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A promising direction that could allow us to make progress with computing the inner product measure is rooted in the BKL conjecture, which states that as one approaches a space-like singularity, spatial derivatives become negligible {{cite:da778f700dec2a4b7e4a5aa7217ea625f38c6471}}. In the context of the Kodama state, this means that only the cubic, non-abelian part of the action will be non-vanishing. This was already confirmed in previous work where the Kodama state was evaluated in Bianchi-type spacetimes and it was shown that only the non-abelian terms in the action functional is present {{cite:81a3aef8f9612e7cc9a8224d72e64478c20f171b}}. Conversely, it was also shown that when the spacetime is homogeneous and isotropic the non-abelian in the action term vanishes. This is reminiscent of non-abelian projection proposed by t' Hooft, to exploit features of confinement of gauge theories. We expect that in BKL limit, as the spacetime enters a space-like singularity, this mix-master behavior, proposed to avoid singularities, could be described by a Chern-Simons matrix theory, which could be obtained from our proposed inner product. We will explore these connections between the Kodama state, abelian projection and the BKL conjecture in an upcoming work {{cite:5375612faf1eff238696ba84273652b13e2b28e6}}.
| d | 60df26057fd7ea4bdaeed549978814ee |
Along with the success of unsupervised pretraining applied in deep learning, others are studying unsupervised learning algorithms for generative models, such as Deep Belief Networks (DBN) and Denoised Auto-encoders (DA) {{cite:90e6789a0faa30851a2d9d3609ce82ff709cef44}}, {{cite:845504b2ee11a6b81ce998413fc49dcb4d008338}}. Many deep generative models are developed based on energy-based model or auto-encoders. Temporal autoencoding is integrated with Restrict Boltzmann Machines (RBMs) to improve generative models {{cite:4f11dbe114543e9caa1b49f65debfc0083c3f6ee}}. A training strategy inspired by recent work on optimization-based learning is proposed to train complex neural networks for imputation tasks {{cite:282bc0d4014a250a4f77d09596b4f47ade69ae18}}. A generalized Denoised Auto-encoder extends the theoretical framework and is applied to Deep Generative Stochastic Networks (DGSN) {{cite:4d09022cdd3f2c3eadc2ee94de3c2d0ab23fd740}}, {{cite:c904ccc09ab57a3255c17cc85af967bdfc9e5ed1}}.
| i | 9f993b0f993dc3510d4758c0fea8bf53 |
When a vessel containing a liquid is subjected to vertical oscillation, nonlinear standing waves form on the liquid interface, which were first reported by Michael Faraday {{cite:c32d00a1655afc2e3611f69b21f74c36e397c460}} and are called "Faraday Waves" after him. Many studies have been performed on Faraday waves, investigating their patterns {{cite:bc965d179c14b95f692ed39e162c8567752f70fa}}, {{cite:93634518d00c4d7008acc8113cdf1a9d2fae54a4}}, {{cite:017a6a867ecb0657ecb84cbbd2833da9652eb355}}, {{cite:0506c8b280feed59bb364e118ddfc4a5067dfb07}}, {{cite:9329afc9da6934105260e4087470956dc25b1a7c}}, threshold amplitude for their formation, and their wavelength {{cite:88bcfa98a1dff49e0a689efff6ce8bade26164b2}}, {{cite:93634518d00c4d7008acc8113cdf1a9d2fae54a4}}, {{cite:253dd3c2f3dbdc29ea3b4382a4f0ed70049f2a6a}}. Other studies have investigated the effect of different parameters like the viscosity {{cite:0869ab7a017baa8469d11ae9bf9df0f39ef4d0de}}, {{cite:3143d976f2cc1812f48d54e757068d43197fa36a}}, {{cite:23abd8f8b027b94bcf32972a1fcae44ae88ea531}} and surface tension {{cite:39851f2b4a140a5ccdb420dde3d07c1aada2e178}}, {{cite:40827ff39716a1f6e59231cb8af3edfe75562153}} of the liquid, the filling depth, and the shape of the container {{cite:0869ab7a017baa8469d11ae9bf9df0f39ef4d0de}}, {{cite:619c7ce66bfa0984564695ecd49e6c7830783be0}}, {{cite:f5e46afd08fd411c0edecf7416a33a7f1cf1c931}}, {{cite:c428392878053a6ae6c2481026b39a1f500ff273}}, {{cite:7388c02d3ccc3b98fca8971c0101199623f1db52}}, {{cite:644b0e08a7d7118d9a7ebb8964259e09d9724082}}.
Several theories have been developed for the formation mechanism of the Faraday waves, namely the linear theory of an ideal fluid by Benjamin and Urcell {{cite:75ddea14b9fa6aa2d0c32096239050d4e5646a81}}, the linear theory of a viscous liquid by Kumar and Tuckerman {{cite:48cd819ffacc553bc51916ff7a120803cb5a37a9}}, and the Lagrangian method of John Miles {{cite:2e962d4af747c76ac7fc2bfec6dc2e77cbccd405}}, {{cite:ef95acd3fe9758f0811409f569a7b4f9a9c4b82e}}, {{cite:aacf9c75c7c0ddfbdc49510729aa39fc33aad89d}}, {{cite:0bea680aa6c22e78e82586f0aab870afc7f09ec5}}, {{cite:405848bb438b851879bd8346ee390f5dc2626444}}. Experimental studies have been also performed on the subject {{cite:aacf9c75c7c0ddfbdc49510729aa39fc33aad89d}}, {{cite:0869ab7a017baa8469d11ae9bf9df0f39ef4d0de}}, {{cite:e3d42775d46d8794f3e4ea6f626101dfa2f03a75}}, {{cite:0e1c40f351ba8428967a5fec55ad3b8088ce5872}}, {{cite:0524ed72ccb2fdbe9d7960a9e7051f1353d2ae11}}.
| i | 9bad4622a357c707a23364fd4bcaafef |
In this work we focus on evaluating the expected information gain (EIG), a commonly used utility function in Bayesian optimal experiment design (BOED) {{cite:19f25a224d3b13f190a26cd2e3b5ce380b8aee9d}}, {{cite:6483c497464ea6db7adf3b18d7aee2edcc349947}}. We specify our model, composed of a likelihood and prior {{formula:2be72c10-7cd6-4fb2-b2e7-1972adc89f75}} for design {{formula:b2150cfc-74b4-43aa-9682-59d5d43d5ffe}} , possible experimental outcomes {{formula:cbfd5f38-b372-4e27-9f4a-fa9c704cec81}} and latent variables {{formula:39406b96-05a5-40ce-895f-9c24a7ac7c35}} . The EIG is then defined to be:
{{formula:25d28e27-ad55-4618-9629-31039fa66098}}
| i | 967446855a515fca5a94fbc6e91d7b30 |
As the average probability {{formula:42a051cb-3181-4836-8ce8-055dac272006}} of {{formula:c1709cca-9da7-4665-a3fa-b7dd7ca64a28}} and 10 shown in Fig. REF , REF and REF , we can clearly see that as {{formula:3747bc0a-754c-407d-ad37-bbadd948dd5d}} increases, the transition is becoming increasingly abrupt near the critical temperature, and the phase transition part is getting steeper. Compared with the continuous phase transition of {{formula:1fa9b4d7-ed76-4e22-a268-ec966df11a95}} in Fig. REF , it is obvious that the values of {{formula:79227f15-dbe5-4c42-b57f-f9625baa9fb1}} are distributed very discretely in the phase transition region from states {{formula:967e7e63-a180-405d-a412-2422788daea5}} to 10. In particular, for {{formula:abf32876-491f-4df8-a278-207fa89d0744}} , the probability of belonging to “0” breaks almost immediately by classification near the critical temperature. This corresponds to the theoretical phase transition properties of the {{formula:4193f3a7-8dc6-481e-b089-49f6d0afbd05}} - state Potts model: The phase transition is continuous for {{formula:5b6b7650-7054-47ad-b910-5983f6249311}}
as the second-order phase transition and discontinuous for {{formula:02a2f1a6-a556-47ec-a742-31af3abc63c4}} as the first-order phase transition {{cite:1dfa99d20edeb2b16c1c9387eb498d0e421b532d}}, {{cite:0b153c48dcbd9bb14ad49fbd773cbd448a93d465}}.
{{table:18418d1b-9532-4436-b5e2-9c95e53669a1}} | r | 14767acbc2b13843e483a8dbe42abb52 |
water,
resulting in an aggregate degree of child poverty between 0 and 7 with 0 indicating no poverty and 7 indicating severe poverty.
Due to the sensitive nature and the accompanying ethical considerations, the IMF dataset is not made publicly available and can be requested upon from the original authors of {{cite:02de90d1b4f1038811106d9c6417b1226fbdd504}}, {{cite:a88b54afa0e0ae210f5c0bd973732c7a4a63e6bd}}, {{cite:ba5f3432bdadc1e289261e025331881a3ee35d7b}}.
Since deep neural networks are prone to overfit, we split the data into 1,922,316 training, 9,709 validation and 9,709 test samples.
We run multiple simulations for the hyperparameter selection and select the best hyperparameters with the best held-out validation loss.
We strictly use only the training set samples for training and use the held-out validation set for early stopping to get the model with best validation loss.
We further validate the generalization of the best validation loss model on the held-out test set.
We use three fully-connected layers with [40, 30, 20] hidden units for the graphical conditioner and three fully-connected layers with [15, 10, 5] hidden units for the monotonic UMNN transformer.
We implement c-GNFs in Pytorch {{cite:1fd0f00aa8edc8c7c1fbca4a0fc573426f5b6959}} using GNF baseline codehttps://github.com/AWehenkel/Graphical-Normalizing-Flows and AdamW {{cite:d7d562ec203db1f36372f0fdf232d98f4af9e500}} optimizer with learning-rate={{formula:8e996143-addb-44f7-ae7d-33563297a2a3}} and a batch-size of 1024 (4GB of GPU memory) for all our experiments.
Fig. REF (a) shows the child poverty statistics sorted degree-wise for the entire Global-South observed across multiple treatment strategies for multiple simulations. The invariability of the boxplot corresponding to the strategy {{formula:7cae6815-3f52-4c4d-8451-9d156f7d4441}} (i.e., naturally observed treatment) validates the consistency assumption of the c-GNF model, as the same outcome is observed for the same observed treatments across multiple simulations. Thus, the c-GNF model satisfies consistency by construction.
More importantly, Fig. REF (b) shows the IMF program advisability statistics or the proportions of personalization across multiple treatment strategies.
Since {{formula:d09049fb-65ff-4411-afde-d63650ff1c81}} provides the finest personalization at the individual child level, we observe that IMF program is harmful (discouraged) for 7.25{{formula:86b9cbc5-55fe-41f6-a8ec-0322034a84bf}} 4.89%, beneficial (encouraged) for 61.22{{formula:942fffee-49a5-4744-864f-42a0ea58765d}} 4.08%, and neutral for the rest.
Contrast to {{formula:7be89a32-f37e-4c40-a8c8-cfdd4d877587}} , {{formula:86712e63-b825-4cac-9dc2-c62664babdfd}} provides intermediate personalization at country level, hence we observe that IMF program is harmful (discouraged) for 10.8{{formula:f9425b08-6e52-4068-b918-bc6fb1b4618e}} 7.1%, beneficial (encouraged) for 88.1{{formula:ae97c8d5-a7ed-47d7-956d-8cc928ec6029}} 6.04%, and neutral for the rest.
It should noted that the invariability of the {{formula:6bb1ca10-0133-4c99-b8db-64c85dc246e0}} and {{formula:529c607f-fa3f-4c4f-9dcb-91431f558c3d}} is due to the fact that the treatments for these strategies are fixed beforehand.
As for {{formula:c24bbfed-6398-49b7-b002-c5b958f09a5a}} , our findings also indicate the importance of considering all the seven poverty degrees in the analysis in contrast to {{cite:ba5f3432bdadc1e289261e025331881a3ee35d7b}} that considers only the indicator of child poverty, as the IMF program may help children move from severe to moderate poverty. This may get obscured if a binary indicator of poverty (poor vs non-poor) is used, leading to the erroneous conclusion that personalization is irrelevant.
The fundamental oversight from over-simplification by grouping poverty degrees 2 to 7 neglects the improvements within the group, e.g., 7 to 2 is a significant improvement for which the IMF program will be rightly encouraged in {{formula:da90fa59-025c-4126-be94-024def229fbe}} . However, {{formula:ba0d1a53-516e-42bc-8ef1-f55c96553095}} considers no change in the indicator of the poverty and hence wrongly assumes that the IMF program is neutral for resource optimization. In other words, {{formula:f020e119-8ff2-40a2-aaf3-1ab8a6e5647b}} wrongly values a change of degree from 2 to 1 more than a change of degree from 7 to 2.
This is specifically seen in the advisability plots of {{formula:f6413941-eed0-4b6b-93ea-71a6d574da96}} where, compared to {{formula:8bd10ada-519c-4787-83ac-c121778022d7}} , there is an increase in the neutral advisability over the encouragement.
This important finding of ours reinforces the need of the radical rethinking of {{cite:b2a8a29a6f40c590c07bf6436f3bf1117779a5da}}'s Nobel Prize winning work stated previously in Section that suggests one should not resort to over-simplification of the poor into cartoon characters by ignoring their individual characteristics in all their rich complexities and relative improvements in their living conditions.
Fig. REF (c) shows the variation of the average degree of child poverty for all the treatment strategies obtained from averaging Fig. REF (a).
From Fig. REF (c), the treatment strategies can be sorted in the decreasing order of their expected degree of child poverty {{formula:09b3cbd7-9260-49f4-b9a5-b461b3f7e186}} : {{formula:e57e71b3-d68c-472d-b7ee-b7a7cc5ba252}} . This indicates that the IMF program is beneficial for the Global-South ({{formula:81dccd00-2997-46dd-9973-aacbf58c40a9}} ).
Fig. REF (c) shows that the personalization at the country level due to the treatment strategy {{formula:f26485fa-69d1-43dd-8d8b-2a148ae2d26f}} (purple) represents a significant reduction in child poverty over the `one-size-fits-all' treatment strategy {{formula:f418cb89-d5b9-4f75-a199-9a161cf91312}} (blue) and the sub-optimal naturally observed treatment strategy {{formula:c2cc45b1-c743-4e07-9dc6-07a8ca816b16}} (orange).
Moreover, personalization at the individual child level is even more beneficial ({{formula:272096a0-2b3c-4cf9-9960-4810014d6216}} ).
Fig. REF (d) reconfirms the beneficial nature of the IMF program across multiple simulations as the average degree of the child poverty is observed to be reduced by {{formula:829eed74-b532-458d-a1ea-632cdac7355f}} degree.
Similarly, Fig. REF shows that most countries experience a reduction in the average degree of child poverty from the IMF program, and hence the program has beneficial effects on the Global-South as a whole.
Figs. REF in Appendix provides a qualitative visual analysis of the country-wise average degree of child poverty in the form of the six potential (interventional) worlds under each of the six treatment strategies from one of the 5 simulations. From these results, we see that it is indeed possible to perform P{{formula:51b98ad1-e2f2-4a88-8cd3-58182d585e81}} A, under the assumptions in Section , to effectively combat social ills in contrast to the `one-size-fits-all' approaches.
On interpretability and explanability of the c-GNF
Since the c-GNF is able to provide the encapsulated-SCM, this enables to go beyond total causal effect estimation and into the mediation analysis dealing with natural/controlled direct/indirect effects {{cite:2e8832e282982a1873f2eabc691ae8f6fcd54d37}}. The probabilistic nature of the c-GNF further enables one to analyse important causal quantities such as probabilities of causation {{cite:7f5bf8389a604b657724ca0ec41569d0dde3881d}} to dive deep into the causal aspects of the social system under study and enable policymakers with personalized policies. Finally, the c-GNF/encapsulated-SCM is able to successfully navigate across all the three rungs of the `Ladder of Causation' {{cite:487b8050f070ef06a12cc4c0c642067050a768d8}}, i.e., (i) association, (ii) intervention, and (iii) counterfactuals, to be able to answer every causal and counterfactual questions using `The First Law of Causal Inference' {{cite:2e8832e282982a1873f2eabc691ae8f6fcd54d37}}, {{cite:487b8050f070ef06a12cc4c0c642067050a768d8}}. Of all the 16 macroeconomic variables that cause child poverty, we observed that political will is the most impactful as it defines the way of the nation and hence impacts in a macroeconomic shock that trickles down to the individual child level, via microeconomic family-level factors. Observing the c-DAG in Fig. REF of Appendix , it is evident that the political will of a country determines other macroeconomic factors such as public spending, polity, governance, and also trickles down to individual child status via intermediate microeconomic factors. For example, consider Pakistan or Iraq where a negative political will is observed and hence the IMF programs are seen to be harmful (recall Fig. REF ) due to the tendency of the monetary funds being misused for state-sponsored terrorism instead of the primary objective of economic stability. In contrast, countries such as India and Bangladesh, where positive political will is observed, are seen to be benefiting the most from the IMF program both economy and child poverty-wise. Similarly, for instance, the most number of current CEOs of tech-giants such as Google, Microsoft, Adobe, IBM, Twitter can loosely be attributed to the positive effects of positive political will in India.
It was also observed that the macroeconomic shocks on child poverty can be isolated if the microeconomic factors at the family-level such as family wealth, family head education, number of children/adults in the family are well conditioned. This strengthens the belief of personalizing the treatments/policies to effectively combat/isolate the macro-level shocks trickling down to individual family or child. In summary, our major observations are two-folds: (i) political will is an important macroeconomic factor that defines both macro- and micro- socio-economic status of a nation, (ii) the IMF program coupled with a positive political will is seen to be beneficial for the child poverty status of the country.
Conclusion
In this article, we deployed causal-Graphical Normalizing Flows (c-GNFs) to draw insights from the real-world observational data on the impact of the IMF program on child poverty.
Our findings in terms of ACE indicated the IMF program to be beneficial for the Global-South, in expectation.
Apart from considering the traditional `one-size-fits-all' treatment, we also proposed an empirical framework to formulate different personalized treatment strategies at different population granularity levels by computing ACE, country-wise CACE, and child-wise ICE.
Our findings reinforced the radical thinking proposed by {{cite:b2a8a29a6f40c590c07bf6436f3bf1117779a5da}} to address the problem of child poverty without over-simplification of the poor into cartoon characters.
Even though we demonstrated the personalized treatment strategy formulation framework in a social science setting, our framework can be extended to the field of personalized medicine as well.
The transparent nature of the c-GNF that is able to provide the encapsulated-SCM enables one to successfully navigate across all the three rungs of the ladder of causation to provide an end-to-end causal inference tool.
IMF dataset country-wise observational samples
{{figure:80a03afb-e9ed-4171-ac69-1f7697a5d244}}
Summary of the six treatment strategies
{{table:8cc1669c-9311-453b-87ff-51e37f0ed9da}}
Hypothesized causal-DAG for the current social system under study
{{figure:0ada5781-83b7-4549-8e2f-7ce09621f4ee}}
Counterfactual worldmaps for different treatment strategies
{{figure:a19a5687-e3bb-4151-9e56-ec53e00c5542}}
Algorithm for Gaussian dequantization
[htb!]
Gaussian Dequantization
Input: Discrete variables {{formula:10b3d29e-bf49-4e56-8bee-8b6adc24e6d6}}
Generate {{formula:d14e3de9-0b2d-44d1-a8e9-07d390444606}} .
Output: Dequantized / continuous variables {{formula:d9e7fcbe-eae9-4a7c-8b04-b435e312f461}}
[htb!]
Gaussian Quantization
Input: Continuous variables {{formula:2c53bbdf-44af-42a9-8646-cb862935bead}}
Generate {{formula:8df10b80-9d1d-443c-a48d-74fa04ef073b}}Output: Quantized / discrete variables {{formula:4e0bdeb8-2353-4d4f-b6a4-de316c050c0f}}
| r | e7e46713256c769d29f06575e0d31aa6 |
A wide range of important work actually trust SentEval {{cite:c277b4da6d500760f81885eaee94e0732dfb7dd8}}, {{cite:bd9b917a2245d4300e262f56809fbef4a72df821}}, {{cite:f82caca027112bc8cbf15a85afd1431c55c27f18}}, {{cite:f4ede6475a6dc6a815b1bbc3ae7ed04974e9d418}} or GLUE {{cite:6c41f38aa1aaee6ef91316464da69e9766a75eb0}} in order to back up the claim that encoders produce universal representations.
| i | 92c09138c2e6664737a59d26948db700 |
The exponent {{formula:4c43b32d-668f-43dc-90de-7f22ea81ab9d}} = 0.6 is close to 1/{{formula:056ae0b8-1e4e-4c06-9563-90f1698305ad}} for the non-degenerate Fermi gas with {{formula:04943348-83de-4d8b-8ac1-9ffa5381adb5}} {{cite:9e95cba56c223465a2f200211fc0c206a753cd0a}}, {{cite:914ad666f435caed49bde884bce62f87e545d514}}.
Theoretically, the degenerate Fermi gas at {{formula:de297996-2ee3-478f-a96f-38cc812f9cb3}} (the Fermi temperature) yields the Korringa law, while the non-degenerate Fermi gas at {{formula:a42eee0b-c303-4d6f-97a8-b02f48956a26}} yields 1/{{formula:7417ac19-c43a-42e1-a12c-3e823cd0e484}} according to the electron density of states {{formula:9bc21cd3-a1b9-49b3-b64e-e9e49b5f9928}} {{cite:9e95cba56c223465a2f200211fc0c206a753cd0a}}, {{cite:914ad666f435caed49bde884bce62f87e545d514}}.
However, no report of 1/{{formula:f79e9ede-f234-4252-8154-9bd3120635b1}} has been found on actual semiconductors.
For doped Si:P semiconductors, 1/{{formula:e32eba84-d57f-495d-bd96-97ac5a3ac47c}} was reported {{cite:961bcc5136fb2006526aec7f10abb889d37bec93}}.
| d | dd264213ea240087ce17c223be9d9272 |
Multimodal methods. We evaluate two varieties of multimodal models: i) unimodal pretrained and ii) multimodal pretrained. In the unimodal pretrained category we explore MMBT {{cite:e8432eaddbf63656eebcc6abadbdd7f9f1104aae}}, MoViE+MCAN {{cite:4e3f090a27f5ef2b26edcaae217f3154ee82e158}} and UniT {{cite:30ced543abd79a1988efca68ad21a2284fff597b}}. These models are initialized from unimodal pretrained weights: BERT pretraining for MMBT; Imagenet + Visual Genome {{cite:a1917fc8bf4541227a8d5eb9becaa74cf06e214b}} detection pretraining for MoViE+MCAN; and Imagenet + COCO {{cite:208f2fc305663779bd8f690b6e81d6b190d7c052}} detection pretraining for the image encoder part and BERT pretraining for the text encoder part in UniT. In the multimodal pretrained category, we explore VisualBERT {{cite:3257f848b8aa8abd31b461ab20695f10661a4e41}}, VilBERT {{cite:194e8ff878370d9334ef54a30ca4dfe6f4654d44}}, {{cite:44f8491b8ef20cdf997d35507d8818c55dee5216}}, VilT {{cite:6a43eaa6ef1f49b65819dbb5b9dceae057547944}}, UNITER{{cite:4ea47d8ff9ce80347080dad00346dce2178590f7}} and VILLA {{cite:6d22a199a1da2cf03413e0b01d26dde19c5380ec}}. These models are first initialized from pretrained unimodal models and then pretrained on different multimodal datasets on proxy self-supervised/semi-supervised tasks before finetuning on VQA. VisualBERT is pretrained on COCO Captions {{cite:2dfcff11aefc6e1856f84f5d8309ef0eeaaef505}}; VilBERT is pretrained on Conceptual Captions {{cite:d9db5b8649544dfd364f78a1b2817e4eb5e54194}}; ViLT, UNITER and VILLA models are pretrained on COCO Captions {{cite:2dfcff11aefc6e1856f84f5d8309ef0eeaaef505}} + Visual Genome {{cite:a1917fc8bf4541227a8d5eb9becaa74cf06e214b}} + Conceptual Captions {{cite:d9db5b8649544dfd364f78a1b2817e4eb5e54194}} + SBU Captions {{cite:e7005d6c49fd0c73f7116d36ccacaceca92600db}} datasets.
| m | a95a3454b07cea543aa4b0a0b1d203f8 |
Semantic label to face generation. The quantitative results for semantic face generation on the FFHQ and CelebA datasets can be found in Tables REF and REF , respectively.
As the choice of comparison methods, we use the current state-of-the-art method for semantic face generation TediGAN {{cite:c5c85813ed1a15ee76eff6076343c4ba7d11197e}} and several recently introduced semantic to face generation methods {{cite:0e4005493994bcde6773140bcfb5f809287be515}}, {{cite:9a855463f5f687dfa6c54b55056c3b57ea6cb9c2}}, {{cite:7b2648c3bceb2bf22db16684cc80b8f8ae67d643}}, {{cite:515ab205ec1935450b76ac2ed73f326087394d8f}}.
The fine-tuning-based multimodal generation and the combined unpaired
training-based results are shown separately. TediGAN {{cite:c5c85813ed1a15ee76eff6076343c4ba7d11197e}} has been trained with paired data across all modalities since it supports such a provision. From Tables REF , and REF we can see that all the methods fail to produce reasonable results when trained in the finetuning-based strategies. This can be seen in the high FID scores, low SSIM, and parsed mask accuracy metrics. The alternating training strategy produces reasonably good results, and improve all the evaluation metrics improve. But training this way introduces dataset-specific bias because of which the quality of the existing semantic-to-face generation techniques deteriorates when used on an independent test set during testing.
{{figure:2ad41650-2753-4604-a915-d2791d39dca3}}{{table:74fb5bf7-688b-4e76-a69f-676b1af151a4}} | d | 380eba1f635a3ec39a68c76d9f713bc0 |
Finally, we return to the question of whether rotating the applied field away from the {{formula:f953aca5-77df-4713-8198-cf752d43456f}} axis will break the VL domain degeneracy within the L phase.
Such an effect was previously observed in TmNi{{formula:8149724b-8b21-4597-928a-265c1b598802}} B{{formula:514323dc-a462-492d-a5e0-b4a98860c377}} C where the VL undergoes a triangular to square transition with a degenerate intermediate rhombic phase,{{cite:566d4498fdb8c18de3c21c49a640c35f3354b83a}} and where rotating the field away from the {{formula:2087b333-ece3-4f34-87c3-b1a1e7ac0636}} axis by {{formula:56180f6a-f8c5-40b8-ab06-7a496c567aa2}} is sufficient to suppress one of the two rhombic domains.{{cite:b9419422843923ce9733dbb0dca50f5b0f3216ab}}
In an ideal uniaxial superconductor with an isotropic basal plane, London theory predicts that the two-fold anisotropy introduced by field rotation will favor a VL orientation with Bragg peaks on the minor axis of the ellipse in reciprocal space.{{cite:b9c49c28803fe3ec2ceb0b2a7811a053d74752ff}}
However, any real material will exhibit some basal plane anisotropy which may compete with the uniaxial effect, and the relative strength of the two will determine the VL orientation.
As an example, one can consider NbSe{{formula:27a7a2c4-eecb-4471-aa4e-8a4b08bbcdd5}} , where the triangular VL is oriented in a manner corresponding to the maximal energy according to the London theory.{{cite:4f1717f0b7b9628356cacac43775aef80d8a8cf6}}
| d | f8d2d9dae7efe88981c1e50ef7229013 |
The policy is trained with a Huber loss ({{formula:5c0fa57c-d9e1-4b01-a7d5-3a1feccf2509}} ), that in practice is usually just an MSE loss, since predictions almost always lie within {{formula:a6dceb0d-223d-4711-8684-e4b87de8d6a1}} . A deterministic policy trained with mean-squared error can be viewed as max likelihood with a unimodal Gaussian policy, with learned mean {{formula:b97778c2-b71d-4749-9df3-53cb5e03614c}} and fixed {{formula:ec48f606-5812-47fa-b767-b92c0db26b06}} . We tried a stochastic policy, with a learned {{formula:df64c92c-2226-41ef-9900-671869f91925}} based on the current state, but found it did not help and seemed to make training less stable.
Similarly, a mixture density network (mixture of 10 Gaussians) did not improve performance.
Using a larger model architecture than ResNet-18 (ResNet-34 and larger) also did not improve performance.
To address the small action problem identified in Section REF , we tried decomposing XYZ prediction into direction and magnitude. The hypothesis was that by making it easier for the model to predict small actions, it would prevent the model from predicting small actions at every state. This did not outperform predicting XYZ directly, and eventually led to the adaptive algorithm used in the final results.
We initially used a spatial softmax layer in our policy and video encoder. Visualizing those spatial softmax layers made it easier to interpret policy predictions, but performance increased when the spatial softmaxes were removed.
Conditioning the policy on proprioceptive information, as well as previous robot poses, did not improve performance. It is possible this was due to causal confusion between that information and the expert actions {{cite:82ad38496746fb352d1344b71fcdc94ce09af036}}.
Using more video frames (40 instead of 20) did not improve performance of the video encoder, and slowed down training.
We experimented with including human videos that did not correspond to any of the robot tasks, using them as negative examples for a contrastive loss, to encourage the task embeddings to be more continuous. We found this did not help, and the negative examples were too easy to embed far away from all other videos.
Pre-training the ResNet on the ILSVRC2012 object classification dataset did not improve performance.
We obtained better results on manipulation tasks by representing angles as delta axis-angle, rather than absolute axis-angle, absolute quaternions, or delta quaternions.
At each state, the policy predicts a 10 action long open-loop trajectory, then only executes the first action. Stopping the gradient from the 2nd to 10th predicted actions of the open-loop trajectory was inconclusive but generally did not help.
Applying mixup regularization {{cite:cd6b3e9df3e260bc45bd41fdc4a941b5a237a5ad}} to the images and robot poses did not help. We suspected it played poorly with the continuous outputs, and might work better if actions were discretized.
Predicting gripper residuals instead of the absolute open/close angle.
We found that while validation error on predicting future poses was correlated with task success, different models with similar validation errors could have wildly varying levels of task success. This made selecting the right checkpoint for evaluation challenging; it is quite possible that performance numbers would be higher with additional evaluation budget for specific checkpoints. This is likely because validation accuracy is most critical on specific states (especially near contact), while there is more tolerance for error on other states.
| r | 52e1c9920a57dc17ece51b0052ae62c1 |
The mean average precision (mAP) results comparing with state-of-the-art methods are shown in Table REF . The CNNH {{cite:dec23ffe2d8651ace04f4b511ee02c5d10503af1}}, DNNH {{cite:97d96dc337f2fb92ccbb07bd1ce7efa89bcd8a04}}, DHN {{cite:3903a399de76c85f164bc7bbfbdb4d13770aaac1}}, HashNet {{cite:369551173cc8ce173f976ed49127913a399ec6a7}}, CSQ {{cite:e47901ff8bc92b71a0d93d2ca2c2fac95dbd105f}} and our proposed CSCE-Net are based on ResNet50 backbone; TransHash {{cite:471d08ffc3434999052665409cd77017736434e2}}, CIBHash {{cite:4da2bf8dcd14e3c38696def38529af5db39871bb}} use the Vision Transformer (ViT) as backbone.
From Table REF , it can be observed that our proposed CSCE-Net substantially outperforms all ResNet50 based comparison methods even better than transformer-based TransHash by up 8.4% on ImageNet(16bits) and 14.4% on NUS-WIDE(64bit).
Specifically, compared with the state-of-the-art ResNet50 based methods CSQ, our CSCE-Net achieves average absolute boosts of 1.5% in mAP for different bits on three benchmarks except for NUS-WIDE(16bit).
Especially, the performance boost on ImageNet100 dataset is much larger than that on others, which is very impressive. Note that ImageNet100 has the most categories with variations among three datasets. Therefore, our CSCE-Net has the strong capacity for extracting critical local detailed information guided by semantic global context.
| m | 3d9d9cf06cf4f6c1e7e2be28544dc2d5 |
(i) Root Count: Consider the example system (taken from {{cite:c6866f42917230a7560cabb0c61293c80d46cc85}}) with two unknown variables {{formula:591fca45-55e5-49f1-8cc9-1c55e18d5ed7}} and with 4 solutions.
{{formula:81e7ab21-affe-4f3e-8ebe-8cf25b6d90c5}}
| m | f90b4eb992378395c3bcbb923e4a99f0 |
Nonetheless, there are several directions towards which our results may be improved which we aim at investigating in the future. First, future work will be devoted to adding explicit dynamic reasoning withing the neural network, for example by introducing recurrent layers {{cite:e28546d4101bb570cde5e3045f5490cc031524e7}}. This should help boost the capability of the neural network of discerning between exposed and infected, and between infected and recovered (or dead). Indeed, these transitions are essentially time dependent and can be extracted from associating an internal dynamics to the initial recognition that a node entered in the exposed state.
Yet, it is worth mentioning that stacking LSTMs layers in between the GNNs did not produce a statistically relevant increasing of the network performance and as such has not been included in the present work. Similarly the use of attention mechanisms {{cite:e6e2e0a0ca76434efcd4dd7098129ce093176309}} have been tested but not included due to the negligible increment of performance that they resulted into.
Finally, we believe that a very important assumption to be relaxed is the full knowledge of the social network (see Sec. REF ). Several algorithms are being proposed that can extract the social structure from GPS localization and other mobility information provided by contact tracing apps {{cite:d0a26513eed10ab80fcd74b89bb9becbebc73f8a}}, {{cite:25809026b034ed82988fb444dc33546b65210f94}}.
Data driven methods can then possibly be used to infer the graph topology itself {{cite:c9dc74288a40d2465c55e47034aedcea8d500c44}}, {{cite:56a10918a94462e60ce72b805120cd60c952f53d}}.
| d | 05a22863b015ebfe96d56535c98d0c64 |
Differential rotation on tides should also be taken into account, as it
affects propagation of gravito-inertial waves, leading to a large variety of resonant cavities as well as chaotic zones {{cite:fe33520fff5f005a93664c8fd4df80a41f0f96cf}}, {{cite:c7093aba620cb4822bdd6a672627904a38853dd3}}. It also allows the deposit of angular momentum in critical layers and therefore interactions between waves and mean flows {{cite:c51cb84d93e0ba556d6e72f1ee838c0405deb700}}, {{cite:cedbd2acb6be1362d074594df1c06a5121381264}}, {{cite:0737f070e5608dbe9d6a1617e54a873912a14f20}}. A strong differential rotation may set up during the PMS due to stellar contraction {{cite:2b245c80ccacf7c65bcbfd1ebbc032215ddd9f69}}, {{cite:aea3c67fe516089256b8d143410560461ba52cd8}}, {{cite:54c94df079655e43ac9221de7ba15e08d60df900}}, when the tidal dissipation through gravity waves is maximal. Such an effect can therefore have a significant influence on the evolution of binary and planetary systems. The presence of a magnetic field may also affect tidal dissipation, modifying the propagation and the damping of tidal gravity waves {{cite:50e94abc18d3ae4d2b6ef23a4d9066f17a2502ce}}, {{cite:46798c461e0defe2eedb1700cbfe7784d797560a}}.
| d | f0dde0b5f504226170b4d821bf131d86 |
In Fig. REF the mean and standard deviation of the {{formula:7aee4d84-45ce-4eb6-a611-1bf979f79129}} spectra are compared for pp, p==Pb and Pb==Pb collisions at the same centre-of-mass energy per nucleon pair of {{formula:14a2ff9d-2f3e-401d-a06d-4ec7344230ab}} .
All three collision systems have similar values at {{formula:8d45b7ce-86c4-4346-a364-e590c8ec1b74}} and then coincide until Pb==Pb deviates at {{formula:3fe1e1a3-4108-4930-92f3-ca76466b67e9}} and p==Pb deviates at {{formula:7c395493-cf3f-4927-aaa9-8bc57b9561e4}} from the trend observed in pp.
This observation is consistent with an earlier comparison of the {{formula:a17f7ef5-b8de-4bc4-8bc6-cf9ba6b7b591}} –{{formula:6c1ff5a6-fc1b-4111-875a-4a716fc7bd71}} correlation for the three systems at different centre-of-mass energies {{cite:f9abb906a7279ddd5b6402c07f38d7596e5c09bf}}.
Figure REF shows the mean (left) and standard deviation (right) of the transverse momentum spectra as a function of the charged-particle multiplicity {{formula:2f2206cc-fe45-42c4-933d-4f42f1b7622b}} for pp (top), p==Pb (middle), and AA (bottom) collisions at different centre-of-mass energies per nucleon pair.
For all collision systems, a clear ordering of {{formula:3b4fd57c-2f40-4ae0-bb2b-808084da8d30}} as well as {{formula:b752ad7e-981f-481f-b389-dfac48837eb4}} with collision energy is observed, which can be attributed to the larger momentum transfers involved at higher {{formula:c42e06c6-78e6-4121-a0aa-25e70f49bd29}} .
For pp collisions at all centre-of-mass energies, the average transverse momentum increases monotonically with an almost linear trend up to {{formula:cce66751-0e17-4373-859c-632b7edc1c93}} {{formula:8d314c58-25f2-4d60-8217-d6731a60df64}} and beyond that continues with an again almost linear dependence on {{formula:88e7fcfd-f1e0-49b8-a2e0-359f959ea7b4}} but reduced slope.
In p==Pb collisions, a similar multiplicity dependence is observed up to {{formula:fe1c4bf9-bd81-48e6-bc5e-b3bac389756d}} .
At higher multiplicities, the increase in {{formula:e23ce805-4b78-4b1b-9a18-7a4c3f8a6aac}} is slower than in pp collisions.
In both pp and p==Pb, {{formula:f78cfd69-5970-4142-b1a1-49bd4e82bbb9}} follows a similar trend as {{formula:364e1ac7-e6c2-4a2d-8064-aec3a6cd7d1c}} .
On the other hand, for AA collisions one observes an increase of {{formula:a3f34641-6cc4-40fc-ab44-136c1ebd282b}} with multiplicity up to about one third of the measured range, followed by a constant trend for the rest of the {{formula:43c1501b-ac81-4681-baaa-6d35aa857cbd}} range.
The {{formula:9e489c70-a1c7-4085-ad98-ca0aa123b4b3}} increases for {{formula:76ad66f5-a57f-411f-85e5-85b24506e094}} to a maximum and decreases afterwards.
This is unique to large collision systems and is presumably a consequence of flow and jet quenching {{cite:2fb32fbd0c1abd6910e97300f7edde74511c6bb6}}.
The high {{formula:16e44b36-6547-4958-82d0-54c62b384991}} resolution of this measurement makes it possible to spot differences between the spectral evolution with multiplicity in Xe==Xe and Pb==Pb collisions at {{formula:94337780-83e6-4bb7-b5b8-db4589900e56}} and {{formula:cd370d2b-2abd-46d9-93e9-b4bd4a5dbfb7}} , respectively.
The observed difference in the trends might be a result of the slightly deformed Xe nuclei {{cite:79e6c5ff6dac64a70d82d083024cc00f4f1c429d}}.
In Fig. REF both the mean (left) and standard deviation (right) of the {{formula:ab21c924-eef8-46ab-8171-8a72652294b0}} spectra as a function of {{formula:3677671b-4390-4051-8282-b9c158c72cfd}} are summarised for all data sets (top panels) and then shown as a function of relative multiplicity {{formula:e212d236-230a-42ce-a0cf-8a8cb5b9b6ea}} (middle panels) as well as divided by their respective multiplicity-integrated values (bottom panels).
In the latter scaling, the overall energy dependent increase of average kinematic energy and number of produced particles are accounted for.
As a result, the values for each collision system align almost perfectly for the {{formula:f77a74f2-3687-4f96-a7d0-00b3ed1066ab}} .
For {{formula:6776c832-f42d-4069-9b3f-a9af37150181}} , for a given system the scaled value increases slightly with centre-of-mass energy.
This small remaining ordering may be due to the larger available phase space at higher centre-of-mass energies.
{{figure:e6828292-f017-47ee-9c8f-369f0b9b7cc2}}{{figure:1366c2d8-ceec-4b92-925a-e8059aafdce4}}{{figure:fe7bdcae-a9d0-44eb-8209-005da593c684}} | r | fb4922a3b15b1b86203186416b9ace5c |
The inception of deep neural networks has revolutionized the landscape of medical image segmentation {{cite:527f6cdbce3e32f393c5005c8f6a4fe58ef682d0}}, {{cite:d66c24202c59ad47130ef335a6f8ac909badb028}}, {{cite:59b4b56ed873d7a1e9053c28136b99892db10626}}. Despite their tremendous success, however, depriving them of sufficient quantities of labeled images limits their effectiveness. Unfortunately, obtaining abundant amounts of expert-level-accurate, pixel-wise annotated data in the medical imaging domain incurs significant time and expense {{cite:6e26ea86e4a2330e5a19b557da256db5447dee3f}}. Therefore, it is imperative to explore new medical image segmentation techniques that can learn from scarcely annotated data.
| i | 493a3407e5b2f3b559667721d81b772a |
+ Cutout {{cite:2d3adb4be9993263cd366c1e24bdd5918ac98efc}} - - - {{formula:1dab5b94-5507-4b01-b366-869c51762ff1}}
| r | fcafdbdea5fd071fa8866034c7307093 |
There is widespread agreement that there are limitations to network generalization {{cite:90ab722e02caf2e33ea1ced8cc54a59da7f1c282}}. There is also consensus that modern artificial networks do not generalize as well or in the same way as humans {{cite:a841b3e0ed6bcd5a588253bd1567d1375f2666fb}}. There are conflicting views as to whether generalization is specifically poor between simulations of camera images and camera images {{cite:374762c41bd313e7de75f705532b963e00567c5f}}, {{cite:fb52802dc427b4c5799206097045763f3fe8464d}}, {{cite:ff8824fc18e24983af97902f1ec85d9a009329af}}, {{cite:89593fc5c44b2d10fea495a7617f991b6395270e}}, {{cite:1505b68c6b7ad18bcbd349bf6c065d6ed7f882c1}}, {{cite:e8a996350d2eb526ecaafad820e40b5f0c066342}}.
| d | 9c307376850716940b2d0891c79aaba3 |
Neural-network image classifiers are well-known to be susceptible to adversarial examples—images that are perturbed in a way that is largely imperceptable to humans but that cause the neural network to make misclassifications. Much research has gone into methods for constructing adverarial examples in order to understand the nature of neural-network vulnerabilities and to develop methods to make neural-network classifiers more robust to attacks {{cite:2761039f3a8bcfe6461685e03a5e9f832e83b7b8}}, {{cite:14a6e86126391c77580e1af4d284949b2bd321a1}}, {{cite:81cba9bfc72275ab22f32b185c2c3429d92a1acb}}, {{cite:f145b4cc76bbcebd6db43ee7518e0d0f819c8e74}}, {{cite:a90109e0eb89c59a23072d59c37f0870b124a46c}}, {{cite:63fdab508d58868febb4081042b0d95475130069}}, {{cite:c57421f5ce11b8ee497187829f80b9d179b70799}}.
| i | 3628f60e20c62384c3d17ba2107141f6 |
The strong interaction in a fully heavy multiquark state is not clear at present. The Chromomagnetic Interaction (CMI) model provides us a simply picture to quantitatively understand the spectrum of multiquark states. In the framework of CMI model {{cite:7f24989299b7a49302980c76bc6e2d336886e467}}, the strong interaction between quarks via gluon-exchange force is parameterized into effective quark masses and quark coupling parameters. Despite its simple Hamiltonian, this model can catch the basic features of hadron spectra, since the mass splittings between hadrons reflect the basic symmetries of their inner structures {{cite:c0190e21eefa7a0624dd11b1f68b21cb4f4fcb1a}}. This model has been widely adopted to study the mass spectra of multiquark systems {{cite:bd108f85818a4c018f69eb2d251a3e3722c26f8f}}, {{cite:d2dd3c2a25feebe477eb52d4d5b93a7d009afcac}}, {{cite:bebb5c8d1c71349d67a80541586047b05903a997}}, {{cite:8f94a0a96dd7306bb131f133dde0c0b35059c46c}}, {{cite:eb76952f231ffd956b198492f5cfd1d657ed1c16}}, {{cite:d6a5853955195381dc8894bc196abc9b2d8cb698}}, {{cite:a5ec78978755ef7d91ca4dae2a3b1d46cae972e1}}, {{cite:a348334ce9cd3c6ab5042480155ea878fd851124}}, {{cite:7e9c856651499aaacf9a46290bc5cfdbb21682e3}}, {{cite:0f6ee9763a5cd7124eb6fd75fd476eb03521c24e}}, {{cite:dce023ec1ae1a3d87eb6430542af09c3d6d2dc39}}, {{cite:bbb29d3794fd5bd16f5061e78fffc457fc3ab740}}, {{cite:fc02004656d7a8df46ea80a993bf75df4cb16f8c}}, {{cite:a885b561104eae0ed300cba0c46d8e6fdb9d9dcf}}, {{cite:24c6877172feed58a02628b185f4b911cf7d53af}}, {{cite:99b2424d4e6f9927b9417bb7201528561b743bbf}}, {{cite:46dc8c3a7fc7c3a4d75e05c4569159994eff4a31}}, {{cite:8f7bd1b7ac352fd32f282cf77d20ad967bd0d8e8}}, {{cite:56e7386938a0133e0302e072059ed21c90187f7d}}, {{cite:8f94a0a96dd7306bb131f133dde0c0b35059c46c}}, {{cite:d6a5853955195381dc8894bc196abc9b2d8cb698}}, {{cite:a5ec78978755ef7d91ca4dae2a3b1d46cae972e1}}, {{cite:7e9c856651499aaacf9a46290bc5cfdbb21682e3}}.
In this work, we systematically study the S-wave {{formula:6eb72354-2be2-4730-ad4a-86efba9878b6}} pentaquark system within the framework of CMI model to calculate the mass spectra, the relative partial decay widths and find possible stable pentaquark state.
| i | 9837ff53f018c0f2a8a6bfdeb25c984f |
Note that our problem formulation is same as that of existing works
with the distinction that we replace the requirement of a large-scale
corpus by the availability of pre-trained word embeddings. This makes
our setting more appealing and flexible, as pre-trained embeddings
are widely available (e.g., word2vec, Glove, and ELMo), and they have
arguably high coverage and quality due to the
gigantic training corpus. In addition, they are available
for many languages {{cite:21898e1bf1c512644960579b5a1f904679dd6895}}, and are easily adaptable
as one can customize the pre-trained embeddings by further training
with domain-specific corpus {{cite:8f4ed1e15ad7cd3d68511b8991df1a616ac34a60}}, {{cite:a214a7686c3c74e99dc7317c9bb22d0c84508af4}}, {{cite:818f7ad8b96b47c5e88a92309974544c90690617}}. We summarize the major contributions of this paper as follows:
| i | 383aa54556ded0d3a71d0cfc59b5bb54 |
We compare our method with DENet {{cite:0ac20a8d8c59848da79c2a710fb07e893e0becdc}}, CAPL {{cite:d02424dba819075252059625b5795ba848f01ec2}}, PFENet {{cite:1e0107c7bbf058c7521836a384e75a054464aa7e}} and ACASTLE {{cite:ccb7fcc643f1684a3b9f3d31554e000962db7142}}.
DENet and CAPL are two state-of-the-art GFSS methods. PFENet is a state-of-the-art FSS model which is naturally extendable to GFSS.
ACASTLE is a state-of-the-art generalized few-shot recognition model, which can also be re-purposed for GFSS.
All results are produced based on their officially released codes except CAPL {{cite:d02424dba819075252059625b5795ba848f01ec2}} that does not release code (citing results from their paper).
In addition, a baseline using normalized score fusion only is also compared.
| m | 44a0b240aabe97f0b2424aabe377c987 |
Previous research on supporting user goals on the web has primarily sought to understand and categorize a person's intent manifested through search queries.
In their seminal studies, {{cite:a14f08f2ae02c2c0af277ae2eb2871afc5de6efc}} and {{cite:5576e6849bb27ae5be46fa91beceaa3506c53c55}} classified the goal of a user query into one of three categories: navigational, informational, and transactional.
Successive work refined intent categorization by introducing purchase, sell or job search intents {{cite:1ac09b455569230ff65ab7228a511590b969ee5e}}, {{cite:55d0db8552668a1ffd4bf05888e3b0a7e0b5a5bd}}, as well as examined the variability of intents across different users {{cite:d94a527dc9fc4039c0c38969a4099addb65953c8}}.
The main objective of research in this field is often to inform and improve the search process {{cite:a14f08f2ae02c2c0af277ae2eb2871afc5de6efc}}, {{cite:aa5dec9c2ea83047a60d881cda041bd9a5b8bee0}}, {{cite:5576e6849bb27ae5be46fa91beceaa3506c53c55}}, {{cite:6e0b11a03e117eb25753f344bb5a8c2f59f7cecd}}, and the characteristics of user goals tend to be task-oriented or situation-specific.
In contrast to that, we emphasize incorporating the fundamental human goals into the context of web browsing, since they are recognized to be key to the core values in people's lives {{cite:90a644de47b1591a9bd94c18b03bd5a21f644ed2}} (e.g. health, well-being, sustainability, and learning).
| i | 79470c87d446d4403aad37f8e8645932 |
We used a rather general approach to analytical
evaluation of the 2-point and 4-point zig-zag diagrams.
This approach leads to a fairly simple
proof of the Broadhurst-Kreimer conjecture
that is different from the proof of {{cite:a9d48067d1f4e0c43f73c221e59a0285e042a99e}}. Here
we make use the operator formalism {{cite:54e44caa936c165a611fc779579690dfddb9aefc}}, {{cite:9f596ef6cca4ff95525ee9dd432119d1ed7173fd}} and
methods of {{cite:6d18aa65ce81da3099c6f56e7aba5e20d03a5784}} based on the Euclidean multi-dimensional
conformal quantum field theories
(see {{cite:3c03fdf2997bcc71cbf91e06d7f9b9fb1f9bc4c8}},{{cite:c06123614257a88c5b80fa59bf2b0cfe880715d9}}, {{cite:e94e514849c0f7c19a4dd4f688749920de5aa857}}, {{cite:f0a333dae93d9afb2019b7f159e60928fe9e4743}},
{{cite:2740b12f9749237ad7d1160180568f09ff4a3af6}}, and references therein).
| i | 1ae80d28b9faa87b433fde062758c301 |
The symmetric Lanczos {{cite:8754e9dd06eb0682a56f4455b4b7995b98b05c2b}} and the GK algorithms are closely related: indeed,
multiplying the first expression in (REF ) from the left by {{formula:40d5dd52-fc42-4b2a-a38e-9bdda15ec7b5}} , and using again the second equation in (REF ), one obtains
{{formula:10047f45-4a83-4f92-967f-cac5f26cd6c3}}
| m | c5080888e076aa5fc20fa5a7a72be12a |
Application to Performance estimation problems (PEPs). PEPs were introduced by {{cite:840c49cfabee540c8ab2ec8e3177a734d94b7c2b}} for developing new analyses of first-order methods; see also {{cite:18bd9b6e419785a8e2c04194f61ce016a0010bb1}}, {{cite:84e9e87af300271ea2f40a2517f0085757859fa4}} for the first works on this topic.
PEPs were later formalized using the concept of convex interpolation by {{cite:c150fd1713316d85a579ecbbc54a6adfaaf66d44}}, {{cite:11916605a6f41e2c3a90eaa6a0ba2d3b700fe543}}.
PEPs formulate the search for worst-case guarantees as infinite dimensional optimization problems over the considered class of functions, e.g.,
{{formula:20e3401f-b78a-472d-94d8-bae4d88e57c4}}
| r | f2db8f14db466f8aaa5fb74cc555165a |
A matrix with real number entries is said to be totally nonnegative if each of its minors is nonnegative. Totally nonnegative matrices arise in many different settings, for example, oscillations in mechanical
systems, stochastic processes and approximation theory, Pólya frequency sequences,
representation theory, planar networks, ... . Two recent books which serve as useful references for properties of totally nonnegative matrices are {{cite:b4d99ed56eea9e0cb5bf15fdd9498685d7892ef6}} and {{cite:ef5ab27ae121e7cb52c26d8f01549aea8439c4ce}}. (The reader should be aware that, in {{cite:ef5ab27ae121e7cb52c26d8f01549aea8439c4ce}}, Pinkus uses the term totally positive where we use the term totally nonnegative.)
| r | a06bf6d9cb04f5989118dc0161a46429 |
To investigate if early warning signals are vulnerable to this fallacy,
we simulate a system that is not driven towards a bifurcation such as
in Fig reffig:1(b). This simulation approach allows us to determine whether
examining historical events is a valid way to test the utility of these
indicators. We simulated 20,000 replicates of a stochastic individual-based
birth-death process with an Allee threshold {{cite:e04d9b3a4e0ff83e003af7a4984247b4a7030411}}, which
arises from positive fitness effects at low densities. Above the Allee
threshold the population returns to a positive equilibrium size, whereas
below the threshold the population decreases to zero. The model can be represented as a continuous time birth-death process where births and deaths are Poisson events which depend on the current density with rates given by
{{formula:c8f845f1-36f6-48d3-a31a-247001dde70e}}
| m | 698acfb3b0f701994b6b07bec4bc7965 |
We want to evaluate if our method qualitatively improves upon ILO {{cite:072aa8697aa30c37d7c522369c02c42c45ce5021}} which is the previous state-of-the-art method for solving inverse problems with pre-trained generators. We also compare with vanilla CSGM {{cite:5ae1771503323a77674c2adec5430e777a755377}} which performs much worse. For a fair comparison, we choose 8 real images from FFHQ to tune the hyperparameters for each method at each measurement level, and then measure performance with respect to the ground truth on 30 FFHQ test set images (never seen by the score-based model). For ILO, we also tried the default parameters (300, 300, 300, 100 steps) reported in {{cite:072aa8697aa30c37d7c522369c02c42c45ce5021}}. Finally, to make sure that the benefit of our method comes indeed from the prior and not from optimizing without the ILO sparsity constraints, we also test ILO without any constraint on the optimization space. In the Figures, for the ILO we report the minimum of ILO with tuned parameters, ILO with default parameters (from the paper) and ILO without any regularization. For the denoising experiments, we tried ILO with and without dynamic addition of noise (Stochastic Noise Addition) and we plotted the best score.
| r | 3f718ba3c487f6037b178b1c13417aa5 |
The special case {{formula:676a3110-e92b-4f52-a465-aefa739d9945}} corresponds to the ultraspherical or Gegenbauer polynomials {{formula:f64b29ed-2ea4-4dd4-8315-7c5b3cac85a8}} with slightly different normalization, and the case {{formula:7bece5eb-7778-4e33-8484-da362b1e6eb5}} corresponds to the Legendre polynomials (see e.g. {{cite:2f5a0229ccc6ae99886e381b7804bbbe42417ff8}}).
| i | b5fde6f1f67df9f22134f6aacf230d3b |
Based on the impact parameter analysis of Swift bursts, the corresponding volumetric rate density is {{formula:0e4f11b2-b94c-4116-877a-4ece41215bf9}} {{formula:09ad4aed-d62b-46fb-bdd8-d6566ec2ffe5}} . This falls below the {{formula:ea6eb8bd-ad87-400b-9671-ae03399e62cb}} range estimated for NSNS mergers by {{cite:0ab9958d4b19ba2c43abcea2493e8648f0c92faa}} of {{formula:82b883cc-e958-4472-90ae-d096d018befc}} based on the the single detection of GW170817 during the O1 and O2 LIGO science runs. Thus, if the true merger rate is as high as this, then only a small fraction of future GW detections is likely to be accompanied by detectable gamma-ray flashes. That could be understood as a consequence of anisotropic gamma-ray emission, since our line of sight was within {{formula:ebb5c229-fb96-411d-b90b-dbfc8b1aabe3}} of the primary jet axis in the case of GW170817.
On the other hand, estimates of the NSNS merger rate based on the small sample of known Milky Way double neutron stars continue to point to lower figures, albeit also with large uncertainties (e.g., {{formula:7668fa3d-307f-4e88-a75e-d492e5bdde9c}} in {{cite:26001839bb099fed153f3ab16201e06f8f597eaf}}).
| d | a95d8d701dae53fb2b8bdecc7910668f |
With other parametrizations, relative contributions of horizon and dark
energy entropy decide the evolution of total entropy. The signs of {{formula:8dfc6ff5-c561-461b-9fd0-d541275cd0bb}} and {{formula:557f603d-24d4-4e0e-b6df-10f9016060f7}} are
decided by the terms ({{formula:3eca5dc8-0fbc-4103-a40c-765aef268e92}} ) and ({{formula:b025e4fa-f93f-4f89-817c-7345a1604bef}} ) in Eq.(REF ) and Eq.(), respectively. Further, the
magnitude of {{formula:7a49cee6-0e47-4917-8888-d7c0229cd26f}} and hence {{formula:8030848a-80d4-4b84-9a1f-c67f503704b4}} is modulated by the parameter {{formula:142c5e18-dfe9-4339-bbd4-49a618a750a9}} as shown in Ref.
{{cite:82b1f19516e63bd90ad134a10c43ba34012ee019}}. Presently, {{formula:a7cf6d51-97cf-4428-816f-7f11de8909a5}} is used. In Figs. 1 and 2, variation
of {{formula:ef0650ae-8962-48cc-9b45-6e16bf40139f}} vs. {{formula:da9b267b-eb08-459d-8dd5-53f6809f5d12}} due to different parametrizations is
plotted within range {{formula:e8fcbb5e-af53-4e19-8c52-2679e6fd7418}} –1000. In all cases, the peak in
variation of {{formula:41514de7-5c04-4161-9de6-e5bc4027d239}} is observed to be at the transition epoch
corresponding {{formula:17c3bfd7-f11b-4fd8-a14f-898411f77a61}} . This is expected as the sign of {{formula:1f6072db-5eb3-4bc8-8a22-97d9c516fb7d}} changes
at {{formula:3be10519-4e09-4ec4-8b31-1cf1080fc2a4}} . It is also observed that models
presented in Fig. 1, namely {{formula:197e8463-fa56-4a52-bf76-778ec9eb0466}} CDM, quintessence, BA, PSY1 and PSY2
have {{formula:9cbadafd-ad9e-4c98-a060-33d7f7f6adff}} and {{formula:0fdddc62-75f2-4173-919f-f07baccbe534}}
due to phantom, UIS, FSSL1, FSSL2 and MZ parametrizations displayed in Fig.
2 have {{formula:037afba4-769d-4627-8312-2befb3966ed8}} . However, thermodynamic
viability of parametric models cannot be decided due to the unknown value of
arbitrary parameter {{formula:2e00ccd6-32a7-46fe-b1de-e333fbf58504}} .
| r | 935839d836795470a2cbcf1ce8463705 |
It is hard to exaggerate the importance that fairness has now taken within Machine Learning (ML) {{cite:c3056bc66f0f48c9781734b234e3f6bfe0653c2d}}, {{cite:048133cc7e6e32fb1eb182b6bc4601dab50af504}}, {{cite:2d716777e06ea21e40ea232303a73072f9ff9e3a}} (and references therein). ML being a data processing field, a common upstream source of biases leading to downstream discrimination is the data itself. A recent paper has extrapolated the max-entropy (max-ent) principle to debiasing the underlying data domain distribution itself {{cite:048133cc7e6e32fb1eb182b6bc4601dab50af504}}. The approach, designed for binary domains, proceeds in two stages: it first modifies the data distribution to get a fair `seed' and then finds an approximation to this seed via a max-ent problem (or equivalently, a minimiser of the KL divergence) that meets domain constraints on aggregated statistics such as marginals.
{{figure:3df026c0-e482-4036-b7cf-ad1fd9bdc9e8}} | i | 6e60d3a6a28b98a1099d675832b8a7d2 |
Several theoretical methods have been developed for the global polarization.
These theoretical methods can be roughly put into three categories.
One category is related to the quantum statistical theory for particle
systems with spin degrees of freedom in equilibrium {{cite:ea83158f3f694d0c159b4639e753519d59ca8b45}}, {{cite:9893c008ff6ebcb1428e206454f116eef01ea8e3}}, {{cite:0b09088f12e82032bb3a12c4b6b6f4d002475451}}, {{cite:e4749616b6b4ecb3b780fb9abb43bf15703a5464}}, {{cite:a25261a2fa139089a4e652010e1eb734f757340a}}, {{cite:7dca0abe64ff499e46a9b2096b70f0a42881d85b}}
[for a recent review, see, e.g., Ref. {{cite:1048bdab337bc81fca43b67965bd7a63ea8aa364}}].
One category is the microscopic transport theory based on kinetic
or Boltzmann equations for spin degrees of freedom {{cite:6a6a24d5a7da6fe695e5f02004067bb39a6e991a}}, {{cite:9f06d6500f0aba3cc413836126181b9dd982e36c}}, {{cite:a22abbe2da230355c35bdec6ebcdb9b6eedb3586}}, {{cite:8577f06d4a26acbdb06a1f43cebb1448931be152}}, {{cite:b30a9906b692f5d3c74339f7fd9dc31e6cdf22b0}}, {{cite:98baf5f95ff362c5d16e0ab5f46c890be7d835bb}}, {{cite:8901e6cdac477a00dfb4fcc26e018c47b1e4b6bc}}, {{cite:ddf20202aacd3948f7e187617e82d8f1618cdfa8}}, {{cite:e92f33d807074e5508228080d8be0827d6f75ce7}}, {{cite:a34820224c95401928dc0e9e7d2f6a730c0fbbab}}
in terms of covariant Wigner functions {{cite:9b5318eddb4533b04743418379c2b70613112aba}}, {{cite:69a93c345585a215566a6d46f692115b903ca0fd}}, {{cite:c02b07108165298f539a2371f84fbe8ad545d378}}, {{cite:8bd295ad5516c558adc0652ee0127500add54c3d}}, {{cite:c4286973f23fc81fa78a92b6e80efe53720460f0}}
[see, e.g., Refs. {{cite:3bf2273680611fbc41387bd8ed62d3ec2e6d2812}}, {{cite:a259b0e7c220295795ebe0bbf364690e9a9108af}} for recent
reviews]. Another category is relativistic spin hydrodynamics {{cite:48e0dd03d602edcf705185fb237b841270959158}}, {{cite:1bf2e030fc786a50af63e815ab725d90ec56afc8}}, {{cite:dcb656f1b23d7eed6ed7b7b0050ca249140a8af7}}, {{cite:a25261a2fa139089a4e652010e1eb734f757340a}}, {{cite:73b5cf30a0725d43fe91bd130a6392bde2287a38}}, {{cite:0547bd4a8dd5e390b7ece382e27f74e559c2f880}}, {{cite:a0b5813a8a164bc59a64c2ddfb0da8a47bb270f4}}, {{cite:672c20d43c62c1798b0f5991894a0fcc291ed995}}, {{cite:c1b797181ee9bf16a7b1ab0a8728c7e5341ee83a}}, {{cite:a7cbb5d6156e19489d1c9ebb5afcb523f2638965}}
[see Ref. {{cite:1bf2e030fc786a50af63e815ab725d90ec56afc8}} for a review], which incorporates
spin degrees of freedom into conventional relativistic hydrodynamics
applied to the strong interaction matter in heavy-ion collisions {{cite:01fdfce9f857feec3305a0d0383243d3ecfbc219}}, {{cite:746a6e9bf7171172535bd3291a69f733c06fff9e}}, {{cite:b58c75e1583b6f9d2bdb00c0cbd12ff719379227}}, {{cite:021eddfce29664dbb7f5d0309c398dfc1a94b96c}}.
There are many phenomenological studies of the global and local polarization
using these theoretical methods to describe experimental data {{cite:1a76e65fb242ec7a3b2ec87fd8a1cb43edfe5037}}, {{cite:f3591329b87211e7fe3e371ff69dbd58819dfcd3}}, {{cite:74f6b187f7d81ce2a4cc091109d46463de816bbe}}, {{cite:1f023287b1a80aab97425d37cd2c237253fa99db}}, {{cite:cb6e72d34f84b0302ee8426919134bf450f6da0f}}, {{cite:9c7905dd5916af8026c3bb97bb5bc2305ba9bebe}}, {{cite:80e74aca613d6645aacad8ab7fed7aaef1ac1bf2}}, {{cite:6013cde043c0b03f40d7acf17f079d1dd79eb2d4}}, {{cite:3f5bcd16d46a10a2901da74f957f11ba6b5d1820}}, {{cite:4526dfb1bb283ba219eb30b9b717f20992a5d660}}, {{cite:5d84fec5d336c82509b25cae1ee62ca3e3c5ea61}}, {{cite:b4b5f9c9d9bc0d0967e92ebc179fd5c67d70dfbc}}, {{cite:2cea3814c87d24a106a32be15595b391aae2069f}}, {{cite:cfcb3f1dcd738113ed5edbaee2d5c33038988de3}}, {{cite:e5c561821187a0e7a73a4998c1adbc10b75b25cb}}, {{cite:c1b797181ee9bf16a7b1ab0a8728c7e5341ee83a}}, {{cite:e250fcb1895b8e323c62e48a7ecadf7194785bed}}
[for recent reviews, see, e.g., Refs. {{cite:df5add59e927bf5a6e4ac4258fafe359a0179a16}}, {{cite:3b11e0a62646193e827fb881cfc22ef05915df52}}, {{cite:03f8416d12903a099e152db4b004cdf34d7832a9}}].
| i | 04ab31bf6c599ea2f23bd4a4734db388 |
Throughout this paper, we use the 2018 cosmology as our fiducial cosmology. We take the values given in Table 2, in the column 6 (best-fit with BAO), of {{cite:faf2a6b748ad7fad05a12ab8d0581c68c2d3e3e2}}.
We use the following naming conventions: observable refers to a spherical 2D field built on measured quantities, such as counts, redshifts, or deflection angles, while probe refers to the combination of one or two observables into a summary statistics. In practice, our probes will be the two-point angular power spectra {{formula:fb753604-832a-40fa-a81e-d6dfc5396cf7}} .
The redshift due to the Hubble expansion is denoted by {{formula:febaebd9-5771-4137-80e2-35667602cb7a}} , while {{formula:601638fe-9e5b-46b2-8d49-fe760d7f688f}} is the measured redshift (which includes redshift distortions induced by radial peculiar velocities);{{formula:0f927380-4847-4a34-b620-aeb00e85c7c4}} is the density of matter at {{formula:31958d56-7f3e-46f3-8476-d3d274581f71}} in units of the critical density and {{formula:19c99ded-08a3-472d-bc51-2405bb70a04e}} is the Hubble constant; {{formula:0b6e0748-8152-46fc-8b80-7d7c30ab367c}} is the line of sight comoving distance, and {{formula:6d62f41e-a670-4f03-b4a7-654d583480db}} is the comoving volume element per solid angle, with {{formula:46d9dc61-cad8-4c32-9b5d-0ec3db9af3eb}} a differential solid angle element.
Vectors are in bold font and a hat denotes a unit vector.
| i | 370560535d799e4dd7335dcc9c4ddfd1 |
Integrated Gradients. Gradient explanations are often noisy and suffer from saturation problems {{cite:4bc83980c609b5b14243c852df077e39cab9b97b}}. Integrated gradients addresses the gradient saturation problem by averaging the gradients over a set of interpolated inputs derived using node {{formula:f0693d8f-1a04-4687-b149-cb7c037df085}} 's attribute and a baseline. Formally, integrated gradient explanation for a node {{formula:8cb955da-7bb5-4955-b0dc-bef7dbe8201a}} is an {{formula:c2800d46-1306-4fb9-b439-27e5f59d4c8a}} -dimensional vector given by:
{{formula:6dda545b-e0c8-4ae2-9def-d81cc42f5576}}
| m | 0824bfc719b8ed9fdb9049c258f4adc3 |
LOCCNet not only unifies and extends the existing LOCC protocols, but also sheds light on the power and limitation of LOCC in the noisy intermediate-scale quantum (NISQ) era {{cite:c9c81b2e460c8591e714120a53d5a123207cc822}} by providing a plethora of examples. We developed improved protocols for entanglement distillation, local state discrimination, and quantum channel simulation as applications. As a showcase, we applied LOCCNet to establish hardware-efficient and state-of-the-art protocols for entanglement distillation of noisy entangled states of interest. In addition to making a significant contribution to entanglement distillation, LOCCNet finds direct practical use in many settings, as we exemplified with several explicit applications in distinguishing noisy and noiseless Bell states as well as simulating amplitude damping channels.
| d | 91d35a82bd76afc823352625cd98bda6 |
In real-world situations, running randomized controlled trials uncovering causal relationships for BN can be costly and time consuming. Sometimes, it is even impossible due to ethical concerns. Thus, it has been of great interest to develop statistical methods to infer the structure of BN purely based on observed data. This problem, called structure learning, has become a research hot spot in machine learning (ML) community.
Traditional applications include gene expression data analysis {{cite:1f94be7c2a194000da53db0bad4fc1006434c8d9}}, {{cite:9a7786adb434f4a04bc17cdcd8dfd4873b317f7c}}, error identification {{cite:e10f22fd00ab2ab892251b29b776a286406ff90b}}, model factorization {{cite:60ede90e128a4379a5c38c2ea0fc5c23376e137f}} and system optimization {{cite:2c9d52f2f4fc79d7a972570e975c0c21c248f41b}}, to name but a few.
| i | e2459e8755b4b52eb390ebb1a34f4317 |
Remark 1.2 In the development of this article, we learned that the authors of {{cite:953d04ea12e60a92854f285f9bcb9aef33e5bb5e}} were also studying holomorphic symplectic structures on augmentation varieties, working on a different construction with plabic graphs. Their work is yet to appear but, once it does, it would be interesting to compare these symplectic structures, as the constructions seem to be significantly different and a potential link between weaves and plabic graphs could be fruitful.{{formula:1f9bfa0f-e646-4807-b6f4-0822ffe8e78c}}
| r | da0f1464ea8ec9d60b1f11fceb3cb456 |
Although several algorithms exist for training NN models, the backpropagation algorithm {{cite:3d156d0b060d7284f270fd0d01397d33411cd24a}}, {{cite:f535d01efd639ce974f4f4a6d27f9a512958bfd5}} with stochastic gradient descent (or variants thereof {{cite:caa4991ba1a5fcb0da153be83b876d03e0bf0185}}) has been established as a standard for supervised learning.
The backpropagation is a clever procedure to assess how sensitive the output error is w.r.t. a given parameter of the model; thus, each parameter is modified proportionally to this measure of sensitivity.
The computation involves the sequential product of many matrices whose resulting norm, similarly to the product of many real numbers, can shrink to vanish or expand to infinity exponentially with depth.
This problem has been known in the literature as the vanishing/exploding (V/E) gradient issue.
The V/E issue has been firstly recognised in the context of recurrent neural networks (RNNs) in the nineties {{cite:56c0816008d03602927a0a713b2236a7d371518e}}, {{cite:5e93a70a55a487f93ff252f42f3ff89f86fbaed2}}, and then, after the advent of increasingly deep architectures, it became evident also in feedforward neural networks (FNNs) {{cite:494254581c8a96cbb39578c1d81090189ec3f050}}.
| i | e63986bc872f251ac776933373bca682 |
In addition to the results shown above, we also present qualitative correspondence results between neural implicit fields and real-world data in the supplementary. More specifically, in Section 5 of the supplementary, we show qualitative interpolation and correspondence results between implicitly defined surfaces. Then, in Section 6.1 of supplementary, we show qualitative correspondence results in the form of texture transfer between pair of shapes from the CMU-Panoptic dataset {{cite:a2269cd7f491f0a61b25a80c09ddf086fd05adcf}} consisting of point clouds acquired from from Kinect RGB-D sensor. Finally, in Section 6.2, we also show the versatility of our representation in modelling deformation field between shapes that have more freedom regarding such as meshes of the human heart {{cite:b12fb4a826425a0ccc1f46f4bc9d2c34144378da}}.
| r | 521537ba45671b0454b0a0d048e23365 |
Inspired by recent research {{cite:8fac9444d4996db26fa03ae7a0ed7851a52234dd}}, {{cite:884275d1bdf4f97550a99748b4d8840a116053f7}}, in this paper we present an optimal control and inverse optimal control based method for interactive motion planning in automated driving highway merging. Our method not only incorporates the interactions, but also adapts the joint optimization cost function based on observation of the actual trajectory of the NV, online. Our hypothesis is that the nature of the NV is defined by weight it places on various terms in its cost function. These weights need to be estimated online through trajectory observations. To facilitate this, we harness the inverse optimization theory presented in {{cite:c910331a49c4891efdca51ff5bccc611df119bc0}}.
| i | 5371d454ef3f0d52e500ce8a139f228f |
Several prior studies have considered the role of directionality in population structure on the spread of mutant types {{cite:ca73af6ffa4b9973a4897e81af851c4cd1f28919}}, {{cite:e72ea306afb4516465b08e354c038f6a38c14908}}, {{cite:fcb6d437d9bfd69569d3f56d726f3073d2ed1dab}}, {{cite:f76fd9c39fbc8bdd4141ebcba0d83bb1badb1d22}}.
But in those studies the fitness advantage of the mutant is fixed, independent of type frequency. By contrast, our study considers frequency-dependent fitness effects that therefore describe game-theoretic interactions: an individual's payoff depends on both her type and her neighbors' types. The question of directionality in models of social behavior has been analyzed in at least one prior paper {{cite:bc06ee1ddcf1f5ac1f4b143c58ec087e35b5379d}}, but only in the case of two specific networks. Lieberman {{formula:04eb5f13-72d0-4c0b-92ab-7c62df1219e0}} analyzed a directed circle network, where each node has one incoming neighbor and one outgoing neighbor, and a super-star network {{cite:bc06ee1ddcf1f5ac1f4b143c58ec087e35b5379d}}.
Whereas that work shows that directionality can influence the spread of cooperation, in those two specific cases the effect of directionality is to repress cooperation.
Our analysis applies to arbitrary network structures and we find that, in general, directionality tends to favor cooperation. Other studies have considered distinct networks of social interactions versus behavioral dispersal, limited to purely bi-directional links {{cite:65014bfac147655d9318b60052b666912c76b235}}, {{cite:f6c678ef4bdf92ed61568608e0e8ad3f55c5fa0a}}.
| d | 46a0088c52960a0bf29d511e240b65a5 |
There are situations, however, when even higher-order numerical approximations ({{formula:209b74da-7e0b-49c7-bdc4-a2dd9ce1281c}} ) are
required, for instance in problems arising in astrodynamics. In that case, although generic splitting methods exist, they involve such a large number
of elementary flows {{formula:e5c34d89-2928-4d1d-a0b6-4f7327dcde58}} , {{formula:4ae540a5-0724-418b-bda4-976b1c72e910}} , that are not competitive with other integrators. This is so due to the exponential growth with the order {{formula:3ee4b928-0e99-418d-87b1-2c017357c060}}
of the required number of
conditions to be satisfied to achieve that order {{cite:e3d9b828ee90f4d1d960a5492ddbcd2ed6f533ad}}. For this reason, palindromic compositions of the form
{{formula:7b9576c6-a401-4775-95c9-9dd9458537dc}}
| i | 3cb0029287f91ec5ef7991f325cf2337 |
We in no way claim that CHAMP resolves all of the problems with modularity-based methods(see, e.g., the discussion in {{cite:2fae793edf0531a7f8a1a69f58b38bc8a6f5df93}}). And CHAMP is certainly not the only way to try to process different results across various resolution parameters (see again the Introduction). However, by taking advantage of the underlying properties of modularity, including the fact that each partition defines a linear function for {{formula:0e3ac8f1-72a5-4fba-94e1-b9ff9e2f3da2}} in terms of the resolution and interlayer coupling parameters, CHAMP provides a principled method built directly on the definition of modularity to make better sense of the parameter space when modularity methods are employed. In particular, many of the various other proposed approaches assess each partition at the particular parameter value input into the community detection heuristic that found the partition, that is treating each partition as a single point in {{formula:16880a2e-00b3-4820-8a31-a10e3040e5cf}} . In contrast, CHAMP returns to the underlying definition of modularity with a resolution parameter to recognize that each partition here is more completely represented as a line in {{formula:088581ff-d4ef-4d21-bb1d-3011a28bdc69}} [in the multilayer case, as a plane in {{formula:cce112b7-fad3-46a3-b1f4-5defe0c02a81}} ]. The single point is on that line but does not completely explore the potential of that partition to compete against the other identified partitions. By using the full linear subspace associated with each partition, CHAMP prunes away the vast majority of partitions in practice.
| d | 8ec6ebc095e32c24f3c25b1841bdb685 |
Theorem 9 (Hoeffding Bound, {{cite:365b7a9e1c224b2448fab3798e54a79d09affdf3}})
Let {{formula:dcd8a853-9a39-4c94-852c-7630bef0e651}} be independent random variables. Assume {{formula:a9194299-7aa1-47a9-9eb9-b23445025639}} has mean {{formula:999d0bd9-13e5-4a26-8c12-33a20cfbe493}} and sub-Gaussian parameter {{formula:ef4d8b63-bbee-42f4-86a6-c47165dde8a4}} . Then for all {{formula:ee3a5ec1-10f0-4141-bd94-fe70ae03ae78}} , we have
{{formula:6cb52e68-8df9-4322-8fe1-17b79ca66ec8}}
| r | 810f943b221ea3a2f358465c97d8c6e4 |
Though the focus has been on the applications of fluid dynamics
near local equilibrium of the system by using the gradient expansion,
it is important to explore whether the applicability can also be
extended to fluid dynamics far from local equilibrium
{{cite:ecbb1fb679601c84f0a5b83eb22f77e9dd604152}}.
This issue has opened up a new direction called
"resurgence" giving rise to hydrodynamic attractor solutions.
Resurgence theory
suggests that the gradient series becomes divergent but is Borel
summable giving rise to hydrodynamic attractor
solutions {{cite:2195878026f50032deee8d3abdba38c12f87cc3f}}. It is also applicable to large gradients.
It will be interesting to study the
attractor solution in the present case of three dimensional anisotropic
expansion of the fluid with second and higher order viscous hydrodynamics
(see Ref.{{cite:8a161e47051084034a392aad41b2c39ac5c72afe}} for related discussion).
To conclude, the present study of QGP dynamics with second order
relativistic viscous hydrodynamics and anisotropic expansion of the fluid
using Kasner space-time is expected to provide a better understanding
of the physics of early universe as well as strongly coupled theories.
| d | 4943c0761298b8d796d695a90350497c |
The code employed for this article, ASDG, can identify the connection between a paper and an SDG through its abstract. It uses four different models: Non-Negative Matrix Factorization (NMF) {{cite:d959994775a133fe0bbffb76ac6585fa942beb0a}}, Distributed Representations of Topics (Top2Vec) {{cite:3187b4aa355393aa5c98dcd4223fa6b3bbe5f222}}, Latent Dirichlet Allocation (LDA) {{cite:96e6c9ec66ec550391c23f1bf391fb5c620cc554}}, and BERTopic {{cite:2d6e3b2748723c5cc09c2dd4d667f7bf850605d4}}. Due to their inherently different nature, the information that each model extracts from a text is different. In other words, their functionalities are complementary. To take advantage of this fact, ASDG introduces a voting mechanism. Similar ideas have been used very recently for studying the social network Twitter {{cite:3b644264e9770169a26d004b27639e91cf3d6139}}. In the voting stage, ASDG takes the scores of each model for each text as inputs. Using this information, ASDG decides which identified SDGs have enough confidence to assume that the text relates to them.
| m | e50c0341427220b5cf61199ab94f33f7 |
Whole Heart Segmentation Dataset {{cite:81391d65998dec5833144bb471384f81af5d4a48}}. In total, this dataset provided 120 multi-modality whole heart images from multiple sites, including 60 cardiac CT. We selected the CT images and split 20 images to form the training set, and the remaining 40 to form the test set. We partition the 20 labeled data into 10 training and 10 validation. More importantly, we add up with 50 unlabeled cardiac CT data collected from centers in order to validate different semi-supervised learning.
We employed three widely used metrics, Dice score, Jaccard, and Hausdorff Distance (HD) to evaluate the segmentation results on 40 testing data. The evaluation tool is provided officially by {{cite:81391d65998dec5833144bb471384f81af5d4a48}}.
| r | 76e3f4373dd3ccbeead65c65f9ad8e60 |
A consequence of the above scenario for water formation is that the D/H ratio of water could depend on the physical conditions in the molecular cloud and prestellar core prior to and during the protostellar collapse. Lower temperatures or a longer duration of the deeply embedded phase would increase the D/H ratio observed in the inner warm region. Conversely, a faster collapse or warmer gas temperature could lower the D/H ratio in the inner warm region. This would imply a relation between the bulk water D/H ratio and the dynamics of the formation environment. Isolated protostars may collapse more slowly than clustered counterparts because the stability of the cloud is determined solely by the internal cloud structure {{cite:f77659acfb44750d4b92676c91d24232fc0edbbb}}, {{cite:37026df3eed5c936a718c5456441079da96e32ef}}. Moreover, the temperature in clustered regions could be higher owing to, for instance, more external radiation or shock heating {{cite:d2ddb559ce4089ffced58376b65101832ace5b2b}}, {{cite:051767ea4152d054f8ee6da67b48c7d859024ea2}}. Either of these scenarios would enhance the D/H ratio toward isolated protostars in contrast to clustered protostars, in which external factors can influence the physical conditions. Such a differentiation was recently suggested based on ALMA observations of HDO and H{{formula:78c25df7-309b-4d9c-84ba-5132fd300ee2}} O in the warm inner envelope toward three isolated protostars {{cite:99f0ad7d83403c13d6c23991cf8f867921ce882b}}.
If the enhanced HDO/H{{formula:cfa7574d-2a35-4edf-a880-03cd32319474}} O ratio is a consequence of environmental effects, then the same might also apply to D{{formula:d6921978-3cb4-4745-a259-8bc0df7d8107}} O.
| i | 3eafe04e3455cb70ced215c2d527e8bf |
In the distributed optimization problems mentioned above, the agents decide the same variable while need to reach consensus on the optimal decision. However, in other scenarios, each agent only decides its own variable but the objective function of each agent is related to other agents' decisions through an aggregated variable. For example, in multi-agents formation control problem {{cite:8f62db38b96f6661fe4562013d20195709aec15e}}, a group of networked agents wish to achieve a geometric pattern while surrounding a target, which can be regarded as a goal tracking problem. The dynamical tracking problem can be modelled as an online distributed optimization. In this case, each agent decides its location, while the objective function also depends on the centroid of all agents. Similar scenarios exist in resource allocation {{cite:6e366529c5906996a988c1ad98b5dac9fd3def0a}}, smart grids {{cite:2cd49cdb881fdbcce6557a3afd7fc7d2225714d1}}, social networks {{cite:5877add2adf41c5eb8b60a5b93dbc5822528ec85}} as well. The above optimization problem is called distributed aggregative optimization in {{cite:388fceeeaebc2514158e8d25c8428ddded0d5dfc}}. The aggregative optimization is also related to the well studied aggregative games {{cite:f441e4ceb540a67a853fb0144bcf81f1c5372a8a}}, {{cite:782cbc4e3ba73dd069f0ce3ba093770ed463b096}}, {{cite:f11f07a0af3311b6caa768da23236ff9c6488c5e}}, but can be treated as a cooperative formulation in contrast to the noncooperative setting for multiagent decision problem. Regarding the study of aggregative optimization, {{cite:388fceeeaebc2514158e8d25c8428ddded0d5dfc}} considered a static unconstrained framework, {{cite:7305d6c340fd793e32851ea5fde6ce2d260d1959}} considered an online constrained framework, and {{cite:b6db8c0ff21e2e1cbaa2696927e3ee53ef5a8f27}} considered a quantitative problem. To the best of our knowledge, no work has been done to improve the computational bottlenecks encountered by algorithms when dealing with complicated constraints that prohibiting projection algorithms.
| i | 7df3ba30429a1e87353407c2cb467fe2 |
(i)
How to directly analyze for {{formula:02124a21-d1b1-46a7-8c75-ebc51c00831d}} in Section ? In this case, main difficulties have been described in Remark REF .
Besides, after opening lens, we have to deal with the singularities at {{formula:995002ab-c0bb-45f9-b35e-a6faccb1293b}} under the second jump factorization with {{formula:a88d4588-e700-459b-be90-fdcb47f858ae}} instead of {{formula:05dd8dc7-96b8-4686-a2af-9e0db13f9da2}} when we directly investigate {{formula:3a741501-e4e3-41fe-880c-623fb8943b6e}} ,
which can not be easily to convert the singularity conditions of {{formula:18ace4dd-6c23-46e2-953d-7fa1259a9487}} into the residue condition as (REF ).
(ii)
Asymptotics of transitions regions between {{formula:9cae989f-1521-4509-ae80-08ba7686aafb}} and {{formula:c58fb22a-91a9-4090-afd7-53867103f283}} are still open. From the point of the RH problem formalism, the transition region between corresponds to
the saddle points {{formula:078a572f-c050-4a27-9554-4e642b6c6598}} and singularities {{formula:224b030a-f805-4f77-8f93-9655133d15af}} . I hold the view that the main difficult comes from the origin ponint. For the case of {{formula:3f3a9ca7-745b-42eb-a8a7-65e49c363d78}} , {{formula:cc81ef6e-d0f2-4f28-8cfb-3fafe7673474}} , we see that the leading term
{{formula:3e828adf-18b4-49d9-a599-62dbbbe4b3b6}} increasing oscillations as {{formula:dec7242d-ed47-4bfa-9dd0-9fac8bdd72f2}} , {{formula:e61f76b4-7053-452a-9aa5-ea830cfe1092}} respectively. We notice that in {{cite:722f6e27bfce90c2b31d8ded72ad8fa9bd85cb20}}, Rybalko and Shepelsky give a good solvable
results along the curved wedges in the long-time asymptotics for the integrable nonlinear nonlocal Schrödinger equation for this problem. We look forward to extending similar results to our
forthcoming work for nonlocal MKdV equation.
(iii)
Does Painlavé-type asymptotics exist or not? Different from the local MKdV with step-like initial data, there exists a singularity at {{formula:65e83bc1-591c-4fc7-aa5d-d51d83c5ed16}} in {{formula:994d9fe6-91ea-4d4c-83ab-d7ea2ece0ad8}} rather than a
cut {{formula:6b06d437-5357-4282-a6c3-0a7573b13bdf}} in {{formula:4e203c6d-41ae-4334-b338-3f03c9aad1e0}} as in {{cite:7d2f7c56ac3fb1b369f4e09a235cd2569847d5e4}}. To some extent, besides the singular point {{formula:2450205a-3abb-416c-b877-e6c52814586b}} , I think the properties of nonlocal MKdV with step-like intial values are
more close to the local MKdV equation with decay boundary condtions such as in {{cite:d71dfe636097b92f6fa7a2901e089908901be3dc}}, which take Painlevé-type asymptotics in some transition regions. That's our motivation to
ask this quesiton.
| d | 6c6e38d7471c43a1b4d41bf0ee4c7fb8 |
Where {{formula:1d338bd3-185e-49e2-8943-25a4262e78f6}} is the sigmoid function and K is number of negative samples, typically 5, and {{formula:25938c58-d9b1-4b53-ad61-19d0c8ebcf8e}} is a probability distribution over {{formula:d12b9250-7aec-4ffc-a623-ac6acada56ac}} . It is often based on the degree of {{formula:4ed4d752-35b8-47b5-9dca-3aa4d5a0ca6d}} and the task. DeepWalk compute these losses for every node in each random walk and update the {{formula:1dc81a69-b0fa-434d-bd48-05eef54d19ea}} by using gradient descents methods {{cite:0e9888176de39a0449e309c78f39a27f18dcba04}}. We note that the next node is selected uniformly from the current node's neighborhood in each random walk. DeepWalk also shows that these learned representations can be utilized in downstream tasks like node classification and missing link predictions. LINE is a direct extension of DeepWalk. They modify the DeepWalk loss by restricting co-occurring nodes to be directly connected. Furthermore, they add the following loss as well.
{{formula:acecca5b-b465-4e27-af70-947eac02d8b2}}
| m | 015b3868f98e9cec28b67515b01e02ca |
To demonstrate the effectiveness of the suggested method, we train all classifiers using the standard cross-entropy loss and our modified loss and compare post-hoc OOD detection methods across three NAS datasets.
Specifically, we present the results of the confidence-based (i.e., MSP and ODIN) and the distance-based methods (i.e., Mahalanobis distance).
We also include a recently proposed OOD detection method {{cite:4ccb70f8ffd8e22ce38387dc633d3c538d137eec}} which computes channel-wise correlations in CNN with the gram matrix and estimates the deviation of the test samples from the training samples to detect the OOD samples.
However, in the text domain, the notion of gram matrix is vague, and hence we do not compare against this baseline.
Although this method uses the distance in the channel correlation space, we expect it to behave more similarly to the Mahalanobis detector than confidence-based methods, namely MSP and ODIN.
We also compare with another recent baseline which exploits the energy score to detect OOD samples {{cite:406063857f6a531db2627f54c9a587e7b6e8f593}}.
As the method leverage the logit layer to calculate the energy score, and the softmax score is based on the logit values, we conjecture that the energy score demonstrates detection ability similar to the confidence-based methods.
| r | e86baeeb84bd5283456c0225932fa12b |
While research on noise robust methods for single-label classification is well established in the CV community, with consistent definitions of label noise and benchmark datasets, most research conducted in the multi-label case appears to be more heterogeneous. Some research fields treat multi-label noise partially, without explicitly mentioning it. For example, the research field of multi-label learning with missing labels (MLML) can be interpreted as a problem inducing subtractive noise for multi-label classification. In MLML labels can be either annotated as present or absent or not annotated at all (missing). A common approach to deal with the missing labels is to consider them as absent {{cite:9e322d0928bc6a6825ac07cd27955d6986537a7c}}. This procedure induces subtractive noise in the form of present classes that are annotated as absent. Bucak et al. {{cite:07802b1435299d3ed77722d1bcca7c0cc29dfaad}} solve the problem of MLML by using group lasso techniques and a ranking loss applied to a support vector machine classifier, while Jain et al. {{cite:b578c3fbdc6aabc3c1a9f46abdd54a8e5eed2722}} introduce a propensity scored loss function that is used to train a tree classifier. Further, Durand et al. {{cite:9e322d0928bc6a6825ac07cd27955d6986537a7c}} propose a version of the Binary Cross Entropy loss functions that adapts itself to the proportion of known labels per sample. The loss function is used to train a state-of-the-art convolutional network whose output is concatenated with a graph neural network to model the correlation between classes.
| m | 39c67cb7b682519855afce535a8a694d |
A second ingredient to the distinct behavior of positive and negative disclinations is the asymmetric dependence of conformal crystal structure on the sign of topological charge. As described in Sec. REF , disclinations act monopole sources for conformal distortions of {{formula:c4d082c0-32ee-4543-a32b-13e49897772c}} , and as such lead to near-field singularity at the location of disclinations, {{formula:f872cad4-2a51-4cd9-a9f0-0b9b35785bbb}} , where {{formula:ca9c96ec-d994-4f91-b771-9990c185f396}} is the defect position, as in eq. (REF ). While this density pattern is singular for both signs of {{formula:5ccdfa43-aac5-44fd-b573-e0ec82317d82}} , its value is bounded for negative charge but divergent for positive charges. This leads to a strong effect on the asymmetry of the “self-energy” associated with near-field repulsive cost of locally under- or over-packing the region around the disclination core. For example, in Fig. REF , see the energy to form a single, centered disclination (relative to the defect-free cluster) vs. topological charge {{formula:833321ae-45a9-4b3b-97b3-0990a07520a8}} in a harmonically-confined array of particles with 2D Coulomb repulsion (i.e. {{formula:42325f8d-9d5d-4900-bb24-519ae26a716a}} ). Due to the asymmetry between local density, the self-energy deviates considerably from the symmetric cost {{formula:81499ffd-1289-4960-8443-2949b5072e18}} expected from continuum theory of cohesive crystals {{cite:4341b3867a4153936243f725f8306778d9af5999}}. Note that the energy to form a {{formula:f7ad09f6-25cb-475c-b8c6-be112b0d92b7}} disclination remains finite, while the corresponding energy to form positive disclination diverges at a finite value, {{formula:e1d1bf83-456b-4033-9363-0224d3710249}} . This result implies that energy cost of concentrate multiple {{formula:95de89df-ff3a-4b7b-b9a0-406a809fcc98}} disclinations is modest, while there is strong incentive to split and separate {{formula:a8da448c-13da-4f02-891c-a5ac8a28bfdd}} disclinations into distant regions of a conformal crystal. This is consistent with the observation that positive disclination states are only stable in split-ring configurations in our discrete defect calculations, while axisymmetric patterns with {{formula:641f8619-77b9-4920-897c-605d18e6baec}} are generically stable.
| d | f784e7c09ca5e45120831e4d1a0eb576 |
By studying the three-body hadronic {{formula:fe7619d4-7397-47af-b3cd-f3dbaf21c2be}} meson decays involving {{formula:6d50355a-6479-4081-b604-0e58986c280b}} , one could provide the constraint on the unitary
triangle {{cite:2fc8efa20cdd89b6d39498f9381aa4135c8ed88e}}, {{cite:5db5906cd3a417c039d993a4222f3fc59be3fac6}}, {{cite:c9193e96d1496f352afb001296fc543fef3f976a}}, {{cite:39c99d139247feb3ef9ce52e4d48fff67affaf80}} and probe the inner structure of the intermediate
resonances. In Ref {{cite:78417ea1f04225369fec3806f040b24117b34ccd}}, four quasi-two-body decay processes involving {{formula:a55bd42a-690a-4684-bace-5a7ef849f96a}} have been studied
in the perturbative QCD (PQCD) approach {{cite:3d25ae87c7c83baa07a2559646541a10ae383351}}, {{cite:4ec64bc0fc2aeaf2fa6b97b2d673abe7e8c317e6}}, {{cite:7a9744f09a07464a6555d39e6c33c645135a2c93}}, {{cite:6233b64cf27cf8cdf22185bb2179de7a338e423f}}. In this work,
we extend the study to the quasi-two-body decays {{formula:93b745b4-9695-45b1-91f2-68fe2d4552f8}} , with the bachelor particle {{formula:38449a7c-9f14-4a79-8aac-f0bf32df5b30}}
which denotes the light pseudoscalar {{formula:ef23b13d-4354-4423-8f7d-c0e0344a2f76}} , {{formula:a681cd74-7d66-43ea-aa93-339433f381fb}} , {{formula:c187b111-bfef-4b77-9186-69e5efabf62f}} , or {{formula:e87877fc-713a-44c7-9c9d-8a48b1df10e0}} .
Typical diagrams for the {{formula:cd5b0564-3bd6-434f-b081-e12af76dda70}} decays' processes are shown in Fig. REF .
Inspired by the generalized parton distribution in hard exclusive
two pion production {{cite:a0920fed0e333889e062e2aebb012dfe2f4fd5e6}}, {{cite:07b10ae963a09b5088879d815b47a2ad776659c3}}, {{cite:e188a1e96e175ad96555d171a2cf190b11fc698f}}, {{cite:67602ff9ea142f2ff39c8b953e996b1c7277c4f0}},
the two-meson distribution amplitude was introduced in three-body hadronic {{formula:ee720c9f-5212-4fb1-9f5b-a50f6b079ab1}} decays in {{cite:3d4fb3df775b1d8f868169e7e21927f2977b508a}}, {{cite:d51ef3c823b46e1ad360681730b6757326b9a783}}
as the universal nonperturbative input within the PQCD approach.
The PQCD approach has been employed in {{cite:3d4fb3df775b1d8f868169e7e21927f2977b508a}}, {{cite:d51ef3c823b46e1ad360681730b6757326b9a783}}, {{cite:d7f4bc8eae0841e42ee5b6df5f7352318a492f39}}, {{cite:f42b1537bed55a411b4b4f0461b1bbe363bfb740}}, {{cite:6135280c8694bffc97144e02606a05ee573e2daa}}
for the three-body
and in {{cite:1f2aa32b372f42d7acde0d7a20a8518dfd819ec8}}, {{cite:5027a359ab6b6dd485571da08afa8e322d04d2e3}}, {{cite:73f39f23c76929cb7199e77869bcfb068ec197ff}}, {{cite:4266668fe335eef450bd6f5b5d861362632d9959}}, {{cite:1efd7f209d943f0e10a502127eda7b77c45d0ce8}}, {{cite:e7adfef2c70712607b08443ca51c36c7663e1ad6}} for the quasi-two-body {{formula:b5518d6e-42e7-4e81-81d5-c8f31a68f311}} meson decays.
The decay amplitude for a three-body or quasi-two-body {{formula:e0b6bff4-a2ef-4700-ae83-0ce906f39e27}} decay can be expressed as the convolution of the
nonperturbative wave function and hard kernel {{cite:3d4fb3df775b1d8f868169e7e21927f2977b508a}}, {{cite:d51ef3c823b46e1ad360681730b6757326b9a783}}, {{cite:1f2aa32b372f42d7acde0d7a20a8518dfd819ec8}}. Taking
{{formula:bf163ccd-b8c5-4759-9ca3-a94a351ec33e}} as an example, we have the decay amplitude
{{formula:6f28fefb-920c-46a4-aba1-13e6ba98ae71}}
| i | 53b61ee272503a63d666bf78bbe5098f |
Transferability with regards to machine learning technique: Transferability of adversarial samples {{cite:eee2e77b6d1d5a5aceaa626df20dc1abb6526754}} {{cite:d3c05bf5fd641cddb51c68eb594f3e329ac73fe7}} has been shown to be more effective with targeted adversarial samples {{cite:54469159e35938949297c4540298d39efaa17c7f}}. This implies that non-targeted adversarial samples (reliability attacks) which are solely aimed at causing a misclassification, are more likely to transfer from one model to the other. In furtherance to this phenomenon, we observe that adversarial attacks in network security are less likely to transfer from one machine learning technique to another. Transferability of adversarial defences in network security in also impacted by to the heterogenous nature of the perturbed features. While this is has a positive side with regards to preventing transferable defenses, it also makes it more difficult in real world situations. From our observation, adversarial attacks in problem space are more difficult to generate, more difficult to defend against and less chances of being transferable.
| d | 75303d10b74744efc37477751c37cc86 |
A multilayer approach has been recently suggested to offer a better description of various real-world networks {{cite:27daab30bef2a2e2b0c695f5ef0b63e7efd7d057}}, {{cite:8e9689745c506e1f33dea1eca917fb05c039a677}}, {{cite:ba00a6a2ba59839e9aaec7c76ebfdfeeeb578161}}.
In multilayer networks the nodes are distributed in different layers according to the type of the relation they share. For example, in the case of a neuronal network the neurons can form different layers depending on their connectivity through a chemical link or by an ionic channel. For the investigation of the brain, the multilayer representation allows to model its structural and functional connectivity from a new viewpoint, i.e., combined with each other as layers of a multilayer network {{cite:5cbe6df0a4dfd7e1651647d98d664384b23f817b}}.
| i | 4f918841dbac36677ea558648b38ca3d |
We perform a global analysis of all the observables discussed in Section within a Bayesian framework, using the publicly available HEPfit package {{cite:d1642fab88b841ae996ae9aca1f91e50eeaeca4e}}, whose Markov Chain Monte Carlo determination of posteriors is powered by the Bayesian Analysis Toolkit (BAT) {{cite:23b19e8cf53c6a6f0aad2358f9bc9eef507bdfea}}. With this setup we find an Information Criterion (IC) {{cite:f043fc6f04007933f7ece483163f7c79b6c142e1}} value of {{formula:d5fab2e6-1acc-4b18-987d-2fdc737fa22b}} for the SM. In the following we briefly discuss the results obtained and point the interested reader to Ref. {{cite:39645eadd6fd601a55b67a6fe8f0beb9bc1b1c24}}, where details and discussions of the fits can be found.
| r | c4eb8c0e8e35c4ae6fefc3e74684495c |
To address this problem, we propose our framework,
Alignment-Aware Acoustic-Text Pretraining
(A{{formula:ef93d5db-d83a-4ec3-83ca-c142770f538a}} T),
where we introduce cross-modal alignment embeddings
which make the model easier to learn the alignment between
the acoustic and phoneme
input during multi-modal pretraining,
and significantly improve the quality of the reconstructed acoustic signals.
Moreover, we borrow several useful ideas from recent
text-to-speech (TTS)
literature, including Conformer {{cite:1cf317faa8271995b108047f9e75ea0f518193c2}}, {{cite:34cc5b74586eaec3447ef6aa08281cbaf149c118}} and Post-Net {{cite:59cefb018503ee078a04eb5590d41a8d20ee35ba}}, to further improve
the quality of our reconstructed spectrograms.
| i | c9acd29ec3e9b58857d339ca851e82ee |
An important future direction is to study how quantum advantage becomes evident when we replace classical algorithms leveraging the powerful SQ access with measurement data access.
It is likely that various learning tasks considered to have no exponential quantum advantage are thought of as such due to the power of SQ access.
For example, we established an exponential quantum advantage for quantum principal component analysis (quantum PCA) in {{cite:0608cbe55edc494d8610dc55bd5fff6bf3441725}} when we compare quantum algorithms with quantum state inputs to classical algorithms with access to measurement data.
This result contrasts with the lack of exponential advantage in quantum PCA {{cite:f733d97d0d4511ac396f2a04a7199da12e5c728c}} when we compare to classical algorithms with SQ access.
By comparing quantum algorithms with quantum state inputs to classical algorithms with access to measurement data,
we are hopeful that new and significant quantum advantages could be established, and that the grounds for claiming such quantum advantages will be made clearer.
| d | 57f96015e6892a0fcea457a33fdfa04c |
Testing this hypothesis proves to be a formidable task for the present possibilities. The same mechanism underlying the flavor vacuum condensation is responsible for QFT modifications to the neutrino oscillation formulas. Yet these modifications are mostly negligible except for non-relativistc neutrinos {{formula:9bc885f6-8ba4-4b57-aebf-2998b434377c}} , whereas neutrino oscillations are usually accessible at much larger neutrino energies {{formula:003fb815-8577-4c17-8455-053b5e64b1d1}} . This rules out oscillation experiments as a possible probe of the condensation mechanism. There are, however, experiments aimed at the revelation of non-relativistic neutrinos, like PTOLEMY {{cite:7e31fc4e9155e267858e64c1b60c238124349314}}, where the QFT effects may be observable.
| i | ffa6dbb21dbc2d84522f99b83afc5afa |
Remark: Concurrently and independently from this paper, {{cite:f72a1881b2367d1118cba541c8b67e03878a9840}} recently achieved a parallel algorithm with {{formula:1003fab4-152c-4d06-b249-76635f86786d}} depth and {{formula:c6308ebc-e43b-4f41-ad68-0d61de4a8451}} work by parallelizing the sequential algorithm of {{cite:ed17f07139c626fc48db6c2305c006a1b4a491be}}. The work of this algorithm is smaller than ours for sparse graphs ({{formula:62b8debe-d32f-44d0-9ca6-bdec8abdacb8}} ). This is work-optimal when {{formula:24eef240-ac10-4c93-bce8-bdc94b59ca65}} (but not when {{formula:6112bbca-1a14-4ba2-bd8b-99df3dababe4}} ).When {{formula:94ed95ca-78fa-4267-ad7f-431a356ddf23}} for some growing function {{formula:e83dfdd8-440d-49a9-80e8-f6b3f00187b2}} , we have {{formula:86df2813-d613-4071-9063-38c0ff0d094c}} by setting {{formula:e851c0e5-3617-4b5d-af09-4bc7f99f7cf3}} to {{formula:ed19378d-0901-4b81-90c5-13f2cce14437}} for some constant {{formula:a6d379ce-9231-4004-a036-67ccda2f8e6a}} . Table REF compares our result with other results.
{{table:fc39931c-9cc8-4f7f-bbc0-c6c1ed35a2da}} | r | 41afb5c798059c6fe777e97263105093 |
With Assumption REF on {{formula:cc6a0f39-1fa7-4b64-bfe6-d9c2e92968ac}} -smoothness and {{formula:1a975854-e53a-448d-a4bf-3bf75b9ead40}} -strong convexity of {{formula:9a55fdb3-de18-4323-b03e-ee4d334e7f81}} , according to {{cite:2248992355268d1a65c9aafaec42c0c13c60c410}}[Theorems 2.1.5, 2.1.10, and 2.1.12], we have the following useful inequalities
| r | 06ecc79c304798f06ca492df4f4bbb04 |
The experimental setup is inspired by the one proposed in {{formula:9faf5955-0e3d-4ad3-8309-d147cbf39278}} {{cite:972453db4295fc785ee30b269efdc72b1956ab13}}.
Each dataset of 1000 classes is split into {{formula:500a9207-881a-4ffa-a214-eefd209fa018}} incremental states.
Each incremental state adds a batch of {{formula:41e92875-c560-429e-b890-1ce248b086e1}} classes to those that were already learned in states 1 to {{formula:f30b1f28-47a0-47c0-9a8c-b6bcf0233a26}} .
The same class ordering provided in {{formula:afdd4ed4-6cf0-4a46-9ff0-2eb1a1634254}} {{cite:972453db4295fc785ee30b269efdc72b1956ab13}} is reused for {{formula:5af45660-c579-47b6-a01e-165855630b54}} and a random ordering of classes is created to form {{formula:8d02b7de-ca27-46d7-9b22-1bb97b8633fc}} and {{formula:6b9afe1b-8308-44df-b23e-72741a905eb7}} states.
The size of bounded memory {{formula:7df17ee4-f6f7-467c-a9b1-1c663a3bb349}} was shown to have a central importance for the performance of incremental learning algorithms {{cite:df4f710c5053fc4caf9fec4186dc090ed0bd435d}}, {{cite:972453db4295fc785ee30b269efdc72b1956ab13}}.
To assess its influence on the proposed calibration methods, we report results with {{formula:bad5d760-cbee-44b7-baa0-38cfd7278f1b}} exemplars stored in memory for each dataset and imbalance configuration.
| m | 37208e629982f9529943012152c2611c |
If we use the amplitude amplification procedure {{cite:a260b21cbc0831fdab60dad07fcac6dcecc6f672}}, the time complexity of the search algorithm is {{formula:1cfa0717-3fea-4a46-a87e-4fcd8f159f47}} . Using Eqs. (REF ) and (REF ), the total running time with success probability {{formula:d73c0eae-61c5-4025-8562-34f51762287f}} is
{{formula:83da3efe-8713-4239-9062-26e5e7199d12}}
| m | 6ae21b9a4b6a38f6b3a30553c0bca2de |
We use the fermion mass ratios, mixing angles and CP violation phases to construct the {{formula:81ce405e-400e-4641-afd7-42025712e868}} function, the experimental data of the leptons and quarks are summarized in table REF .
The data of the lepton mixing parameters are taken from the latest global fit of NuFIT v5.0 including the atmospheric neutrino data from Super-Kamiokande {{cite:ab76c444626ed429c73de6a9130a14f28f31f768}} and the neutrino mass spectrum is taken to be normal ordering for illustration. The charged lepton mass ratios are taken from {{cite:034b327008a6b8e20123b6e4346fe4d52bf02135}}, and the quark mixing parameters and mass ratios are adopted from {{cite:ebb4b4a86f219edf8eb055d5563be405cac6be01}}, and they are calculated at the GUT scale {{formula:9a9f10e9-db55-443d-a8eb-bcf43080a617}} GeV in a minimal SUSY breaking scenario, with SUSY breaking scale {{formula:1f613354-ac2e-46dd-8a38-98fbb1d3bfc9}} TeV and {{formula:bc3aa44a-7b30-48d1-8888-542f9fb42975}} . The leptonic Dirac CP phase {{formula:0e03dd1a-29c9-4827-99fb-9e93d26d2f01}} has not been accurately measured, therefore we don't include the contribution of {{formula:a06d128d-553c-4b23-9fe4-198aec4820a9}} in the {{formula:6b856cc0-5f59-43c7-a487-296fbb00afd0}} function. If all observables at the best fit point of a model are compatible with the experimental data at {{formula:e602f3aa-86f1-4080-8aa5-af9e74e30c54}} level, this model would be regarded as phenomenologically viable. In the following, we report the fitting results of the viable models with the minimal number of free parameters, and all numerical results are shown with six significant digits. Notice that {{formula:12826441-5c95-4ce6-8deb-e82909ee8d1c}} and all CP violation phases flipped their signs while all other observables and free parameters are unchanged at the CP dual point.
{{table:7bf82265-cacf-4980-8e1e-869fe2ecf34b}} | r | 4e38eaab9beaec2b396dca40319a2d67 |
The physics of monolayer
transition-metal dichalcogenide (TMD) semiconductors, such as MoSe{{formula:b696f893-fdf2-48c8-b43f-22ce3c443563}} , has has been widely investigated.
Review articles include Refs. wang-etal.12,schaibley-etal.16,choi-etal.16,manzeli-etal.17,berkelbach-reichman.18,mueller-malic.2018.
Examples of studies of these materials include
their growth, preparation and
structural properties
{{cite:5e4fd2fba25eec6991f0a781416e10001c6e9304}}, {{cite:520b961b05a2c5bf375f599be7cf4807a3eaaafc}}, {{cite:c3619d1f5db5acdba777b7baed98d918558b7f00}}, {{cite:64706215e5209def85237d049a26a59d4bb4c749}},
as well as
thermoelectric {{cite:733a3a2f3a5c6f5fa38ab0decd3e8635a6b28c6b}},
piezoelectric {{cite:d4082f8d03b5c2e58f6ff973eca269b914ada45b}},
electronic
{{cite:363e59b9ef749980a8d811f1256f82bfbe2a16d1}}, {{cite:755ebaa6766c7ab37121f38576be3761488d910e}}, {{cite:ec0330807f5390cc04ca07ec2f4a5bac3ec3e261}}, {{cite:8dc6f305a4dce00efbf9e895a6964ac0e2200c8f}}, {{cite:fb36243149116ba61c89cf02f7eaf46e581cbb74}}, {{cite:3e6d0172d5179d00262f9adce253785b3922f59f}}, {{cite:8f0cab66e8164feebbc54b711c2647db895bdafe}}, {{cite:563bb2c9eae5bcfac43693fb2b8bf4b439b176af}}, {{cite:b0f77d936fac5ab8dc134a66c5c977af4d3904b6}}, {{cite:a338884d747961e6e587582e8973b86f56010aba}}, {{cite:759c02906a9b3fe175502b44bcbf74583e655e92}},
electron transport and transfer
{{cite:30aaf5cf316fa6718b07083ff27924f43322b4cd}}, {{cite:9a2d1e3e11f08a7622321618299e1b3292965b2a}}, {{cite:f536e964717cc571a726fca46f530b0e2b41b1cd}},
mechanical/phononic
{{cite:0318b5b58e8dca7a8858af0afe42f074be7df9cc}}, {{cite:a4f3daee6afa36c624bf0855eeab8b0ce19f5e13}}, {{cite:a4f3daee6afa36c624bf0855eeab8b0ce19f5e13}}, {{cite:a718e3b0ef31f447de1eebc07b1bf29f13d27148}}, {{cite:dd2468bb4fffa5b3bcfe9804f944ca89f4a34c57}},
and optical, exciton and trion properties
{{cite:bfd9955c813d915e862b76471aa97bd4fcef6eab}}, {{cite:ad1795ecd0121749f4cc94941dfc2b6066964650}}, {{cite:6bd00577a1f70e825c2c88b11e92bacf229f2049}}, {{cite:8a96c1ea98d10eccdf689901c0e5bb92a7654d97}}, {{cite:52a24b42bc96421a63ec287017a942353ef3ffe4}}, {{cite:a86b2d1ca59db26f339d97c75e84fce2ca175648}}, {{cite:61d06a9fa0c2399c8ea71126b80668400ce082b4}}, {{cite:502e9ee363f74e4412b92ff859ac8615001b9632}}, {{cite:dea3cafc196030ad5d9695bb60a3350f25173801}}, {{cite:55df48d4120c5839284c70809c4500f51f2b6464}}, {{cite:4d367baf3f2ce06416a4298ebcbb0aea2669e9d0}}, {{cite:338570b3cf3e6efe3e526c185848f0810afb08b1}}, {{cite:51098432b0065a8164728d935e02c4ba28b61ef7}}, {{cite:5156849250a0f3d251df003c927f53cb55b0d157}}, {{cite:ee1cdd8f70bacdfe2529da23bfb7c18888626b0c}}, {{cite:96a28ec616aa85d36677cb9bca4690bc4cfc241c}}, {{cite:e3f4266ed83fb12a27570c387947ca7663c98332}}, {{cite:c36a84893f9a59c948d694e22d4ed1c30b799b3d}}, {{cite:c0ebb94797d1f6b20bbabf1a300467aa743ca360}}, {{cite:635a04b96f10b06e204b1b6a86972284363dabad}}, {{cite:e53e088a3a35150df4f2a2e0290e53a8ece3ec06}}, {{cite:37a806a49791596b5f7b4b6fe7efc7f07aeba197}}, {{cite:edb8b01ff4159576ed3fb87fd20d6ba6655ac984}}, {{cite:2ccc420813cf9c08321bbaa26b2138f79a38441f}}, {{cite:2acb78ae81594a5bd114ac7a7efe0a2cc13a8106}}, {{cite:f4dcd78f75a520d2494c3532f56485d60fba8ec8}}, {{cite:668ab1f2c20b97886a90be008e910e951790f00b}}, {{cite:0f6bf67fd12a397a3178e3ea2f2409fbd3c0b46b}}, {{cite:27e76bfc2d33d73733324c12a542d5172d24c707}}, {{cite:419812abceec020d5a2f3d70a88fb0353c46fc97}}, {{cite:fb29eb476d459b4522f60ca1b680ed7548d4883e}}, {{cite:479c9039ca87b3166c0cdd739dab084f73250a47}},
and also
exploration for future device applications
{{cite:6605f9e02b4f59456602c2d020a59a675b76d441}}, {{cite:0aeea750e1a31ee4455fcf13a14554aa94b6ce6b}}, {{cite:05bd4eb430b997533fc610585b7d5bf3e6fe172d}}, {{cite:3818e0232f41bdd1766cc2306d2247596ee9cf6a}}, {{cite:a1ed4b0ea215bdb49aa285bbfe1d2ffba79b9793}}, {{cite:df8ceb200c3dd452e2169bc851cf2b809b6d7f20}}, {{cite:30aaf5cf316fa6718b07083ff27924f43322b4cd}}.
Similar to conventional III-V semiconductors, TMDs have direct electronic bandgaps and host excitons (albeit with larger exciton binding energies than their III-V counterparts). A crucial aspect that is different between III-V and TMD semiconductors is the size of the electron-hole (e-h) exchange, which is on the order of meV in TMDs while on {{formula:aa1ade9e-3366-4e8f-a5b1-deaa41e01140}} eV in III-V semiconductors.
Another aspect that is, at least in practice, different between typical III-V and TMD semiconductors is the presence of trion resonances below the exciton in TMDs. This is a consequence of intentional or unintentional doping of TMDs. The spectroscopic challenge that arises from the trion resonances is that they are generally close to the expected position of the biexciton resonance, a few tens of meV below the exciton. This makes identification of the resonances, which would be easy if they would be substantially spectrally separated, more difficult. It also makes the identification of lasing processes, that have been observed in TMDs
{{cite:a1ed4b0ea215bdb49aa285bbfe1d2ffba79b9793}}, {{cite:df8ceb200c3dd452e2169bc851cf2b809b6d7f20}}, {{cite:30aaf5cf316fa6718b07083ff27924f43322b4cd}}, more difficult, as there is no strongly spectrally isolated signature that identifies the lasing as excitonic, trion-assisted or biexciton-assisted lasing.
Previous work
{{cite:2ccc420813cf9c08321bbaa26b2138f79a38441f}}, {{cite:2acb78ae81594a5bd114ac7a7efe0a2cc13a8106}}, {{cite:caf1ec40887cc54cadac7dc9fc8f42a0ee18387e}}
has been successful at using microscopic theories, including e-h exchange {{cite:caf1ec40887cc54cadac7dc9fc8f42a0ee18387e}},
to identify spectral signatures in experimental differential transmission or absorption spectra to originate from trions or biexcitons.
Also, the effect of e-h exchange interaction on the exciton dispersion is by now well understood
{{cite:dea3cafc196030ad5d9695bb60a3350f25173801}}, {{cite:51098432b0065a8164728d935e02c4ba28b61ef7}}, {{cite:c0b05373433c57f5f91ae28b93971afff9586bec}}, {{cite:caf1ec40887cc54cadac7dc9fc8f42a0ee18387e}}, {{cite:e90d014742407e0e1c8e186a4954b9a5a02359dc}}, {{cite:f5ca4b2780131c51ae91592ebd59fe440268536e}}, {{cite:c2ee976983355c7f174b4a854c2fa7f06434fa8a}}, as are intervalley exciton scattering dynamics {{cite:19bd6a3df5d703935a90ba37f9adb73d64960a4a}}.
But a systematic study explaining the underlying principles of how e-h exchange influences the spectral positions and lineshape in differential transmission (DT) is still lacking.
| i | da2c94d157562b66e5e99db47a6e6215 |
We compare the error exponent {{formula:b0c67567-fdb8-41ef-a7ef-f3e3a92decb0}} given in Theorem REF corresponding to list decoding with list size {{formula:ab48dfd5-7c48-4812-82eb-1061e5965e64}} for the random matrix ensemble {{formula:352302f1-575d-473d-8226-214ae873e619}} with {{formula:6669d0e1-9375-4063-9dde-bd3bde674ac4}} above where {{formula:bca83327-4aa0-428c-8f60-0b06f69fb210}} which corresponds to list decoding with list size {{formula:ed95f951-28c6-43b6-b4be-f6547b814e16}} for the random code ensemble of the same rate {{formula:27d100b4-7b96-41da-a82e-d9453698fa77}} described by Gallager. We can observe that in the high rate region {{formula:5327df4b-7f3f-4d29-a41c-182a122205e1}} , the two exponents {{formula:108867e9-a188-4487-9c14-7085ca2bfb34}} and {{formula:5f3c3702-c000-46e0-9e85-f5c8ff93020c}} coincide with each other, but in the low rate region {{formula:314ddff5-417a-49ba-8fb2-9f69aff61a6e}} , we have {{formula:8c4c0597-5e2a-4616-ace9-59e37edca888}} whenever {{formula:9c1462e5-0dba-400f-ba8d-abfd072adae3}} . As illustrations we plot the two exponents as functions of {{formula:1441bf33-bc1a-41ed-b4e0-d871d53a6128}} in Figs. 2 and 3 for {{formula:4cba6cb6-00d1-40f7-9ace-1d357808c096}} , {{formula:659e3afa-d5c6-4ba4-ad79-14f2cce267e6}} , {{formula:55d85b2a-1f17-4a16-8565-3483be98034c}} with {{formula:e9973c12-f954-4b26-8470-da1ef7fede00}} and 3. This shows that under the list decoding principle over the erasure channel, the performance of linear codes on average is as good as that of nonlinear codes in the high rate range, but is inferior in the low rate range if the list size {{formula:fe033d00-6829-4d71-b5b0-34d0a9b3c867}} is at least 3. It is well-known that they have the same performance when {{formula:4b3d7bd3-a75c-44e6-946e-47a7ab03b14a}} , that is, under the unambiguous decoding and the maximum likelihood decoding principles {{cite:dc57d76d163e239d9bf62237cca249c1de6709ca}}.
{{figure:b1958044-f963-4810-9535-ad61fb4577ad}} | d | ba27d4e57e21c527a6137fdf0c8e8ede |
We remark that finding {{formula:149e4f26-4036-40df-8878-162cd4a42d6e}} and {{formula:6f44b6c6-ccc3-49c4-b2ae-35d53ddfbd61}} in unambiguously discriminating separable quantum states can be useful in studying the phenomenon of nonlocality without entanglement(NLWE){{cite:cac2056f7201698ac189ee6755daeb51f89bafc4}}.
For the optimal UD of a separable state ensemble {{formula:9eb6179a-a230-4074-bcf4-341d690025d5}} ,
the NLWE phenomenon occurs when {{formula:f8a5d534-f73d-4250-b2cd-2986324a0e19}} cannot be realized only by LOCC,
that is, {{formula:b4926073-dd4e-4f8b-9ef9-16194500e98e}} . Due to Corollary REF , {{formula:7169f699-c421-4363-8b92-15022bb2f6d4}} means {{formula:1cce73b7-4286-419f-b40a-044584e89219}} , therefore the occurrence of NLWE. It is a natural future work to find good bounds on optimal local discrimination in other generalized state discrimination strategies such as an optimal discrimination with a fixed rate of inconclusive results{{cite:176e4caad7daab9ad6f22b168dddd6e024f9c401}}, {{cite:a082b1a564915e29dae2ecfc2b7a43334c571f13}}, {{cite:c0a6abb05bb511891e1916d194bf5b73886d0e6a}}, {{cite:bfcdb7c253ceae5f6816d151f2781a439a08e718}}, {{cite:8caf9694c42c38d41847d8145872d6676cb3d5a4}}.
| d | 0c090b912497b365dc351a8c6e5bc59d |
and we also consider {{formula:8aad1ce4-a4d0-4881-93a2-acc6cba84e6f}} that involves derivatives up to {{formula:0bbbab57-3e78-4882-a6c2-b56b26c861ce}} order for a positive integer {{formula:f8ef3e90-09a8-453f-a214-49cd69232d67}} .
There is a reason that we consider only derivatives in the {{formula:5c53ba37-c0f9-42ce-afbb-86ac6238ef0d}} variable but not the {{formula:d93e89fc-7b2f-4e12-a03c-2ca126bdc474}} variable; see the
discussion in Section 4. Like in the case of {{formula:1d068a4d-1610-41ed-907a-a6983df80b47}} , our main result provides explicit construction of
orthogonal bases and a closed-form formula for the orthogonal projection operator. The study requires an
extension of the Jacobi polynomials with a parameter being a negative integer, which needs to satisfy the
Sobolev orthogonality of one variable that is inherited from {{formula:d4ae0a75-9dbd-4ff7-bdc3-114d1fbaf388}} when we restrict the
inner product to polynomials depending only on the {{formula:affc98dc-a6a1-4118-a61f-4436550eedf4}} variable. Such Sobolev orthogonal polynomials of
one variable have been studied by several authors; see, for example, {{cite:1768d7d6d52f1d4252f7683607f1247281cbdab0}}, {{cite:2f67b70ce9ac67a282bc1a471bb455a04d2e1c7f}}, {{cite:f0d74a4c39856148c45bd3ecde80e46ae2bfc2d2}}, {{cite:508bff693cd8de1b84232979b5f8474c0e091df9}}, {{cite:c9676412f47891aa4925d2836821ad068025cfc0}}, {{cite:87cae4f2c2c7c620b27c06933e4b2a5781db8a84}}
and {{cite:d9fac1352fbcd089f711750d93059faa63abe260}}. We shall follow the approach in {{cite:87cae4f2c2c7c620b27c06933e4b2a5781db8a84}} since it is more convenient for studying orthogonal
projection operators and provides a link, in particular, between the Sobolev orthogonal structure and
the ordinary orthogonal structure, which is useful for studying the convergence of the Fourier orthogonal
series in the Sobolev orthogonal polynomials. In the framework of polynomial approximation theory on the ball
and standard or Sobolev orthogonal polynomials, we can refer to {{cite:dac449a49d046906248d6afca35a1899b97a61f2}}, {{cite:0a2dfea3a95ae6b2ce4b1a322a92ac47f6d88a1f}}, {{cite:32b954391ad976b1a4f33c5ea069c7a123b7cdf2}}, {{cite:ce44a36e209bc31ab6bc698cd450e19355b0c05b}}, {{cite:068eda82dfc109ce9cea1318d91024a162e55528}}, {{cite:9e29a4e68c073e508f509cdee4b22c2bb65e56e8}}, {{cite:acdcc3533df342eb2f83670fff1b27658065a2a5}}, {{cite:394cebe0ba083ea5d196fb595bbaa1cd88c69bd9}}, among others.
| i | 6121689548cf306aaf0f7a92b8d2dec5 |
where {{formula:f1a1d15a-0760-4374-a9eb-5b23ac7e49f4}} are the eigenfunctions of {{formula:586b9478-8a7a-4dce-9beb-1082978a17ad}} ,
{{formula:64410d4c-d910-4a5d-b205-361ebf47c160}} are the eigenvalues of the corresponding
Floquet Hamiltonian, and the last equation follows from Eq. REF . This procedure thus allows access to the exact Floquet
quasienergies and eigenfunctions for finite-sized systems. The
stroboscopic evolution, at {{formula:e7257faf-dbdb-4dc9-9bdb-66e6f4fe344f}} ( where {{formula:93f7899f-d7a3-48b3-827b-38f249573004}} is an integer), for
any operator {{formula:68cd130f-b2b7-416a-b367-783f1702bd17}} , can thus be computed as {{cite:7eb228a78ddf9965d5feb3827a428595683da23e}}
{{formula:336344c8-a9d8-4e00-95e0-a9015f9c4f92}}
| m | b7b87e31abeb4a417c2943b20634287c |
which avoids singularities as the denominator in Eq. (REF ) is strictly positive for {{formula:bf7de4af-6fb4-47cf-9941-5d628ba2d271}} .
The implementation of Eq. on commonly used learning packages with auto-differentiable features, such as Pytorch {{cite:1ba9b4d9426033bf9ed9244a94e3bc5b7c2490c8}} or JAX {{cite:aacf1b56af3344076b2e1621d8e864cc3e0752fd}}, allows to train the flow network {{formula:3150304f-edf6-4dfc-bb81-3d6fde6f9026}} in a weakly-supervised fashion.
| m | 54385d89c9212c9c0a062a25c3eb0477 |
A prevailing method to improve the model robustness against adversarial attacks is adversarial training {{cite:1e6622228b3208b486ed8c4da0b3e9dfb571140d}}. In adversarial training, each batch of data is augmented by adding corresponding adversarial examples of the same batch.
In NLP, adversarial training in the input space has been hard, as existing
natural language adversarial attacks are too slow to generate adversarial examples on the fly during training {{cite:62bd21af025597d2c212a3951e6068be91ab0fae}}, {{cite:80ebe062a241abb44ced9ecebb3200fa7b3b02fd}}, {{cite:19adb1f959dac3b3f67c7c72ad4b4ffbd2d68d59}}.
Although there has been previous work exploring efficient input space adversarial training for NLP {{cite:69dbb249b4fcf00f4d145c17f4acae66f49083a8}}, few have paid attention to input space adversarial training for modern pretrained language models like BERT.
Furthermore, unlike computer vision, where one can use standard datasets consisting of tens of millions of images (for example, ImageNet {{cite:db3ded5ae92282fcceb1d518699d0851a0ce3401}}) for adversarial training, NLP tasks typically have much fewer labeled examples, making it harder to improve the robustness of NLP models with adversarial training.
| i | f40135acaacaf826a18b901acae97a11 |
Theorem 2.1 ({{cite:19878d8cbfe36e475fa4ef2ab500e6a12e3bcc49}}, page 344)
For {{formula:6ce1319d-0751-475e-a268-a405a4aae510}} , let {{formula:d7b1edee-9dd7-462b-a89f-99fc008b1ace}} , {{formula:0c7cc9c9-d085-4dce-9556-690688281164}} and {{formula:799e956d-23ed-4e09-bf70-34e6e90b8a99}} . Then the problem
{{formula:678d1541-be30-402f-9da1-bb52b328c5a5}}
| r | 3e9fbb2289fd7eef3206bf338bf1a84a |
Moment restrictions identify a parameter of interest by restricting the expectation value of so-called moment functions, which depend on the parameter and random variables representing the underlying noisy data generating process. Important problems in causal inference, economics, and generally robust machine learning can be cast in this form {{cite:dcc7099775767270e281b80a00190e80af5884c8}}, {{cite:e3b7f5a8b52e36afdd0581c67ab02a63960644df}}, {{cite:060e1ce53bc637b555887aa6dcc89699c022d123}}, {{cite:8684d572583337100fc2ee787b2c5198da2060cb}}.
Particularly challenging are problems formulated as conditional moment restrictions (CMR), which constrain the conditional expectation of the moment function. Such problems appear, e.g., in instrumental variable (IV) regression {{cite:ccb3f208718c91c005628a63045e06a02a11744e}}, {{cite:7153de2b26c284c6e362dbd1467be47d4907d5a9}}, where the expectation of the residual of the prediction conditioned on so-called instruments is restricted to be zero.
Other applications are policy learning {{cite:4907006be0052826ce3bb318c6f2ce4a04c50747}} and off-policy evaluation in reinforcement learning {{cite:be491b2926ea58f7f599e2c6ee892eafc97abe98}}, {{cite:2a89e6682ef99ea3ffdfbe71d6d237ba78df0e8d}}, {{cite:08fd2970a6782a17e42f5442c96f0261f001a57f}} and double/debiased machine learning {{cite:6225d467954fd07c34906ca3df67e645e009ab9b}}, {{cite:5249840556f8d407826a20aea698fd9beffd0a1e}}, {{cite:baa95d08a35c61429370a22314efd99ef90a6230}}.
| i | b90050842c478d573ef846e7a5398f52 |
However, it is not surprising that the CME is significantly more efficient for the amplification of PMFs than in the case of the axion interaction with magnetic fields. In the induction Eq. (REF ), the helicity parameter {{formula:20d00020-7df6-4251-bae6-cf057cd303ce}} , that enters there the PMF instability term {{formula:35f9e1fe-d38f-4ae7-91b3-8be0591f2b75}} , occurs to be much less than the corresponding CME parameter {{formula:73919185-39d4-472e-a669-590b48f0f971}} , where
{{formula:503ffb68-ec53-4d9d-9ee0-e0d92f9d0e85}} and {{formula:d5750d45-714e-4f3a-a000-d872bc3eac93}} are the chemical potentials for right and left charged leptons. Indeed, the CME parameter, {{formula:f132a32b-5278-4a5d-8fee-aa3b0fde2f4b}} , is given by a great pseudoscalar {{formula:07ec6dbd-cdcf-4f28-81be-204d0faa769a}} at the temperature {{formula:a5b71af0-a174-41c0-9760-7a3ae5aa5777}} , or {{formula:c5ec214d-87a0-4279-89f3-1e36a89373f8}} (see Fig. 1 in Ref. {{cite:554d37f3addf0a48745d03e9411f72a320802261}}). While in the case of axions the pseudoscalar {{formula:5eaa84f7-9ef4-41d6-a5dc-6c9fa611508e}} , when accounting for the initial derivative {{formula:c6223ea6-d9dc-4819-b5be-26ff8502ada0}} [see below Eq. (REF )], is estimated as
{{formula:ca9f4a6a-65b1-47f6-85a0-d877b5497912}}
| d | 27d7ff8b37f6c14939105690e8664231 |
Considering that learning the end-to-end translation between RLRD to HRD from unpaired LR-HR data is challenging, part of the one-stage domain translation-based RSISR methods {{cite:d0af3cae52387dc0a9c78e3d19b7ec5271307160}}, {{cite:61ee6d56c1d430878809f1333b5ade4550c223dd}}, {{cite:a9e78c9013e27b9384102770246bd3b3141485b3}}, {{cite:884b4dc49e2c3d0044615a0e432555da418645a0}}, {{cite:35a1961827df3b5f12197b16bc92e8a3ed027022}} also use the synthetic LR image as a bridge in the training phase. Given unpaired realistic LR and HR images, Fritsche et al. {{cite:61ee6d56c1d430878809f1333b5ade4550c223dd}} first bicubically downsample HR images. Bicubically downsampled results are then translated into the realistic domain to make them follow real scene characteristics, using a standard GAN-based domain translation network trained on the bicubically downsampled images and realistic LR images in an unsupervised fashion. Taking the pseudo-realistic LR images and corresponding HR images as training sample pairs, the ESRGAN {{cite:4e1bbde7576903b293cd1b10b01b2e76454bd23f}} is trained for upsampling in a supervised manner. In order to generate images well matching the target distribution, both domain translation and SR networks are optimized with frequency separation-based loss functions. The source code of DSGAN {{cite:61ee6d56c1d430878809f1333b5ade4550c223dd}} is available at https://github.com/ManuelFritsche/real-world-sr More specifically, the color loss, the texture loss, and the perceptual loss are employed to the low-frequency component, the high-frequency component, and the whole image, respectively. Note that only the SR model is needed to upscale real-world images in the testing phase because it is trained on the image pairs that follow real-world image distribution. On this basis, recently Umer et al. {{cite:35a1961827df3b5f12197b16bc92e8a3ed027022}} improve the GAN-based SR model following the real-world image observation model, thus exploiting the powerful regularization and optimization techniques simultaneously. The source code of SRResCGAN {{cite:35a1961827df3b5f12197b16bc92e8a3ed027022}} is available at https://github.com/RaoUmer/SRResCGAN Rad et al. {{cite:a9e78c9013e27b9384102770246bd3b3141485b3}} convert realistic LR images to bicubic look-alike images based on their copying mechanism and bicubic perceptual loss. Different from the above works {{cite:61ee6d56c1d430878809f1333b5ade4550c223dd}}, {{cite:35a1961827df3b5f12197b16bc92e8a3ed027022}}, {{cite:a9e78c9013e27b9384102770246bd3b3141485b3}} which use a single direction domain translation model, Lugmayr et al. {{cite:d0af3cae52387dc0a9c78e3d19b7ec5271307160}} and Chen et al.{{cite:884b4dc49e2c3d0044615a0e432555da418645a0}} propose to train a bi-directional domain translation model with the cycle consistency constraints for better robustness.
| m | b771fd95e3ab7ce80efe8efd2b0979e8 |
For the purpose of our study, we computed the power-law integrated sensitivity curve {{formula:f2097695-e368-41fc-905d-8bdf94a71a72}} , starting from the noise spectral density in {{cite:2a36945450ab95ecc974dede08df53e7098b2d9e}} for ET, {{cite:778c4232132b0095401d77dd57696d87b4cee208}} for CE and {{cite:18c00ec3693d6f670ef3f6c4d519c4233622dbb9}} for BBO/DECIGO.
For pulsar timing arrays EPTA, NANOGrav and SKA, we directly took the sensitivity curves from {{cite:e89873bd4665744c40b30376f9409d73e919d6e9}}. The signal-to-noise ratio can be improved by using cross-correlation between multiple detectors, e.g. LIGO-Hanford, LIGO-Livingston, VIRGO but also KAGRA which may join the network at the end of run O3, which began on the 1st of April 2019, or LIGO-India which may be operational for run O5 {{cite:9812c54385b06329b03cc837cebf922ab21a5df7}}. We computed the SNR for LIGO from the expression {{cite:5449ba85609de6c841bfe643c0059f50dd691781}}
{{formula:e6fb893b-eb6f-4129-9fb1-fffe6ece563f}}
| r | 6a0867d123da88fb7f812099bc1c9cba |
Bayesian networks {{cite:a15e40a0a71a05854a62752b2f601435159b5865}} are a popular framework of choice for representing uncertainty about the world in multiple scientific domains, including medical diagnosis {{cite:63ffa17adb578fc7668e07e09ac3f86b4d25be2f}}, {{cite:e08e962731fbf71244062800acbceae5317425ef}}, molecular biology {{cite:a93ae336f884122a96838510c617c4f04279a6b9}}, {{cite:6ffd9a958211d81413eea380a5f9e239b1258bfd}}, and ecological modeling {{cite:0b754353e1bcbc64cc870b822fe6890010617eab}}, {{cite:d5170d1e7753f84a82a95c6016acc35f715684bd}}. For many applications, the structure of the Bayesian network, represented as a directed acyclic graph (DAG) and encoding the statistical dependencies between the variables of interest, is assumed to be known based on knowledge from domain experts. However, when this graph is unknown, we can learn the DAG structure of the Bayesian network from data alone in order to discover these statistical (or possibly causal) relationships. This may form the basis of novel scientific theories.
| i | 3a2c5b5cf2b200e58accbcd709bfbd29 |
for some probability kernel {{formula:049e4463-2af1-4a02-ade8-a85273b3490d}} . Here {{formula:5dc3667d-812b-4ce1-b95d-837a26c6a97c}} acts as mixing distribution and {{formula:cd0dac8b-2bf8-4092-8e04-f7461af2a4a7}} represents the random number of mixture components, thus providing a flexible way to model unobserved heterogeneity in the population. The mixture is characterized by the component distribution {{formula:f30572ea-7109-4cf7-ac6a-bc0865f3f43b}} , usually referred as the {{formula:beba52bb-dde7-46b3-ae98-bbb66709f018}} th mixture component, and the mixing weights {{formula:abe58022-b7d8-4604-94da-5f1dc9b0f4bb}} . See {{cite:1613337c3305a3cec8524f6686d4e65f96a883a0}} for a recent review on the inferential implications of different choices of {{formula:b7fffabe-96d7-4973-9f52-3770da02ba50}} .
| i | 170e8d11b77ce90a6b4e5bfd35c6ed71 |
Jelinek-Mercer and Dirichlet prior are the two most common types of smoothing for MNB models. One view
of smoothing is that smoothing methods discount seen occurrences of words in order to redistribute the subtracted
probability mass {{formula:361b918e-05fc-4eeb-9021-912726dec1f5}} to the background model. Under this view both of these discount the seen counts linearly
by {{formula:224957fe-e9b8-41ab-aff3-ce77b42e81f9}} . A third basic type of smoothing is called is called absolute discounting
{{cite:f914954399dc611229c1f90ea138660a66d9ba2e}}, {{cite:0790815270825263d6d9e94f86a81fa285b36d5d}}, {{cite:362013f565585925f00360c7c0da92d3a3657678}}, {{cite:93402ec5fd190ebc0b98222ab361b4115db29475}}, {{cite:2398d0ace7b5cfa702874f3306aff0e43a835cb8}}. This works similar to Jelinek-Mercer smoothing, but subtracts
a parameter value {{formula:11eebc65-40c8-4f59-b2b7-5c8835e8bc86}} from all counts for a label, and uses the subtracted probability
mass for choosing the smoothing coefficient. The discounted counts can be denoted {{formula:acca233d-f420-460b-bed3-1aa8f31703fa}} . Using Equation
REF and choosing {{formula:99415bfc-c3b6-4f05-939b-7dee6c527c6c}} ,
and {{formula:091efc34-26ac-4ae0-8b2e-9e39a0074c03}} produces absolute discounting.
| m | 0deee987263b831ab92d6521a9319755 |
We also show a denoising example based on the “ROF” method (which
consists simply in minimizing the total variation (defined
by the surface tension {{formula:5efdc71d-ec4c-417c-b0ec-58d34dc9ad33}} ) of an image with a quadratic
penalization of the distance to a noisy data, in order to produce a
denoised version, see {{cite:5991befb7e674d88b1e9a41b96e04660bf185e72}}) with the anisotropic tension {{formula:2a28606b-459d-4dc3-891f-c2215a051a40}} (“{{formula:b44b68a6-42b6-4023-911e-0e98d71bf5d3}} ”)
and the optimized homogenized surface tension for {{formula:bcd26ab7-a7f3-4751-b314-7092c7c2dd5b}} .
The original image is degraded with a Gaussian noise with {{formula:6a5e72f9-4b31-4062-9d22-77cf41e4bbcd}} standard
deviation (with respect to the range of the values).
Here, the difference between the two regularizers is hardly perceptible (since the data term strongly influences the position of
the discontinuities), yet a close-up (bottom row) allows to see a slight difference, for instance on the cheek where the {{formula:baf43d6a-cb3b-4cbe-819a-64637aaa707f}} anisotropy
produces block structures.
{{figure:c9d6eaac-a13d-4293-9e93-9fa51dcde8b7}} | r | 7977735ba78d9d2bc59f4a3647887bf3 |
Recently, value-based methods have been applied to multi-agent scenarios to solve complex Markov games and have achieved significant algorithmic progress. VDN {{cite:7b44534cabff9626e2f3da659c317f1ff4456d5b}} represents the joint action-value as a summation of individual value functions. Due to its poor expression factorization, QMIX {{cite:a18699a276848c71662c8fd485d4c185d6bcc10c}} improves VDN {{cite:7b44534cabff9626e2f3da659c317f1ff4456d5b}} by using a mixing network for nonlinear aggregation while maintaining the monotonic relationship between centralized and individual value functions. Moreover, weighted QMIX {{cite:b8f2de3678a832bcc44d77f488cf321c99a36a5c}} adapts a twin network and encourages underestimated actions to alleviate the risk of suboptimal outcomes. The monotonic constraints of QMIX and similar methods lead to provably poor exploratory and suboptimal properties. To address the structural limitations, QTRAN {{cite:a3c3359fa2d0440550620188eea4620c361703c9}} constructs regularizations with linear constraints and relaxes them with a {{formula:0a7f910c-26c6-4a0b-8825-1f1982f39220}} -norm penalty to improve tractability, but its constraints are computationally intractable. MAVEN {{cite:3a4fba67c7ac770e1fc83eed6558ccffda3ea8e5}} relaxes QTRAN {{cite:a3c3359fa2d0440550620188eea4620c361703c9}} by two penalties and introduces a hierarchical model to coordinate diverse explorations among agents. In {{cite:f61ff830136be4d821ae751171d2c6adadd67af1}}, a duplex dueling network architecture is introduced for factoring joint value functions, which achieves state-of-the-art on a range of cooperative tasks. Additionally, some more advanced methods {{cite:5e35fb5ef834144cec60c687b1fa9b744ddef66b}}, {{cite:0be0a35aa5da6bc9ba5c3d8f390bc0dbd02a150c}} introduce role-oriented frameworks to decompose complex MARL tasks. In general, these methods mainly focus on aggregating local agent utility networks into a central critic network, while our method improves the structure of individual agent networks for more robust performance.
| m | 3f0abcaf33992e90a9fda8e84ab41bad |
Given the significant computational effort needed to generate a
network, we propose a strategy that limits the amount of such
generation steps. While it is common in evolutionary algorithms to use
large populations to prevent local minima, this is not the only
possible strategy {{cite:e47d4cd3028cd8e2b24ae31612b074faf1b2df9d}}, nor is it guaranteed to work {{cite:fbf4060b49c4a41ead62016778b3d7cd3aa0b6df}}.
| m | 425b1b16a4ff106d84f7c329c8eec6ee |
HOCH{{formula:819a9f77-2e7d-46a1-9492-6202561e2a26}} CN is thus far only detected in two sources, SMM1-a and IRAS 16293B {{cite:52bf3ae49d3fb3e8597b4faaf2fe6e357e72caa4}}, and therefore a chemical comparison is limited to these two objects. To use molecular ratios that are unbiased by observational parameters, only data of the chemical inventory of IRAS 16293B obtained with PILS survey data at the full-beam offset position is used for the source comparison. This means that the tentative column density of HOCH{{formula:6d108bdb-82ba-4719-9be3-be7b48371ad2}} CN in IRAS 16293B is used. Figure REF shows the abundances of molecules detected in this work to CH{{formula:673e2cd3-c26b-4ec9-806f-ecc21c0c60df}} OH and HNCO in SMM1-a and IRAS 16293B. For IRAS 16293B, the analysis performed in this work is combined with results from {{cite:900644d0f627625f6e2eab6a9533d421cf995029}}, {{cite:8a1e3030b6d052f3e3e259d40490c6a7b327b96c}}, {{cite:e47972eb68a79fbc8a6d34a1674b1d6ceb46ed66}}, {{cite:d3115feaff04c4cc4fbe544c8cfbb45d663399a1}}, {{cite:b9693081c44f0594a415440a4de0b5c34aa76122}}, {{cite:49d11b931c59b320b8ef236cfd35e14c2cd3ed93}}, {{cite:66a9ca4f9c6ef1f0b4ce0ba8a3c2ffcaa218bbc0}}. For both the [X]/[CH{{formula:519e1946-2f88-49b4-ac71-aac5f2556f6b}} OH] and [X]/[HNCO] ratios, all the oxygen-bearing molecules, CH{{formula:b727cd1e-1058-4eef-a9ed-7e7e1ddf213f}} CN, and NH{{formula:ce062473-3609-444a-8be4-a4bee7e579d9}} CN are found to be more abundant in IRAS 16293B than in SMM1-a. For [X]/[CH{{formula:d629db62-b10f-4b52-80ff-5971b3ab7a5b}} OH] its ratios are generally a factor of a few lower in SMM1-a, while for the [X]/[HNCO] ratios the difference is usually more than a factor of ten.
| d | e9feb96e42a24febe7111e89e4698dcb |
The vast majority of published video compression research papers provide results using the objective metrics Peak signal-to-noise ratio (PSNR) {{cite:55bd64e0ecf0bba6338e8e25dc150d1e3dbf084c}}, structural similarity index measure (SSIM) {{cite:9aa3c6b7cc661daf95d311b5ef0974caffdf4bb0}}, multi-scale SSIM (MS-SSIM) {{cite:65e12bb9cfec5e3549939e2ae29602bf98136db0}}, and Video Multi-Method Assessment Fusion (VMAF) {{cite:25c72fc2d1ae221cbf9b60f82dc838dbf0848844}}, e.g., {{cite:f2a209e3b40cf4fa58ed0e818bb6d7e006bd2404}}, {{cite:884d79f15f11d5a1708cee8e88e0c5b30d837109}}, {{cite:cbaefecab65081b4a13316a8bff906091975fcf4}}. However, it has been shown that PSNR, SSIM, and MS-SSIM are not well correlated to subjective opinion {{cite:25c72fc2d1ae221cbf9b60f82dc838dbf0848844}}, {{cite:a7d019863d82968f9ba6d6515914375ee409b0d9}}. VMAF has been trained on traditional DSP-based video codecs such as H.264/AVC {{cite:cfcb639ab0178f581d13b006fe2f4286419d5cde}}, but has not been shown to correlate with the newer deep learning based codecs. Moreover, VMAF hasn't been trained for longer term effects like recency, primacy, and rebuffering {{cite:85a6fa2d77ee99c665e0c662727664d90ec6cdbf}}. Therefore for video codec research there is no alternative to subjective tests to evaluate and compare codecs at this time.
| i | 7c34a6d97752eaa48d881403fdada593 |
For more details about the loss and optimization procedure see {{cite:282c4e00848f5c7a2764b1edc1ea9c5c079d0ef5}}.
Our agent implementation instantiates the policy via {{formula:67f9d569-11f6-4d60-8005-fa087a937329}} where {{formula:5459e5f6-2c16-45de-a943-05da0fdca1c5}} and {{formula:27cbe081-6d87-4cf2-a11c-2dbdfb8b1e9b}} is the Kronecker delta.
The memory {{formula:d8ba9b08-7279-4fee-b1ba-518d65a60f43}} is reset at the beginning of each episode and it is updated along the trajectory.
| m | ad3416684a242c021855d12d5bd06d29 |
Support vector machines {{cite:2a06a9c650d9412efa5fd463b4233c8c3703903a}} partition their input space in regions
using hyperplanes that separate the training inputs according to
their labels.
They hyperplanes are chosen (i.e., learned during training) to maximize
their distance (called margin) to their closest training inputs
(called support vectors).
Figure REF shows a very simple support vector machine in a
two-dimensional input space.
When the training inputs are not linearly separable in the input space, the
input space is implicitly projected, using so-called kernel
functions, into a much higher-dimensional space in which the training
inputs become linearly separable. This allows a support vector machine to
also learn non-linear decision boundaries.
| m | 528b6ffeb3fc515cc5467ed1ad139d44 |
Hand-designed networks found in the literature {{cite:585273b83cbde6082aeca723f8a6253ed3bf77a9}}, {{cite:f382db3ba761916da2ea1893ac69cd5bd766b090}} are compared to the best weight agnostic networks found for each task. We compare the mean performance over 100 trials under 4 conditions:
| r | c19db17b9a4a54f0ee01c28d41026c98 |
{{cite:080d7c15a02a0b378134849b2e5caa79d4009bbd}} 2021
{{table:8082d1bf-8827-4bc6-85a1-2bff5bf9ba41}} | m | c3208ad4f660f44a3cfcea2edf402078 |
Third, there is a fundamental mathematical question of characterizing the attractor whose existence we postulate in Claim REF . It is likely that symmetric bifurcation theory {{cite:6b4b6f7d10850e661e2b72480928ce11bfeced4b}} will provide a set of tools to enable this analysis.
Answering these questions will push forward knowledge of how the unfolding pitchfork can be used to coordinate high-level autonomous behaviors.
| d | ab1d2f787bfb320079abea0d3bd61827 |
Recent advancements in Internet of Things (IoT) and 5G wireless networks have paved a way towards realizing new application such as surveillance, augmented/virtual reality, and face recognition, which usually are both computation and caching resource intensive. For battery-powered and resource-constrained devices, such as wearable devices, on-device sensors, and smart phones, it is therefore challenging to support such applications, in particular, delay sensitive applications {{cite:9c197c64f0d95b9feacc05c46f5c1296860fc655}}. To alleviate computation limitations and to prolong battery lifetime of IoT devices, Mobile Cloud Computing (MCC) leverages offloading computation intensive tasks to the centralized cloud server. MCC however may result in high communication latency, low coverage, and lagged data transmission thus limiting its applicability for real-time applications such as automated driving and smart navigation. Edge computing is a promising paradigm to address such issues associated with MCC, by pushing additional computation resources available at the edge servers {{cite:a9a67b3d713f812fb1e1aa0d75e7a608ce9e7085}}.
| i | 871a9575ebac8430e62bbd5fd4b7d2d2 |
Our implementation of the copy generation in the Transformer is inspired by {{cite:534a278402ba29476c1cddc488754b23dd9ad4bc}}. We use the final encoder attention vector and produce a copying vector emphasising each input token relative to its attention weight {{formula:ae0ffe00-1dff-4e67-954a-155e9da274bb}} , Equation REF . This is then interpolated with the original vocabulary distribution {{formula:22fc78e6-7ec6-4d8b-b1dd-5fb2cae9609b}} through a {{formula:f61216c6-5f6e-4a1f-812f-bbca3b65bc1e}} function. The use of out-of-vocabulary tokens for very rare words, described in Section REF , allows for even more generic copying of words that haven't even been seen in the training dataset.
{{figure:3b5c5822-a99c-42f3-867b-554c11b6555c}} | m | 14f5d42c7086ac51c55b1d58632a694d |
In the modern era, observations may have a comparable or even larger dimension than the number of samples. So the dimension of parameters cannot be considered as fixed. In order to perform consistent estimation, statisticians need to assume the underlying parameters are sparse(i.e., the parameters contain many zeros), and proceed with statistical inference based on this assumption. Lasso is a suitable algorithm for this setting since it conducts an implicit model selection, i.e., zeroing out parameters that are not significant, see Tibshirani {{cite:42dd3c115b91421ef7d0006b6b02be4d695e03cc}}. More recent work includes Zhao and Yu {{cite:fd61ac680e80e61da632345afee1d93df67ff929}}, Meinshausen and Bühlmann {{cite:4c385829467c08c458994508ec1b27ab2052deeb}} and Meinshausen and Yu {{cite:ffaeb00dd64a84edd12905d5d43e1818a363b047}} for model selection; Zhang and Zhang {{cite:f7efee8b0371a6de88d37b642f5d449712219e79}}, Zhang and Cheng {{cite:29cbd15b0c54c3b3135822367a1bb5eb62861cdd}} and Chatterjee and Lahiri {{cite:489deb73abc33d4c7b19fa771ec76cd8c2559f4c}}, {{cite:3aa68282df4aa263789b2d0ce6c5c626d09e0323}} for statistical inference and hypothesis testing; Greenshtein and Ritov {{cite:cba891197200986ca27da28862e46b95cdd6c885}} for prediction and Zou {{cite:58f77eb78eae867129348fcaa1423ef614ece14f}} for algorithm improvement. We refer Bühlmann and van de Geer {{cite:72aea395be46dc5b587a51c1fbfed498a9c677d5}} for a comprehensive overview of the Lasso method on high dimensional data set.
| i | c39136899f897084aad720637a473ede |
We may and shall assume that {{formula:8b282bff-4577-4db6-8164-493f889f183b}} otherwise the statement trivially holds.
Let {{formula:e9555893-c12a-4061-b6ba-42762e7e6569}} , that is, {{formula:83e3a7b2-53be-432a-aed0-792d7f449df8}} and {{formula:a692ef1c-316a-4b96-a271-3adb7967462a}} .
It is easy to check that {{formula:7f3deeb3-0182-409c-ab9b-4cabf6d2191a}} . Thus the
property (REF ) yields
{{formula:011dd4ee-0065-4143-ba17-525399f13d96}} .
Hence {{formula:83b448f4-cc71-4f23-b06b-8e5a793d01cc}} .
Passing to the supremum over {{formula:4906eb43-f227-489c-9ca4-3ac68d47991e}} we get
{{formula:80231fd0-b30b-4217-a7a1-c7d08dd65b50}} .
To complete the proof, we must find {{formula:8d0e2c99-7407-4072-99af-1fb1dd230e9d}}
such that {{formula:6cf2f88e-59cd-40de-af8a-450f6cfeba40}} . Then we will able to
write "max" instead of "sup".
We consider two cases. First assume that {{formula:a5d74bce-41be-4187-a225-df9303e79236}} and {{formula:3dc78b57-55af-4db2-b4ba-067086736a67}} are linearly dependent, i.e. {{formula:8e23b9f3-dde8-4961-80a2-06737ebdd73f}} with
some number {{formula:04d42a26-1cd8-43ac-b9eb-112ca501eeaf}} . Fix {{formula:0694b11c-94a6-4325-939d-4d148dec77fd}} . Then
{{formula:3c2beebd-e99a-4aca-9425-be8b8e49c807}}
So, the first case is complete. Now, suppose that {{formula:7f0342d1-6904-4d60-adc4-84710941bc4f}} is a linearly independent subset.
Let us define a real subspace {{formula:c8272695-dc09-43c2-a7c3-f96063062854}} by the formula
{{formula:235c8fed-a84c-4282-b507-ca9b7c5cb23d}} .
Put {{formula:5d4a3d8f-2052-41d6-8a09-09b68ff066b5}} . It follows from
Lemma REF that {{formula:d7767b64-9af5-47ed-969a-d2e875d33517}} . This equality yields, in
particular, that there exists a sequence {{formula:579fb407-33d2-4dd4-b716-0dc8765d03c0}} in {{formula:53e80f51-7a74-48b9-93f6-97ed4342fcd6}} such that {{formula:14611cd1-822e-450d-bdae-f0fb710d1cd7}} and
{{formula:8f74e222-7242-4afc-9015-891fd337652d}} .
Let us define for the moment a closed subalgebra {{formula:947291a2-f1b6-495b-91d4-5a82888fe377}}
spanned by the vectors
{{formula:5afddd4d-aa2c-4eed-a417-d3eb45885c40}} , {{formula:722ae819-1c19-40ac-ba6a-7498b576b9e0}} , {{formula:71902cb5-44bd-41da-91c1-76947bc0c062}} and {{formula:6c246b80-2e6a-46f1-af0a-e3eb25978a82}} .
In particular, we have
{{formula:c133598d-7b24-4ecd-9f7d-1c429c42fa6a}} .
Moreover, it is easily seen that {{formula:5bd903ca-9314-4c4c-9345-297d36ce4190}} is separable.
Also, there exist states {{formula:de5ee51f-7801-43ab-8612-d37adbc1c2ac}} such that
{{formula:e1b63712-dc9f-4637-8873-8ff845db1e52}}
Now our attention must focus on the real two-dimensional space {{formula:2f2d13a5-cea5-490b-8a7b-0d80bb01d96a}} .
Fix {{formula:03c199f7-efa6-47a7-8fb5-36c837388cff}} . It is not difficult to see that
{{formula:edf70520-b83b-4899-b66a-82dc6707785a}}
is a {{formula:3fccc15d-6b05-486c-94d9-b19a66b5b6df}} -linear functional and
{{formula:b3bfe054-4a54-43bf-8151-9b739587556c}}
The space {{formula:0aa449b6-3c0b-450f-9a06-5e2f76088bd7}} is smooth at {{formula:daf79cad-01ae-43db-b2e1-c8e0dabf63df}} . Thus, from (REF ) and (REF ) it is known that
{{formula:e3324b44-163a-43e1-be07-40a466300385}}
By Alaoglu's Theorem, we known that the closed unit ball {{formula:fe6ba830-ecf7-46db-b74e-dd46e65b6a9f}} is weakly* compact.
It is easy to check that subset {{formula:61dcc215-b403-4c59-97c7-a9211485b9e6}} is a norm-closed convex
subset of the weakly* compact ball of {{formula:ffb08ebe-bac2-41d9-a9f2-23418c1ae7ad}} . Therefore {{formula:ef2dbfbe-98c2-4282-a3af-e11fc7fb8cb4}} is weakly* compact.
Since {{formula:d8429123-74eb-4e89-8574-219734426538}} is separable, {{formula:2d17d280-5cec-4057-b453-7b2152099bd0}} is weakly* sequentially compact.
Thus, there are an element {{formula:c668bf37-db42-44e0-b238-ee179567c480}} and a
subsequence {{formula:eb6f571e-1a2f-4888-a02c-60dc6e541922}}
such that {{formula:076bffab-7806-4088-a1e2-86d82475e84c}} .
Since {{formula:5f8e3fa3-baa0-4355-a0c6-bcb0be132be9}} , we conclude that
{{formula:a0fe8eeb-7ede-4981-abad-af0ff0d4acf7}}
Similarly, since {{formula:55445a4d-46f7-46c8-9de8-746ea814f129}} , it
follows that
{{formula:965b7ab2-41d3-4c2a-97c4-a25ead8d5909}}
Combining the three conditions (P5)-(REF )-(REF ) we deduce that
{{formula:e42d45da-aa94-4692-b2ea-f46e1ae49c96}}
Furthermore, combining (REF ) with (REF ) yields
{{formula:30bcdac5-c255-424f-bd92-e20e8586f980}} .
Now we back to the {{formula:de9f6321-350d-4762-b8ad-69b329f3b789}} -algebra {{formula:0145f155-5491-43f2-b18a-005e56f66f68}} and we go to the dual normed
space {{formula:9ef91eb0-011a-4360-87e6-b5009b84bf3f}} . Namely, since {{formula:6dc52c15-8dc0-480a-88bd-28db790e4d77}} is a state on {{formula:a99e6d1a-8a9a-4386-bfda-6d4b5be29ece}} ,
it follows that there exists a state {{formula:77997653-d565-4588-bded-8c3c88a4c99b}} on {{formula:c493fe4c-0e7d-4fab-bd32-d70b7b597497}} such
that {{formula:d85b42a8-3509-416e-b2bd-f1cf3c07a80e}} (see e.g. {{cite:0daefb8b0334086cd89bad8e4322c690991d51ca}}). From this
we get {{formula:8eab3658-90df-4f27-b306-8a33bf44b4c1}} and
{{formula:754b0b3e-c7be-4974-897a-2b84980d8424}} . The proof is completed.
| r | 520c1e9f4df254cd801ab29b506cb26c |
With regard to the second-order derivatives, we have the following counterpart of Yau's {{formula:6e851a23-a4df-4699-bafc-98d058149288}} estimate {{cite:cc5cf144d996e52b5933a42da0e15e47d9ecda79}}.
| i | dcecccb95482e4bb2afafe2a50225504 |
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