text stringlengths 54 548k | label stringclasses 4
values | id_ stringlengths 32 32 |
|---|---|---|
We note the similarity of (REF ) to the approximate quadratic Hamiltonian of Fetter {{cite:ed405a25dd3ad8838d0b86db4917269b8151d697}}, {{cite:8f65cd48b0786c4089ef50f427e8bb7761d68959}}.
| d | 5b987ec01e862bd29a91fa9327dc2162 |
The bulk of the research on deep-learning super-resolution methods considers the use of a single LR image to produce an HR output {{cite:b2075be1a2d7afd4dac4ee7f755f05f8c9266a9f}}, {{cite:6fb47d68d0251e315a351f81b31b0b2e346124b7}}. In contrast, video super-resolution schemes exploit the temporal correlations in multiple consecutive LR images to produce an improved HR reconstruction in exchange for frame rate {{cite:2f6d6715b10b5532d68c51870c0017a988b43cf0}}. Most of these approaches are based on a combination of two networks: one for inter-frame alignment {{cite:fb37e3d3f975d60b93cb41328d99f8901bb978fd}} and another one for feature extraction/fusion to produce a HR space {{cite:5f4eeddee846cbbcb595bcd682354b7588b8cee0}}, {{cite:d983773537f776c9052d5be198f1eb04688cbdb8}}. Other methods do not use alignment but exploit the spatio-temporal information for feature extraction using 2D or 3D convolutions {{cite:55262ad6fbdc67f7b81f58b01bacf978e11d8482}}, or recurrent neural networks RCNN {{cite:e0910ee0cf76d73125ba84d29f2b0b8838b8d700}}. All of the aforementioned video superresolution schemes work best in the case of sub-pixel displacements between consecutive frames.
| i | 1f4c6296d73ab06a09b07ca78360fa45 |
Shots Aggregation Most prior work {{cite:1185c3ef79bf193de4412a760530f1b4e4ae6a59}}, {{cite:524910ea307f2fd2b61771d93e3dc61cb92bae50}}, {{cite:93f68ce706cbbab76b0dd15f37d18f4284420207}} simply average multi-shot support images to obtain a class prototype for detection head. However, this cannot fully exploit the little but valuable information from the support images. Again, we construct a shots aggregation module by learning the relationship between the multi-support images to obtain an effective shots aggregation feature, which is named as global-local relation network (GLR). With GLR, AirDet can achieve significant improvements with more shots.
| i | 91a9cdb27c1a861e42aff6d91c9db57c |
Spanier {{cite:db33bda32b9cbe18586e2133dab07ac18a040993}} introduced a different topology on the fundamental group which has been called the whisker topology by Brodskiy et al. {{cite:61149024b9e0cf3f4f0b5967826acc7cfb0a973c}} and denoted by {{formula:f19d59c7-123c-48cd-b31e-b8b57eb67195}} . They showed that {{formula:2555b7ed-4541-4f93-9767-b029fc01ecd5}} is a topological group when the inverse map is continuous {{cite:61149024b9e0cf3f4f0b5967826acc7cfb0a973c}}. Although {{formula:0fd0ea8a-9348-407e-95a3-b2a16bc37792}} is not a quasitopological group, in general, we show that it is a homogenous space (see Proposition 3.2). In Section 3, after recalling the whisker topology and presenting some of its properties, we intend to describe its influence on the notion of generalized covering subgroups. Trying to classify the generalized covering subgroups of the fundamental group, we give an example to show that the whisker topology is not suitable for the subject. Moreover, we find some properties of the whisker topology on the qoutient space {{formula:6b71a54b-7d02-4332-9849-676a9b7afd84}} , where {{formula:fe5c4b49-c5dd-4dda-a7af-416394eaaf44}} is a subgroup of {{formula:ae196ea8-2e2a-44ad-823a-5fb9ff1e7000}} .
| i | 3363820684e46ac542f85dc2ac5fb6bd |
While there are a large number of alternative clustering methods available (such as STING {{cite:ad36327c6f8f7d08d279a9e919594cc95175ee81}}, BIRCH {{cite:296feb1ec0a82e653195e223441c420b7e42a961}}, CLIQUE {{cite:04d1d6226b9d2e1605eacf23ea97851058ebdf4a}}, WaveCluster {{cite:394cb1976a843016cde685d1b052236043c876ca}}, DenClue {{cite:7a318e9a8ed6dd2c6092d6d5be15834c33278a81}}, spectral clustering {{cite:15f3a6f9602ad1a6a0b7459be82a4b176f5d2bd7}}, Gaussian mixture model {{cite:da57001c941f0acc804d3515d640e6c8f53bb297}}, {{cite:622119fe3b81da92505dd22299b17c5a56d027fe}}, {{cite:52e64111d27959e3dfd97be6e261c80dcce257e6}}, DBSCAN {{cite:75bc4d6e35bb42a6eb67ad346d3df96de784bb84}} and HDBSCAN {{cite:3d36b7146b4c3684cd93d94484fa169f6a8c0a26}}, to name just a few of the more commonly used), many of these are inappropriate for time series data and/or require difficult parameter choices. For example, the density-based DBSCAN algorithm is not appropriate for time series pieces because there is no reason to expect that similar pieces {{formula:d0b55005-ed57-4bd2-87d4-ae84cbcf4809}} would aggregate in regions of high density.
| d | bd201aa9df53c458447af84a54a58b47 |
Comparison to Slim: Table REF shows that {{formula:f582a040-e984-418a-be88-c1602e639959}} achieved notably increased accuracy compared to Slim on all the data sets. This suggests that dropping the L1-norm regularization as well as the non-negativity constraint on the learned weights is beneficial. Our analysis indicates that the latter is especially important: as illustrated in Figure REF on the Netflix data (the histograms for ML-20M and MSD data look almost identical up to re-scaling, and are omitted), the learned weights in {{formula:5fd8f27f-c351-4437-8af3-0c25b858251c}} are distributed around 0. Interestingly, it turns out that about 60% of the learned weights are negative on all the data sets in our experiments (regarding both papers {{cite:e124726f415b7178453af1607740bc4c5d1fbeb7}}, {{cite:4cdfee280715cf85f18bd1aaee05789ee28a6fb6}}). This indicates that it is crucial to learn also the dissimilarity (negative weights) between items besides their similarity (positive weights).
Moreover, when we simply set the negative weights to zero (see {{formula:d3521c9d-6b77-49ff-ba11-1df7e41c69dd}}{{formula:19015be9-3105-4029-a85b-26e92e64f1dc}} in Table REF ), which obviously is not the optimal non-negative solution, the resulting accuracy drops and is very close to the one of Slim.
Apart from that, note that {{formula:c030dd51-ca96-4cef-85df-fc1d3fecd0ba}}{{formula:13742e96-cc96-4144-be34-e288416739dc}} is still quite dense (40% positive weights) compared to Slim, which indirectly indicates that the sparsity of Slim (due to L{{formula:fc5eb2c0-647b-4930-91c0-f8ce4e4014eb}} -norm regularization) did not noticeably improve the ranking accuracy of Slim in our experiments.
| r | 4efdcecae093c28d33c32673864ed561 |
In this paper we explored synchronization of phase oscillators on hypergraphs with heterogeneous structures, generalizing the results in {{cite:346dd99d9a94e11d682a6de85cdd3a0c3da36347}}, {{cite:00a955a1eee53ee1bdcb495811277e81d86ff4b5}} to more complex scenarios. The mean-field approximation allowed us to predict the onset of synchronization, explosive transitions between synchronized and incoherent states, and their bistability as a function of system parameters. In the absence of hyperedges of size larger than 2, we recover a smooth transition between incoherent and synchronized states as found in the standard network Kuramoto model {{cite:6465060be91f34e63ff48ba35909998e0f237420}}, {{cite:c477e71af3e204f6705c2249be834ce5faabab06}}. Sufficiently strong higher order interactions lead to an abrupt transition and bistability of incoherent and synchronized states (see Ref.{{cite:e176e30bbf56289f8f92932d2dc2fcc4c6848cc4}} for a broader perspective of this issue). For a hypergraph with correlated links and triangles, we showed that the onset of synchronization and onset of bistability depend on the moments of the degree distribution. For the hypergraph model we considered, higher order-interactions only affect the onset of bistability, but not the onset of synchronization (however, see additional discussion on this point below). We have also verified that similar results hold true for networks with power law and bimodal degree distributions.
| d | 4fbd17cbe429e1a87be795356ea9a3ca |
Since the MNIST-360 dataset has no task boundaries, many methods that rely on task boundaries are inadequate for it, such as LWF {{cite:fa56e47f9eabda9fb58d3809064c260cd90fee53}}, oEWC {{cite:2690187fabeb1e5af54f41bee10e191e1913cf8b}}, SI {{cite:bc3d9631725c69a900d94a4c8dc991ec485dcdcd}}, GEM {{cite:0bab1d4ecd9b815128cc9c4910fe42a645cc5bf4}}, iCaRL {{cite:9b448d970d0ed0cd59398d908f645c1938a35120}}, FDR {{cite:32a5772fa521df1ee4660279747379f0407b6ab7}}, and HAL {{cite:be63a388a1640855a979ae0578c7d9bb97950337}}. Thus, their methods are unavailable on MNIST-360 dataset. We could observe that our CoCa framework achieves top performance across all the different buffer sizes, which surpasses the suboptimal method at least in 5%. It is quite impressive when the buffer size is limited, such as 200, with at least 12% gains against the other competitors. These results indicate that the collaborative distillation and self-supervision greatly alleviate catastrophic forgetting by mitigating deviation in the absence of task boundaries.
| m | 0eb659caa39edb3099129315e8bd994f |
Baselines: We have compared the retrieval and ranking performance of our system with some of the other state-of-the-art face image retrieval and ranking approaches including MARR {{cite:c4af31cb7f1c5d475fc2601d3aea4a4bb282a9d6}}, rankBoost {{cite:400911b40170ed1e59f5ec321ce98f0a3c14f308}}, TagProp {{cite:82429f94e00d35acabd3e32e9e57de33c7385972}}. For fair comparison, we have exploited the VGG-19 architecture pretrained on Imagenet dataset, which is the same as the initial CNN of the image modality in DNDCMH, to extract CNN features. All the above baselines are trained based on these CNN features. Additionally, we have also compared our algorithm with the state-of-the-art deep cross modal hashing algorithms DCMH {{cite:a0a0a7fe6ad9a05e30ad0741f155fd483473da77}}, pairwise relationship guided deep hashing for cross-modal retrieval (PRDH) {{cite:25b593906b17ae7c0af8c5970a5eb455be360cbc}}, and triplet-based hashing network (THN) {{cite:165781157718cfb96c9419788445173b1ac4a4a1}}. We have also compared the DNDCMH framework with only the ADCMH network; i.e., training using only stage 1(a).
| r | db448a8facc5ceb0fd5c41109e213d52 |
Linear optical networks are the basis of quantum technologies.
Many important applications of quantum technologies such as quantum key distribution {{cite:8ac10f6ef356d9410e6ef88ef93c3218deec819a}} and boson sampling {{cite:c8b03ace2d04d53623b613fff12005013488d219}} were demonstrated using linear optics.
At the heart of these linear networks lie optical beam splitters (BS) and phase shifters, since it was shown that with these two components any unitary matrix operation can be implemented {{cite:3b8b068755d6ae8d0999907fb1a9c79fecc53a31}}.
| i | 5f5a3505e1e8772ac44453e9295b3da6 |
For simple models, sampling may be an unnecessarily slow mode of processing when the whole distribution is sufficiently encoded by the weights and hence by simultaneous neural activations in the output layer.
In more complex models, sampling may be necessary in the same way it is necessary for serial computing: to approximate a complex distribution over many unobserved variables.
Population codes provide the capability to fully encode highly complex distributions, but in practice, applying those distributions to a particular action or perception may not be straightforward or possible without sampling.
Different intervals of the learned distribution over one layer may correspond to mutually exclusive actions.
Sampling allows the network to control its search across arbitrarily complex domains by engaging in random activity in the simpler, earlier stages of processing leading up to them.
This idea is analogous to sampling from the lowest-dimensional encoding layer of a variational autoencoder to search the final layer of complex reconstructions {{cite:4e788fd628499381b0bd7805a907040da5175cbb}}.
| d | 675e9396dc1968d643556f459f4ad4c5 |
One potential benefit of the regression approach is that it allows for the development and study of non-separable estimators. We can incorporate covariates and structural information that are useful for estimating the unknown means by including additional inputs in the estimator. The need to include covariates and structural information is prevalent in settings where there are replications that can be used as covariates {{cite:8cc435a7bfb15639c085eafbb7ed9f6a5fcd52e7}}, where there are results from auxiliary experiments {{cite:a4373a0804beb9d969714dc17dd723fba9c7181e}}, where there is a regular dependence structure, similar to AR({{formula:b4aa2e86-0a83-44a7-bf94-7fd32cc851a8}} ) {{cite:b65c799fdb5ed07df64a1332fb325ffc27a5dacd}} or pixel neighborhoods {{cite:56a529570be8c212969b736f803ff37eb054bd18}}, and where the heteroskedastic variances are known {{cite:92789fca8e06e0cbbf6055354ca18f8eed59e471}}. In the general problem, we want to estimate {{formula:eee9bb64-74b2-40af-8028-e0ea4f813ae7}} using {{formula:74390ee0-19db-4e7a-92e3-12bfb0240b31}} , {{formula:40faa44b-a880-4d02-94a8-c11901d72936}} fixed covariates {{formula:575037a1-8bec-40a5-a350-15699121ff2c}} , and {{formula:5634507f-53b6-4ff6-ad78-7f57a02fde6e}} of the other observations {{formula:417811e4-91b7-4f9e-b0f4-818ebb1fb98e}} , the regression problem becomes one of modeling and fitting the function {{formula:2fcf9d2b-9682-49a8-9cec-3b24cbdb85db}} . A multi-dimensional version of Stein's lemma can be used derive risk estimates that can be used to fit such non-separable estimators. A natural approach to modeling this general estimator is to use the generalized additive model: {{formula:b165ba38-b475-42c0-ac51-8dc0632a40b4}} {{cite:5e586f93cd9a09b1650ca3af97aa97d672b6619f}}, {{cite:5baf63aff9763856fecff1e53b2623b896bd3ce5}}. This additive model decomposition breaks the modeling and the fitting steps into separate problems so that any penalties and shape constraints can be specified separately for each function. This decomposition is closely related to the hierarchical Bayesian model studied in {{cite:1d78f03e7d6b6dd730783a4477515432ff113c39}}. In this model, {{formula:46c7cc28-c041-4d70-b64b-d673d8498411}} can be interpreted as an estimate of the unknown mean and {{formula:83db33b6-00c0-420a-91f9-661115421c62}} is a shrinkage estimator adjusting for additional noise.
| d | c3162a29facc74a9f9602602c4d3c0ed |
This paper presents a new embedding transfer method that overcomes the above limitations.
Our method defines the knowledge as pairwise similarities between samples in a source embedding space.
Pairwise similarities are useful to characterize an embedding space in detail, thus have been widely used for learning embedding spaces {{cite:104ee4f8eb54f18fc7326f470141888448fd6817}}, {{cite:2b835b5389eb973ffa853bd5168a6db04ee0884a}}, {{cite:39e1afa8bf77aba7f0ca0d443f71a976ca12b201}}, {{cite:598c2df23933be6d27c4051df116ae109d1a8413}} and identifying underlying manifolds of data {{cite:dc939e74536b6e90002078d4b2f522fb5e0359bb}}, {{cite:db6e768abeebf7e34525beedbcfccdf519f89db5}}.
Also, they capture detailed inter-sample relations, which are missing in probability distributions {{cite:fe1e71b11f43ca8e39ff949ba8eb1e6921d4a8ba}} and the rank of similarities {{cite:3a49814a88dbe96db5a2607bd1af9947c4e931e2}} used as knowledge in previous work.
| i | f805ffd26ee15d23b4dd1e9d92638cf8 |
We first report the results in Table REF . We use the FiD {{cite:1368bfc1c21e1340c563ecf4ae3ce0a1882fbfb8}} base reader model on Natural Questions Open {{cite:83ae428cce7731944da691be18a2ab63e5a8d8c8}}. To verify that the model overfits the top-rank passages, we purposely mask top retrieval passage representations based on the mask position. We observe huge performance degradation ({{formula:f9d196b7-71ac-46c8-966f-943939b32a1e}} , {{formula:d7ae6059-88ab-4c72-b347-73ad22f1b2e5}} to {{formula:cd708576-a2aa-4d9b-a397-5325f1746acc}} ) by masking the top one passage representation and even larger performance drop ({{formula:afcbc7ed-3319-44f8-8da1-fbe5b9a920e2}} to {{formula:d88d4609-618e-4743-badd-6cb8011a5252}} ) by masking the top five retrieval passages.
| r | c6b753d4763f9804df0c2ae7d5036b98 |
The shifts of broad emission lines may originate from the non-virialized BLR, e.g., outflows or inflows. However, gas outflows can generate the blueshifts of emission lines, e.g., narrow forbidden lines [O iii] {{cite:2b0c14bfaa63b54b73866832aadc906db46ea645}}, {{cite:7f9e814da3bc75dbe13ba671dec08810e78afae0}}
and broad emission line C iv {{cite:d3377e75d52061c001322210d58a958de98c94bb}}. The [O iii] emission lines can be decomposed into two components:
a narrow Gaussian component and a blueshifted/blue-skewed broad component. According to {{cite:5c32a13219651e97755aa3fb0297e51f6d180426}}, the shifts of broad emission lines are derived with respect to the narrow Gaussian component of [O iii]{{formula:ea929f08-ba77-4e18-9cb5-5b76721ff205}} 5007. Thus, the shifts of broad emission lines taken from Table 2 in {{cite:5c32a13219651e97755aa3fb0297e51f6d180426}} are not influenced by these blueshifted/blue-skewed broad components of [O iii]. The outflows in AGNs can be pushed by the line-driven force {{cite:a192061eb677016846d8df4739173749a81d1c38}}, {{cite:0dc7eca2ef615eb61fc775bb4a0989c15afd9fdd}}, {{cite:f31bcfcce8518dd2b97ff9ee2c80eb283013cdef}},
and accretion disk winds driven by the line force have the increasing velocity with roughly decreasing acceleration
from the black hole to the far {{cite:22cdc01d36c6c404d96ad60b149b9311f86913ef}}. Observations show the various outflows at accretion disk scales, the BLR scales, the NLR scales and the kpc scales, driven by {{formula:b59f2955-0f4b-46fc-b0ac-c384c7836e39}} from AGNs {{cite:40cdd0af5e98cb302133969f410b674b0600f063}}, {{cite:d1a4ece7ebb3de5d9e507bee103724163f206f4f}}, {{cite:acf0f4cf34a943431cabab7124a4790b825b150f}}. Thus, {{formula:d0101529-4891-4880-9c33-0eec362e9c89}} is prevalent, and might contribute to the force budget for inflow, e.g., {{formula:ef32351f-24ca-41c6-b5e9-4e4b3c0767ed}} decelerates inflow {{cite:a2059ce4c59c7994ede43b45db098cd426826b2c}}. RM observations of PG 0026+129 indicate a decelerating inflow towards the black hole if {{formula:888c001a-bff1-4e0b-bfc8-09b52f1297c1}} originates from inflow. If the decelerating inflow is prevalent, {{formula:f1eebe50-244c-47fa-87ea-df7d99016626}} will increase with the increasing {{formula:739b8172-e246-44b2-ad2e-4edd5eae6aa0}} , and this expectation is not consistent with the trend found in Figure 3.
Thus, the inflow seems not to be the origin of {{formula:ee87b61d-c393-450a-9f57-05c7120042ff}} (H{{formula:0e02c23d-23f4-4047-96ab-e44c5c9ed6cb}} ).
| d | 1d2894897e692aea4a11ac3957500a37 |
Feedback Alignment (FA) The weight update (REF ) of layer {{formula:c3f86692-118e-4419-915f-ef301729f9fa}} requires the knowledge of the matrix {{formula:dae9a053-ef2a-44c9-bec5-a765040bc13f}} and is biologically implausible because it requires that neurons send to each other large numbers of synaptic weights (i.e. weight transport). This fact has motivated the substitution of the matrix {{formula:b2b75ec3-4a22-4eb3-abd3-67f6a08ad720}} with a random synaptic weights matrix {{formula:417f0ddb-a32d-43d1-be93-7e9ea78e02c6}} to account for a separate backward pass needed to avoid the weight transport problem {{cite:fa481171cca95d63f881d62b41a1c66a2fa6b787}}. Therefore, the weight update becomes:
{{formula:3f8edc50-aa4a-451a-b977-b93d94b3b869}}
| m | 8af516e10bb526f51d5fc4cc038c9675 |
Using {{cite:e3392111662844a552036c6d1058ed68ef8cb822}}, the sum {{formula:3a92950d-4cfb-48ec-886c-c9e57b7e3244}} is maximally monotone and hence, its graph is closed in {{formula:a02df759-c0ea-46d3-9d72-d8c19602d69a}} {{cite:e3392111662844a552036c6d1058ed68ef8cb822}}.
Therefore, {{formula:78e93f84-cf2a-4902-a71e-0bc0cd506833}} a.s., that is {{formula:9d21a11e-df8e-42fa-964c-9ab0dd0f21c9}} a.s. By Lemma REF , the sequence {{formula:c0c50f62-281a-45a3-804b-f736e816a15e}} converges weakly to {{formula:eb61386d-a1ab-4e0f-8092-b32bd4769333}} a.s. and the proof is completed.
| r | 7aea6cf1f37904b151eacf28978d00ad |
Table REF shows the result comparison with three recent Transformer variants, ResTv1 {{cite:19992446946f1a7c4c2030ca40b788faf48e6aa9}}, Swin Transformer {{cite:567d7d49d3796290d0f28081e92875084707e0fe}}, and Focal Transformer {{cite:25fe03d566c1e4cba9de32288a69c2dc432f9967}}, as well as two strong ConvNets: RegNet {{cite:cd61249392fa16a056ba12b317d941febe31b34b}} and ConvNeXt {{cite:c42c2da6d058a6fff22e7ab3474e4faf8eb2263f}}.
{{table:a76f5023-69a1-4a69-bbcd-c4e3f9e50002}} | r | dd639060e61e31b205ca6898c83ab3e9 |
This work opens up four avenues for further research. An on-going extension regards the case of categorical and mixed variables, taking inspiration from discrete GANs {{cite:e15ff841597a28d6b809daa6cb521cae502435ea}}. Another perspective is to relax the causal sufficiency assumption and handle hidden confounders, e.g. by introducing statistical dependencies between the noise variables attached to different variables {{cite:9fea3e8c7466ca6eaedc8392eca358d07c490b10}}, or creating shared noise variables {{cite:61507db9fcc603557e6ba7e2510118608827de84}}, or via dimensionality reduction {{cite:b6dda0b1df0b3c11698d1a379d285975be40dcee}}.
A longer term perspective is to extend SAM to simulate interventions on target variables.
Lastly, the case of causal graphs with cycles will be considered, leveraging the power of recurrent neural nets to define a proper generative model from a graph with feedback loops.
| d | f804067366debdbc1afb57aec42df7e2 |
As studies have shown that VQA models can be reliant on single modalities {{cite:fb25ea8410f6e98db06fe32da136b3d3ee4b4426}}, {{cite:fc16b54d6c927ce911c9bcd17b7ab3ddcfec9199}}, we define a novel pool-based AL strategy for VQA by leveraging mutual information of the multiple inputs, image and text, individually through a multi-branch model.
In this multi-branch model, we denote a “main” branch that relies on all modalities.
If a single-modal prediction {{formula:5dd3b8c5-8f3f-41aa-9981-d39999d31825}} or {{formula:5dfba3d0-91a9-4e8a-9d50-d4ea7e912220}} is different from the “main” prediction {{formula:33a5c622-817b-4033-9fc3-4fdd8ec97bf0}} , it may signify that the missing modality is informative, where {{formula:2a8e09b0-c6a5-4778-b495-dfc40798c35a}} , {{formula:63ad1beb-bd2c-4f61-bdc2-80f5f4141029}} , and {{formula:7c389fc5-b775-44c6-8835-14a5aa5a0572}} are the answer output, visual input, and question input respectively.
Hence, we propose a method called Single-Modal Entropic Measure (SMEM) that selects instances for labeling from the unlabeled data pool based on the differences among the predictions from the single-modal and “main” predictions.
We also show that we can take the differences among the predictions from the single-modal and “main” predictions into account by simply computing the entropy of the single-modal predictions.
In effect, we propose an uncertainty based sampling paradigm that enables simple inference without any ad hoc steps to measure uncertainty by relying on multi-modal uncertainty.
In addition, we
use self-distillation,
not as a regularizer, but to directly aid in sample acquisition by forcing the single-modal branches to generate outputs similar to the “main” branch.
If the discrepancy between the single- and multi-modal outputs of a sample are still high despite self-distillation, that sample is highly likely to have large information gain.
| i | 87a8b0a76caea59d86a58e64f6eb06ef |
Classical sensor fusion strategies normally rely on the handcrafted physical models and algorithms. For example, in the case of visual-inertial odometry, filtering methods update their belief based on the past state and current observations of visual and inertial modalities {{cite:673711cb8920a755a68e80f18f0dca5033eaa724}}, {{cite:85eec949cd315d36e183291f2d4e7c949f3d417e}}, {{cite:ee2f066e7f635beeeca31e369a28cc55e10825e1}}, {{cite:f4f0ab56edbc95a9f81656ed266c45981803d23c}}. "Learning" within these methods is usually constrained to gain and covariances {{cite:a72c36049952d83ca8e2fcf38ab5e2c955c55122}}. This is a deterministic process, and noise parameters are hand-tuned beforehand.
Deep leaning methods are instead fully learned from data and the hidden recurrent state only contains information relevant to the regressor. Our approach models the feature selection process explicitly with the use of soft and hard masks. Loosely, the proposed soft mask can be viewed as similar to tuning the gain and covariance matrix in classical filtering methods, but based on the latent data representation instead.
{{table:2d14f52f-7cb4-407f-9ad7-3c104ab54c09}} | d | 59f7ac03d2d9324c784f2197e4e70e46 |
This notion of solution was introduced in {{cite:abec768e8e4348646562ca841a111626c5ac871c}} for the case of the interaction with the logarithmic
potential, see also {{cite:9a16d78e188495bd5fd0fde628b437967ccded1d}}.
We shall construct weak solutions to problem (REF ) by applying the Jordan-Kinderlehrer-Otto {{cite:e129d1f4cc866dc5e8c4bf860ee23a24dbbc687e}} scheme. Therefore, denoting by {{formula:9688b6b0-0e7f-4ec1-aa1c-154e13c45341}} the Wasserstein distance of order 2, for a discrete time step {{formula:30ed5adf-9014-4942-875f-f1ba40c0c53b}} , we shall solve the recursive minimization problems
{{formula:5f46dd67-9f04-4f3b-a505-8192cf10f4a2}}
| i | 023259578614163f425e3b60b3223378 |
Universality has been established for wide classes of Hermitian random matrices. We refer the interested reader to, e.g., the book {{cite:2c6698875cbda2bf4346209f5637a91a049b99a2}} for an overview of these developments as well as to the seminal papers of Tao and Vu {{cite:fa8849b9ac4106dba2e6ddc0c2578cbeb04a10f1}}, {{cite:20773d4585aa367ddba965db6b87feb482d6d215}}, and Erdős, Schlein and Yau {{cite:0c437fc6682866a2fde9de266d81ea5baa09deec}}.
| d | 6dff39a8c4df8b2d3ec0542c80c6a3c9 |
Therefore, {{formula:b82459e6-f9ed-470d-b0d8-62d9d8d08d26}} is an equicontinuous subset of {{formula:ce412abb-cc6b-40c3-a3f4-fa3c5944f1f8}} . By Ascoli-Arzela Theorem, see {{cite:1140c2bbc2620ca2879b2340a41329191636b091}}, {{formula:6856d472-c291-4c13-a4fe-3cc9a5ba754a}} is compact.
| r | dc5cc4797fad285f5d84b3eba6cb7434 |
In this section, we provide additional details on the baseline methods and cite the implementations that were used. NOTEARS {{cite:8a311aa9eeea28ce6f8b35b032c03815acc86079}} was extended to handle perfect interventions, and to use a Gaussian likelihood (with unequal variance across features). In contrast to the original implementation that used a second-order optimization method, the reimplementation used in this paper relies on first-order optimization. A similar GPU reimplementation was used in the NO-BEARS manuscript {{cite:2555ab4a8ac6978a13cc075eb9a7ba369fce4beb}} and shown to be 100x faster for {{formula:eff7bf0b-d54b-4efd-9d5e-046dc3092988}} . NOTEARS-LR {{cite:1b2ec33ec78b32ebfb51dd4e4b18a09882094794}} and NOBEARS {{cite:2555ab4a8ac6978a13cc075eb9a7ba369fce4beb}} were also reimplemented to handle interventions, and use a Gaussian likelihood.
| m | 45ade146678cc11774c8e58e247d337b |
||Pt f||L2(X) (-2c1 t) ||f||L2(X), fL20(X).
In addition, time relaxation property (REF ) is equivalent to {{formula:a2212919-6a3d-439f-825e-04ba74dc3620}} -mixing of the process
{{formula:acc6c83a-9be1-4801-845a-e121fbc77e82}} , {{formula:de98a84b-3c94-4c52-9944-3f17e8df9b3b}} . Specifically, let
{{formula:69ec1b6d-4dc5-4d10-b749-c0b9fa473ec0}} , where {{formula:207c70c9-3bd2-42e3-b8f1-abf760ad1bdd}} is the correlation function. Then, (REF ) or (REF ) implies that {{formula:afeef354-fcbb-447a-b6c3-84c303603a35}} ; see {{cite:2df7e7537297fb6c2452fa7a98de0181f8b3dfe0}}, {{cite:5c99e1a1bd75e112a2630c4d527741f6a7415f39}}.
The time relaxation property (REF ) (or the exponential decay property (REF )) plays an important role in proving the existing of the effective diffusivity. We will numerically investigate this property in Section .
| r | 273293ffe4f509887f82cc10cb3fa1b2 |
PartNet Semantic Segmentation. We present semantic segmentation results on PartNet segmentation task. We evaluate our MulPro final model with post-processing technique {{cite:4738bf6871961f19e9535e767279d64039b15f95}}. We also compare our results with WeakSup {{cite:4738bf6871961f19e9535e767279d64039b15f95}}, the large margin suggests the efficacy of proposed mutli-prototype classifier.
| r | 88adf4bf5d4b2b09030e8b0b4ff562c5 |
It is important to note that a Deep-RL agent is trained for each proposed environment. We compared our method Depth-CUPRL with the CURL {{cite:83c0eb4bcbaffc93dce6f525327381041fa2e2fc}} having as input the raw pixel image, and with an own version of the CURL called here CURL (Depth) with depth maps as input but without prioritized memory. We also compared with a SAC (CNN prio.) as adopted in Grando et al {{cite:2ff361f62e17dbf9a552a4f3548014b5d53509c3}} but with convolutional layers. The SAC (CNN prio.) uses depth maps as inputs of the network and has prioritized memory. All networks tested in the work followed the architecture proposed in Fig. REF . The initial position of the vehicle for both training and testing in each of the scenarios is defined as the Cartesian position (3.6, -2.6, 2.0) for the aerial environment. Only linear and angular velocities are applied to the {{formula:5dee9907-33ab-4801-8b2a-ae29f15d75ef}} of the vehicle.
| r | 83d79954bab9aca409c840dfff82e6e2 |
Corollary A.1
{{cite:0b3fb6bf9848f4061ec9a60ea2a727775eb0e137}} If {{formula:4f0cf63a-fdba-4688-8fdd-81609d35d1ea}} is a Hermitian {{formula:013ce770-6cf5-4062-947f-4bcee40f81a7}} strictly diagonally dominant or irreducibly diagonally dominant matrix with positive real diagonal entries, then {{formula:e27c899b-ee88-4888-bc7d-72e2d9a2064a}} is positive definite.
| r | 36540a2b8e6c834979218a10d1dd63a4 |
A limitation of the QCCOT-GAN algorithm is the uncertainty brought by the gradient approximation using the straight-through estimator. Differing from VQ-VAEs and VQGAN whose approximation only applies to the gradient with respect to the encoder parameters, QCCOT-GAN has to estimate that with respect to both encoder and decoder parameters. To investigate the impact of gradient approximation, future work could explore alternative methods such as the REINFORCE algorithm {{cite:1671e775db1029c2aef026d3ca7413f396c7f316}}, approximation using the Gumbel-Softmax distribution {{cite:afcd19b5cd4886d7b668363d69dc838a419330e0}}, and stochastic perturbation {{cite:e8add0175f8038a108d42a00345c82b70f1dbbc2}}.
| d | 3319ec9d9135ef8a5ceda224ce7dda86 |
BadNet-SL {{cite:42a2ed2920a283cf17e5c9b1e8420aec0a33e498}}: This attacking method follows the same data-poisoning and model re-training procedure as BadNet-RW, but in this case, the trigger is chosen as a long neutral sentence to make the poisoned sample look naturally. Thus, it is a sentence-level attack.
| m | 094ef2852cf901867a74ddd77ffc28ee |
The derivative {{formula:91133a7e-47d0-461b-8a94-15de79c24a77}} of {{formula:7eeb3eff-7dd9-45d7-8735-7d805a48124f}} in the sense of distributions is a vector-valued Radon measure having total mass {{formula:858f2cb7-ec3e-4660-a1e3-0e8e70be828a}} see {{cite:7a8cdff0b82500fe4deec61f4ebe32d5a3633439}}, {{cite:294b4bab877ba7bbba046545688f1f6e9fa862e3}} for more details. The
main advantage of applying total variation regularization is its ability to preserve sharp edges in the image.
| m | 0831530389f4f3ff32c0f3698a2e8d76 |
We reduce from Positive Not-All-Equal 3-Sat which is a {{formula:3035c398-06dc-4374-bfd5-5d8f0a238744}} -complete variant {{cite:1acb80e2f0106e4dad17d7184215a138ea75ebbc}} of the 3-Sat problem where given a formula in which all literals are positive, the problem is to determine whether there exists a truth assignment such that in no clause, all three literals have the same truth value. Given an instance {{formula:ddd54fa2-a9a2-4b46-8ed5-cfc1e0b8d9d7}} of this problem, with variable set {{formula:639208ac-e57c-4720-bda8-5bfc18cb717d}} and clause set {{formula:a5e261f3-e58a-411a-95d8-5b3d5509c8cb}} , we construct two instances {{formula:ed038bdf-5002-407b-ac9f-499b39337bcf}} and {{formula:4320defb-c625-4ad2-bad2-fc9894d0bbed}} of Contraction Number({{formula:d9cd2a32-01b3-451f-b016-1eb741adddff}} ,2), one {{formula:a37ecf19-cd56-469c-a04e-24c7234f8cb5}} -free and the other {{formula:f75c36f9-e554-4ee4-9602-ed11308532c0}} -free, respectively. For both graphs, we start as follows. For every variable {{formula:e46d2516-e3ad-4b97-b5d3-a07684fc80c7}} , we introduce the gadget {{formula:66915f3f-d394-4196-ad09-26249869827d}} depicted in fig:vargadc3c4std2, which has two distinguished truth vertices {{formula:59fcf7a7-5fcf-468a-85c1-fe6efce70a4b}} and {{formula:a31af026-421e-412c-b000-57e26be76401}} . For every clause {{formula:1d02174d-610b-4d38-965b-3394266ea469}} containing variables {{formula:10c95d6d-0e5a-47b8-829e-f357d2a76582}} and {{formula:e9ba02eb-fbff-4347-8139-73eb1e8c1093}} , we introduce two clause vertices {{formula:0cd4e8c0-fe40-412b-960d-db4f20d56fc5}} and {{formula:78a8d2d9-b223-407f-a842-d7188ef802dd}} , and add for every {{formula:245586d7-191e-4827-98ce-778d4badce09}} , an edge between {{formula:a9b970ab-5bea-4c3a-b4d0-204eb6d8e8f5}} and {{formula:084e23d3-b16d-4d4a-a021-60dd27bf7ba8}} , and an edge between {{formula:38cb9071-8988-486b-a05d-107b5481384f}} and {{formula:1aea513b-1206-4150-a08b-8887340ba453}} . We denote by {{formula:80694a69-23e3-4d58-bbf6-63cac716a82a}} the set of positive clause vertices, and by {{formula:a0c6ebba-0367-40c6-be38-74e3fe01006a}} the set of negated clause vertices. This concludes the construction of {{formula:1e1c6d0a-a589-4d06-ac24-219119422b38}} . For the graph {{formula:c5bcf909-c9f1-456a-9f3a-35060754843c}} , we further add edges so that {{formula:66ffc34c-cb06-4724-a474-ee4045f3166c}} is a clique and {{formula:9cf58ebe-ef42-4062-b328-42050db4c4e8}} is a clique.
{{figure:2c9d1ac2-4bc6-400d-9071-a5d2c51786ff}} | r | d131a870247328a51bd41d23d07ac12d |
with the three errors coming from the variations of {{formula:d3cd8e4c-4306-44b2-8d66-94c51f36df5c}} GeV {{cite:f322496936240faa9b4e637edf7fd81f8ecbf7ab}} or
{{formula:6631a392-a067-4475-8903-af59538ba4c3}} GeV, {{formula:e5189f16-9330-4a01-96e4-a9e847869876}} , and {{formula:3c331fc0-d02c-4d11-acc4-320bb8b72374}} GeV. It is seen
that the above results are not sensitive to {{formula:17cbb5a9-9e48-4c34-b340-e228bf20250c}} , so the central value of
{{formula:50bc9b02-abe2-4e80-b451-97b1694fd754}} is actually mainly determined by the {{formula:62b85196-8858-4e67-a7b6-58c6c9a6876a}} data. The errors induced by the
variations of the Wolfenstein parameters and the mean lifetime of the {{formula:51df2184-19df-4806-a37a-2350bff0717e}} or {{formula:427c34ad-0ab5-4799-8ddd-4c3600dda380}} meson are
tiny, and have been omitted.
| r | c700452fc30a02fa700c6d551020fce8 |
The 1d case of the random geometric graph has appeared in three major places. Firstly, as random spatial models in the physics of complex systems, see for example the 1d soft random geometric graph {{cite:e38a1f620e90c6eeddcf70c63f30c7b198010952}} used in complex networks by Krioukov et al. in network geometry {{cite:e632c3f2a2253f37a3dca142c8cbfdd00de59fd4}}. Secondly, in Poisson-Boolean continuum percolation {{cite:f554526afb28729b6c0399c5afcce7d7937704ce}}, {{cite:08ed1f57fa66341633dca902fd13cb32746ae578}}, {{cite:7bb66303f8ead8b1f7c71f13babf44be8ce10080}}, {{cite:be57552574141c8f65ae58201048fcafa1c59f98}}, and thirdly, in vehicular communications {{cite:013f967cd4a8a31a4a25d1329b2cebfaf4adc752}}, {{cite:70c7e2e4f3281cbcf886d09ad9f591379406faec}}, {{cite:b8511e922dc6516e94e870b3f8aab2005571dcbc}}, {{cite:e38a1f620e90c6eeddcf70c63f30c7b198010952}}, {{cite:7c8bd171d09f9bc9d2185b3cd5c75a3fe74ce441}}, {{cite:19db0b4944ddcc87d7d49b9a02e0a9cf33f342a9}}, {{cite:c3033f3a76c3f9cedae0e8b0ff62e03b2f6a86db}}, {{cite:bf03b701065b032f1272e8a82aeb5d60ddf08937}}, {{cite:ac15c6d54a1f134f9a6d7e838c05c2c43aec58cd}}, {{cite:1e13e5fb8dd0cca59c98b65209a76c231ce6cad1}}, {{cite:f43c31cb108eae9f608ef3b2ebaf13a647c284dc}}, {{cite:f2dcfae5fb06a6316ba1673085070cf48aac8845}}, {{cite:9a6a42763b1760a97f8bf942f310ff0579a91f41}}, {{cite:f43c31cb108eae9f608ef3b2ebaf13a647c284dc}}, {{cite:da304fddbc726edcb46ac5811bc89469dae57725}}, {{cite:b3fff35fa0ae4c0c38c7b42daac6cc09597a5930}}, {{cite:fa89c56a6ae42f06f6f208aef87de5ee4a7dc58c}}, {{cite:db3b82f651a39c53f70948a7b6ab593745be79c8}}, {{cite:e9ccdf6aa0d537d0a44fb94122a5097fecffeea1}}. For 1d spatial models similar to the 1d RGG, see the 1d exponential random geometric graph {{cite:08a1d08f89cddec210b20f2970bb4f414a84a1c9}}, random interval graphs where the connection is between overlapping intervals of random length {{cite:0ce835d4343dbba57f0ff22b1f026fd19ed928e8}}, {{cite:c3033f3a76c3f9cedae0e8b0ff62e03b2f6a86db}}, or various models of one-dimensional mathematical physics {{cite:f554526afb28729b6c0399c5afcce7d7937704ce}}, {{cite:e99030229cb95bfdb769583594ac5ccc0172b895}}, {{cite:24dd1ce1c74de5c7be9d3145ba72ee49d1cf7146}}. For a historical introduction to the similar problem of covering a line by random overlapping intervals, see Domb {{cite:581c84597e02915b4a4f0e1a41c325a754d88bf2}}.
| i | 760ccc53d7c0c94c77896c2646335933 |
The results in this section are for {{formula:d51ff6ab-1192-4bf3-88cb-2ae852ba0e28}} REs, {{formula:8c7fa4aa-a78b-48bc-bfc9-f6ca5148a9bc}} Monte Carlo runs, {{formula:cc7090e0-3639-4254-bb68-0d602f639e04}} , {{formula:989da863-1db9-47ca-9af1-8e1c50c3924c}} , {{formula:8eeb2493-4a2f-4497-8591-c911e13d1f9e}} , SINR threshold {{formula:873e4046-a1ce-486d-bacb-bfb57692c137}} , MSBL threshold {{formula:55f8c858-ac9b-4f07-966e-e0f45091f9f7}} , cell radius {{formula:b1aa5a13-cf85-4329-8560-bde291a32fb8}} m, and reference distance {{formula:5e2ce143-5589-4a6b-a4ef-b6a8815e7ebc}} m {{cite:744e3e309b6de9850440941d2069a5d6c00be6be}}.
The number of users contending for the {{formula:8aa37ddf-8f7e-4962-8981-68a714fd3470}} REs is computed based on the load {{formula:9f59c57d-6a21-4659-850e-adb6c1678e7c}} as {{formula:f09fe08a-3c13-4764-a574-2783173199bc}} .
The soliton distribution {{cite:5116cd81f97e313f15322e29f74418e0d52b3a4e}} with {{formula:d691b6d7-abb0-45a4-9e69-9e85fc74fa2b}} maximum repetitions is used to generate the repetition factor {{formula:4240ed02-d937-429b-8b60-a200ed220be2}} for the {{formula:a998ce4d-34e1-4112-966d-39ade63740f3}} th user, whose access pattern is formed by uniformly randomly choosing {{formula:90ec5ad2-df1c-41b8-bdf4-1671003fed72}} REs from {{formula:89707cf1-0714-4e9f-bdfe-e4a6aaef7b21}} REs {{cite:210ff4662f325dd01a15dc0073af6d232d5354c4}}.
The APM is formed by stacking the pattern vectors of all the users.
The location of each user is uniformly sampled from within a cell of radius {{formula:97452eac-b93f-4b59-831f-75b888fd7961}} centered at the BS.
The path loss coefficient is calculated as {{formula:1c9e44ba-2f87-4828-8507-a34fab56067c}} where {{formula:4c3f9b67-12f7-4e6b-a46d-87b104414091}} is the radial distance of the {{formula:bb2ff52c-d07f-4b9c-ac2f-2a99cc5aa2b1}} th user from the BS.
The signal to noise ratio (SNR) for the {{formula:e7b3bc00-b222-46bb-9505-dd6538589790}} th user is calculated as {{formula:0f192296-1903-4845-bb11-e297f8c4e56b}} .
The received SNR of a user at the edge of the cell at the BS is termed as the cell edge SNR, and is denoted by {{formula:5564e3a9-f4a8-48ed-ad1c-b3b718bfca3b}} .
The power levels of all users is chosen such that the signal from a user at a distance {{formula:6d3b2186-31bd-419c-96e2-b11aebc554f2}} from the BS is received at {{formula:aa68f872-a5f4-48cb-b155-a096bbd8d151}} .
This ensures that all users' signals are received at an SINR that at least {{formula:f7766f08-8076-483e-bc03-17ef62fe95e2}} on average, in singleton REs.
If {{formula:3e328c9a-afa7-4099-950e-510e3d0304ed}} , i.e., it is such that the cell edge user's signal is decodable, then all users' signals are decodable with high probability in singleton REs.
The power levels of users is set to {{formula:5edfb67e-add9-4875-ad0d-cbf1d34d0aac}} dBm {{cite:744e3e309b6de9850440941d2069a5d6c00be6be}} and {{formula:84fae620-4ab9-4764-af39-803ae2a7adaa}} is chosen such that the cell edge SNR is 10 dB, unless otherwise stated.
The pilot sequence for each user is generated as {{formula:2a505446-92eb-4588-a4b0-459ca27bd5a2}} .
{{figure:1ea5178b-4c24-47ef-bab3-411ab4a9592a}}{{figure:276436fb-f8db-48a9-89e9-b0807d364706}} | r | 0aba0f3175bd4271f93ebcc7db656942 |
Graphene is an ideal candidate for such a composite structure due to its unparalleled carrier mobility. This allows for extremely enhanced and tunable electromagnetic response spectra when doped with other plasmonic materials, or fabricated as a component of a multilayer structure. Monolayer graphene has a response spectrum dominated by absorption peaks at {{formula:3e2d9298-891b-41ec-8727-783cb4a1d9d1}} eV and {{formula:5eb23d09-bff8-4cc5-8acf-2bffc699fba0}} eV, the {{formula:63c0dbb8-54d1-45c7-ac37-ad7defddb60c}} and {{formula:65233d65-d255-45bb-b3ff-78973ba4f623}} + {{formula:9b70b981-3ad3-4eb0-8266-fdb18d22555f}} surface plasmons. Graphene plasmon resonance provides low losses in the frequency regime below the optical phonon frequency of {{formula:3c0af609-1c10-4556-b616-3fff44f0a16a}} eV, where large losses are typically present for metallic plasmonic materials. {{cite:ea917812330e378a12445b0c9f2a701602595907}}
| i | bae593e3e8684b267f631063e779d4f1 |
The training process of the Faster R-CNN keeps the first two convolutional layers of the VGG-16 network fixed {{cite:a69a37486084ac8e576f548285218b8833e3299f}}. Changing this, so that the weights of all layers are trained worsens the results by 1%-2%. A similar effect was observed when a dense-sparse-dense training {{cite:641d42ac06344b0cc6c9d401d8bd4142054a3b67}} was performed in order to regularize the model. In further experiments, we have evaluated the use of standard *NMS instead of Soft-*NMS. As expected, the results achieved were inferior to those presented.
| d | 49183dce191cfd9c92276e0bd14833f3 |
Consider now magnetar MG J1647-4552. According to {{cite:bec1f68715aae204018536a8ef6a7afa60bb7227}}, its radius is
estimated as {{formula:3b43dfcd-0991-4125-8ba2-1ff418e8c6c3}} cm, the period of its rotation is 10 seconds, and
the magnetic field
induction on the surface is about {{formula:7917c8c5-69c7-4222-b65c-18bd0f1b9cce}} gauss.
In this case, the expression (15) takes the form:
{{formula:507369df-b9d7-41a7-b233-e5cb531766ee}}
| d | 07d93e73ffc92f810648ee0111073ae7 |
We reported, in the previous sections, on the long observations of the bright quasar RBS 1055 with XMM-Newton in 2014 and with NuSTAR in 2021. A {{formula:76d826ae-1fe0-4d15-801a-d512d566f052}} drop in the 2-10 keV flux (1.38-6.88 keV at the rest-frame of the source) is observed after seven years, from F{{formula:10b3a221-8ab3-4b03-8759-8b64857bd727}} erg cm{{formula:2c094e9d-cc15-4d12-b437-4232a14013f1}} s{{formula:f2e2e324-8a03-4f30-9d62-bf4284007b4a}} to F{{formula:06f4c1df-609f-44b3-bb3b-80dd3a655761}} erg cm{{formula:b6d7ba36-ba89-4777-8995-34ad8f6b68d1}} s{{formula:48d78a04-fc24-4131-817b-00993db3a366}} . At the redshift of the source, these fluxes correspond to L{{formula:016f29a2-5136-4e4d-a299-9009aad737b9}} erg s{{formula:d10bb179-d75a-4890-b2ab-9e74a9c76b44}} and L{{formula:c2a094d4-071e-4b80-9dbc-e6b84e22670c}} erg s{{formula:95541327-cadd-4f5b-b4af-bff609c2772e}} , respectively. Assuming a black hole mass estimate of M{{formula:24f9e913-a53e-44ca-824d-1b12901ecf29}} M{{formula:e5f01c87-9881-4a5a-927e-b84a713c6b6f}} (see Sect. 4.3) and adopting the bolometric corrections {{formula:59e008b4-3e1a-417e-af4c-2727a161d1f4}} from {{cite:654312d42fdf75771315049e30180e9f8df5d41b}} (Equation 3) we retrieve bolometric luminosities L{{formula:3f567861-af78-4e21-9440-ba9def29c4f8}} =7.4{{formula:e2c5a90a-f6e9-4cf3-b123-33f3093a5ccb}} erg s{{formula:070e77df-cd57-4349-901a-c6a703db7a1a}} and 6.4{{formula:7c2fbd90-dfbc-4a74-954e-789e329589bf}} erg s{{formula:f23861d1-edc0-4ddf-809a-7982cd21224e}} for the 2014 and 2021 epochs, respectively. The corresponding accretion rates are {{formula:7365fcfa-3319-4613-8781-2e3f656d3136}} =0.9 and {{formula:883c16bf-237c-4dad-b243-931d422a9e2f}} =0.8. The 2021 bolometric luminosity calculated from the 2-10 keV luminosity is a factor {{formula:4a2db9cb-c743-4b08-aa26-ba7112a9ab75}} higher than the one estimated from the continuum luminosity at 5100Å. An important proxy of the interaction between the accretion disk and the corona is the slope of the power law connecting the rest-frame X-ray luminosity at 2 keV and the rest-frame UV luminosity at 2500 {{formula:3f1ae9ab-42e8-4a13-9487-fa506429dbc4}} i.e., {{formula:1244471d-928f-4caa-b657-ba10bfcc7a0f}} ({{cite:e9aad1e9f9f51bd49dcccb65e757032e97529ae9}}, {{cite:673164851ed23a6203a7c90bcbb5dea35e88b2e3}}, {{cite:e413146265d73b01ee2e5c9c8052acd69aae7482}};{{cite:fc521221729736e3087446d92fdc47fdd02fbc8b}}, {{cite:85b8774eec8a1892ac46255efde72aca02167adb}}, {{cite:ba2fac7137184ef0986bb7954caf4f034bc4f964}}). Interpolating the UV luminosities inferred with the UVW1 (2910 {{formula:1b2610cb-3474-405c-bcd4-5c4af49e2f7d}} ) and U (3440 {{formula:37b96399-95dd-49ce-bb4b-5e7c1827beaa}} ) filters, we obtain a monocromathic 2500 {{formula:a75db60d-036a-49be-9e73-c6463a074f54}} luminosity {{formula:6d1efe91-4187-4724-a651-1b89ab1b0ab4}} and, using the best fit discussed in Sect. 3.2, a 2 keV luminosity {{formula:a71188f1-2a18-494b-96a1-62b60fcf004c}} . We therefore infer an {{formula:440a6579-df39-4d49-b160-5a75e133fba9}} . This value lies at the very low end of the {{formula:67475651-a10a-4d32-bc45-17359b214db8}} distribution obtained from high-redshift quasars samples. If compared with the WISSH (WISE-SDSS selected hyper-luminous) quasars {{cite:c225660db5934a4b4aae114496ac35b11ee1c158}}, using the best fitting relation (3) in {{cite:dac27ab64bb4bab6626e02a99b2449ee7bf53d9e}}, we obtain a difference {{formula:a02ef5a6-5936-4965-b0fc-21dd7e2c3447}} . From Eq. (8) in {{cite:273b2aa769a1d824685be121244c9b33e870901a}}, in which Swift observations of sources at {{formula:a15ea584-3356-466e-83e8-f850de8029e4}} 0.01-0.4 are considered, we find {{formula:d4f92edb-8641-40b7-9440-a8c8fbc7c693}} . Applying the L{{formula:dd64596b-7fb1-4d3b-8c9e-a62f9f3b803e}} -L{{formula:5a3e6e8a-4b31-4f28-b231-bfaf4fca17c2}} relation reported in {{cite:ba2fac7137184ef0986bb7954caf4f034bc4f964}} to the measured monocromathic 2500 {{formula:95798d9d-f874-4433-9ac1-d5fe0eed96bb}} luminosity a {{formula:77086740-5a18-450c-8d6f-5d8863a20a7e}} is retrieved, well below the {{formula:6901e5e2-ff69-4861-a5ff-46d01dabc9c5}} observed value. This difference is in agreement with the one between the bolometric luminosities discussed above. We therefore conclude that RBS 1055, despite a {{formula:33eea139-b9cd-4de6-822f-74897579c4ec}} decrease in the total 2-10 keV flux in 2021, continues to have an extremely X-ray bright SED, 10-15 times higher than other objects in this redshift range.
| d | 3b37b7d2fb7829085e732be6d21843b6 |
In terms of the peak-to-average power ratio (PAPR) of transmitted signals, the
former case corresponds to the worst case, i.e., the highest PAPR case that is
{{formula:53df85d7-0967-4fdc-a4b0-60655171daf5}} , while the later case corresponds to the best case in the mean sense, i.e.,
the lowest PAPR case that is 1. After saying so, the above i.i.d. weight
{{formula:66dc217b-b57e-4ed5-bfb4-05d84cb34a40}} case is only in the statistical sense. In practice, a deterministic
weight sequence {{formula:345dcfb9-f465-4c08-bc66-6b35485cd807}} is used, which can be only a pseudo-random noise (PN)
sequence and therefore, its {{formula:d4137133-6e84-421f-91d1-7b2b76818471}} -point inverse discrete Fourier transform {{formula:e6d121ef-c40c-4f86-870c-12b2e4961e91}}
(and/or its analog waveform {{formula:cba5e49d-f63c-410d-ade3-d5768c49ef4f}} ) may not have a constant power and in fact,
its PAPR may be high (although may not be the highest) compared with the LFM
radar or the random noise radar. This will be an interesting future research
problem on how to deal with the high PAPR problem of OFDM signals for radar
applications. Note that there have been many studies for the PAPR reduction in
communications community, see for example
{{cite:b77304525917d892e4f1ddeab7c33d7dc4d4dfe7}}, {{cite:fdd8772fbf3de5938f4ab76474fa4ac4ce6b7c5c}}. If we only consider the finite
time domain signal values, i.e., the IDFT, {{formula:f7f7495e-3971-414b-a976-460abd553a4b}} , of the weights {{formula:3e8f2add-b5ce-4548-a70c-b6a13c392ca8}} in
(REF ), we can use a Zadoff-Chu sequence as {{formula:ab8c6706-9def-400a-bf63-05cd7a16a06a}} that is, in fact, a
discrete LFM signal, and then its IDFT, {{formula:fad30d13-89ea-4ad8-ac9b-061cd14f723e}} , has constant module as well
{{cite:94f1761855d56a95a038293a9eb8970a6a01a829}}, {{cite:aa4d38eb958fdc7a55125e86413d558d54d66ee7}}. In
this case, both the weights {{formula:5e654c6d-0353-47f4-852d-84a5c1265072}} and the discrete time domain signal values
{{formula:4585213e-5f65-4d1f-b89b-942c2185c292}} have constant module, i.e., the discrete PAPR (the peak power over the
mean power of {{formula:8eb706a1-a111-4362-bdae-dca81aaf80f0}} ) is 1.
| d | 3de499dd0c0ebc4ed6430049455c62a0 |
We also show that the Gelbrich risk provides a finite-sample upper confidence bound on the true risk under the population distribution if the radius of the Gelbrich ambiguity set scales with the inverse square root of the sample size. This finite-sample bound is dimension-free in the sense that the rate does not depend the number of assets. This result contrasts sharply with existing out-of-sample guarantees for the Wasserstein risk {{cite:9f14c497517a2647ba5358d9be0e81cdb86797ae}}, which rely on a measure concentration result by {{cite:39c76ca093b67625ff9b5d277a6b890e047586e4}} and suffer from a curse of dimensionality. Our result is also orthogonal to the dimension-free finite-sample guarantees for the Wasserstein risk by {{cite:7338262d9d4fd8fc1617ea5fad6b2eee91e6a77c}}, which rely on concepts of hypothesis complexity such as covering numbers or Rademacher complexities and which apply only to worst-case expectations but may not easily generalize to other risk measures.
| i | f6de63df7e506bb1fb6c88600cc71e96 |
In this section, we test the effectiveness of RDA on feature extraction tasks and classification tasks. RDA is compared with four variants of multilinear discriminant analysis (i.e. HODA {{cite:f8e63ab9e887a8f1e9fbe24790d245a46e7a897b}}, DATER {{cite:df7679504bed96e16a9b0baef7821aceae76fbdc}}, CMDA {{cite:89ed1330f591a917d27918117713a5d515d6c055}}, and MHODA {{cite:2fc3d650100ddb1d9b3d4632aaa49c702b059cc6}}) and four variants of tensor decomposition (i.e. NTD {{cite:f960e4aa6c91d25f844dde93f5a5f97d6c167594}}, LRRHTD {{cite:8efbd642c98d5ec4f4a0265eb6b219882ca3214f}}, HTD Multinomial {{cite:2606e5fd3176a16720c0f06689ef3ba2dfe3964a}}, and HOSVD {{cite:3ec2bab782ec754f7adc121cd0696719a0d787c3}}). All subsequent numerical experiments are carried out on a desktop (Intel Core i5-5200U CPU with a frequency of 2.20 GHz and a RAM of 8.00 GB). Each experiment is repeated 10 times, each time using different random sampling data.
| r | de1a23da8ce3cda7b1e8a3247959eab4 |
Furthermore, two split-merge algorithm {{cite:7461b5805c885f7d3dc53f3681f65394260f3446}}, {{cite:e43633e0485be4d6a4013c11b481001ee49921f6}} with unknown number of initial clusters also posted in Table REF , with more details of algorithms to be found in Appendix . For fair comparision, the inital cluster number k is setted as {{formula:f7204a50-e33d-44c6-ac81-e970253be2e7}} .
| d | 6b08c555ced6dc142580146fddf66e93 |
see for instance {{cite:92d10a6a546efc3685221ba3123d156627391934}}, {{cite:36802b2fcab019035c2e11b26af57897d9d996e3}} or {{cite:147e3f0fa2e561e7d9b7512fbe7e9485eb109609}} for further details.
In particular, the derivative is uniquely defined, up to an additive constant.
In the rest of the paper, we will use the notation {{formula:9c7cefd2-2ee4-4184-a099-33e55d136ca8}} and {{formula:b0dde1a2-8688-4fa9-936f-c89d1cb5ad88}} for the {{formula:53f4e5dd-91e1-4280-99b8-818a30f04760}} -derivative of a function {{formula:77fc2997-26e6-4f63-8445-98c76bdb99b0}} in the variable of the probability measure {{formula:f0cc9c78-772b-48b2-b9dc-401401054cc2}} , {{formula:1ab28542-52bd-49de-9842-1f4810cf101b}} and {{formula:344d2d2d-6017-4b81-af2b-e87e332e32aa}} , respectively.
| r | 5f297130bcb43acfef6dcf70d7876b6f |
Recently, the versatile CLIP {{cite:8105dd8efa36c5f02b098db2042182bdf1f1886c}} has been proposed for zero-shot 2D image classification, which is pre-trained by large-scale image-text pairs and obtains strong open-world recognition capacity. Inspired by this, PointCLIP {{cite:afe3493a21f58689fe632dd1814ee08e9637e40b}}, for the first time, indicates that CLIP can also be adapted for zero-shot point cloud classification without any 3D training. To bridge the modal gap between the 2D pre-trained CLIP and the 3D input, PointCLIP introduces two modules for visual and textual branches, respectively. The visual one projects the `unseen' 3D point cloud sparsely into 2D depth maps, and the textual one modifies the general 2D prompt into handcrafted 3D descriptions. However, as a preliminary work, the zero-shot classification performance of PointCLIP is far from satisfactory. As shown in Figure REF , on the widely adopted ModelNet40 {{cite:2877781fb9b811516a96f3656d6903c9e5a788e8}} and ScanObjectNN {{cite:3ba9f057a83534b16ef0bf3a5a5ef2e9679d3311}} datasets, PointCLIP only achieves 23.78% and 21.34% classification accuracy, which cannot be put into actual use. Therefore, we ask the question: what actually restricts the performance of CLIP on point clouds and how to fully unleash it for 3D open-world understanding?
| i | d04dc2d36178bbd096b8e1c9a26ae0bf |
Solving the ill-posed linear inverse problem of estimating the subsurface reflectivity through the classical least-squares formulation {{cite:9de5a239d354080abb0a42fb46d75076e889fcfa}} leads to nonuniqueness issues arising out of a convolution with a bandlimited wavelet and loss of low and high-frequency information {{cite:dbea19bdf8a339d3694db1c4fe249e3dd92ae8c4}}, {{cite:7a0b8d4dd14d48423f630426ab7946823d7b0b68}}, {{cite:fe52cf706daa146c719af26ec76447f3bb60c536}}. The nonuniqueness aspect can be tackled through regularization {{cite:b538c83147f6f624e90c4171cd787ee88d898d5b}}, for example, by imposing a sparsity prior on the solution through the {{formula:5d843e9b-64e5-45ce-9622-3b352691bf53}} -norm {{cite:dbea19bdf8a339d3694db1c4fe249e3dd92ae8c4}}, {{cite:9de5a239d354080abb0a42fb46d75076e889fcfa}}.
| i | 2f46cb7e566bba62a39bac8b1dae2b75 |
Our method has two parts and is shown schematically in Fig.REF . In the first, slow, part we initialize the parameters to zero and perform Bayesian optimization using Gaussian processes.
This method is well-suited for this task, since querying the QPU is expensive and results in noisy outputs {{cite:fb7b65e7bc2c9bf57a2dd896306d38c644fe21a9}}.
The computational complexity of Bayesian optimization increases as the number of samples {{formula:fb6399a0-a0f6-46c0-9e6a-27a414bbbf68}} gathered from the QPU accumulates, due to the {{formula:f67c404e-3f88-41c5-808e-4b285a54cd13}} scaling of the calculation of the co-variance matrix inverse {{cite:4b34b9a8db548a8002daa5e1bb8de960264d1533}}. Therefore,
this method is not suited for a detailed local search.
| m | a7c1b06686d047b37719266e376a23a0 |
Our main motivation comes from the Eigenfracture approach to brittle materials that has been developed in {{cite:ca49cb4102b0ea7cbdd06f7557ddb6e4f014e8c3}} and further considered in {{cite:217756cc511934cee1e5b448531f299fe2c7dd62}}, {{cite:d9b4b02926331e36d8f8f9cf4968b057a229b758}}, {{cite:ddc49175ce4aef76518e0a3af9a773af4a2dd14d}}. Our main aim is to extend this model to a ductile fracture regime with a significant damage zone. The variables of the model are the deformation field {{formula:17a9befe-1fed-4201-bb19-b299aede6b35}} and an eigendeformation field {{formula:748d5ee4-19d1-433e-92c2-d9837e0c89f2}} , which induces a decomposition of the strain {{formula:b48da50f-b4c5-4de7-9043-2835ca08bd34}} into an elastic and an inelastic part, the latter describing deformation modes that cost no local elastic energy. (We refer to {{cite:2edb48d4ba605095cca0d17938a4f72581942890}} for more details on the concept of eigendeformations to describe nonelastic deformations and, in particular, plastic deformations.) The energy associated to the formation and increase of damage is accordingly modeled in terms of a nonlocal functional acting on {{formula:bdb5fe1d-ecc2-4a9d-b037-d70cdf1d0e03}} , which replaces the nonlocal contribution defined in terms of a simple {{formula:5ca7f628-3e46-4055-bfd3-7ad1034e24f2}} -neighborhood of the crack set in the original Eigenfracture model by a more general (and softer) convolution approximation.
| i | 8fa86292c27807b3c7448b9e71b95ba8 |
The phonon spectra for the T{{formula:a41c4be8-1acd-4a13-b01d-2f5af3c8e7c8}} phase of ZrI{{formula:0d6303a2-93b0-462a-ad2e-fc4c12875a2a}} were calculated using the method of frozen phonons as implemented in VASP and Phonopy {{cite:976c7b63a973af2256b33fa7c155713215ec8e08}} and density functional perturbation theory (DFPT) as implemented in QE. The calculations within frozen phonons were carried out for a {{formula:2d3f5c62-dbc0-443d-9a0d-0c031caca41d}} supercell on a {{formula:38460086-fc16-4921-b965-27a4e39ccf56}} {{formula:9ef4b630-11a8-441c-a1be-36a6b30a15e0}} -point mesh. The calculations within DFPT were performed on a {{formula:9501711f-b0c9-4f2f-823f-94f4ff6340e8}} {{formula:b9f633d5-47f2-4080-80ca-a351a6a4948d}} -point mesh. The calculated phonon spectra are summarized in Supplementary Figure 6.
| m | b789c0cab54c35f0ecefbc8464867c1b |
Since the limit in (REF ) holds in {{formula:4f6dea18-4b4f-45ac-84de-7bd8e090ddc9}}
(see Stein {{cite:9388e27ffd927205b407c3c36c0fbb43de4f3963}}, Chapter II), we have
{{formula:32045bb1-983f-44c7-ba9f-d3f27b728284}}
| r | 6dc560505bf07ded3a7e8ade57523aa6 |
The training and attacks performed were similar to those in MNIST and CIFAR10. Table REF shows the results obtained without regularization, with adversarial training, and our proposed method. There were no analysis on this data set in the Input Gradient Regularization {{cite:2dadd503331d3bafffaa93b69f1dede1d27a7607}} and Jacobian Regularization papers to show with our results. Similar to the previous experiments, our models show higher {{formula:882365bc-db40-4de4-bf53-f30888e4dd5e}} values compared to normal training. When combined with adversarial training, the model shows the highest {{formula:dd634b78-2e26-4e7e-9a81-86efb2f2b546}} .
| r | 116ea67eb1fce53ed32a4ae83510f0b1 |
In our model, we have two free parameters, {{formula:314b0c2b-cbd8-46ca-ad18-da2e7ad2acaf}} and {{formula:88d7db3a-21a9-43e4-bf91-2940a148b49f}} . {{formula:d877a472-8559-4985-8c31-fdd2f5aec11d}} is a global factor and its value does not affect the shape of the {{formula:2603ef17-72f4-4ba6-87ca-e640b23647cd}} invariant mass distribution.
As mentioned above, the value of {{formula:12682406-f365-4a5b-8713-09ca30ce0e3e}} should be around 3. In the first step, we take {{formula:4e49cc16-2125-4fdd-968d-414f259c47f7}} , and show the {{formula:b8310f5e-a274-4be8-92ea-414146a2df5e}} invariant mass distribution up to an arbitrary normalization in Fig. REF . Instead of the cusp structure as shown in Fig. REF , one can find a dip structure around 980 MeV in Fig. REF , which could be associated to the {{formula:9f0bd939-08b1-45e7-b2d9-d5dd3ce9dc4a}} . Although the {{formula:718ec24d-b874-44cf-a642-bed7d139d0fe}} , as a dynamically generated state from the {{formula:a4564acf-9d55-493c-9198-cd53d7f48465}} -wave pseudoscalar-pseudoscalar, manifests as a cusp structure in many processes, such as {{formula:2d24cfaf-e683-4521-b767-e70602007748}} {{cite:69013791e81a49b0eafb7b9f03ff638c97956a53}}, {{cite:fa420f27739af127ee6b282d4fd4f87020b7b4b7}}, it shows a dip structure in the process {{formula:26b96a40-7e73-46b0-8de7-7141561ca232}} .
As we known, hadron resonances are observed as narrow or broad peaks in the invariant mass distribution in many cases, a resonance may even show up as a dip, depending on the interference between the different contributions, as discussed in Ref. {{cite:75bbed3e4d5367aafeb019f4e114f3e95821997d}}. Indeed, this behaviour is relatively common in hadron physics. For example, the {{formula:85a5ca73-19a8-41df-a738-7583515316f7}} manifests itself as a clear peak in the {{formula:6f0fb146-4940-4d37-a862-d9df15588254}} invariant mass distribution of the {{formula:fa4afd68-d14d-4f56-b433-103047e6148e}} {{cite:d9fb3e9e382e29a38421159c32a9bbc56ba12477}}, {{cite:6b3433ebf4ea8fddfa69af2e9ea4a7bd3d4d6b8d}}, and {{formula:c8b3b5bc-43b7-4e04-8138-80a6e1eb6884}} {{cite:2fa71e406069d09a61480b1e1b46fd262c2e7961}} reactions, but shows up as a dip in the {{formula:b75c6149-b7ac-41fd-ac5d-89d242a24042}} -wave {{formula:f85a3851-1649-4022-8d4a-3389a2690ea3}} scattering amplitudes {{cite:ad1a13b08bc69d1d05470e879c226cb6d3d5830a}}. The dip structures have also been found in experiments {{cite:de2c0c15d2c2ffc72b03f6127c124eef4d265bd3}}, {{cite:22efde0f20fdfc5d60a04fc2ab92ab9c0cd714d6}} and theoretical studies {{cite:e19216237e845d5b0b46fa21eb0ca435fdac6aed}}, {{cite:c396783d286d49eff8cf5de089306407a03f6de2}}, {{cite:57d602e8adfdec229494cd137a1a812ecf660747}}, {{cite:7d85b4c507ea4aae331b06eafe8dd0b145e93353}}.
| r | 05e72bf649b782bbd30fa14316ad0169 |
There has been a great deal of activity recently regarding correlation functions of local operators in planar {{formula:85fcb86d-4646-4f54-894e-204c765aa2e0}} SYM and in its holographic dual, IIB superstring theory in {{formula:6c78a5c1-fea2-4c49-8d98-610dbf8dcb81}} . On the one hand, building on Mellin space techniques {{cite:d3eafd3ef1c502671cb02df54c15d4cc43bf365b}}, {{cite:ab37b9b88b9a634671cf42bbbc5271538052492a}} and bootstrap ideas, new approaches have been developed {{cite:8e9ca203122d4010c9edbff6ffc3ef9ec1691e05}}, {{cite:6b4c16ba77545e2183af5f5a1f2d2f926227de6f}}, {{cite:3f43fa7b5ad67337e53f5940e329b9ff47fbd2bc}}, {{cite:956a3310e8c9440af395ca36e8cafdd48c298d46}}, {{cite:9278180b6b4b74cdee8e4a2fc1d0434284bc9172}}, {{cite:d21a4db94e7fdfcb866af26d4461875d85288138}}, {{cite:09bdfcdd4b082753bccd1057af6290de37db4cf6}}, {{cite:2d2b85581ec2221b7fb9ace0ed26ee7dc49679d8}} to deal more efficiently with the supergravity regime, corresponding to the strong coupling limit, {{formula:a716d51f-ddc3-4b9c-870d-eed3fbce4bfe}} , of the large-{{formula:0e5140c9-f644-4bb0-9ba4-ebe06aa047e3}} gauge theory. They led to spectacular results, starting with a conjecture {{cite:8e9ca203122d4010c9edbff6ffc3ef9ec1691e05}} for the {{formula:02ccfc02-1810-424a-abea-e69551008c27}} correction to the 4pt functions of single-trace chiral primary operators of arbitrary dimensions {{formula:ae66bdba-c5ba-412d-8477-e63f1e668c36}} , which generalises earlier results and proposals, see {{cite:5229e81357743386c29d9d27717bba1f71137ee1}} and references therein. Further considerations unveiled hidden symmetries of the supergravity regime {{cite:d21a4db94e7fdfcb866af26d4461875d85288138}}, {{cite:9278180b6b4b74cdee8e4a2fc1d0434284bc9172}} and yielded lots of new OPE data for double-trace operators at strong coupling {{cite:6b4c16ba77545e2183af5f5a1f2d2f926227de6f}}, {{cite:3f43fa7b5ad67337e53f5940e329b9ff47fbd2bc}}, {{cite:038ee2a56cb06a1ef9db4da460c8023d9f78e4b8}}, {{cite:956a3310e8c9440af395ca36e8cafdd48c298d46}}, {{cite:9278180b6b4b74cdee8e4a2fc1d0434284bc9172}}. They suggest the exciting possibility that more general correlators can be found in the supergravity regime without ever using a single Witten diagram.
| i | dba215a4e98609818f90cbfc395705fc |
The statistical uncertainties of Eqs. (REF ) and (REF ) have been obtained through bootstraping, while the direct substitutions of expectation values would yield to 3.3 of gain over the shot-noise limit {{formula:816dad7a-dc85-408a-9bda-7deac4d5422f}} .
Based on Eq. (REF ), this proves the presence of metrologically useful entanglement {{cite:88ed2bd0ed25b4ad866bb6fe2b2552e51f61373f}}.
Based on Eq. (REF ), it even demonstrated that the quantum state had metrologically useful 4-particle entanglement.
Assuming an error of a standard deviation, Eq. (REF ) still proves 3-particle entanglement.
| m | f8e181a67e47baf0ec3dfcdf6bfd110f |
where {{formula:25d2db35-d1fd-40c9-8d1f-fcd6e40ebcab}} is either a uniqueness or a minimal function. Furthermore, given a time-independent barrier function candidate {{formula:dfc8d01c-8155-421d-b60e-96d73c2d5d85}} , according to {{cite:6ad8080e832438e205d9a44fcb56b26ca86f13a3}}, {{cite:bcaa74d894d826cf558a9d7478311a3ce293232f}}, {{cite:88eedda0df8cfeaa5b4785ea82a3dd58a3055339}}, the following condition implies forward pre-invariance of the set {{formula:e42cf968-32ac-4846-a286-16e9eced441b}} in (REF ):
{{formula:8f1278f1-85e0-4316-b5dc-a08829ea9027}}
| r | 13254f9ce85bcdd421c58fea5e5b68a6 |
Traditionally there exist two different pictures on random fields in space-time, one results in space and time being treated separately {{cite:0a80652b0f1530adb98ef68ec89ab8c2e07ac2b7}}, {{cite:8406b46b98164a38d1dc914cda8780a9f8d75cb0}}, while the other models the field as defined over a single space, namely space-time {{cite:fef9467e301aed7408d1ded107b130ee61690077}}, {{cite:77aeb07485e9d8f5964336076db6a13d6aa12157}} (see e.g. {{cite:2aa84df60bd0a93066c591b4719c4eaf51aeb37a}} for an extensive discussion). In this work we rely on the latter picture. Consequently the corresponding inference problems can be regarded as the task of inferring a field defined on a single space, given a finite amount of measurements in this space.
| i | 40bf00293741f56ffd494bc6fd485029 |
The Momentum Contrast (MoCo) {{cite:407dfeb7038334ac16065838d9e0f4646725d09e}} is a memory-based contrastive learning model. While the SimCLR {{cite:dd9bebd64129e0149218f0f6e56f6cf0b81e4062}} treats other instances over a batch as negatives, the MoCo instead uses a memory bank to store negatives queued from the past iterations.
| m | 985c048ec2315fadcd15ac79b7d51231 |
In the quantitative experiments, all compared methods generate diverse images except Pix2PixHD {{cite:6ee24f5ba11136528eadb5eb83b2fbfea813cbb1}} which does not support diverse generation. Table REF shows experimental results in FID, SWD and LPIPS. It can be observed that IQ-VAE outperforms all compared methods across most metrics and tasks consistently.
DRIT++ {{cite:e5fe27761528335015d20a1a438f8a8f9e59a803}} and StarGAN v2 {{cite:a8c64f7125c610e9ec45b0943971b467c1ac3a81}} achieve relatively high LPIPS scores by sacrificing the image quality as measured by FID and SWD, while SPADE {{cite:b9aada948be241b9f9424946f5ee37ee12517026}} and SMIS {{cite:1aad1d52497c6c635af91f8202b37c269470a2c7}} achieve decent FID and SWD scores with degraded LPIPS scores.
The proposed IQ-VAE employs powerful variational auto-encoders to achieve high-fidelity image synthesis and a auto-regressive model for faithful image diversity modeling, thus achieving superior performance in terms of image quality and diversity.
Compared with Taming transformer {{cite:a3e2e5b82ae9970c165ece18a272fc8dc1f2bc2f}}, the proposed IQ-VAE allows to quantize the image sequences and conditional sequence jointly and boosts the auto-regressive modeling for better FID and SWD scores.
In addition, the proposed Gumbel sampling introduces uncertainty of distribution sampling into the training process which mitigates the exposure bias and improves the inference performance clearly. As the mixed sequence serves as certain extra data augmentation, the Gumbel sampling also helps to alleviate the over-fitting of auto-regressive model effectively.
{{table:efeed6ae-4699-4aa9-b444-1d85b3063de0}} | r | 60b67cdf72b9c624a499483891051123 |
We believe that our model should prove useful help in navigating data collected on complex networks. There are still ongoing discussions on how the claimed scale-free networks must be characterized {{cite:b129fdf766585dcaf56a28c33d12186d77a78e88}}, {{cite:e9512d74194249ba47e02770c1bf1ffda63df1e9}}, {{cite:b5b5cebb442b2e479e8779728f5059f48b061d49}}. In the context of our model, we would simply encourage researchers to measure the slope of the empirical power-law {{formula:f70a1d89-3b65-4aea-85cd-92d82009b7ed}} in their data together with the average clustering co-efficient {{formula:9dad2ac6-5fd9-4fcb-816b-b50cb243ef22}} and see if it lies within the red shaded area in Fig. REF B. From there it is possible to identify the values of {{formula:56cce8c2-5d9b-47a5-86bb-94634e153d00}} and {{formula:6817f8e5-ad06-4102-a399-acdf9406aa29}} consistent with those values. The 'friend of a friend' model with those values of {{formula:25b02f56-b9ce-4b26-9ef7-9d67692cc512}} and {{formula:f7476a9a-0643-4ffb-8241-5fb2ab9d3675}} thus becomes a candidate mechanism for generating the network.
| d | 885bd78e97f601915f8979550a52ad48 |
It means negative value of {{formula:496c75ed-0acd-4b96-b5f5-1a11db472c5b}} microcanonical corrections {{cite:963fffa6bfe2b7ed9f97ae09a2ee979e93e908c5}}, {{cite:6a6da970cdd7f9fd133e5dd681983fbb47652f8e}}, {{cite:0c77c850692223f928747396b0d21cb9a3ee2fe7}}, {{cite:c287c817d1887190e7eaa6f705bef75982457c82}}, {{cite:709937a178f0e4137d69b26d7ded5a76ab6466c2}}, {{cite:b838388d5440e4f4882c9c67df055c4aa3fdd857}}. Note that the positive value obtained from canonical corrections due to thermal fluctuation {{cite:963fffa6bfe2b7ed9f97ae09a2ee979e93e908c5}}, {{cite:6a6da970cdd7f9fd133e5dd681983fbb47652f8e}}, {{cite:c287c817d1887190e7eaa6f705bef75982457c82}}, {{cite:709937a178f0e4137d69b26d7ded5a76ab6466c2}}, {{cite:b838388d5440e4f4882c9c67df055c4aa3fdd857}}. Therefore, from phenomenological view the sign of {{formula:76f0f396-9b4e-4354-87fc-c3fcbabbda45}} is determined by combining both corrections.
| r | fb72ad88ca4c83854613c6587937bebb |
Although both models should produce the same output {{formula:1462107f-8ebd-4362-bb81-e1af8572b230}} , we use {{formula:e16e99aa-6688-41fa-8618-b19d1d5d1025}} and {{formula:125d9afb-6fed-49a9-a6bb-33c001cee872}} to differentiate their outputs. To train both models at the same time without introducing extra parameters, we use the concept of Classifier-Free Guidance (CFG) {{cite:2038e3d65a21feee7741cd8ca4fe7402408a4366}}. More specifically a dropout layer as shown in Fig. REF , is used to randomly mask {{formula:616f0896-b59c-49a8-a3d8-32a771f305ac}} in each batch by {{formula:d610e3c3-dbdc-4f0e-81a0-5c04b80294c1}} with probability {{formula:cb9948df-ecf6-41e4-a8a0-13d9f38c69ed}} . We chose {{formula:1312fccf-ba5c-43e9-9761-92043be0f824}} as the dropout value due to the fact that 0 corresponds to silence in {{formula:d5e3bdd2-4646-4c2f-a156-1354f5e97a28}} and we want to avoid confusing the model during training. The model is trained to minimize the L2 loss between model output {{formula:b7d6f774-2594-4e4b-acbd-1d1295d17446}} and ground truth label {{formula:dc1c83f6-4ffe-4945-b41e-e3bfaa1673e6}} , as shown in Eq. (REF ), similar to previous approaches {{cite:75a10807b3089062c5f9eaa46aeec0d35bd667c8}}, {{cite:183bb10f0637f956e119886856fea3604bb7d2cd}}. A full explanation of this loss is provided in the supplementary material[1].
{{formula:208e5a44-68d9-4cb9-8a9c-399b5f52ea34}}
| m | 8f61663a6476a670f90fbe82cc2bc23e |
Table REF summarises the comparative study
in terms of their theoretical and computational properties.
Denoting by {{formula:cb466a45-6d57-4d00-8d1f-a22d3ae98dfd}} the size of change between the {{formula:f65bfaf1-eaed-4f37-8114-5cb9b63d7179}} -th and the {{formula:0e70890d-b767-4359-8d90-942d5b4435f8}} -th segments
(measured differently for different methods),
the separation rate refers to some {{formula:89d8aa62-973c-4815-b8b6-a692ec01bbcc}} such that if
{{formula:c804084a-0366-496d-b0cb-7eeab4d7060b}} ,
the corresponding method correctly detects all {{formula:6e2e08a3-d96d-456f-a503-42981f0b37c8}} change points;
for Stage 2, we set {{formula:96949c37-84c1-48fc-8baa-417482769914}}
and for the others, {{formula:b19d221e-4ac0-4f1b-afe9-32d7555ff1e9}} .
The localisation rate refers to some {{formula:3929199e-6382-4055-9521-06c3dfdb4817}} satisfying
{{formula:a8f25c12-d88e-429e-bbfc-e30a4fa54e96}}
for the estimators {{formula:1be95b55-1194-4d6c-99e0-07e4e7edb38b}} returned by respective methods.
For Algorithm REF , the weights reflect the difficulty associated
with locating individual change points, i.e. {{formula:84c653e8-2976-4433-a517-ea56efa4de5a}} ,
while for {{cite:16eab74e4bca010f2d6b9da9abb079f0637ddcc2}} and {{cite:f5106d424ec3cbe52182f8b2320c6fc91c004c41}}, the weights are global
with {{formula:ada3a5a2-1baf-4a53-96b2-8b48dd495ae7}} and {{formula:4ccc7293-11d8-4ec0-9198-8195291fafda}} , respectively.
{{cite:f5106d424ec3cbe52182f8b2320c6fc91c004c41}} further assume that
{{formula:ccc4773c-28bf-4021-be10-d6ef17c63a86}} is bounded away from zero.
We suppose that {{formula:928067e0-7850-4a77-b05b-a14348e4fc9a}} ,
a sufficient condition for the stability of the segment-specific VAR processes
{{cite:248d086336b44ec8a7a008f1cc2b4c1b353ae6f0}},
which is required by all the methods in consideration for their theoretical analysis.
| m | 034644f2ac84e757b062eab843386351 |
Results are demonstrated on the IAM, RIMES, and NIST offline handwritten datasets. The IAM {{cite:5f3fc38e2d00696d6832755bfade1189c4de6c76}} dataset contains 115,320 English words, mostly cursive, by 500 authors. This dataset includes training, validation, and test splits, where an author contributing to a training set, cannot occur in the validation or test split. The RIMES {{cite:5433b55f261c7d6679f95afd64553366cada608a}} dataset contains 60,000 French words, by over 1000 authors. There are several versions of the RIMES dataset, where each newer release is a super-set of prior releases. We utilize the popular ICDAR2011 release.
| r | 3a18ae29388fc736f180ab01653837f0 |
Another class of approaches apply machine learning to model predictive control {{cite:be93bd3394fe63064fc73082232b9169744deda1}}, {{cite:54867263c786a0b89d63ae273479041a16a73366}}, {{cite:f00fcaf243a0c36f2159c35cc5df29b6bd18ab69}}. These approaches however either use simple learned primitives for modelling dynamics, or are geared primarily towards process control, and have not been demonstrated to be capable of controlling complex robotic systems at high speed in real time.
| i | b1811fb4bad674051e35d24ca0d15e2c |
Universal conformal symmetry, requiring local Weyl scaling
covariance{{cite:80a85595125a01f8b89a63701d2e45263319d426}}, {{cite:99d13d90db08b3de94546966109b6aa3f29ff5d2}}, {{cite:5a94256f5c0fac52870573015b334d03375e68a3}} of all elementary physical fields
{{cite:a5b33b015407984a7e9dfaff4269676780623859}}, offers a paradigm alternative to consensus {{formula:f27bac44-43ba-424b-82e3-f95a7ded4994}} ,
motivated by the absence of experimental confirmation of conjectured
dark matter and need for explanation of currently accelerating Hubble
expansion. The conformal Higgs model (CHM){{cite:df59c8e0c07aea1d49234f926edd5b8e04c57170}}, {{cite:6279da0a7a2c5944ea8fd871c0b5ebace9c3e93f}}, {{cite:0711edfb0bcfe1f6d343da95a2343fb6ee261979}}, {{cite:3f83fd1fc67eada19bd370c13bc7c7d9ae385933}}
retains the Higgs mechanism for gauge boson mass, but acquires a
gravitational term in the scalar field Lagrangian density. The CHM
determines centrifugal cosmic acceleration accurately for redshifts
{{formula:f2ee9d58-6fee-4975-b788-96bba2799f93}} (7.33 Gyr){{cite:df59c8e0c07aea1d49234f926edd5b8e04c57170}}, {{cite:6279da0a7a2c5944ea8fd871c0b5ebace9c3e93f}}. Conformal gravity (CG) replaces
the Einstein Lagrangian density by a quadratic contraction of the
conformal Weyl tensor {{cite:eb29519e32415501db533605de74c9350dd599b7}}, {{cite:d8ff0699bfc06478db8db7a40efff8d5985d286d}}, {{cite:1f358091069c78bd35286d39d9eda82be9a160fc}}, {{cite:ca40a79b9ceeaf7cdad112f6c211e086233e3331}}, {{cite:99d13d90db08b3de94546966109b6aa3f29ff5d2}}, {{cite:288a9b8859ffdb3e0c91f3e664222c9cd4f452b7}}.
Substantial empirical support for this proposed break with
convention is provided by applications of CG to anomalous galactic
rotation velocities. CG has recently been fitted to rotation data for 138 galaxies{{cite:fdfb5f89a3d6e349bb3f6130076ee1e1ccb67930}}, {{cite:c9c1eea394d2dba3323b9bcebb45d6e21c67bbb2}}, {{cite:9b9e7a921b921c72ec0ed7e128af73e4d2c01789}}, {{cite:0c38fecb4193db3dba06d5fe190fd4435bb596e1}}, {{cite:a452394795fed07d139d0c8c059195bada078899}}.
The CHM precludes existence of a massive Higgs particle, but conformal
theory is found to be compatible with a compound gauge diboson {{formula:daf6f146-95b5-4f75-9b64-33b866e7a8bb}} of
mass 125 GeV{{cite:d5cc2c9229892fd3e1c5efcaf32be9ba803fcb95}}, consistent with the observed LHC resonance
{{cite:92b3e2e52e39879fe16bec94e0eb3ee47afc45e4}}, {{cite:9751bf579b80f0e7f4e937f0027333fbf94b32be}}.
| i | b3e9fd6c0f3714efa8346643d2356643 |
While an all-multiplicity proof could be found using the methods employed in {{cite:6b61560a73ecff5fe8cd9fa96f59e5ef59821076}}, which relied on position space Feynman rules, they soon become cumbersome. From our experience with the tree-level amplitudes in the usual plane wave basis we know that there should be more compact descriptions of the S-matrix. For certain classes of celestial amplitudes in four dimensions all-multiplicity formulas already exist in the literature: tree-level Yang-Mills MHV and NMHV amplitudes were computed in {{cite:432e7f11c3a2979ff282118687b597224b632562}}. These computations are done by performing Mellin transforms on the energies of the external particles which, while doable for some low point amplitudes including loop {{cite:41201603c804e48c7857d05e7bd97dba004dd4b3}}, {{cite:920b488ad9cbbebda3f66a38b66d727bbc52ab33}} and string {{cite:8cf469df84626a82d8e9e29ac882c8ef5c36db06}} amplitudes, become highly involved for generic amplitudes. CFT inspired methods have also been used to holographically constrain MHV amplitudes {{cite:2d9b77206a1ccb9d567be4f1fa7de6664ae8cbb1}}, {{cite:080d693d0031dc1f590174557fdf804867071292}} and it might be that further understanding of the celestial OPEs {{cite:8eea0c19bcfe742a217909192d4295847e143fc0}}, {{cite:54c4c2838534e6ba0bb9755fa3cdb11d1ee7bee2}}, {{cite:f37be11efa2a00ea6867348bac942e424a942b7b}}, {{cite:7050cbc1ab89f23e696a44fff040dc1e8e43f7f2}} will lead to better methods.
| i | 79ccb1953c6276f0b9082dc59abc53b2 |
Similarly, Figure REF shows the class-wise vulnerability of the EWC online {{cite:29d78f2d1cc7634fc207c0bc4b4d7a4efbb61dd4}} against the FGSM, PGD, and CW {{cite:cceff7ffb4d3b29c215d08507950b6a5e69f61c6}}, {{cite:c3fccf0ff9253b92c42d2bf0bfc9f109ecfd1a1a}}, {{cite:3519d381d3816b9d84b2d65e2bb04bb34bae094c}} adversarial attacks under Task-IL setting of continual learning. The initial two rows present the class-wise vulnerability of the EWC online against FGSM. The next two rows depict the class-wise vulnerability of the EWC online against PGD, and the last two rows present the class-wise vulnerability of the EWC online against CW. Moreover, the first sub-figure in rows 1, 3, and 5 presents the EWC online average performance under standard evaluation of continual learning. The second sub-plots in rows 1, 3, and 5 present the degradation under untargeted adversarial attacks. The subsequent sub-plots show how targeted adversarial attacks degrade the overall performance. The sub-plots' headers point to the labels that are being targeted. The number on x-axis indicates the task number while the y-axis presents the average accuracy over 10 runs.
{{figure:577a16fb-deac-4d9d-b715-6c60f053d005}} | r | bd26a835e3b1a2002f3a0e204c124c9a |
However, given the limited availability of resources on many devices, performing FL on such devices is impractical due to increased training times {{cite:c2def3048e210e223191322bce6cbfe7e2145f72}}. One approach is to leverage the computational resources offered by edge servers (located at the edge of the network) for training. The concept of offloading computations of the ML model that may be a Deep Neural Network (DNN) from a device to an edge server for FL by splitting the ML model has been introduced {{cite:e7c0d4ab48107f4008596643b8576bf46313e353}} (this concept is referred to as edge-based FL).
However, a major challenge that has not been considered within the context of edge-based FL is device mobility.
| i | 64e40728e9d6852e866f2f626892965d |
While not mentioned explicitly, our evaluation toolkit is also useful for evaluating matching methods {{cite:08deae46f36217cf17eb4396842d994f126f9f15}}.
Matching allows the estimation of counterfactual outcomes and is therefore applicable for outcome evaluation.
It can also be considered an integer-weighting algorithm and can therefore be evaluated using the weighting evaluations.
Furthermore, specifically, propensity matching requires a propensity model and therefore lends itself to propensity evaluation.
| d | 45a20e7140f450b2c0f0fde3cd0270fa |
Background.
The transformer model {{cite:431fd494742f3627971c33b53ea2f2addb8505e6}} has revolutionized deep learning research {{cite:fa49e5ee46995812de5c40ab88b396ea52277324}}, {{cite:1983be73cbe3a4017c7fa76e37ed60c784087d47}}, {{cite:bdcf25c38b33ada086b5517ba44edb9ea89ccae8}}, {{cite:4758ddc2f71ad3005420960fddbd92d20e9d65a4}}.
After being proposed for neural machine translation, transformers were adopted for self-supervised training over large language corpora with the proposal of BERT {{cite:fa49e5ee46995812de5c40ab88b396ea52277324}}, allowing models to be pre-trained, made publicly available, and fine-tuned on downstream tasks {{cite:fa49e5ee46995812de5c40ab88b396ea52277324}}, {{cite:0bbc22fb4a4b060b5d8b4d093331757cc0c05c7c}}.
Due to their remarkable performance, transformer models became popular in domains beyond natural language processing (NLP), such as computer vision {{cite:bdcf25c38b33ada086b5517ba44edb9ea89ccae8}}, {{cite:4758ddc2f71ad3005420960fddbd92d20e9d65a4}}, multi-modal deep learning {{cite:6884069f8a38690da5d9cf5058271864c654b0a5}}, {{cite:2c616532383f30ed01ce1b2ace4408a6c80eb2af}}, and even music generation {{cite:c59fc35b9e7fea199e9e4f829229b96222ab9ff1}}.
The use cases for transformers are constantly expanding as deep learning practitioners develop new applications {{cite:827c10fea03edbe317044987fa62b56fec9205ba}}, {{cite:92b1cee45099b02eee5d337f99ee741b7118a845}}, {{cite:38acadf474cdc4eff60d4e823bcfc7049c88e9eb}}, {{cite:83099dd8fbdd21b9a736486e67430e21bf15440b}}.
| i | 5ff99858fb15bb438723dcd96cd5baaf |
In contrast to ParCNetV1 which applies large kernel convolutions only on later stage CNN blocks, we unify the block design by mixing large kernel convolutions with local depth-wise convolutions in all the blocks. Both types of convolutions are operated on a fraction of the input feature map channels. The exact portion is determined by its depth in the model, following a general rule that the usage of oversized kernel convolutions grows when the block is deeper. This progressive design combines local convolution and global convolutions in one convolution step, unlike many other works that stack the two sequentially {{cite:16d898ef99110279ac11baf08c8fe0b4a3291c94}}, {{cite:781abc1c1ed81be4980c1fb87b7899a3450891a3}} or as two separate branches {{cite:61d973ee4f01edeb3a1498237afacf370c663c81}}, {{cite:18835e0d988470ab51e55d1e6856abbf413d7720}}, {{cite:1874e84eff7078786372a6c4c34f2ca6ff9800e1}}, {{cite:58f98a703ffb3203848a4dd6616082cc904831ca}}. To this end, the resulting redesigned ParC V2 structure is capable of performing local convolutions, global convolutions, token channel mixing, and BGU-based attention all in one block.
| i | 5f5cb807c1be60a655d54db1809eebaa |
After initially validating our models on several toy datasets (see Appendix ), we focus the bulk of our evaluation on four RL tasks. As running experiments with people is costly, we use the standard RM approach of generating synthetic preference data (here trajectory return labels) using ground-truth oracle reward functions {{cite:5d55e64563e44324e6415700134a357a3b898016}}. Unlike prior work, these oracle reward functions depend on historical information that cannot be recovered from the instantaneous environmental state, thereby emulating the disparity between the information that a human evaluator possesses while viewing a trajectory sequentially, and that contained in the state alone. In this section, we introduce our RL tasks (Section REF ), evaluate the quality of reward reconstruction (Section REF ), investigate the use of MIL RM models for agent training (Section REF ), and evaluate their robustness to label noise (Section REF ).
| r | dd344b2f3e8ab14e762bc1f9b887dc19 |
We
started our simulations with a burned central region which, in size, corresponds
to about 1 to 2 seconds after the thermonuclear runaway in models of central
ignition.
This is the onset of RT in models with central ignition {{cite:c88c66a74f33804b4deda7cfb659df1025a8904f}}, {{cite:1e6363eaee36027ff7e4188f4f7ef83a5d82a99b}}.
In off-center and multi-spot ignitions,
the development of RT instabilities is faster {{cite:785aa0256a40654025410794f40df2c29b184c8e}}.
Though we do not follow the deflagration front during the regime of distributed
burning, the tangling cannot be expected to decrease. Rather, in the absence of
a large scale flow to order the field, it can only be
expected to increase during the regime of distributed and detonation burning.
We show that the density
distribution remains spherical to within {{formula:b02718aa-f42d-4e74-a58a-7bf554293fce}} in the most strongly magnetized
case. This is due to the dominance of pressure
equilibrium and gravity, a result found previously by hydro-simulations for
QSE of explosive oxygen burning regions {{cite:185b3e18cf3368a580748a4f5f5c20933ce74eb3}}, {{cite:4486b10420e932e87f45dc6066435ab6ddf6bab7}}.
| d | 6297e808b3b22f888f3251c936873a61 |
With fully error-corrected quantum computers it becomes feasible to define kernels with a strong bias that do not require exponentially many measurements. An example of this kind was recently presented by {{cite:b769cb1b7dc8fe221e472a765647ea75430be5f6}}: Here one knows that the target function is extremely simple after computing the discrete logarithm. A quantum computer is able to encode this inductive bias by using an efficient algorithm for computing the discrete logarithm.
| d | ceec4b6713fd294e9dccbd6ad6db3a15 |
In future work, we plan to extend this work to the setting of multiple variable groups similar to {{cite:b1ced0da8c4af0bed81426bb4c8aa04b83e7608c}} as well as to use partial dimension reduction techniques. We also plan to relax the i.i.d. assumption to better deal with autocorrelations following {{cite:7ac40d2aa97a4d23bdaa7d30df21544869f621dc}}.
| d | 4467038cb3c125f2dd0c692dbe39357c |
The measurement is carried out in
a wider {{formula:7293a296-454b-489d-9803-ba79a32f72e4}} range with respect to
previous measurements in pp collisions {{cite:dff053cdac1caeb4a193dbe7af2e8fbc37c8c415}}, {{cite:f504105074950a863f508e27d0d0e5e492a12fc1}},
the {{formula:934eafa4-102a-4f98-9cdf-c5d096d19964}} reach
being extended from {{formula:d0a35a81-9b53-4968-afad-35dbd096f09d}} = 10 GeV/{{formula:4df5a252-4eb3-45ff-b082-df29d4128553}} at {{formula:d3111fe8-69e3-4efa-bcbb-83422b683f24}} = 2.76 TeV ({{formula:200b8b81-b7f5-4d2a-8967-7f0d057f5cdd}} =
12 GeV/{{formula:10e04fcf-2efa-40a6-9869-a12ff31c16fa}} at
{{formula:43ee18c0-4b30-40e7-9772-a0523d3cb6d3}} = 7 TeV) to {{formula:67756c35-dd9d-455d-b355-ce53755c1f10}} = 20 GeV/{{formula:ec08f254-35bb-4e25-8443-1669b7207c4b}} by
using MSL and MSH triggers. The total uncertainties (quadratic sum of
statistical and systematic uncertainties) are reduced by a factor of about {{formula:fb2a3302-ec95-4b15-b26b-5b424f2d566c}}
with respect
to previous measurements. These improvements have various sources: i) better
understanding of the detector response, ii) new data-driven strategy for the
estimation of the contribution of muons from light-hadron decays, iii) larger
integrated luminosity and iv) use of a high-{{formula:14c6054c-c5ad-46de-9346-8cbf0dbd0188}} trigger. The measured production cross section
(Fig. REF , upper panel) is compared with FONLL
predictions. The FONLL calculations {{cite:c6bad7ed350ba01bbab5f3d78e9b88174eac79fe}}, {{cite:2f5be64536db4d6c0475e6eb1c64860e9fc4e806}} include the non-perturbative fragmentation into open heavy-flavour hadrons and their decay into final-state leptons. As described in {{cite:597e2d297f932f9f206cbc2ffff2a307960031bb}}, the production of leptons from charm- and beauty-hadron decays is controlled by measured decay spectra and branching ratios. These predictions which use
the CTEQ6.6 PDFs {{cite:c7173d6aae5fe2466a5d4477303adfb526ea5a2f}} are represented with a black curve
and a shaded band
for the systematic uncertainty.
The latter contains the uncertainties on the renormalization and factorization
scales, on quark masses as well as on the PDFs.
The FONLL predictions are also displayed for muons
coming from charm and beauty decays, separately. The latter contribution
includes
direct decays and decays via D-hadron decays.
The FONLL predictions are compatible with data within the experimental
and theoretical uncertainties. However, one can notice that the central
values of FONLL predictions systematically underestimate the measured
production cross section at low and intermediate {{formula:f9b2e73c-3af5-447a-ae82-0f14cd826df6}} , i.e. up to
{{formula:fd50b02c-4dd2-44fd-94f4-3afafc3a52e8}} {{formula:0c7c713a-2865-4699-80d6-3667a8c23231}} 8 GeV/{{formula:dcffaf8f-a2e1-44b7-9eee-b0a835cc2124}} .
This is also illustrated in the bottom panel of Fig. REF , which
shows the ratio between the measured production cross section and the FONLL
calculations. This ratio is about 1.3 for {{formula:a8bbb7d1-f5cf-4189-9426-89652c38ab34}} GeV/{{formula:4eb8ea00-1ba3-4ce5-8723-9bf2ce88a2c4}} and then
decreases with increasing {{formula:40c00b0a-b96d-495f-8d03-57f1e7415849}} to tend towards unity in the
high {{formula:f4fb2b96-9f1b-4b66-82ce-7430794431de}} region ({{formula:01ee6e2e-1cec-4af5-bad2-c57892289e65}} GeV/{{formula:39d3442e-ace2-4870-8f80-89b6d20b45a1}} ).
Qualitatively, this behaviour was also reported at forward rapidity for muons
from
heavy-flavour hadron decays in previous
analyses {{cite:dff053cdac1caeb4a193dbe7af2e8fbc37c8c415}}, {{cite:f504105074950a863f508e27d0d0e5e492a12fc1}} and for D mesons measured
in pp collisions at {{formula:bd72fee8-abcf-4f4d-a4a2-df902f145b59}} = 5.02 and 13 TeV with the LHCb
detector {{cite:2366bad30f7ceac96cefda9bfc94386aeb488f4d}}, {{cite:1611d19fe3526daed07bd3912baef03f0c35d324}}, as well as at mid-rapidity
for D mesons and electrons from B-hadron and
heavy-flavour hadron decays measured in pp collisions at {{formula:032312b9-9cfe-4273-a0d2-6135ef6ca223}} = 2.76
and 7 TeV with ALICE {{cite:1b4e44d1f9e209112dec60f86291f4e38c6167e9}}, {{cite:62c213c7014dd8dc77454084a601c3e39fadf90c}}, {{cite:85216e24cf714f3098d690070abd1de8e323c858}}, {{cite:39ac637334078a099b3d98148ce07cfdb8d9a27b}}, {{cite:aef537e511ec05aa690038df770829fdba4a4d0b}}.
| r | 6fec73295472a5ce8f9be5e72ebdc3cf |
Since FST is intended for post- and pre-processing, comparisons to other post- and pre-processing methods are most natural as they accommodate situations a)–c) in Section . For post-processing, we have chosen {{cite:21aed915a28406fd3632c635f2c871d5a05483ab}} (HPS) and the reject option method of {{cite:1a21ce2f99e3f14f1ea25a4c6504489cea34e0d8}}, both as implemented in {{cite:39dfa614ac741d82208c70f7775d437ca7fa5f1e}}, as well as the Wass-1 Post-Process {{formula:3c2816d0-74e5-446d-9132-1d8d387dcdbe}} method (WPP) of {{cite:99d990bd6c59bcce492720d0244803077786f884}}. For pre-processing, the massaging and reweighing methods of {{cite:7194750d28fe64a3e045c1d2c4f9c6fafafe3591}} and the optimization method of {{cite:1d1e42e80fe6fc1dae4acd302f1569a42cbd2f74}} were chosen. Among in-processing methods, meta-algorithms that work with essentially any base classifier can handle situation b). The reductions method {{cite:e7610e77c93c94ac7b1c7c5565eb42c71822a078}} (`red') was selected from this class. We also compared to in-processing methods specific to certain types of classifiers, which do not allow for any of a)–c): fairness constraints (FC) {{cite:fb7e5bc8c26b4b2791c32f2c98853a204b6f0c67}}, disparate mistreatment (DM) {{cite:c2feef1ac5fca0bbd63a88dadc9bec09e08bfcfe}}, and fair empirical risk minimization (FERM) {{cite:eaf769cc64479285bbecccfef612c8a13451cd03}}. Last but not least, availability of code was an important criterion.
{{table:bfad86a3-07c8-4e54-ab5f-3fa19be63378}} | m | cfdcc34ad2708f500471071aa872c876 |
Experimental observation of the space and time-resolved plasma emission based on Phase Resolved Optical Emission Spectroscopy (PROES) {{cite:0f4202b35f060a6259f32d5c49a167688267e74d}}, {{cite:3311636f171946fea274d677c4724786a09c0ef6}}, {{cite:2c697c4e19b6d1ef0bfc10d3fb3b1a0310b52d84}} provides invaluable information on the electron power absorption and excitation/ionization dynamics in low-pressure CCPs {{cite:d133b18e5ca5221a17c147c7800d3ddd1bc58abd}}, {{cite:eba74b83bac86e37eb3a57dad2a2bc3d92844548}}. For PROES measurements, Ne is often used as a tracer gas due to its favorable spectroscopic properties. By adding Ne in a small concentration (typically 5% – 15%) to the background gas, and measuring the emission from a carefully selected atomic transition (e.g., Ne {{formula:40881eab-e13a-4808-966a-bc89246acb23}} with a wavelength of 585.25 nm) the spatio-temporal electron impact excitation rate from the ground state into the upper level can be derived. This way, by selecting an emission line resulting from an excited state with a high electron impact excitation threshold energy, information about the dynamics of high-energy electrons (which are typically responsible both for the excitation and the ionization processes in the discharge) can be obtained, making PROES an effective non-intrusive diagnostic technique. Although PROES provides information about the spatio-temporal distribution of the electron-impact excitation dynamics from the ground state into the selected excited atomic state in the discharge, it is generally considered to probe the discharge operation mode (which, in turn, is determined by the spatio-temporal distribution of the ionization dynamics) as well.
| i | 1a5b922a9dcae174f225eaffae3b8b77 |
Experimental set-up. Our colloidal model system consists of silica beads of diameter {{formula:49d1d8bc-8045-4219-bddc-079a2450eb6b}} (Sigma aldrich, 44054) suspended in a {{formula:289fd186-40d9-4263-bfd1-49be6dd2210c}} solution of hydrogen peroxide {{formula:e03ed85e-eede-46d4-b648-e3dce8b31b9a}} in deionized water (Millipore, {{formula:ee33faf6-6308-412d-a6f6-402c7d425e65}} ). Within a few minutes, the heavy particles sediment on the bottom wall of the sample cell to form a dense monolayer of area fraction {{formula:04c96227-323b-45d2-b25f-d748e97c8beb}} , where {{formula:13e6711d-70d1-424a-9766-8958aaed626a}} is the number of particle contained in the hexagonal area {{formula:a7fdd5b1-2af6-46f8-b370-3aaa0058deaa}} . The equilibrium gravitational height is much smaller than {{formula:62ab465d-9005-4ab3-8c99-632bad774472}} , so that out-of-plane thermal fluctuations are negligible in the absence of swimmers and the system is quasi two-dimensional. When active intruders are introduced in the layer however, passive particle are observed to slightly lift from the bottom surface as smaller swimmers pass by. The numeric fraction of intruders {{formula:14581637-b406-4f7c-b4de-133b5fcec624}} , with {{formula:1f117252-3c31-4fab-b5cc-e4228f5ac427}} the number of swimmers, is varied. They are light activated {{formula:c9153e0e-d357-4bb1-9ef2-6d0894caabc4}} m-diameter particles, consisting of a hematite cube embedded in a polymer bead {{cite:cefc7b87fb2678672940f5711d46172ddc2af296}}, {{cite:308510f8f2c4381bb9b88e3a49ec4190d58b10f8}}. Under UV-light, the photo-catalytic hematite triggers the local decomposition of the hydrogen peroxide contained in the solution, creating a gradient that sets the swimmer into motion through phoretic effects. They then exhibit a persistent random walk along the bottom surface.
| m | 6c27760a8cff3d55d0b67f44a839a595 |
SHAP. Lundberg and Lee {{cite:7ada4801ca775943f515f11ad1bbe0823094bd28}} present a framework of Shapley additive explanations (SHAP). This framework builds on Shapley regression values, inspired by the game theoretic concept of Shapley values {{cite:5311096384ed67913d627643e466174b8cde7577}}. For the {{formula:00acc321-0edc-44cd-aef3-21f357a1c695}} -th variable, the Shapley regression value is given by
{{formula:6ca0f03e-3113-42ae-982e-50f3bb0025da}}
| m | a54d555b1fa13f663c70c9ab1abc8367 |
Another limitation of our approach is that, because we only considered the effect of intervening on one treatment at a time, we cannot directly address how to select combinations of medications that would be expected to optimize the probability of treatment success. Previous work evaluated the causal contrasts between different regimens of concurrent medications in MDR-TB. {{cite:66c822d3b606bd798a8510dcf4ada21146651b99}} Future applications should directly address the more challenging question of treatment-treatment interactions on the outcome which would directly allow for the evaluation of optimal medication usage. Other ongoing work in our group involves using LASSO, {{cite:0c1a1ba8bffa6f0551790808fa73be9fa67aa0a8}} rather than hypothesis testing, to select the effect modifiers in the linear MSM for the CATE. This may improve upon the current work by utilizing a superior approach to variable selection.
| d | a3f24d1d2114e61d0eb5ab0d9a5514fe |
Li et al. {{cite:6f0168d0f9a5d4559fe1295af48c84b61817d06a}} proposed a Faster-RCNN {{cite:cf7c0790b1225874abe418aa20c6219308891edf}} based convolutional detection method and reported a performance of 0.93 F1 score in the TableBank dataset. They have used Resnet-101 and Resnet-152 very deep neural networks as feature extractor backbone.
| m | 9b9634ef3e68c98bbc1a960db2b23acb |
Denoising Diffusion Probabilistic Models (DDPMs) {{cite:c335059ab0d5defdacd9eae36d8de2428a4cb1cf}} are a class of generative models that have received growing attention in recent years,
due to their promising results in both unconditional and conditional generation tasks, such as image generation {{cite:455171601491d0d6b5417318588ab5da0162cb89}}, {{cite:ff0945bfb570d24847204cef9bc5bb2d920b4b95}}, {{cite:9dfe5c69f507eec152622e8adaf9cdbd8226cad7}}, image manipulation and restoration {{cite:9dfe5c69f507eec152622e8adaf9cdbd8226cad7}}, {{cite:284d2fa13bc9e5c98ef36e93be392502da79faac}}, {{cite:e2f387bebcc701792428ee1cde7a2b204c228161}}, {{cite:c40ac95e520a1a826cfd9ce4e1dbff0a38a7cbd0}}, audio generation {{cite:4197775dfbe4bdca5ceafdfed0218146a4a14d5a}}, {{cite:d40306eb9b12c7d22404ad1db40371111f0f87c1}}, as well as 3D shape generation and completion {{cite:914611fa08d537ef931ceeb17f0b230fde687472}}, {{cite:e27636ee48da811dddca30834636fad4aadaaf3a}}, {{cite:54f0fcd11343ec1887d6c8b5723cca8401fb6a28}}, {{cite:e27636ee48da811dddca30834636fad4aadaaf3a}}.
DDPMs regard the generation procedure as the reverse of a diffusion process, which gradually adds noises to data samples and transforms the data distribution into a Gaussian distribution.
Therefore,
synthesizing a sample from DDPMs is achieved by denoising a randomly sampled Gaussian noise iteratively.
| i | 3a2c457f32b6849250b1007a0c3b6682 |
The term {{formula:cd3ee48f-17d7-44e7-a0ed-375b1f58a24e}} is the usual single relaxation time Bhatnagar–Gross–Krook collisional operator {{cite:5d40f8237b5bdfc91e776c6d85bf96eb70b976c0}}
{{formula:581f2671-16d9-4569-b9f2-6528d52fc96a}}
| m | 82c19c82dca843d103f3475745d6bd4a |
FGSM {{cite:576cc15bc25ea88ce86ace5fd75d91e5710bfbef}} perturbs natural example {{formula:784806b6-c84d-4520-a4d8-65a6a9df9178}} for one step with step size {{formula:e7b6a5e9-ca5d-443a-bbe3-b7d3ad81fe72}} along the gradient direction:
{{formula:56952cf9-8654-49b0-9b55-18a61fc6f724}}
| m | 9ce046316c4ce54c444888f00767ed61 |
We implement and compare several PINN-based machine learning approaches. These become very attractive numerical schemes for PDEs as they are very flexible when tasked with solving parameter identification tasks. Something that is notoriously difficult in the context of finite element methods as for these schemes a careful discretization of the optimality conditions often requires rather technical derivations as well as the solution of complex systems of linear equations associated with the first order conditions or linearizations thereof {{cite:429f975818d9fdc47df8cfd7cf52e0e850ffa982}}.
| i | 5e3863b9f31dbcecffc55e477c045264 |
Given the wide popularity of {{formula:d88966a2-bb0d-4e88-8426-bda60947e9a2}} -AT, in this paper, we propose SNAP as an augmentation that generalizes the effectiveness of {{formula:04c24927-e412-4edf-8cd2-5cf597a511ff}} -AT to the union of {{formula:5c311bcb-6f58-4804-a38d-02dda7d8126e}} perturbations. SNAP's strength is its simplicity and efficiency. Consequently, this work sets a first benchmark for ResNet-50 and ResNet-101 networks which are resilient to the union of {{formula:9a0d6ac7-a7ed-483e-92f8-7851fcfa314a}} perturbations on ImageNet. Note that norm-bounded perturbations include a large class of attacks, e.g., gradient-based {{cite:34a48cbbd964fd9ed93c33215b04dd80116dba7d}}, {{cite:11e06c94be016396adc4d3813a4984bd3923a1cc}}, {{cite:58d2b74de7223f9a9920c8595848b221f5c80dde}}, {{cite:ed9c9c661846df080cfaae5df7b5a7213ea6a217}}, {{cite:c01c58a40ec7366177adfc8cbc900b3832db968a}}, {{cite:9c4b4bbbf3e7731c6e62d040ef0a95ea618fae36}}, decision-based {{cite:2849fe2ccc5a45c8261118097e8035b09e285dfb}} and black-box {{cite:3d48db6a070214ae91c1de34d770a871d077751e}} attacks.
| d | c54b0cb35d3724532a06370f392d9de6 |
To do that, first let us observe the fact (van der Vaart and Wellner {{formula:fc9c49bf-6236-4305-be63-223c767e801c}} {{cite:34b5fccb4fea991606dd7f65223f2eea3c37dd0c}}) that any appropriately measurable Vapnik-{{formula:bbb29e85-2325-44b0-8f5f-5b1a1696655c}} ervonenkis(VC) class is Glivenko-Cantelli(GC) provided its envelope function is integrable.
Hence, it is enough to show that, {{formula:56eabcf2-7268-4ad6-a552-b97963850b39}} is VC. But to conclude that {{formula:aae89662-b334-4b36-b970-77f815c58ad6}} is GC, the integrability of the envelope function is very crucial. To achieve this integrability, we need the compactness of the parameter space which is established by Lemma REF in Appendix , in the almost sure sense. The significance of Lemma REF is that the estimators are almost surely included in a compact subset {{formula:6170a20c-5c42-4180-972f-b8131fdceb0f}} of the actual parameter space {{formula:aa631524-f00d-426b-b0ae-a4b75449777b}} for sufficiently large sample sizes. Hence, it is enough to focus on the compact subset {{formula:10fcdcbd-fe7c-4e04-98a7-2effa52b0e71}} instead of the entire parameter space {{formula:41b87fd1-2780-48df-a563-54be68c7b7a9}} which is unbounded.
| r | 765966721b2c092a5b9910bf1ec63155 |
(i) From {{formula:c68475a4-4fbe-447d-bc22-61ff6cdb03a5}} and {{cite:6f18bc683b1447536ec5fee1ffe983d8ddc96ede}}, it follows that there exists {{formula:920f2300-0c52-45ce-8440-fb48c7f173fa}} such that {{formula:0b43e5f7-c557-48d0-949a-a58114782829}} for all {{formula:3a40cbd6-3f18-4650-9d46-5a07bdd58d55}} Since {{formula:18c22c58-46a0-44cc-9cbb-6989b5934fd4}} is a multi-smooth operator of finite order, {{formula:72cd6114-44a5-4e05-ad9a-1b32360de0fb}} is finite-dimensional. Now, {{formula:418a1f32-d664-4440-94b9-712222b140aa}} being a non-empty, weak*compact, convex set, by the Krein-Milman theorem, we get
{{formula:3771f7eb-c32c-460d-9bce-81157a440d97}}
Using {{cite:dc246189a418dc5eee3751e505ede65f58fbe206}}, we get extreme points {{formula:61e50390-49e3-484a-96f1-34531842015d}} of the unit ball of {{formula:30b52a56-2383-4c12-93ec-66d2f443fcd4}} and scalars {{formula:962eb7d8-c18f-4bb8-a2bc-2615eb772ead}} such that {{formula:66661152-53fa-48d1-95c2-4433099d6894}} and {{formula:f223c1af-d2a9-469f-a2f6-b07a8e4129c4}} Now, it is easy to check that {{formula:620d3126-ccad-4e90-a00a-294c242ed17a}} for all {{formula:98931cfd-7472-4dc2-bdcd-e4112bc0c16d}} Since {{formula:5dfb7ed6-aae6-4cf2-942f-a2c81a338946}} is an extremal subset of {{formula:f1fd73eb-52e4-4db9-be40-46a06a1d6e16}} each {{formula:ccaec6ac-5b14-4b19-a859-2b7c671651f3}} is an extreme point of {{formula:51daa3d3-7974-4242-881f-bef07f5656b7}} Therefore, there exist {{formula:524865ac-b136-4474-a052-f9c55c3893c7}} such that {{formula:24f9abf8-a615-4d4a-abfe-4e0e4120996b}} for each {{formula:81ea5d07-8392-4031-bdbc-cb7a8eb5163a}} Now, {{formula:b7681e2d-224a-4ad2-9610-4dc3c8661802}} implies that
{{formula:e43207f0-b734-42bf-a9a3-f19c63105c2f}}
which yields that {{formula:ea97c00f-c000-4943-8d77-ccf4ddc4870d}} and {{formula:c1d37425-eb7f-4eb9-be25-91f2b120b14a}}
Since {{formula:9e9926a0-ec86-45f2-a4ad-02a883194807}} is an {{formula:7fc0f874-3aed-44df-a24e-c9edd5f54e5b}} ideal in {{formula:83fd19b2-3d08-4642-8b12-9e126215f920}} by {{cite:18859c767491752f0d53b1e0423e0da5eaff4163}} we have {{formula:a5d5a7fc-bead-4526-8d8c-47fca7337310}} and by {{cite:18859c767491752f0d53b1e0423e0da5eaff4163}} {{formula:7926f19f-1845-45c7-a35c-8c33f1f35a5f}} Thus, {{formula:c104c2b4-6f4b-4095-b42c-8592495973e8}} for all {{formula:cd981b34-fe5e-49ea-babc-2bc0338e785d}} We claim that for some {{formula:f314dda2-7417-4c54-90c7-31540bdc86d6}} {{formula:bc14670c-56dd-4b3b-aa60-cee13eda3b54}} If possible, suppose that {{formula:b8adfd9c-4a90-4c02-a32b-25258dc4125b}} for all {{formula:1e324528-034f-40fb-9d36-65cd1f643f0e}} Since {{formula:8948e897-4cbe-4373-b43e-9b54939cf280}} is an {{formula:6be83877-60c7-45ac-9118-7df89307204b}} predual space, either {{formula:023f53a9-3e4a-4bdb-b813-fbc2c7eb5de3}} is linearly independent or {{formula:3d038a48-e4e0-417a-9374-9ba7feeb4af9}} for some {{formula:f9742348-00f5-4bc2-b853-fada13eac653}} In the next two paragraphs, we show that after suitable modification, we can write {{formula:4f55c4df-dfe5-4e23-9ff8-aaa3c373e5cc}} where {{formula:49295c97-596f-4e05-bb58-e8eb50a74cc2}} and {{formula:c6994b5d-ded2-47a0-84ac-bb83d0b8e191}} is linearly independent.
Now, suppose that {{formula:4eea756a-96e9-4966-8904-5efa9179b181}} is smooth. Observe that if {{formula:8409df74-e80e-4371-b7f4-e921db78372a}} for some {{formula:23c70574-58de-4e7d-8d8f-8ee62988e5e4}} then {{formula:ec0ed7b5-bb2f-4fa8-b853-4db458dc5d91}} i.e., {{formula:94f2ef95-4e49-4774-8b16-a1e8adc94136}} The smoothness of {{formula:ed44a15d-fcf4-4ece-806b-7cd83a7034ca}} yields that {{formula:0b7e45b1-b44c-41c4-be2c-166aa01eb18f}} In this case, {{formula:1e328cf0-60e5-4cd3-be4e-852ff3443be9}} Therefore, in case {{formula:cd51831a-1eff-4c60-ae64-ed298d012fed}} is smooth, if necessary changing the scalars suitably, we may write {{formula:7d7ffe84-1623-4f8c-b44a-1f7643776be8}} where {{formula:73693f76-0ca0-4925-907f-a6f9326ae211}} and {{formula:0d8ee70e-6fd3-456d-95fa-e664cd65e8a7}} is linearly independent.
Now, suppose that {{formula:8706cc5b-f75d-43d4-9749-38536f5f5dcc}} is not smooth. Observe that, if {{formula:ca9c9737-c83b-4631-b78a-da9ea410d39c}} holds, then considering {{formula:3d11387e-1680-465f-ba7b-beb4e8b47534}} we get {{formula:2b2ddc32-eed6-4763-b4e0-11c11cb9b870}} and {{formula:b2eb77b7-cb10-4aab-9816-6519e90fe520}} In that case, {{formula:e405597e-279d-423a-9279-eec5e27f1930}} and {{formula:c71505c3-2503-445c-b398-f5e26653c6af}} may not belong to {{formula:6bda0fc2-8d6c-4075-8b59-a638786a1691}} Therefore, in case {{formula:046a2778-1e77-48fc-a774-5b819d7bbe9f}} is not smooth, if necessary after suitable change, we may write {{formula:5cff2116-9916-4b5c-98ed-8ed762181953}} where {{formula:0681f75e-07c8-460a-bdda-a3252a869e49}} and {{formula:f9829ada-4624-4995-9e18-a658fd10f212}} is linearly independent.
Now, choose {{formula:abcff9b1-fd16-4737-94bd-1ac09d0b8d9b}} such that {{formula:3b0d3dfb-0ef3-4887-bab6-8a6e4e91c6af}}
and {{formula:84921639-3e02-4c7e-9159-379cb94d14d4}} Define {{formula:eb2f0de9-ba10-4470-b926-47db1e81d95a}} by{{formula:0d5bc5b0-91e1-4440-ba8a-2b2c34034cea}} for all {{formula:e4fa87f8-63f9-40c4-a5d4-1dd0f1ba80cf}} Therefore, {{formula:4497b415-0d59-4aa4-8d7b-38b43fa19701}} is defined as {{formula:73e75a1f-d7f1-4300-b3bc-6ec76c100009}} for all {{formula:b5e63cc4-c634-4468-8412-dfaab4a50997}} Now, from {{formula:8bc8a3c3-8613-4059-94bc-a16f6747ba45}} it follows that
{{formula:4b6e8884-df7e-4d33-99ae-37cfb2e7c81c}}
which is a contradiction. This proves our claim. Thus, we get {{formula:89522dba-4a3b-4a5c-8d43-4b92753aca97}} such that
{{formula:5bc12f1a-51d5-4b7a-9710-34cd58935c99}}
Now, for each {{formula:bc0aeeae-1d05-4c17-a565-fe552807b967}} and for each {{formula:73182943-e0e7-46a6-96da-548dd8ee73be}}
{{formula:c40bc1a4-9382-4622-83d7-c2bcbf816e73}}
Thus, taking infimum over {{formula:ef1e1065-6820-4086-9fea-90858cc490f7}} we get for each {{formula:1a4cac51-ca4c-4ffe-bf77-39b2a57b0926}}
{{formula:d070b869-c982-4776-b418-bf7bc610b0e9}}
In this inequality, taking supremum over {{formula:5481a0b5-9228-4558-87f0-bf74cded48ad}} we have
{{formula:2bfbd08a-61df-4ed8-8d5b-fa29ef09e27c}}
Therefore, {{formula:be363ef1-0cf9-4c09-a71d-27608356fc08}} On the other hand, from {{formula:57529c2b-486c-4943-bd29-df011cedeb78}} it clearly follows that {{formula:94f879a5-3f04-40f5-9cd8-eb85b555bc8a}} This proves (i).
(ii) Let {{formula:99518202-0265-4029-9db1-79d15dfd0b84}} Then using (REF ), we get {{formula:a066e6c3-3e8d-4cc6-a92d-e160e6c26f7d}} Thus, for all {{formula:2b2017c1-1d19-41c4-be37-160f16b586f4}}
{{formula:df09745a-11e6-4ac5-aa95-d3cd7116f733}}
(iii) Let {{formula:d271ed48-612a-4964-b91b-8269e39bf9ef}} Then using (ii), we get
{{formula:a76654bd-a914-4139-b5f2-4e07bb8565e4}}
Thus, {{formula:db4a7324-95e0-487c-bd33-3f14ef4957f0}}
(iv) From (ii) it follows that {{formula:af2f0581-1d04-42fb-8216-8f409a628462}} and from (iii) it follows that {{formula:80032588-1a39-4d16-975c-11fe4f791e6b}} Therefore,
{{formula:c39bf23c-b46c-4d4d-824e-2340160c3929}}
This completes the proof.
| r | 7298900b662c781c65fca1239008b875 |
For implementing NGP, we used different neural network architectures such as self-size estimating feed-forward network (SSFN) {{cite:995d5035ec70485c8cd2ad85b54e8fe9280c16b3}}, multilayer perceptron (MLP) {{cite:2d9906508c7685e7e1babec8ba3bc6f7cd2f0fb7}}, and CNN to show the universality of NGP. We used a single layer SSFN with 100 random neurons, and a single layer MLP with 500 hidden neurons with ReLU activation trained over 10 epochs. The CNN model used in NGP is the same as in DeepLIFT to have a fair comparison across the different competing methods.
| m | 32d85a9696577710cf236ca873d05532 |
The optimization objective in eq:objswmtl is nonconvex with biconvex terms in inequality constraints. Moreover, there will be a huge number of constraints when the numbers of tasks and features are huge. There is no existing efficient methods that can handle this challenging new problem with theoretical guarantee. Although efficiency-enhanced methods such as Alternating Direction Methods of Multipliers (ADMM) {{cite:1ca4573aa9946696b18524627f0dc92e425f693c}}, {{cite:a0926379ce92887dccfb73bfb51d5d840c78520e}} are demonstrated to accelerate classical Lagrangian methods, extending them to handle nonconvex-inequality constraints are highly nontrivial. To address such issues, this paper proposes a new efficient algorithm based on ADMM for handling such nonconvex-inequality-constrained problem. Theoretical analyses on convergence properties, generalization error, and complexity analysis are also provided.
| m | 1938391aaf8eecb908adc56270761747 |
Ethical considerations.
SLIP faces all of the same ethical considerations as CLIP, both in terms of the harmful applications it may enable, as well as the potential for amplifying and perpetuating problematic behavior in the real world.
CLIP's ability to leverage noisy and minimally filtered data scraped from the open internet has already spurred researchers to begin collecting data in a more careless manner than previously possible for supervised learning {{cite:85facac570f73baf8fef27bf289018b744b966e8}}.
A more cautious and responsible approach to selecting training data may alleviate the most egregious model behaviors.
| d | a537113ed3142d877239a765d0bcfad4 |
In this work, we were able to write the full anisotropic metric as a function of these critical exponents, which correspond to the respective scalings of each coordinate of the holographic dual field theory, together with a flowing structure with respect to the {{formula:b04bd305-e6c2-49ac-8c78-ae95809ca3e2}} parameter, getting closer to a general description of non-relativistic holographic systems with Ricci flow. In this respect, it has been reported that the Ricci flow is the Holographic Renormalization Group flow {{cite:7b7f05923aa86a022c59b4c17037660c758b50eb}}. The latter needs to define the stress tensor for the gravity bulk space-time defined in an {{formula:0e48a93d-2125-48f2-8901-f6b6ccbdb723}} constant surface, using the {{formula:62c0ed0c-829b-45bd-a302-0c89c0e67d32}} decomposition. The Hamilton equation for the canonical momenta is the Ricci flow but with the radial coordinate as a flow parameter. These canonical momenta are holographically dual to the induced energy-momentum tensor of the field theory defined on that surface. An interesting question is whether the DeTurck vector has meaning in this holographic construction knowing that in {{formula:68b2f0ea-64ce-4004-9a85-ca5c7c0b9566}} decomposition, corresponds to a particular choice of phase vector (with the corresponding lapse vector). The freedom of the choice of phase vector must be reflected on the diffeomorphism invariance of the DeTurck vector. As far as the authors know, this question has not been considered yet and is a motivation for future work.
| d | 88f7b18719df477338b54151ae06beaa |
In addition, the strength of the N-Jet representation lies in that it can learn filter sizes, and thus the receptive field size, during training.
However, recent work has demonstrated that the effective receptive field (eRF) size of networks can be considerably smaller than what would be expected from the kernel size {{cite:b27ac150f4f41963d397e5909da7b3b44710aeb6}}.
We investigate the change in eRF size in our N-Jet models by visualizing the gradients with respect to the input image in our models trained on the multiscale Fashion-MNIST dataset (Fig. REF ).
We find that, as expected, the eRF size of N-Jet models grows with the size of the training images, proportionally to the growth of filter sizes.
The baseline U-Net model with {{formula:177946fc-ee31-41d3-b999-d1a4bd0eb53e}} kernels cannot learn to adapt its receptive field size during training, its eRF size remains relatively constant as a function of the input image scale.
| d | 70ae6171aab362a6b32ffebd4cbeec21 |
Domain independent fusion.
Inspired by Wang et al {{cite:582338c630879b8ae1fd7ecc79d953b7bf84b3c7}}'s work on bias mitigation, we perform domain independent training, where we treat the real and synthetic output space as separate. To do so, we create a new set of classes that contains tokens from the synthetic set only, and extend the real set answer token space with these new tokens, as show in the third method of Figure REF . This approach can be viewed as two classifiers with a shared backbone that has access to the decision boundary of both the real and synthetic domain.
{{table:47c4a358-d9f6-46b6-bf55-a79b57e4084e}} | m | 374d0e472934b1cc814c87fb4f5e1b7f |
In the end, we compare the performance of our proposed method with the state-of-the-art methods {{cite:a4f72552aed0440df9b7a366be09212e5e94fc0b}}, {{cite:c3f0d7d7f108e7158663193a656282d710a46993}}.
From Table REF , the baseline model has worse performance than the state-of-the-art methods but it achieves a competitive performance by integrating the proposed VOI map.
It is noted that the ensemble of Kamnitsas et al. {{cite:c3f0d7d7f108e7158663193a656282d710a46993}} contains 7 different types of models but our proposed ensemble only consists of five 3D U-Net.
| r | acb0e1938273ee2430bcb5b3c7fc1a6d |
as subsets of {{formula:13565b40-a62e-40b4-a4df-00e7f972bd2b}} .
Our approximation analysis considers the above bounded hyper-sphere determined by {{formula:bd4ff23f-7b44-4579-8f7f-92006d96bf4e}} instead of {{formula:f70e7bbf-626b-4cb1-b713-574ab10094da}} used in problem (REF ).
Following {{cite:a42b7ea30ebce82d52ae76e73aa30d6a3ec38a6a}}, {{cite:cb52519975b501920f1a02b87b832dc573714b30}}, {{cite:d9fbd3bd57c387fb51b6e6a4f516c8ace7b3a0ab}}, we assume that for some {{formula:a1569652-56ad-4e38-a7ff-1965be8f4cac}} and {{formula:d24790f2-4cb2-4212-b4b7-21c7891fd29e}} such that
{{formula:d80f4bc5-2e3d-454a-a3b5-080291517439}}
| r | a17984af4c63637db1041270255b9f8d |
Asymmetric Architecture
Another line of work exploits an asymmetric architecture {{cite:a3c9faab7e7f288f0ee88579464a3c3c142a7daf}}, {{cite:7c4f77845c54f5c9697a29c4ad6bea7b9439199d}}, {{cite:00705b4d4a24c561cf9e2a018c75a5645947bf1b}}, where the high-to-low process is heavy and the low-to-high process is light.
{{cite:a3c9faab7e7f288f0ee88579464a3c3c142a7daf}} proposes a Cascaded Pyramid Network (Fig. REF c) that detects the simple keypoints with a GlobalNet, and handles the difficult keypoints with a RefineNet.
Specifically, the RefineNet consists of several regular convolutions, integrating all levels of feature representations from the GlobalNet.
{{cite:7c4f77845c54f5c9697a29c4ad6bea7b9439199d}} extends the ResNet {{cite:063d76a2a3b4d18763d79f1d0e8a741c642b4d02}} by adding a few deconvolutional layers instead of feature map interpolation, which is depicted in Fig. REF b).
These methods employ a sub-network of classical classification networks (VGGNet {{cite:cac4f38826f1c20409dd3c181b60711a8a83569e}} and ResNet {{cite:063d76a2a3b4d18763d79f1d0e8a741c642b4d02}}) for high-to-low convolution and adopt simple networks for low-to-high convolution.
Undoubtedly, such asymmetric network architectures suffer from imbalances in feature encoding and decoding, which potentially affects model performance.
| m | 74e29d5d37a4cb04a813ceaa60e40e79 |
In this section we present the results of the forecasted sensitivities using the methods and experiments detailed in Sec. .
These are shown in the {{formula:f85c0b43-1ef0-45c2-bf97-55b35b556e0d}} plane for DM masses {{formula:cd186304-b237-4bfc-8c1a-6d5cf380125a}} GeV. This region is interesting because ample areas are unconstrained by current experiments and, as we are going to see, the LHC experiments listed in sec. REF can probe large portions of it. In the same region we can also have thermal DM production. However, we do not restrict only to the parameters that allow to obtain the measured DM thermal abundance, since we can imagine a non-thermal DM production or a modified cosmological history that could dramatically change the picture. In all our plots we fix {{formula:e5d58694-0529-459e-9afb-22224296bc43}} .
To illustrate the complementarity of the different future LHC experiments, we focus on four representative benchmark scenarios, considering two different values for the mass splitting ({{formula:80f1bcc0-e254-48c2-8312-acf3a12edc32}} and {{formula:9ea093f6-b3e0-4146-b57a-efcf190d0edd}} ) and for the ratio between the dark photon and the DM mass ({{formula:8ff97d9c-2797-49cc-b3ac-aaa03276e489}} and 6).
The main results are presented in Fig. REF and Fig. REF .
The shaded grey region depicts the current experimental constraints on the invisible dark photon already mentioned in Sec. , coming from BaBar {{cite:578d25b0a1dbb0705eeee3645f26d40032926a8f}} and LEP {{cite:185145b1c9b484ef270e695a09bffaa430637e29}}. Since in the region {{formula:d33e2cf1-bda1-489c-8b90-0afa0b1ceadd}} the {{formula:843bbfc7-df0e-480f-9d4f-d0ece5a36cb1}} boson coupling to the dark states is not suppressed, we also include the bound coming from the {{formula:f36f444b-b196-4fd1-b5f7-0ac4d538f02f}} invisible decay {{cite:8d1dd90808054c2b1efc34181af44c9e2e6bf9c3}}.
The colored contours, on the other hand, show the projected future sensitivities of the experiments listed in Sec. REF . Finally, along the dashed black line the {{formula:876cfd61-d2a2-43ed-8950-c487828bc2cb}} abundance matches the observed one.
Fig. REF and Fig. REF correspond to the fermionic iDM (see Sec. REF ) and scalar iDM (see Sec. REF ) models, respectively.
| r | 6b10309ca96982de5f2f904d72f1fa22 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.