spatial regions with correlated temporal activity, with {{formula:7a3343e2-3207-4ccd-853c-b45a078e626c}} encoding their spatial footprints and {{formula:1617c8d4-4389-42c6-9b77-fd1f636b65f6}} encoding their relative intensities over time. However, one of the assumptions in NMF is that the spatial footprint of time-varying activity is fixed in time and does not model the possibility of motion.
| m | a520d557632a7257777e3ea9503c8fda |
Our primary focus is on fully Bayesian estimation of GGMs, which remain relatively uncommon in practice compared to classical methods. While several classical regression strategies have been employed, only recently was a Bayesian lasso regression characterized {{cite:c1bee73d8128f2869a82ce4e25f365d48d8c284b}}. Perhaps the most noteworthy Bayesian approaches makes use of the {{formula:46249adb-3136-4958-a2ea-8035664b20ef}} -Wishart distribution, which is conjugate for {{formula:05dd1455-c018-4b01-85e1-3a39f90035eb}} whose covariances are constrained to be zero {{cite:1bf79146d84c9e4a5ad20bdbac53ad46841fb10a}}, {{cite:7895a857a1b91755314a328b1f4d5b346a83dcf1}}. The earliest approaches utilized reversible jump MCMC {{cite:99c11ce3e1991cfbae488905b61dba432bd58332}}, for example in {{cite:6788e54ee68bb3f73c6db29dc37c6f2d2d6bca67}} and {{cite:483233c3e3f9a80e134397f2d08a89a3713c7dd4}}, whereas the most recent work use a birth and death MCMC algorithm {{cite:4e6c401e261f1fe9028b41c59256ab0e7d82991a}}. Both provide a familiar framework for Bayesian model selection, in that covariance selection uses an indicator function analogous to customary stochastic search algorithms for general linear models {{cite:565886b92418098701c13bc7601efe9cef188f32}}, {{cite:2f2897eda513eafc98f0319f16049e5e6e48b992}}. That is, the underling conditional independence structure can be obtained with either Bayesian model averaging or maximum a posterior probability. Alternative Bayesian approaches, on the other hand, determine non-zero relationships with credible intervals. Recently, block-wise sampling algorithms have been developed to estimate Bayesian versions of the graphical lasso {{cite:6788e54ee68bb3f73c6db29dc37c6f2d2d6bca67}}, {{cite:988a81c56fca99ee5305e851544649293409f9a1}}, in addition to an adaptive version described in {{cite:6788e54ee68bb3f73c6db29dc37c6f2d2d6bca67}}.
| i | a2fea96013c81482f85e78a07cdc4432 |
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