text stringlengths 54 548k | label stringclasses 4
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In addition estimate {{formula:714c9a5b-213c-4262-b2ec-e215d7367763}} , p. 110 of {{cite:dd3af34d8f282d287901bd886b44b8cf5bee3bc8}} for system (REF )
gives
{{formula:d182cf5b-4e9e-48c8-a884-118210c544f7}}
| r | e1bfd8a3c8b3d65885d7581a0ff12857 |
LazyFox relies on nodes iteratively joining and leaving communities. Therefore, it could generate empty, disconnected, or communities fully contained in other communities. We provide an additional post-processing function to eliminate those types of undesired results. However, note that it can be computationally expensive to perform this post-processing on large graphs, or graphs with many detected communities. Sometimes, communities that are fully contained in other communities are desirable and occur in the ground truth. In these cases, e.g. the citation network in SNAP {{cite:c61dbef4e766a93e05928a0fab1612b027bcc270}}, they should not be removed. The post-processing needed is therefore dictated by the research domain which is why detailed analyses on post-processing is not part of our work.
| d | 19d1b2af42f3139df1c3951591eb533b |
Baselines: We considered the following baselines: Bag-of-Words (BoW) {{cite:d7367ce04ef6f4cc17f352a997d458d64f1eda80}}, Bag of Word Vector (BoWV) {{cite:cba6134a181e5e7161ad09d7d161b8148eeac5e1}}, https://bit.ly/2X0XfBH Sparse Composite Document Vectors (SCDV) {{cite:b3c926203a2ccc2b3e30817bc1abdcae3712d650}}, https://bit.ly/36NxGZh paragraph vectors {{cite:77a1fb0fa79fe4f6a63552b5a4d424ccded27e9f}}, pmeans {{cite:48c514c0adef3aaa4960cbc39d1e2480eed33360}}, ELMo {{cite:7643c4ee4236e850b985f5974644fc6113869fbd}}, Topical word embeddings (TWE-1) {{cite:7cfdc30086cdd1b0620c97a1be311aa3bf8454d1}}, Neural Tensor Skip-Gram Model (NTSG-1 to NTSG-3) {{cite:834bd4f68579290ca58b0cda019b312c6581d891}}, tf-idf weighted average word-vector {{cite:dedab2222c990984ee53a8b5380c8cfe7223287b}} and weighted Bag of Concepts (weight-BoC) {{cite:09988576ea087113e7e4b5a184adaa5a8154b72c}}, and BERT {{cite:957b0aac320225b7f71c8ba39f605477a3f167a5}}. In BoC we built topic-document vectors by counting the member words in each topic. For BERT, we reported the results on the unsupervised pre-trained (pr) model because of a fair comparison to our approach which is also unsupervised. In Doc2VecC {{cite:51686071256393802297e1a768a009b3b4832bed}} averaging and training the vectors was done jointly with corruption. Also, in SIF {{cite:e01d9324aead2337d2107cae31464803f192c789}} we used the inverse frequency weights for weighting while averaging word vectors, and finally removed the common components from the average. The results of our proposed embeddings is represented by SCDV-MS in Tables REF and REF . We also compared our representation with topic modeling-based embedding methods, described in the related work.
| r | c7d185d8311c6cf9f4aeae14778ce7bd |
By definition, the SDR is sensitive to outliers corresponding to near-silent segments {{cite:6e2856b9a1daae59339731e8802779484990a876}}, which explains the big difference between the segment-wise median and mean SDR, and also the higher mean SDR reported for the HTMD-Net, since it performs better in near-silence. This effect is visualized in Fig. REF , where the kernel density estimate (KDE) of the segment-wise SDR values is displayed for the HTMD-Net (blue), superimposed with the normalized KDEs of the subsets of the SDR values that correspond to near-silent (green) or non-silent (orange) 1-sec segments, as classified by pyvad. We observe that the vast majority of the outlier SDR values correspond to near-silent segments, since their SDR distribution almost overlaps with the overall one in negative SDR values. A similar trend was observed regarding SIR and SAR as well.
| r | de36255bd007b63d5dc552c20332687b |
We have
{{formula:16b12589-1b6b-47d9-abbc-6d7b0c1f9c4f}}
where the last inequality is a consequence of the spectral properties of the interpolant operator (see{{cite:a1b4697b183e11b6cb5a0e66f5616b52d89bddb1}}).
| m | cdb75c1680ac0fa79521785ac2fe6682 |
Previous works on topology learning with GSP models have focused on mono-layer networks that consist of a single network ‘layer’, and the tools developed are applicable to single-way data only. However, this may not yield a faithful model for many complex systems since networks and graphs do not simply live in isolation. Instead, many networked systems are better described by multi-layer networks featuring coupling interactions within and across network layers. Examples include: opinion dynamics on correlated topics {{cite:db1a2d3cee6905edda5a891e90866a04b04df50b}}, multi-dimensional diffusion {{cite:e14c5651281854e979a45d2cf62d9cf34d1b0358}}, protein-protein interactions {{cite:0f8b9a8337eb609e67ecce4a941929cfb7e991bc}}, animal networks {{cite:74dc5b83c6566dd567630024d2086d751485db39}}, and relations in image pixels {{cite:e0f27d7221f2d8ec2bb3079f72136a958ed97855}}, etc. Observations made on these complex systems are usually generated from two or more coupled networks, and they give rise to multi-attribute observations on nodes, i.e., multi-way graph signals. Naturally, the graph structure embedded in these network data shall be treated using a multilayer graph model as they can not be captured by simple individual networks or flattened networks without structure.
| i | dfaf67eff453cb278938136743ea0b17 |
The push-sum framework was introduced in {{cite:249aaec9156fd951ef2d5d8f15078ac388e9c09a}} to avoid systematic bias in the solution of multi-agent optimizations problems on directed graphs. The analysis of distributed consensus with delays was first given in {{cite:11287003998dcc72fdfe8e2cfc21a67b6e09c981}}, who introduced virtual nodes which model information as passing from one to the next as one less delay until it arrives at the real-time node. Note that these are purely theoretical instruments, and need not be stored.
| i | 4c220ab7be6e291a1e2ca3f81a03e092 |
In this work, we propose a new framework for continual learning to expand the network more sparsely and utilize previous knowledge better. Faced with a new task, deciding optimal number of nodes/filters to add for each layer is posed as a combinatorial optimization problem.
Inspired by Bayesian optimization (BO) for tuning hyperparameters {{cite:8b6e62e2a9a3c261348f92043356de1e1b0ac9e9}}, {{cite:32333a55f119311f34952d6033ae1a08d57de506}}, we utilize it to determine the number of nodes/filters added for each layer. In order to speed up the search process, we will initialize the search points based on previous tasks to warmstart the Gaussian process model. Inspired by attention mechanism in image caption {{cite:46477ffb84ac2a15090479934352cd7fb3229e1d}}, we employ attention mechanism to learn how important the previous knowledge is for the new task. To the best of our knowledge, the proposal is the first attempt that applies the Bayesian optimization and attention mechanism for solving the continual learning problems, which could strike a significantly better balance between performance, network complexity and training time than existing approaches.
| i | 1152d48deb107225f2d12084334d82bb |
This is as in the proof of Theorem REF . The theta divisor is algebraic if and only if {{formula:4254c3a8-c4ea-4ad1-8475-61b02ddf6f7a}} , meaning that {{formula:9b7a3a12-586f-4fc0-bad4-ab7c1147c54a}} is unipotent. Now we refer to the notation of Remark REF . If the curve satisfies our conditions, then we first see that {{formula:ed288363-a667-475d-a36f-fc9f03e94001}} is a disjoint union of projective lines, hence {{formula:b0aedda0-bce7-4b56-b4c1-e1f9eaf50096}} . At this point, our conditions and {{cite:711b72f469a121fa64b04955d08c7c86f403b566}} imply that {{formula:d0d07ef8-5d37-4643-b841-c68cd324957a}} , where {{formula:67e7c7f9-400e-47fb-8cea-ac4adffe5cff}} is the partial normalization of {{formula:cf8b33f3-cff5-47b4-81ee-d57af09bab3b}} . Finally, {{cite:711b72f469a121fa64b04955d08c7c86f403b566}} shows that {{formula:12623b76-5da3-4ba8-87ad-886fa2d134de}} is unipotent.
| d | 7e0b393dda424992565bfbbc8a138087 |
(i) Weak-Lensing Mass: Using deep, multi-band optical images from Subaru/Suprime-Cam, a mass estimate for each cluster is derived by fitting the shear signal expected from weak gravitational lensing of a projected Navarro–Frenk–White (NFW, ref. {{cite:b6799e3b83b600ddf753c60d1a93d60dc31031f5}}) mass density profile to the measured tangential shear pattern {{cite:efe077dea061f2b4905f7bbb74018859724c137d}}.
| m | 4277d1c4db52c34a33e965d8cb33ad17 |
Due to recent technological advances, large multi-modal datasets are being produced; these include imaging as well as multi-platform genomics data. In complex disease systems such as cancer, integrative analyses of such data can reveal important biological insights into specific disease mechanisms and its subsequent clinical translation {{cite:59c631a6251f71c8d319c3c67a2990d9c19698d8}}, {{cite:026c6465f7f238f29f29950c252e06edcab54524}}. Genomic profiling technologies, such as microarrays, next-generation sequencing, methylation arrays and proteomic analyses, have facilitated thorough investigations at the molecular level. Such multi-platform genomic data resources have been used to develop models to better understand the molecular characterization across cancers and especially in gliomas {{cite:29bd15f5860845cdb945d9ce42c994d8efd229a7}}, {{cite:b627c827219e444280d33261435043037a7d058e}}. While genomic data provides information on the molecular characterization of the disease, radiological imaging, such as magnetic resonance imaging (MRI), computed tomography (CT) and positron emission tomography (PET), provide complementary information about the structural aspects of the disease. In this context, radiomic analysis involves mining and extraction of various types of quantitative imaging features from different modalities obtained through high-throughput radiology images {{cite:32a3e849e25e91cb595ce135c8cfd1034a6601d1}}. These image-derived features describe various characteristics such as morphology and texture, among others. Integrative analyses of genomic and radiomic features, commonly referred to as radiogenomic analysis, capture complementary characteristics of the underlying tumor {{cite:cd594936cbc6a33f36cc00049e496808b7db4a2a}}, {{cite:f2173a57431c57483440cb60d236af1a172e3b19}}. However, such integrative modeling approaches present multiple analytical and computational challenges including incorporating complex biological structure, and high-dimensionality of quantitative imaging/genomic markers, necessitating principled and biologically-informed dimension reduction and information extraction techniques.
| i | b5e13e0641bb1e90ae9ef099560151b8 |
To treat adversarial attacks, some defense methods are first introduced. In general, adversarial training and input restoration are two common methods to improve adversarial robustness. Adversarial training method considers a model training on a mixture of adversarial and clean examples. Input restoration method considers preprocessing on input data (before feeding to the model), to eliminate adversarial perturbations.
In terms of input restoration, the Simple Random Sampling (SRS) {{cite:9087e7d22758574903bab93537024d59e3f738d9}}, Statistical Outlier Removal (SOR) {{cite:fa731dfbbd88627eabc9342967a0f09edf3a4e46}}, adding Gaussian noise {{cite:8ab2fd5bd12cc409980042ad0805654135ad8570}}, saliency map removal {{cite:1bb60eb42b6780c786e1b16e22a72a67b1ec1266}}, and Denoiser and UPsampler NETwork (DUP-Net) {{cite:fa731dfbbd88627eabc9342967a0f09edf3a4e46}} are some defense techniques that enhance model robustness against 3D attacks by adding a preprocessing step before feeding input samples to victim models. Wu et al. {{cite:31849caf6a2b2b51568bcd0d412bba3ed9fd2392}} proposed the Implicit Function Defense (IF-Defense) to optimize and restore the input point coordinates by limiting the point perturbation and surface distortion. Some defense techniques {{cite:8e42a59514bd71e5765c35115ffabdead2ff3782}}, {{cite:b85e8f0643086cbcc3692a9f37f57b73325d761d}} directly modify the victim model structure to robust it against attacks.
In terms of adversarial training, Liu et al. {{cite:1bb60eb42b6780c786e1b16e22a72a67b1ec1266}} extend it to 3D point cloud. They train the model by point perturbation adversarial examples and the original point cloud. Liang et al. {{cite:f6bad12974c63d66e65107cd179e5098f1efd32f}} adaptively generate perturbations by embedding the perturbation-injection module to the model, to generate perturbed features to improve the adversarial training performance. Sun et al. {{cite:cc94eb6a36cd7f7127b9844925a6120aa21bde9e}} proposed a type of pooling operation to enhance 3D adversarial training performance. Also, in another work, they use the self-supervised learning and adversarial training together as a defense method {{cite:b5cbe530c49f73d0b0a4d9ecb632a22fc83932e0}}.
| i | 77667931282a62af1c0d7e0d4f3261b9 |
Once the softness of particles is considered, on the other hand, another time scale due to this softness appears in the system.
The kinetic theory of soft-core gases has been constructed in many systems such as that having the inverse power law potential or Lennard–Jones potential {{cite:bfb0736173c926d858f0af2a2603ab6ccf172bcc}}, {{cite:28d77aaefda5a98da932580440d6468d140119ab}}, {{cite:00e4bb0378058b3098f70c54f8f9cbfa784654eb}}, {{cite:a7897d7e336eff4a54384e45bbb35c585bbcebfe}}, {{cite:ef8dd31d28bc0cb769afeb2f1f085e0bc51d7d74}}, {{cite:4c8bb2c63ab9cc6f0d094d967ad3dc95913cf0c9}}.
Recently, Sugimoto and Takada {{cite:309885231a9f3056aac0c972baac895a7d562b99}} extended the kinetic theory to soft-core gases having the harmonic potential, where the collision angle is explicitly written in terms of the elliptic integrals.
| i | 42c2beb68fbcb8059b9e62771edeb7e1 |
Datasets. We use CIFAR-10/100 {{cite:a2a35ee5a1f984a7a9bd680124c9767b04811f6e}}, ILSVRC-2012 ImageNet {{cite:e2c7311943c87130519b277bc41bf0cb4dc58a9a}}, and ImageNet-LT {{cite:b59ddb8c27006d04970d3ff86d1c806af6cf082c}} to compare different sampling strategies. CIFAR-10/100 with 10/100 categories has {{formula:dcf3818e-5a70-4bc3-b236-ee126f2bfc48}} images of size {{formula:09d9a681-9d73-49a2-98f8-6e93c0d2ac84}} , where {{formula:34d12994-b9e5-489d-aa68-c96ec5eb9997}} are training images and {{formula:9105a554-4ff1-4dd0-a82c-2c55857d786d}} are test images. ImageNet contains more than {{formula:5bcc1cc3-a64f-4d5f-b49b-8daed89873cf}} million images that are almost uniformly distributed over {{formula:a354fcdc-e760-4416-a91c-1abce6647d91}} categories. ImageNet-LT is truncated from ImageNet and has the same {{formula:13d1f2c0-2530-4b5a-a0b2-6dfed73e8418}} categories, but the number of images per class ranges from 1280 to 5. We resize ImageNet/LT images into {{formula:572df82b-d1ba-44de-b62a-7b700a18e0e0}} pixels. The validation set for ImageNet-LT experiments is the same as of ImageNet and contains {{formula:85af8e96-8833-47c3-bab9-481f50594d9b}} samples. All datasets are augmented by horizontally flipping the images.
| r | ebc48bd487cb80774e85abb9f397a280 |
We showed that the relationship between the depth of decision path and explanation accuracy, as shown in {{cite:f7338ca468c6a6224299079f5a3c1ba11fba00a8}}, are only visible in cases where the frequency-based ground truth and Euclidean similarity are used.
| d | a0f65b0cf6b6747166d3d34fc6d72083 |
More generally, geological data are commonly available as examples (called statistical samples) of a conceptual model. These might be facies maps from geological cross-sections, from field outcrops, or from geological process model simulations, and each of these might require a specific set of physical processes (a conceptual model) to be invoked to explain their geological origin. However, while the true parameter matrix or image in our tomographic volume may be explained using the same conceptual model, it will never exactly match one of those observed or simulated samples. Therefore, the parameterisation method must be able to generate other geological cross-sections or three-dimensional facies maps that conform to the same concept, in other words which are similar but not identical to the given set of samples. In addition, our goal is to explore the space of possible subsurface geometries to find those that are consistent with the observed geophysical data. However, exploring high-dimensional parameter spaces is extraordinarily computationally demanding, a phenomenon referred to as the curse of dimensionality {{cite:73f8589d574342243228c08e0bd1fd29f814a86c}}. In order to make this feasible we must represent the geological information using fewer representative parameters, usually called latent parameters. In principle we expect that this is possible because geological facies maps are not fully independent (they are spatially strongly correlated as observed in all geological outcrops – {{cite:bb881b49a5d5ee8c7cf44fd57ba5be6691bc57b4}}) and so may be supported by a lower-dimensional manifold of latent parameters {{cite:77dbff87b70bd9e5ab1e2dabcf1c0b6c3506b4e4}}. Two common mathematical constructs that can be used are Variational Auto Encoders (VAEs) and Generative Adversarial Networks (GANs) – both being types of Neural Networks. In this research, we choose GANs for their demonstrated generational quality over VAEs and the near-instantaneous generation of samples which enables more rapid inversions in our applications {{cite:1034d21f253b94300e85aaa8066f6720a31af168}}.
| i | 3bfa96f451a674b6ab5c3ff4d80bec80 |
This assumption is a very mild condition for the loss function {{formula:8b6965f1-b5e4-4696-aa52-c6b763a1f816}} , thus we, in fact, do not previously assume the form of the noise (for example, optimizing the square loss is to optimize the maximum likelihood objective of the Gaussian noise, and {{formula:0f59b5d8-be08-4a9e-859a-c2a297b64f81}} loss is to optimize that for Laplace noise) and our result can even apply to not only the the regression problems but also the classification problems. In this aspect, this result improves upon previous methods to learn linear dynamical systems in {{cite:041163d3642c69dc6e3225668927f1a03883fa99}} and {{cite:b4684d833a475990cbd0f6e8eccd5483a64b3648}} which highly rely on the form of the square loss.
| r | 3dd6223c58367fd3eebcd4b57b12e3a9 |
This notion was largely investigated and characterized in second-order variational analysis with various applications to constrained optimization. Besides the seminal paper by Poliquin and Rockafellar {{cite:2f878dbf857f52f6e9a58cbcc748fb3c4c60d403}}, we refer the reader to Chieu et al. {{cite:8d54640ee1d79b2d26330e97437f1bf05c1da031}}, Drusvyatskiy and Lewis {{cite:6dd32917cf63941869c77238e23f30b23723b85f}}, Drusvyatskiy et al. {{cite:47d47e0066b3aecf62880852cbb6ffcec3543885}}, Gfrerer and Mordukhovich {{cite:e489ccd073a1ec7c44183c688fb651ea7b80eb94}}, Mordukhovich {{cite:8d0fdc89de57b3713be25e532ef3f88406f87d85}}, Mordukhovich and Nghia {{cite:48d543d653dafcb880e4541840708de392777426}}, Mordukhovich and Rockafellar {{cite:e6cc3004126abd26193b44f6b08126253fdd5c9c}} with the bibliographies therein. Some of these characterizations are used in the proof of the following theorem.
| m | a258b795890732d571be9c8a11be71c4 |
As discussed above, {{formula:43b8b6a1-563c-4bc1-accc-f124dd6afc5c}}
depends on the parameters {{formula:a5a4c467-50c0-423b-a15f-5ccc425fc508}} and {{formula:ff98a1e8-ceda-4a1f-9bd0-a81f2812d455}} which are responsible for the
generation of the observed value of {{formula:f1a65e76-43b5-4f0a-8d19-d697299472c7}} , thus we use as their input
ranges {{formula:8d459311-8d39-4bd3-bc50-c61bb527df75}} and {{formula:aa07dc27-e44d-4acc-a100-7ad47f0e697d}} , respectively. Then, we plot in the right panel of figure (REF ) the correlation between {{formula:dbe28e60-ba9e-4de6-a844-3e421511e717}} and {{formula:a20b245c-45e2-4533-a507-bfb3abe30f18}} while the color palette
shows {{formula:78d6d4ec-8bd7-46e5-83d3-726eaef52311}} . We find that the
observed value of {{formula:952caf1f-34ca-4de7-8655-dd10bd1f62b0}} is predicted for the following ranges of {{formula:a7849cc7-9232-413b-8a5e-9cd5e6858336}}
and {{formula:7387db9a-eea1-45b5-a5a4-327cf4e6a0ef}} : {{formula:c40ed4c5-5b51-4c24-afc6-97b7aea89d57}} and {{formula:172f3523-cc0c-40fb-8ab9-48a0d58b4edb}} . We find also that the {{formula:5d414245-3c98-4c31-927f-fef870f2a4c7}} conserving values {{formula:54120dbf-aa42-4277-98a6-9e7645b03f91}}
and {{formula:358be606-34d1-4ad3-b90f-c100e9778f96}} as well as the regions around them are
excluded. Thus, this source of {{formula:6c31b4d2-54cf-4d4e-a919-3918c31484b6}} violation plays a crucial role in
generating the baryon asymmetry in the present model. A detailed study
concerning the correlation between {{formula:48ee89f5-918d-42ef-936c-01e99900dae4}} and the other oscillation parameters has
been performed in ref. {{cite:63859d3b70f212406c24241575ab1fda5cc01571}}.
| r | a9a8d9dcd615c676fb8e8c019643c66d |
However, we observed effects of error cancellation where mitigating the quantum measurement readout error alone may not always yield better results, despite the improved state fidelity after post-selection. In some cases these mitigation measures may even deviate the obtained results further. This highlights the importance of reducing quantum gate errors to further increase the state fidelity, which unfortunately remains an difficult issue in the NISQ era. Current quantum error correction (QEC) techniques are infeasible to implement as it requires many ancillary qubits of multiple factors {{cite:5b21f57ec9d1f0dbae5ff20730f66706840c5179}}.
| d | f7645f2ad4bf212274b225d308911894 |
This work introduced Conformity, a novel strategy to measure the homophilic mixing of network nodes w.r.t. their categorical attributes.
The proposed measure aims to address some limitations of the well-known assortativity coefficient, in its classic definition given by Newman's work {{cite:ae973516a1c6d214f7dcd93a9f101afe21ae754e}}.
The main reason behind Conformity is the need to take into account (the often neglected) impact of node distance on the homophilic/heterophilic behaviors that, in social contexts, favor the creation of social ties.
As shown, the proposed measure can unveil interesting nodes' behaviors and can, in practice, be fruitfully adapted to support several tasks (e.g., the identification/measuring of echo-chambers or polarized islands among users living in a social media ecosystem).
| d | bec4bddf76af94d03043cb81c3610cec |
For the Image Captioning models in our first approach, we use two implementations. The first one is an implementation of Show, Attend, and Tell by Xu et al. {{cite:c2c872e7c53c5d7acc6bd43075af34408a6183a3}} and second one using Bottom-Up Top-Down approach by Anderson et al. {{cite:eb49e4789576145033354e0afb7b8fa8d2538627}}. We take the top 10000 words from the vocabulary and process the images via Inception V3 model. The pre-trained Bert model used to encode generated caption has a dimension of 768. These two result are then fused together and then passed via an MLP classifier.
| m | 03d8b0a2da0ac437a0abc2ba7be6559d |
This was also achieved by {{cite:bef99e00115d61066ce659e1ae210d9e22c7ca6f}}, a
work belonging to the line of research that leverages pretrained
language models. There, a sequence-to-sequence model with a single
encoder captured the style-independent semantic representations using
auxiliary matching losses, and two decoders for each target style,
jointly trained for bi-directional transfer. In
{{cite:e545c4d0e13f18f935cd7cf20c2912501085f369}}, a pretrained language model-based
discriminator helped to maximize the likelihood of the target style
being in the output, and a mutual information maximization loss
between input and output supported diversity in generation. Lastly,
formulating formality transfer as a task of grammatical error
correction, where informal texts often contain slang words, character
repetitions, spelling errors, unexpected capitalization, and so
on. {{cite:cf74135481e78bea957a727b2eb9556eea536fa3}} used parallel data from Gyafc
to fine-tune large pretrained language models, Gpt-2
{{cite:fab7e4e5cd11806eb052dee995fe02899ddd0cce}} and Bart {{cite:8306fca955f6098245732d9ebc180945ec4874dd}} and
augmented them with rewarding strategies based on style discriminators
(targeting the transfer of the attributes) and Bleu
(targeting content preservation). They argued that pretrained models contribute to
better content preservation, even with restricted training data.
| m | 6b847483698db5c33ed75286201dbd66 |
We use pre-trained UniCoRN model to initialize code embeddings. Then following {{cite:5910a99ef61cd597c8b17ef712e1f5e1250c6833}}, {{cite:a979e5b6be7e30f03cb09c42842b8d48d8e15d3e}}, we predict method names as downstream tasks. The method name is treated as a sequence of subtokens (e.g. getItemId {{formula:977c2c20-a723-43de-b5a8-8bd5c002a616}} [get, item, id]). As in {{cite:5910a99ef61cd597c8b17ef712e1f5e1250c6833}}, we use independent linear classifiers to predict each subtoken. The task is defined on the method-level: predict one name for one method (code graph). We use attention pooling {{cite:cf5660772e81f09a42557a28e2f93682344c8071}} to generate a single embedding per method. We follow {{cite:5910a99ef61cd597c8b17ef712e1f5e1250c6833}}, {{cite:a979e5b6be7e30f03cb09c42842b8d48d8e15d3e}} to report F1, precision, recall for evaluation. Below we show results on Java and Python separately, as they are used for different testing purposes.
| m | e982d9ea58bec7e721775361459056cb |
Large-{{formula:48c3e169-3bca-4ad0-b9a4-e45195dd6bc6}} volume independence of {{formula:e97bf498-2d1f-43a6-a760-65bf995b0f9e}} Yang-Mills
and similar theories is a topic
discussed since
long {{cite:2bef0759365865bd5419bfada327a1cf338f12dd}}, {{cite:2cf17970c453142bfebf849248e548d7d1c1c4f3}}, {{cite:60fa3d9f8be3412bcd36058b5318ac4d5f2ffc9b}}, {{cite:baee4906fab08f1d24c150ebadf2fcf0b10e8253}}, {{cite:61eaad0bb733040b6da1f536bd5c66ee8ed39b61}}, {{cite:e30c2df323fb5e1c92752aa03526566a95787a68}}. The possibility that the non-perturbative
properties of the theory might be encoded in a simplified model with
small compactification radii is very appealing, also in view of the
fact that the inverse compactification radius sets a high energy
scale, which makes weak coupling approaches viable. It has been clarified
since long that volume independence holds only
when no transition, leading to the breaking of
center symmetry, takes place:
unfortunately, the breaking happens in most cases, e.g., at the thermal
radius where the theory deconfines.
| i | 563d0071f5d64ca116bdcff5c5a79a31 |
Tab. 4 reports the detailed performance from different models on all four protocols.
Overall, our method surpasses the previous best method on source and target domain evaluation in all categories, with the only exception of the target domain performance in the illumination protocol ({{formula:197a2f9d-14a9-417b-8339-e0e495efd0d7}} worse than {{cite:36c38547eafe1aacd23c7e2ab8e66782266a6c0d}}). More importantly, regarding performance on source domain data, it is impressive that our method surpasses the best previous method in all protocols by a large margin (e.g., {{formula:ce77ce02-3bfb-4fc0-8ffe-7d5644120ee6}} , {{formula:cb7562bd-1edd-480a-bd3e-97db8db12bd2}} , {{formula:8d5fd9e9-2716-4bc5-b256-4295659ca614}} and {{formula:126a3487-d242-4cf0-ad3d-52a53edfe586}} , and {{formula:9fd8a62c-62d5-4aea-a881-8b2759a9bb6f}} on average). We believe that, the proposed SRE can largely alleviate the catastrophic forgetting as mentioned above, thereby yielding the superior source domain performance than prior works. However, the improvement diminishes on the new ethnicity protocol. One possible reason is that the print and replay attacks account for a large portion of data in new ethnicity distribution, and different methods, performance on these two common presentation attacks are similar.
{{table:5efe5a13-4846-4d33-99a0-3c8ffb1a5173}} | r | a9cd193fac0c38fb3e73139a2d369956 |
For MS-DCNN {{cite:347c003ccabdfb789d12ee77b2fd269695819045}}, we removed dropout and added InstanceNorm {{cite:a891203b8140d5b3101232a2da5f3d6c67e62524}}, which greatly improved training stability and performance. We also extended the method of Zhang et al. to handle 3D OCT volumes instead of en-face projections, it is referred to as MS-DCNN 3D.
We extended the approach of Nguyen et al. {{cite:10c35867193d3d014bbdb6a7a2cf7765b83175e5}} to handle the imaging data instead of tabular features, introducing convolutional filters into the recurrent blocks. The work of Gigon et al. {{cite:e6bc069a2c68e85e2ded6a35641017cc8616ff39}} was implemented as in the paper, however, we used {{cite:237faa73acbf97b83d1582cd7cd50d05beae0608}} for layer segmentation. For implementation of the Deep Glioma Growth{{cite:78bf1cb1d9f3fac1b29622d8eb4a3884a025edce}}, we used code provided by Petersen et al.https://github.com/MIC-DKFZ/image-time-series, with the exception that only baseline image and its segmentation was used for generating the prior.
| m | 0ea1dc86ac04dedb29171072c294d0c2 |
to name two possibilities. Often we want to understand how the two are related — what is the impact of specific modeling choices upon performance. A common approach is to fix some parameters while varying others to find out their impact on performance. Whenever one implements the classifier and has full control over the experiment, this white-box approach is relatively straightforward. There are, however, situations where one may not have access to exhaustive classifier details and configuration settings but would still like to learn about similarities between alternative solutions. One such black-box scenario are public machine learning challenges and technology benchmarks. Whether it be NIST speaker recognition evaluations {{cite:23ee4426760ee604ec33a805a1774382532a2e78}}, {{cite:f9ad519b220cef45d4a7446a37b58da3b4dd0bb3}}, VoxCeleb {{cite:13378423d47c23086e071501991851cd6cc096b7}}, ASVspoof {{cite:d2509b1202a98c393f1ff457f4829b8e9b133cea}}, or indeed any other competitive campaigns, participants typically run their in-house systems on a common evaluation set and submit predictions (e.g. scores) for unlabeled data along with a system description. Since source codes or models are often not required, there can be uncertainty as to why specific challenge entries outperform others. The authors' personal motivation for the presented work stems partially from difficulties encountered in our efforts to link classifier properties to their performance in a recent challenge {{cite:d2509b1202a98c393f1ff457f4829b8e9b133cea}}. We wanted to find out what can be learnt about classifier differences based on detection scores.
| i | ee1acd135b221f16fc7e46b79fa3cd31 |
In contrast, we show that gates are not essential at all to construct a well-performing recurrent unit. To this end, we develop a recurrent cell not containing a single gate. The proposed cell surpasses not only GRU and LSTM but also the so far best Mogrifier LSTM on many commonly used benchmark tasks. Our cell is based on a residual ReLU network employing normalization and ReZero {{cite:9051dcbd837f4e646f9a7cdfe63b0ee8976b5970}} recurrent state update.
| i | 32658cb99c59f9702d71448ab2b63e01 |
The idea that new particles need not be heavier than the electroweak scale, but rather can be light and feebly interacting draws increasing attention of both theoretical and experimental communities , , {{cite:253f98d92f2b98b5c82fcb2c9a71b7668752ffb4}}.
In particular, the idea that heavy neutral leptons are responsible for (some of the) beyond-the-Standard-Model phenomena has been actively explored in recent years, see e.g. {{cite:011aa1ee0ee1c791bc72210c859e601953ce115d}}, {{cite:240219bad59fda17ae1905b1b7b28e3610faccf5}}, {{cite:6a85ef50f5450274941811b7920d389c6721062a}}, {{cite:9f14a6fb0b0524632313cf31be9aa7dd9052b670}} and refs. therein.
This idea is motivated in the first place by the type-I seesaw model that explains neutrino oscillations.
Furthermore, the same HNLs with nearly degenerate masses in MeV–TeV range can explain the BAU and refs. therein.
| d | 83a5fb81e9d5904ef81ab0c83a9fbffc |
The {{formula:0b752ebe-7dfb-49c5-a0f9-a0771c54d66b}} harmonic number is the sum of the reciprocals of the first {{formula:8c5bd846-a951-481f-91ee-f2ae86a7b12b}} natural numbers, expressed in the following form {{cite:d259e72b5b32416ad7a436f9220881dfca8c354a}}:
{{formula:952c1890-3baa-4418-acfa-7dbcb8b5b07e}}
| i | 90b05237a6837da1c9797a8b935bd9dc |
If {{formula:7c979181-ab1d-43d0-9ae4-cc2b9caf3e6f}} , we interpret {{formula:f24aa64b-8c85-46ed-b480-175b4a54738b}} as the confining potential {{cite:82312f2bc1b6cd54f80e331cc00d996505df4df3}}. In some cases, Eq. REF describes an equilibrium statistical mechanical system, in particular if {{formula:e0e3775e-31c1-42a2-bab4-dc12a4753d2a}} and {{formula:a6f1da2d-47a8-425f-a88d-752426081c4a}} is proportional to the identity. More generally, equilibrium conditions are realised when the drift term - the deterministic component on the right hand side of Eq. REF - is proportional to the gradient of a function defined according to the Riemannian metric given by the diffusion matrix {{formula:72fd480b-524c-46d3-98e7-a27d4f7d092e}} {{cite:ff43ec095c5b1b939d04f73e950fb0e76117fa86}}.
| r | 4c61d07cb191855ee188c660e7df0365 |
Quasicrystal (QC), an ordered but not periodic structure, is famous for exotic tiling patterns with fractality{{cite:f79846f3c22aa969290060d72a0c703397aacbc3}}, {{cite:e996ced85ec1f5a930e374991c1c0a2cb5566872}}, {{cite:38cd3fd2126c5a3c7fb22f7fdefc87bd0b909234}}, {{cite:25fd347f4efdde93b41fca439415f4019489ebf1}}, {{cite:c4eb8b65cf97d585c94dbfb39557b710ea061998}}, {{cite:d565e00e622ed9ef564dd2de3d0eec0661da8d2f}}, {{cite:a860dea9dcf822ab0c51bdc00db6a2a6836af1ab}}, {{cite:729805bceff4b87ffd8e6ce521ef5eba5e1993cc}}, {{cite:7bf6bee635007ecb5f38c1847b9f344f0931b0ef}}, {{cite:b1d6db56dbf75e647bc481ad324e0d9790d5967d}}. They are represented by self-similar structures as a compensation of the absence of translational symmetry{{cite:5f5d3165aef23f50afbb8f465aeeae33c9c8a4c5}}, {{cite:7d5ad9b260f358731d32002cfd2b097cf972335f}}, {{cite:3cddeddcdda9c198081470fd1b0285ef5869d576}}, {{cite:b1d6db56dbf75e647bc481ad324e0d9790d5967d}}, {{cite:4df58f51e79a614e869f04393aeb2c66da3e6245}}, {{cite:2bc74870b208f08e1f059ae1c757d82a526fb4d3}}, {{cite:729805bceff4b87ffd8e6ce521ef5eba5e1993cc}}, {{cite:79005346bfb5a08432c945203843d5a466c3ba57}}, {{cite:5f5d3165aef23f50afbb8f465aeeae33c9c8a4c5}}. The tiling patterns of quasicrystals are important because they give rise to novel quantum states, for instance, a critical wave function, a power-law decaying wave packet, which has been discovered in many distinct quasicrystals{{cite:4845dccc2cb66c5d5119f0be505767176649551d}}, {{cite:75ebef46aa0bdba712ba3804852b566c62203738}}, {{cite:1ccfcece1a606db5454c7a0d2cd97f4830c2f612}}, {{cite:5194e8583cc5c11a3da97fdf2cd34ae079afa738}}, {{cite:3b1512cdbe5f249bfec70b68be357c64f404e557}}, {{cite:75ebef46aa0bdba712ba3804852b566c62203738}}, {{cite:1ccfcece1a606db5454c7a0d2cd97f4830c2f612}}, {{cite:5194e8583cc5c11a3da97fdf2cd34ae079afa738}}, {{cite:4845dccc2cb66c5d5119f0be505767176649551d}}, {{cite:7b67fee67cc935bd8a32b41d2d431cdb3fbc8be9}}, {{cite:5194e8583cc5c11a3da97fdf2cd34ae079afa738}}. Beyond the critical states, another quantum states in quasicrystals have been recently discussed under magnetic field{{cite:16741272480bd9ba737cee85b9480438db8e4cef}}. In this case, electrons are strictly localized forming each island with particular length scales, similar to the Aharonov-Bohm-like cage, and such islands are extensively distributed and interfere with each other under field control{{cite:fa289b50a06d0e557c1608edc34ef9f495216564}}, {{cite:16741272480bd9ba737cee85b9480438db8e4cef}}. Such states are uniquely present depending on quasi-periodic pattern. Therefore, discovery of exotic tiling patterns and understanding their quantum phenomena are important tasks.
| i | e48075a704e67659b8976a7cee0c68b5 |
We should also mention that {{formula:c7901ab8-41db-47d6-9afb-842a2e3173ee}} holds for the function
f(w ; Es, ):=(w) (-n m 2 MSE(w ; Es)),
with the mean square error function
MSE(w ; Es):=1n m i=1m j=1n(Yi j-I(ki, j ; w, Es))2.
The Bayesian analysis treats the statistical ensemble of {{formula:114822a8-0fb4-4ab4-85ff-c3434e6c7b24}} subject to {{formula:475e9dd7-6890-4315-8312-d163038c6c43}} as an extension of the least-squares method. The mean and standard deviation of {{formula:6e78f757-f145-4186-ad37-a090f94316c0}} is respectively adopted as estimator and its error bar. We also estimated {{formula:6e93b3da-4ac3-4b55-a40d-0371abac7dab}} and {{formula:ac72f54e-a193-4cb3-b8f4-7af8873c4c11}} by treating them as random elements subject to the conditional probability distribution function
p(Es, Dm n)=Z(Es, ){Es} Z(Es, ) d ,
where {{formula:713fcfa0-eef8-4f45-9e59-ddeeae16cc73}} is a collection of candidate forms of {{formula:5cd8e634-a855-446d-8ef4-61c82d205acd}} . Note that this equation is derived from Bayes’ formula such that {{formula:735aa65e-8be1-4f33-b98d-be739e614906}} is an uniform distribution. Especially, {{formula:b91e8447-02a7-4d4b-9077-18fdd4867c2a}} and {{formula:d826113b-110b-40ca-bc10-7ea8729b90f7}} that maximize {{formula:bb927cf8-690c-4bd5-8f2a-6c484990a876}} are adopted as estimators. This type of estimators is known as the empirical Bayes estimator {{cite:8517bbbed5831040321c8fb0d58b17bb9f45f8a9}}, {{cite:db762b1071995b51b2a4075927296deda964bd57}}, {{cite:f0873d22b1aef25f569c1a0cc9d0c1a3ae32ae87}}. We also quantify the uncertainty of each {{formula:676d8fbb-f4cb-4581-9219-e59e69ecf727}} by the marginal probability
p(Es Dm n)=p(Es, Dm n) d ,
as shown in the inset of Fig. REF a (see also Fig. REF b).
| m | 0ca7f08abc98f33b643497781ffc1770 |
To answer RQ2, we calculated the proportion of annotators from each group (i.e., gender or age group) that mislabeled (failed to detect) or misunderstood (failed to comprehend) each text. The resulting distributions were non-normal, so we chose non-parametric tests, which do not assume an underlying distribution. As we have only two values for gender in the dataset, we used a Wilcoxon Signed Rank test {{cite:5277e145c4ae1298e6814e532fd25fea065b887d}} to examine the null hypothesis that the samples from male and female annotators came from the same distribution. This is similar to a paired t-test, and it ranks the absolute value of the pairs of differences to calculate the test statistic, w. With this test, we report the Common Language Effect Size (CLES): the proportion of pairs where the values for one group are higher than the other.
| m | 02ef9cd61bbbc7687b60ebba45e19bfc |
This assumption is commonly used in the literature {{cite:8a006d097508ee8846774d3f9d33907ec84c155e}}, {{cite:6b158c5a9b42bd66aafb8be096a2ab25f04f24e3}}. The Fisher-non-degenerate setting implicitly guarantees that the agent is able to explore the state-action
space under the considered policy class. Similar conditions of the Fisher-non-degeneracy is also required in other global optimum convergence framework (Assumption 6.5 in {{cite:d27124844001c30c1966c3cbfd359ee92a565fe4}} on the relative condition number and Assumption 3 in {{cite:07fcb8f345f7e9b5e7357da3b924477e632cd97a}} on the regularity of the parametric model). Assumption REF is satisfied by a wide families of policies, including the Gaussian policy (REF ) and certain neural policy. Without the non-degenerate Fisher information matrix condition,
the global optimum convergence of more general parameterizations would be hard to analyze without introducing
the additional exploration procedures in the non-tabular setting {{cite:6b158c5a9b42bd66aafb8be096a2ab25f04f24e3}}.
| d | 1993a16477c3f99a0dfdb53556f64ea4 |
In this section, we provide the numerical results of several applications of the proposed GSAT framework. In our experiments, we used the following datasets: MNIST {{cite:49a39c68571512371ac58f5bd69f736ac4648b13}} and CIFAR-10 {{cite:dc7988849720d9137871fed1d1e079f9cbf75baa}} for image recognition, and HapMap GWAS dataset {{cite:220224e29a63fffa61ef3b38699a18c52ad6b8a8}} and TCGA cancer atlas dataset {{cite:8835dc83b4c48e968010a83da73df5be7e50c14d}} for computational biology problems. We implemented the GSAT Algorithm REF in TensorFlow {{cite:f55be405e5a43761cf5941460a0b5e5fecc49765}} and ran every experiment for {{formula:ba9c0d36-d9bc-4e68-9a50-38cc0bfafa24}} iterations. In the experiments, batch-size and group size were chosen to be {{formula:0fd02e27-8c61-402a-8bce-eaac25bf2c39}} . For the MNIST and CIFAR-10 experiments,
we applied the AlexNet architecture {{cite:74ad6624695f66404ea133ce51ba0ac624deadd1}}. For the experiments on GWAS and TCGA data, we applied a 1-hidden layer neural network with 100 smooth ELU {{cite:28e843f630aab2fa42df577d57d31978a0d05133}} neurons.
| r | 578aa56eeb36d1b68a2142ea86828de7 |
The alignment is calculated at each training step on the fly.
To mitigate the negative effects of unreliable alignments in early steps, the CTC-based model is pre-trained with Eq. (REF ).
The soft labels from BERT can be pre-computed for all the training set.
For memory efficiency, top-{{formula:9b3c9482-4632-4815-8f8a-5b76f557005f}} distillation {{cite:c3c29c3c3c6f7167017bb0b8026d2983fe6ce67d}} is applied, where the top-{{formula:16551813-41e9-45ab-949f-a11be92a300c}} probabilities of BERT are normalized and smoothed by temperature parameter {{formula:a1e41603-03e2-4046-84a5-2f8f058dcb8d}} to generate soft labels for distillation.
In this study, {{formula:5eb782ff-af69-4728-ba5c-ddd1c6602899}} and {{formula:09ea07f0-8716-41ee-a327-dc2a21152c1c}} are used.
| m | e2b4b50bada71d1b48b932725c59ec00 |
Naturally, the subspace matrix size is much smaller in the non-orthogonal basis when {{formula:cee8c6f7-7761-490a-b4d6-39999d527c4b}} , and is also more general than Hamiltonian-based generalized eigenvalue problems derived in previous works. The choice of Hamiltonian function {{formula:f1688ed9-0f4d-46f1-ae0b-9577db2b4fcc}} and non-orthogonal basis, {{formula:90e51f95-5cee-46b5-9271-fe5866942c9f}} , will ultimately lead to a wide variety of different hybrid quantum-classical algorithms with trade-offs in terms of convergence, number of calls to the quantum computer, circuit depth, and classical complexity required for post-processing. Although it might not be implementable in the near-term, it is worth mentioning that a non-orthogonal basis defined by the function, {{formula:8770487e-8e33-43d3-94e8-4dc839aea6c2}} , as used in qubitization {{cite:1344a175dd9945c26e1fe64d53d336ca9e99c310}}, would provide an effective way to estimate both ground and excited-state energies with equivalent circuit depths as a single Trotter time step but avoiding Trotter error {{cite:68f262deb484340d0e25d8ceff77b699ac644898}}. However, this comes at a cost adding a register of ancilla qubits with controlled multi-qubit unitary gates. For our purposes, we will focus on the standard Hamiltonian and real-time evolution operators, {{formula:1e6aa37a-126a-490f-be92-6c6c4255afc1}} and {{formula:ade23a6f-7457-41cd-bc8c-602580ee5fe3}} . We will also consider two different sets of non-orthogonal states, thereby obtaining four different quantum-classical algorithms which provide various advantages and disadvantages as discussed below.
| m | fc13905125daeee597304bcefef17c06 |
SphereFace {{cite:e3add297387c2db48e4787d9dbd16cae4451a226}} provides a new view on the weights of the last fully connected layer, representing the centers of each class in angular space.
Enlightened by this, we draw a theory—minimizing the angle can achieve discriminative features and the fast way to decrease the angle {{formula:ae9a36ad-57c2-4c14-afaf-d2ddd29e0b58}} is maximizing the gradient of {{formula:9eca2e77-39bc-44b8-9c92-49b76325cfaf}} .
| m | 98b1fa1aea2533f36b9c28838341e42f |
As part of future work we intend to empirically evaluate the extent to which our approach can be applied to the task of extracting the structure of PGMs from observational data. We intend to evaluate our approach along two measures. First, how close the learned model matches the empirical distribution induced by the observed data, and second, how it compares in terms of both accuracy and efficiency to constraint-based algorithms that perform statistical independence tests {{cite:e2a3e73fddbd8a0140237948c26e5f732009d1c2}}, {{cite:853456c792b06e32b7f6bad94bd3e7b5f9b3ba9b}}.
| d | 089035d3821cce0998f4fe77b8514b0d |
Our insight to evaluate robust decisions using statistical decision theory applies to the whole literature on data-driven robust optimization. There exists a growing number of applications of data-driven robust decision-making in a variety of settings, including portfolio decisions {{cite:d02cfef395923ab7b4a9b32066005be56b9f56be}}, {{cite:19b3a30e97ac5cfde70b6217afd21ef125e9172e}}, elective admission to hospitals {{cite:1eb4123bfa09e697495777b0bcb4c87a84efa9ac}}, {{cite:a12b17e8525fec20f2e90bd665b65d48829b4689}}, the timing of medical interventions {{cite:75de28ca079999407f7fef380591ea508ca5e5f8}}, {{cite:6cb311dcc73ea711a87d30ad287f43ae4a128dac}}, and managing the production of renewable energy {{cite:f94ca730a32512ad09e0fc335352768a0f8a5df7}}, {{cite:0d350176e2fd42f479b745a54aaeeeeb12a7b711}}.See the recent surveys by {{cite:56c7e824b3bdf5a84d2f4bf827479d94e97333e7}}, {{cite:ea7abd86a9ae619fa8dd11c73bbc32e55cfa7d1b}}, and {{cite:6c64f522c75754938f3955f9ab83fd9af3a1af4b}} for numerous additional examples.
| i | 5821948ef759d930bb678b901e0dc7c3 |
There are various types of digital and physical attacks, including face morphing {{cite:6c788b4dfc60ac01a3d6671c816c29c0a10a1bac}}, {{cite:92a8f4234366cc47019be30865986302f126bdd1}}, {{cite:030a2d70d881ef8740e5ebd1ea68654884fb37c3}}, face adversarial attacks {{cite:91d4c69f9617fc7e34e97cbd7ca327aad2ab2f9f}}, {{cite:86ce839dd26db282914e21ba3597b2779c114256}}, {{cite:9cf1d76e5706ad1fb8baac9aaed0fff248443e38}}, face manipulation attacks (e.g., deepfake, face swap) {{cite:fe775e34b6929e3aea82d64788218fdd27530c0a}}, {{cite:8bf1d93cd732690e5ff4c07b0904a185f2b86a8c}}, and face spoofing {{cite:b32d052087f126b77cad7002c7d254367b7fc862}}, {{cite:80dc3c82247cc4a62fa04f49cf5ad3975aafd6df}}, {{cite:652af06d7e4d8087961a47533adb56b08afe2e2b}}. Among the above-mentioned attacks, face spoofing is the only physical attack to deceive the systems, where attackers present faces from spoof mediums, such as photograph, screen, mask and makeup, instead of a live human.
These spoof mediums can be easily manufactured by ordinary people, and hence they pose huge threats to face biometric applications such as mobile face unlock, building access control, and transportation security.
Therefore, face biometric systems need to be secured with face anti-spoofing (FAS) techniques to distinguish the source of the face before performing the face recognition task.
{{figure:021820b7-da66-4e53-989a-55c44080787e}} | i | b30f29b334de5ec4bf2438ea425a77da |
The characteristic hydrogen Balmer spectral signature of EBs is an intensity enhancement in the line wings with unaffected line core.
For the majority of the observed QSEBs, we found such spectral signatures in the H{{formula:23691221-856f-497f-a97c-7573eeed0e70}} line.
However, 14% of QSEBs manifest compact brightening in the H{{formula:903a53ef-a9b3-4fcc-b6b4-17cb5790bca3}} line core in tandem with their line wings counterparts.
Moreover, line core brightenings exhibit a spatial and temporal offset
with respect to line wings brightenings.
In around 93% of the events, the line core brightening occurs with a time delay with respect to the onset of brightening in the line wings.
The median value of the temporal delay is 53 s, while the median value of spatial offset between areas of line wings and line core brightenings was found to be 204 km.
In the majority of events we found that the spatial offsets in the line core and line wings brightening locations are oriented in and close to the direction of the closest limb with line core brightening appearing relatively closer to the limb.
Since the observed FOV was away from the disk center ({{formula:9432146d-2b0c-4435-a1d1-798799c9f5a2}} ), the QSEBs were viewed from the side under inclined angle, the temporal delay and spatial offset in line core brightenings can be interpreted as upward propagating brightening from the photosphere towards the lower chromopshere in vertically elongated current sheets.
Our measurements suggests that the reconnection brightening in QSEBs propagates upward with speeds ranging between 0 and 23 km{{formula:703882a2-d9f2-4e66-a67d-c12eed576964}} s{{formula:9197697e-6510-4a40-85b2-72185cb0a356}} .
QSEBs with bigger area, longer lifetime and higher brightness have higher probability to exhibit line core brightening in the H{{formula:34f9828d-6585-40f6-8fb3-920313658ebf}} line.
As discussed in 2020AA...641L...5J, the observation of H{{formula:9a2ccb13-f644-4a2f-84e1-520dca9f2142}} line core brightening and propagtion of the brightening aligns well with the vertical current sheets in the simulations of {{cite:547a1cf6d15c191522cd1cb3dc9d706c0f61265f}}. These simulations demonstrate the occurrence of EBs and UV bursts
{{cite:32c67f1b678cd5ca2f94b670b105b52f01df501c}}, {{cite:a252c7c731ede2d036ffc01ae8e081fdc42b34f6}} along extended current sheets with EBs located in the deeper part of the atmosphere and UV bursts in the higher atmosphere.
A spatial offset between EBs and UV bursts in off-center observations were observed by
{{cite:7d5bcc38aedea80dc759af66aabc196cb170b6d9}} and
{{cite:fe392e2259ad1c2b0305eddad1581f41fc8900ec}}. The observation of transition region Siiv emission associated with 2 QSEBs by {{cite:44d56ba8a99eb58856cd92d95c33b2855dce739c}} is also consistent with a scenario of reconnection along a vertical current sheet in QSEBs.
| d | b5d04eb2faa029d24da0c1a3ad2edfd3 |
The combination of the trigonal structure and the interlayer AFM order makes MnSb{{formula:9dbcd12b-03fa-4bdd-a5f8-b48a127283c5}} Te{{formula:c3b6eb28-f0a9-4c3c-8e0b-be5bec86b29b}} {{formula:8deb090d-81cd-45d3-88a0-9ad9ae6b1c59}} -symmetric, {{formula:adf9614f-fb5a-46c3-8584-ce75da12f7f6}} being the combination of the time-reversal {{formula:efa0dcac-0fae-4b29-883e-3448aaca77ad}} and primitive-lattice translational symmetries {{formula:bc3bb315-1043-43f2-9f46-0995a3885986}} , {{formula:e3a635fb-516b-409c-9f26-b071d29f2974}} . The presence of this symmetry allows introducing {{formula:81119aa0-d2c7-42c1-a1fc-0e3109246906}} classification of AFM insulators {{cite:548a2da682f11706b2a7de927301c9b6d62b84a7}}, {{cite:a502db816bf7592fbeae47b39d9893ba26e3a0ee}}. To determine whether the system is insulating or not, bulk electronic structure has been studied next for the above discussed magnetic ground state. Our calculations reveal an insulating character of the spectrum, the fundamental band gap value being equal to 124 meV taking spin-orbit coupling (SOC) into account (Fig. REF b). The {{formula:e397a021-829c-4cc2-a93b-f27d955c37af}} invariant can be calculated based on the occupied bands parities {{cite:548a2da682f11706b2a7de927301c9b6d62b84a7}}, {{cite:a502db816bf7592fbeae47b39d9893ba26e3a0ee}}, in which way we find {{formula:8c08bd33-d754-498b-9430-a3f74e970b2c}} for MnSb{{formula:2f7174a9-a79f-404e-8436-242478a3c10d}} Te{{formula:6274abb2-be9b-4466-a6d0-1a303f36828b}} , meaning that it is an AFMTI. The latter means that the bulk band gap of the material should be inverted, which is indeed confirmed by performing the density of states (DOS) calculations lowering the SOC constant {{formula:2e6f1fd7-30d9-46a0-a83a-8ca69232cc95}} stepwise from its natural value {{formula:da3816f1-441b-4b0e-bf2f-5179f68b25c8}} to {{formula:b760b8bd-510a-4914-afd0-f6bf5f608372}} (see Fig. REF c). As can be seen, the system demonstrates the topological phase transition, i.e. passes through the zero gap state, when the SOC strength is decreased to about 0.7{{formula:d48b8a61-9db0-4b40-b1f3-493bbdba2b25}} . Recent DFT studies {{cite:d246f228244d28f9e16b089b116de22f0ee36960}}, {{cite:9ff5d91c0af2e3b7b36b400acf208ad10203c896}}, {{cite:e11f3706a858b45eb019b006cd1a78c8914a6127}}, {{cite:d22539cdb20e2bd3dd8ae11e4e7950027b11c0e3}}, {{cite:937fd70ee31d35f851e601d03f73bf004db983ef}} report, however, that MnSb{{formula:360c1a73-d3dc-41be-9bea-648eb410df2d}} Te{{formula:66f87566-b5b9-49c9-b2cd-05e8e4974cb3}} is topologically trivial, which is in contrast to our results.
As we discuss in detail in the Supplementary Information, the crucial factor causing this difference is the MnSb{{formula:60d969de-e41f-4a86-aa7e-14179bcb5e09}} Te{{formula:ef7af3b6-b498-402f-815b-d44a2acc1f40}} crystal structure, which in our case is fully optimized taking the van der Waals interactions into account (see Methods section). To provide further support to our claim of the AFMTI state in MnSb{{formula:bd3197bd-041c-4deb-b620-d0eb1434aa88}} Te{{formula:a845549b-410b-4673-b738-705623099b80}} , apart from the projector augmented wave method (PAW) calculations using VASP, we have performed DFT calculations using the full-potential linearized augmented plane-wave method (FLEUR code) as well as the Green's functions method (HUTSEPOT code). These calculations predict the band-inverted AFMTI phase in MnSb{{formula:3d36b73c-1aaf-4a54-873e-91f0f743a171}} Te{{formula:0576c92b-d38f-4a0e-9927-ec47cf75652d}} as well (Supplementary Information Figures S1 and S2).
| r | 229e26a604c87f418430ae40b917c33a |
To answer the RQ, study results provided evidence that compared with using interactions, using entity references improved note characterization from fair to moderate on categories and from slight to fair on overview versus detail; the two sets of predictors produced comparable fair agreements on using prior knowledge, based on the interpretation of Kappa values {{cite:745a3279dcea60f1f2265551d7c7d81a62c669e5}}. Referred entities seemed to be better at predicting insight characteristics than interactions, which is understandable as, during visual exploration, insight is still to be discovered, whereas, during entity references, a resulting insight is made more certain.
| d | a6c91a3ba56e6428119df45922abf0f5 |
It follows from formula (5.2) in the book of W. Feller {{cite:186b06c8e1cc9aba5951509c09f4a577cbcb63f6}} that the number of ways of writing a positive integer {{formula:bc577a5f-25cf-49ba-8059-ce89c07696db}} as a sum of {{formula:cdfc66d2-7cbb-480d-a2ac-253b21678462}} non-negative integers is equal to {{formula:0eb228dc-0f7b-421b-8776-d8379b4f840e}} . Therefore, since {{formula:a2d4181a-c2ed-4611-92d6-9bcc06bf5a32}} is the sum of this last expression as {{formula:c6147007-79eb-4651-9ec7-75b07f3e7ba0}} varies from 0 to {{formula:f50e695d-0970-48de-b4d0-14c3e336a903}} , we find, using induction, that
{{formula:354cb6c2-169f-438f-9e3b-e30f6aad5e75}}
| r | bb13cf408c2a2f80c61265da77298354 |
The following theorem summarizes typical convergence results of randomized Kaczmarz method for consistent and inconsistent linear systems{{cite:eaa79075a7a4e106bae6efbf4becde38baaa7ce1}}, {{cite:0d634431f02e9c87bc3d862588d1bf2d27e62c9d}}, {{cite:35138b658f8abe8603dd650bdddf56be6009e888}}, {{cite:67bb7d8e3dc3df5e803e33c333600041216196e6}}.
| m | 15a913474903241e40d6daab05fff992 |
We quantitatively evaluate the quality of disentanglement in Table REF .
We describe two novel metrics to evaluate this.
To evaluate the consistency of appearance with changing geometry, we measure the standard deviation of the average color in a semantically well-defined region, which could be obtained via an off-the-shelf segmentation model {{cite:c80cb0986976f91438e3aa06fdd31b4cee5e27e7}}.
We use the hair region for human heads to compute this metric for networks trained on FFHQ {{cite:e5df29bd436a6e44d54817b6e2a08d57d956dd71}}.
We sample 100 images from the GAN with a fixed appearance code and varying geometry codes.
The standard deviation of the average hair color can be used as a metric, as a lower value would imply consistent appearance across different shapes.
We compute this standard deviation for 10 appearance codes and report the average over the 10 values.
Our approach significantly outperforms GRAF {{cite:c38acf48e81df5a4606eba7fafd1720cabe53334}} and {{formula:e12b2175-2594-4c8a-8e31-269488517dd7}} -GAN {{cite:e80d50fb9b10dfc63d94d4e08f75dd79f0b6d873}}.
Since {{formula:9606eea3-362c-45e0-9549-3510a6bdf6b7}} -GAN does not have different appearance and geometry codes, we simply sample 1000 images from their model and use the numbers as a baseline.
| r | cc71508f6fe513ddd4eae4bc8ed1a58c |
The model used in Ref. [takada2022transport] neglects, however, the collision geometry, particularly, the collision angle dependence of the coefficient of restitution. Moreover, it is assumed that all particles carry the same charge. The situation becomes significantly more complicated in the case of positively and negatively charged granular particles. Here, the theory is similar to polydisperse mixtures, which have been studied intensively in the past twenty years{{cite:79a4cc35fb2e702bcca0f00c600a013723300c4b}}, {{cite:20b914fc61bff387c2f8f15d122f33f7e8c7ae12}}, {{cite:a93d9967b16b1629d6147217f3cdd70241c4999a}}, {{cite:69ea6034136316eb5c9f44c7271ab61a5a787cbb}}, {{cite:c47f6e99537dbb485d77d776df53160ec338c616}}, {{cite:7f0338507290757d42f5f719860b85621e93efdb}}, {{cite:4280476ec77e891b1c0e018369cf6dd7e8add718}}, {{cite:fef66a24eec509f697eef1d484a62b58d55eec04}}, {{cite:35d11e5c9934924ee7f2b4e385decc92d84fbe4d}}, {{cite:e91cceb635efdbaf39ef5de519722d50c95c80ca}}, {{cite:7681da6b5728bee84f34907bcc622390c4d0bc49}}, {{cite:399e6d7581549c51eb929a3ddc8bccb3753ccb06}}, {{cite:2fb56d5bdb6de8fdfe48efe9e7b653dcbe335129}}. The most significant feature of granular mixtures is the violation of the energy equipartition{{cite:79a4cc35fb2e702bcca0f00c600a013723300c4b}}, which inspired the concept of a partial temperature for each species. These temperatures depend on the particle mass and size and the gas density of the corresponding species. For our system of particles carrying different charges, the partial temperature ratios depend, moreover, on the type of the interaction between the particles. In the kinetic theory, the partial temperatures are determined self-consistently to satisfy the energy balance equations.
| i | d1488d6f6b9131bea3e2896519b46024 |
We compare the performance of our tabstruct-net against seven benchmark methods — deepdesrt {{cite:9cc7812741df58ad334f5311ef65f6db884bbfcc}}, tablenet {{cite:6ad9a9bdce3155d8cdc7b3976c811edc3b0e476f}}, graphtsr {{cite:0f6b1c8d73e7e4fc0c1a0b7768b0a9528488c80a}}, splerge {{cite:1210c7b6606545144ea1a98c1842929631ee7348}}, dgcnn {{cite:d10c693d5998ea9f06b78f53584baca961722481}}, Bi-directional gru {{cite:b44a24cefd66198da27f00490a906694449ce53a}} and Image-to-Text {{cite:80bea49d6907d2373ce10c82b982fc2e60f4db6c}}.
| m | d841b1f9a315c600232198f22fb30571 |
Applying the above estimate for the sample size is not trivial
since in general the upper bound {{formula:1731a33e-5c5b-4c58-996a-e14a22e9914d}} on the variance is not available; however it can be replaced with variance estimates
{{cite:e8152ad4071bb7a4d577b9ef30b91e9e17db60ca}} obtained during the computation of the subsampled function values, or with estimated upper bounds on
{{formula:1dbe65de-786c-4f27-9e0b-768820183b34}} and {{formula:b5baa81a-e683-40ce-8101-56a77df4e09b}} {{cite:40ecb93d3b997dd7b72b70ab714c8edc5a2957a2}}, {{cite:c0bd93ce72afdbdf4d145dff0561eecdf85a0852}}.
Alternative proposals consist in increasing the sample size by a prefixed factor, or geometrically with
the iteration index {{formula:baf50e32-e26f-4046-b7b0-4544043be474}} by a rule of the form {{formula:b8b7a39d-f041-497c-bee7-cabd6ae860fb}} for some {{formula:0ec5f90c-5bc5-4967-9ea7-81d0b1d55166}} , {{cite:bb8e13c2bf532e06a6f1c454a2791a15a6e86eac}}, {{cite:e8152ad4071bb7a4d577b9ef30b91e9e17db60ca}}.
As for {{formula:08f225be-9c09-4290-b4df-70fc73ff8702}} , the sample size can be fixed using a specific inner product test that ensures
that it is a descent direction with high probability {{cite:bb8e13c2bf532e06a6f1c454a2791a15a6e86eac}}.
Finally, we observe that experiments with constant sample sizes are reported in {{cite:e8152ad4071bb7a4d577b9ef30b91e9e17db60ca}}, {{cite:e6e18a04ac5b1f9637025a009d2d1a86cdaf4fe7}} but
Byrd et al., {{cite:e8152ad4071bb7a4d577b9ef30b91e9e17db60ca}} observed that most of the improvement in the objective function occurred with a dynamic choice
of the sample size.
| m | cc969db9c6ee19ad7b606fd34e737b55 |
In order to evaluate how the neuron model responds to external stimulus when
interacting in a layered system one needs to know how a single {{formula:41259577-0973-41c1-ba16-9bd821248979}} lattice of
neurons work. First, with {{formula:e61d1419-0dae-4b29-8695-95fa93964a44}} fixed, we explore the effect of the
control parameter {{formula:37db00a3-e787-40ef-a3bc-f3899826d463}} to determine roughly where the phase transition occurs,
i.e, we need to know where are the sub-critical, critical and super-critical
regimes. Then, we can refine our measurements and explore the critical region
for systems with different sizes {{formula:d26053e7-6c6c-4bfb-8236-d2c8f1211919}} and use finite-size scaling techniques
{{cite:7971b71e8820c03a11927d424078b444b9c387b7}} to determine better the critical point of the transition
{{formula:1f564212-70cd-445e-b04a-53e448075539}} , the order parameter critical exponent {{formula:681b2401-5ea8-4fb4-b721-34169ae0625a}} and the susceptibility
critical exponent {{formula:e29fec2b-da0f-4654-802c-5c47ec3c1302}} .
| m | 9b34f0cb18ea45889d31cd70f023593c |
To better understand the effect of populating memory, we analyze 3 commonly used methods that utilize the memory buffer in different ways: 1) AGEM {{cite:e9ad176f676a80daf3b6e2fe5fc247ca5523426d}} which uses the memory as a regularization by comparing the gradients of elements in the buffer with the current task, 2) GDumb {{cite:0d29559a7e157a4459663ef479baa7fe2c80ff0e}} that only uses the memory to train the model during each task, and 3) Experience Replay (ER) which trains the model jointly using current task data with the memory. Following previous works {{cite:e8c3657704f4767b81f42787617b0ec21915cd80}}, {{cite:c29261cb56f0759cd31ae37bdae8ac2261a79bd0}}, we use the memory in ER by concatenating it with the current batch.
| m | 591df37648d2feff29971583f9bcbdce |
Generic non-multilocality of quantum networks with multiple independent observers. The prediction of the quantum theory is incompatible with the local realism model {{cite:bc7ce2e56510ed0c8c61f8cbefe8f5e7088f2c8d}}. This feature is generic for entangled two spin-{{formula:13fce6af-f126-4c95-80cd-88217825123a}} particles {{cite:2b28352bdfa8f0f13343b1605519da7fb9917f66}}, {{cite:45b7483e596204d15c5c59ea731888ea7ae27e47}} or multipartite entangled states {{cite:f17212127b917e6ff5767ace8c0fc18bfdbc9fce}} using CHSH inequality {{cite:e585d1620efed7178d8599e8e1d454dc8e78baed}}. A natural question is whether the inconsistence is typical for quantum networks. We aim to answer this question for those networks consisting of bipartite entangled pure states {{cite:9ecc3f0b3ea4f929f150dd1730ee2bef8f4433db}} and generalized GHZ states {{cite:d2700ddb7cabe650b706f8a9c2f94d2bbd5844fd}} using the presented inequality (REF ). Let {{formula:9ff20655-16b3-4cc7-b52b-90a1e4596a78}} be a finite-size quantum network shown in Fig.1, where {{formula:5268fd1a-f852-40bf-960b-31da98183dc1}} denotes all observers (nodes), {{formula:115cebe8-05f5-467c-9b49-efb71c75a20b}} denotes all particles of quantum resources, and {{formula:f0665772-82ae-4586-bd7c-30a40389cdb4}} denotes all edges (two particles are connected by one edge if they are entangled). Assume that {{formula:90e9ec51-73ca-4577-b985-530ef7ca3bdf}} is {{formula:5ffe4bbb-a763-44d5-a159-24337f54b00f}} -independent, where {{formula:c8c7399d-5983-4b34-9f0b-a84e9b270a40}} denote independent observers. There is an equivalent network shown in Fig.2, where {{formula:d01fc277-3d41-4af0-bd0e-bb3c415a76ba}} denotes all observers in {{formula:20ca3b5a-31eb-47d6-8074-bac7baf784a6}} except for {{formula:1116f08f-49dd-4606-abb7-a0e2a1c7c9ad}} s. For each equivalent network, we prove the following theorem:
| r | 730c4dae31d4ea9a2bfcf7e9da02faa9 |
Early Degeneration for Contrastive Learning
Contrastive learning methods such as MoCo {{cite:88748665c8a366bdc589e27b2ab2fcdf291318da}} and SimCLR {{cite:522508d4f62d66669d22ae4d63b32b88b1a3e4ba}} are rapidly approaching the performance of supervised learning for computer vision. However, their incredible performances are generally limited to the classification problem. Meanwhile, the generative-contrastive method ELETRA {{cite:12c09c2bf8c895002190d9b60bf0cf7d7b61dc20}} for language model pre-training is also outperforming other generative methods on several standard NLP benchmarks with fewer model parameters. However, some remarks indicate that ELETRA's performance on language generation and neural entity extraction is not up to expectations.
| d | f0877bd4cc22ee815a80fe4eb629969d |
Firstly, to model the running of the QCD coupling, we can include the dilaton field {{cite:6972e58b3f7ccec659fe84fe83b822f8a9c58d5d}} in the background geometry and in the DBI action. In fact, various backgrounds with varying dilaton such as the various soft wall models and the Witten-Sakai-Sugimoto models fall into this class. The dilaton profile is also important to modeling confinement and obtaining good meson/glueball spectra. An effective use of the IR cutoff {{formula:9dffe819-121e-4572-aff3-42c63bc05fe5}} could aid in separating various length scales (such as the KK scale from {{formula:3271cf91-ae27-4bc2-83ad-1269e48bad68}} in the WSS models), strong curvature {{formula:ad6d70e6-818b-4d40-8850-162a57eb0eb4}} and strong coupling regions arising deep in the interior of the bulk geometry. Secondly, multiple flavor branes and chiral symmetry can also be included together with a judicious use of the second IR cutoff {{formula:a4ba913e-61e9-4b41-bc0b-d792d7aae7d9}} This also allows us to extend this investigation to finite chemical potentials. In the context of the QCD phase diagram at finite densities we may cite {{cite:38888997c8817256bd2c70bf7cb83f4c0657f668}},{{cite:4519a1d2db77457229f0f65ab1d152703686fc4b}}, {{cite:d67b2762a087298226d320662dbf69da1cf138f1}} {{cite:bdcfc8e4729c576360bdfdbc579b3d9c58c78217}}.
Distributions of polarized branes representing a gas of baryons can be hidden away behind the IR cutoff in an attempt to avoid the problems associated to Non-Abelian DBI actions. Simultaneous inclusion of both baryon and isospin chemical {{cite:3d38d655f8594b8f67099209944e9d802224ccee}} potentials are also quite simple via non-Abelian gauge fields in the DBI as is the possibility of different current quark masses especially the strange quark.
The further advantage of working in ten dimensions is that there is a large body of techniques to find solutions to the gravitational system which can take us beyond the probe approximation. The D7-brane backreaction is controllable to some extent for one (due to linear growth of the dilaton in the UV), and the entire set up, at zero temperature, has a well-defined supersymmetric dual. For instance, {{cite:0cd86249c4e9264833be824abb896d230e8958e0}} present a fully backreacted D3-D5-D7 geometry presenting, for our purposes, useful metric ansatz for more general explorations.
We note here that the AdS/CFT correspondence tells us that the energy density of the boundary theory is obtained as the coefficient of a subleading term in the Fefferman-Graham expansion of the bulk metric. Since the branes are being treated in a probe approximation, the energy density obtained from the FG-expansion will not agree with that obtained from thermodynamics {{formula:9bf21ee1-4733-4ca9-8c13-f6de560a7627}} Thus, the probe approximation is not entirely self-consistent and backreaction will contribute significantly {{cite:10b163eb8b0708e47b16636cc2ddfe8b35e18e03}}.
Even if not, backreaction effects can be estimated and robustness of conclusions can be tested by stability analysis - because the ten dimensional description should be matched up to a complete string theory.
| d | c2c4ca3a62635855c3b10bf18221f6ce |
Despite the generality of the framework, there are a few technical limitations that could be addressed in future work. First, the assumption of the position-based model (REF ) is important in the current algorithmic approach, because it yields the linear structure with respect to exposure that is required in our Frank-Wolfe approach. Dealing with more general cascade models {{cite:dec9cd4b4dae62f56f827455953cb3449b74e44e}}, {{cite:0e31b478658cc9c1b4de5f19af7b1b131129c611}} is an interesting open problem. Second, we focused on the problem of generating rankings, assuming that (user, item) values {{formula:02b6bf49-fdca-4a7f-baf2-a7a762564f95}} are given by an oracle and are stationary over time. Relatedly to this stationarity assumption, we ignored the feedback loops involved in recommendation. These include feedback loops due to learning from prior recommendations {{cite:0a3fda5f9d4727b81bc3fd63c7fc1b3939c4add6}}, the impact of the recommender system on users' preferences themselves {{cite:b426ca7af8cb7d70297fb0d5b5b144ecd9c65671}}, as well as the impact that fairness interventions on content production {{cite:1d0366e12e1b1e65efe0d830ab4c096788a75144}}. Third, our approach to balanced exposure is based on the knowledge of a discrete sensitive attribute of users. Consequently, this criterion cannot be applied when there are constraints on the direct usage of the sensitive attribute within the recommender system, when the sensitive attribute is not available, or when the delineation of groups into discrete categories is not practical or ethical {{cite:e1feaa6e3b21bfbb3adab4b5e2dcf4cb67e35b4a}}.
| d | 3ebdd3669400ec3670a3985caf933db0 |
1) DINO {{cite:17d85d8eff01272bd820504317b1ac9d3d9deb42}} is trained in a self-supervised way by the self-distillation of plain ViTs. In DINO, all transformer blocks enjoy the same feature scale.
The prominent characteristic of DINO is that attention maps of its last layer can learn class-specific features leading to unsupervised object segmentations as discussed in {{cite:17d85d8eff01272bd820504317b1ac9d3d9deb42}}, and shown in Fig. REF . The feature representations of DINO enjoy good generalizations for various environments, illuminations, and resolutions.
| m | f0796a546acfb98626a4f0fc1534d432 |
The origin of such discrepancies between our study and the RGZ study might be a result of different selection criteria. Firstly, the total number of sources in our sample is {{formula:97195082-79a2-45b2-b61e-7ca19f45b77b}} 2% of that of the RGZ sample. Secondly, while our sample includes galaxy group masses in the range {{formula:e4ed2c74-e625-4681-a67c-103aec52b62e}} , the RGZ sample includes cluster masses {{formula:2e6b56b1-bf74-4d46-baae-3976add30ab8}} . To compare the COSMOS galaxy groups halo masses to the RGZ cluster halo masses we calculated the concentration and converted {{formula:e952594b-d3a9-4bc6-add0-09e435cfc68c}} to {{formula:b9b03f6f-fca7-49c2-906a-4ea7d9da8d8d}} using the code Colossus {{cite:8ab26751cf55ba62ed7439dc66e1f634ef1961d0}}. The parameters we used in their code are: Planck15 cosmology and median redshift of COSMOS of 0.9. We obtained {{formula:cae3b081-92f3-4a36-b833-842e96003e58}} . COSMOS is probing galaxy groups with smaller halo masses than probed by RGZ, and these groups are not dynamically relaxed as yet {{cite:2738469ae661f8e3f17065e5aff173991e4d4d6b}}. This could explain the difference in the results between the two studies regarding the BA of BGGs and non-BGGs.
| d | 21c1be88bce6fd3ddc78e296d6ef1072 |
As language models usually fail when generalization requires systematic compositional skills {{cite:b28ed3349cbe06d677569ba48515ff6345e37458}}, it is important to
determine whether the probing model still lacks sensitivity to compositionality. On the other hand, capturing semantic relation from a static word embedding space has been shown not to be robust when used to solving zero-shot learning tasks {{cite:768d112a7243b8c569aaad21436ed49c554c906f}}.
Rethinking how language shapes the way human learn novel objects is necessary.
Therefore, we look into transformer language models and contextual representations to gain deeper insights into how language models help visual semantic understanding tasks by its zero-shot learning capabilities.
| i | 3fa9fcfea9f62ffa396a6d5d1d00fc16 |
Knowledge Graph (KG) represents a collection of interlinked descriptions of entities, namely, real-world objects, events, and abstract concepts.
Knowledge graphs are applied for a wide spectrum of applications ranging from question answering {{cite:c7bf1b330ffa4bceb9fd2a08b89d1329a2b1b391}}, natural
language processing {{cite:63fd7abe36efd73066bd2127582d652b71bab49d}}, computer
vision {{cite:42c735dcbb540859fe655621c696e26e5049fde9}} and recommendation systems {{cite:db4937ab56eb31f4e43653d7cb0b3fc3361d7bd8}}. However, the knowledge graph is usually incomplete with missing relations between entities. To predict missing links between entities based on known
links effectively, a key step, known as Knowledge Graph Completion (KGC) has attracted increasing attention from the community.
| i | fcc17302f40cd9f6cb35f2f1cdfc9066 |
The most common one-class model is the ocsvm {{cite:5588d959b360bfe000fcaf174ece7e589ac4221f}}. {{cite:cae8b50fdf7f3a3b05ff93cb518385666ba77fe3}} are the first who propose to learn one ocsvm model for each class in order to reject novelties using the ocsvm as dependent rejector. Differently, {{cite:0969a4c655bac00588b948dff42a95da5a0b6daa}} use a separated rejector architecture and propose a single ocsvm on the entire dataset.
{{cite:0212370f1a5b92c23e83cb27d212c29ab76ad990}} argue that an optimal hypersphere is not suited for novelty rejection since instances just outside the class boundary would also be rejected. Therefore, they propose a method to enlarge the decision boundary.
| m | 48d40c324a54a27885c7254d4ddaa4f4 |
Domain divergence relaxation.
Our foreground-aware stylization can be thought of as a solution to relax the domain divergence.
Theoretically, {{cite:5b88add4e34e9b03cfd5847f193dbb59147f634c}} showed that the expected error in the target domain is bounded by its source domain error and a divergence measure between the source and target domain. If model capacity is sufficient, the error in the source domain is expected to be small. Hence, the performance of domain adaptation heavily depends on the divergence. As shown in Table REF , the comparison methods' performances based on their own model's confidence (PL, UMA {{cite:6a22646642e6a150c18928a0586da1c3abc18e6f}}, and BDL {{cite:2be29f03b9c95d808f940c6647daaf8f2337fc06}}) are sensitive to the problem setting and handling a large domain shift, e.g., in Ego2Hands and ObMan-Ego, is difficult. In this case, we need to introduce specific heuristics, such as the mask separation in our stylization.
With a few target labels, our stylization performed powerfully in reducing the domain divergence.
| d | e7320c817f7c0b5efb8d90631a69d5e9 |
We test our ZB algorithm's ability to correctly detect communities on 100 network realisations of Girvan-Newman (GN) {{cite:41f14553fe1d683e442e8b69337621b753ff3f50}} and Lancichinetti-Fortunato-Radicchi (LFR) {{cite:dd07716451c6778bb2031127d88c2475aab13257}} benchmarks. 4 examples of these reference networks, {{formula:987364a9-176c-430c-b02f-3fa5ad5e1bf8}} , with predefined {{formula:4c4eeeac-afa6-49e8-a240-e7e4d404a631}} communities, are shown in Fig. REF . We generate these benchmarks by freely available codes from Refs. {{cite:c7ba0c33d738b0f8a5e38e18d82061ca03c95f0e}}, {{cite:3050e594e23de42bbbf477a7b8d9346a1f7243ae}} (GN) and {{cite:ec8f810d763859d99155332626d3399eb1d139b1}} (LFR).
{{figure:f4b554ca-ed44-4503-ac25-2f3ab4ddcdb9}} | m | 61c82bca773a157f03330329eaa0d8c1 |
The past few years have witnessed tremendous progress in deep learning in many if not all machine learning applications, such as computer vision {{cite:8a08710193f66a68973ac5827f1d7b4a0dc0fad1}}, natural language process {{cite:d0b5acdaee28700d922b20fe6de9cdb7103d6246}}, and speech recognition {{cite:8bb65348dc4390d8af5ce32ca62a82a0b7b45022}}. The success of deep learning, in reality, is significantly attributed to the model-sharing convention of the community: adopting a well-behaved and publicly-verified network
pre-trained by others, one may significantly reduce the retraining effort and enjoy the favorable performance resulting from thousands of GPU hours in a plug-and-play manner.
| i | 2179b02ea8f9197ed71f9e49fd39d412 |
Further, taking the {{formula:0514496e-30a1-472b-b309-2fc1a46eb921}} term in the Finite Fourier series expansion (see {{cite:1216d293b0ec51ed14b252c2e36bd386cf4e6e95}}) of the terms {{formula:a91a6591-149a-4e39-96cb-2fc49aad6281}} we obtain the decomposition
{{formula:420def2d-2e9f-47c2-86e1-aee1c07a1b93}}
| m | fcf310589a8cb1cf859fc0c74b711c1a |
Note that, motivated by the idea of the cross-lingual language models {{cite:06150039e8c9af63594e973f58d580340b2135d7}}, we adopt a shared encoder across domains to avoid over-parameterization and achieve further information sharing via parameter-sharing across domains.
| m | d16a43445e2c7422d06855c2931a9bf9 |
Discussion on collider based search is out of scope for
this work and we will focus on the second method. The same was initiated
in the seminal work of {{cite:0cb6072952a5c159c1b9abc154ecc890b4ff735e}} and then followed by many others –
over a considerable period of time.
| i | 6889f1c52831cf2b3ebac9cc0cbb0cf7 |
In this work, we present a Mixed-Domain self-Attention ResNet (MDARsn) to achieve two goals: coping with domain bias among different sources or between training and hidden datasets, and learning the relationships between ECG leads and CVDs automatically. We adopt feature-based augmentation method from {{cite:0c0756309eb2dfe06653bd29fbf2aaa92b3b3995}} and Multi-Head Attention (MHA) layer to reach two objectives.
| m | 042b4bb7bb3817f49f8ec2fbcaff0cfc |
Next we turn to comparing GN+PN's performance to BN's performance across a broad range of models trained on ImageNet. As visible in Figure and Tables and , GN+PN outperforms BN in ResNet-50 and ResNet-101 {{cite:d1002d624a6f341fff57f5c69ecaf76c011069d6}}, matches BN in ResNeXt-50 and ResNeXt-101 {{cite:2d9290420c34198710d48ed6414a6ed80a5bc1f2}}, and matches BN in EfficientNet-B0 and EfficientNet-B2, both in the original variant with depthwise convolutions and with expansion ratio of 6 {{cite:9e68d5578d738d2497a7d221ead9d2dcb33c9f25}} and in an approximately parameter-preserving variant with group convolutions of group size 16 and with expansion ratio of 4 {{cite:dcf3305ec39e13606a47b976066757839a296c6b}} (cf Section ). In short, our batch-independent normalization approach matches BN not only in behavior but also in performance.
| r | 990a86929e03a1a530ed5b3eee3ebfa6 |
The comparative results, as in Table REF , demonstrate that the proposed PAS method with the CT scans outperforms the recent state-of-the-art approach in {{cite:7e4778a436eeb3145177c63d6139bff9751935c8}} by the margins of {{formula:05fbe839-5277-42ba-a0f0-a13d98264968}} and {{formula:c8094af9-8468-4d39-bc5e-9e423e7bc6ad}} concerning the mVOE and mDSC, respectively.
The authors in the second-best method (MMTLNet) {{cite:7e4778a436eeb3145177c63d6139bff9751935c8}} transferred the MRI image information from the source domain to the target CT domain through the adversarial training without considering their spatial alignment, which could be the viable reasons for realizing the WHS multi-modality approach.
The other two well-performing methods (see in Table REF ), such as Multi-label FCN {{cite:0fbae2fcc5d4ac58ce295f6fc55923af905c6511}} and Multi-depth fusion of 3D UNet combining local and global features {{cite:f1318eade26f58d9ca74ddba280fb9def3948577}}, also carry possible drawbacks for being defeated by our proposed approach.
The former strategy applied two stages, wherein the first stage, the VOIs are selected for the essential second stage. The errors in VOI selection could lead to erroneous heart segmentation results.
The latter approach employed the fusion from the different depths of the CNN network, where they fused the input block to the along with other depths to generate the final WHS VOIs. The concatenation of the input block with the same scale outermost decoder's block probably hamper the precise output, as it is also proven in our VGG-UNet and VGG-FCN8s experiments (see in Table REF ), and the articles in {{cite:33ac35debd3aaeac722dd0b87c93d91858b0f152}}, {{cite:5adce650211e97bdf2027570690d0f8d8e856e9b}}.
| r | b086d14169e467cd381ae4c4f61c79ad |
In the event the new model reveals that ODDC in stars can indeed be stabilized against the {{formula:12b5a8a4-0f82-4fd5-bc7e-8e6c3d01abda}} -instability by a sufficiently strong (but still realistic) magnetic field, this could lead to interesting observational predictions. Indeed, {{cite:beb3b600382bd835b902347a2dbbf3f8ff9b4d73}} showed the ODDC-unstable region surrounding the Ledoux-sized core of intermediate-mass stars rapidly becomes fully convective (as a result of the {{formula:c4d84aed-c012-4feb-a179-7cea4b4166e0}} -instability) in the non-magnetic case. These stars therefore have a larger-than-expected convective core whose size is appropriately computed using the Schwarzschild criterion instead.
Intermediate-mass stars with a sufficiently strong magnetic field would, by contrast, remain in a state that has a smaller convective core, surrounded by a region of weak ODDC. Asteroseismic observations of Ledoux-sized cores, should they arise, would therefore point to the presence of a strong magnetic field.
| d | f68bad44760957e4286a49948c2eedc0 |
D*0-Ix+i Iy-(H0+Iz)
,
Here {{formula:33c17ab9-5747-4830-a3a3-3a88e2ddb059}} , and
the expansion coefficients
are written in vector form:
{{formula:20b3f6a9-b149-4aa9-aed2-317e8f92cfa6}} ,
with
{{formula:3c473f07-cf24-43b7-b941-281189b1b9f1}} ,
and {{formula:041964ee-fe47-4533-bf39-854dbd028eb3}} .
The rank of the matrix in Eq. () is {{formula:78fbaed4-fc92-4696-abc9-c32d501c680e}} .
The numerical implementation of the
solver used in solving the {{formula:589eb4df-b185-4d2a-8fd1-454928439730}} eigensystem
in Eq. () was done using
object-oriented Fortran with the
MPI {{cite:a29f1eb68e8b6dc573925521df7feb2a9d35f896}}, OpenMP {{cite:8b904f736602cdb2fea3538881956d12de7949ac}}, and ScaLAPACK {{cite:b57761c5908b01ad7694e5b5bd55f65d48b16723}} libraries.
| m | 69eec706229aca477f5ab79206e6a128 |
The essential ingredients of LVE are the Hubbard-Stratonovich intermediate field
representation {{cite:b50b9243615bd42aeba8ed140a332644f24257d3}}, {{cite:f6a3d91550683fbf3d18814f738b7c6ac0ea7974}},
a replica trick and the BKAR formula {{cite:d346495827a8ca05e44f93a473e04bea65d8a3bf}}, {{cite:180f389822dbcf0fe94682dc5c1d173e2e1af915}}.
The multi-scale loop vertex expansion
(MLVE) {{cite:cfeadd6e1ffdfb626b2c695e845682065062d32e}} is an extension
in order
to deal with quantum fields when renormalisation is present.
Originally devised
for vector fields and limited to tadpole renormalisation,
it has been successfully applied to various general super-renormalisable fields of increasing complexity {{cite:cb2156bab3c6afe5a9658c83f516de8ce1e29245}}, {{cite:bd1db5c1b9a025e6dd359cfaf329b1f16fb4abb5}}, {{cite:fdd05c179b671aea518b32bd19757f6725186516}}.
Curiously the original paper and all later papers are restricted to the partition function and its logarithm (the free energy) and does not include
cumulants (connected Schwinger functions in the terminology of field theorists).
| i | c6adc5979630d67d4dd47c51389b5667 |
Finally, we should stress that unlike the scenario with the Allee effect in prey - which is currently considered to be straightforward in the literature - including the Allee effect in predators can be somewhat tricky since this can be done either by modifying the functional response or the numeric response of the predator. Biologically, this signifies that distinct mechanisms of emerging the resultant demographic Allee effect - a decrease in reproduction at low population numbers - should be modelled in a different way. In particular, the mechanisms such as low fertilization efficiency, a lack of mating partners, sperm limitation, cooperative breeding and similar mechanisms (see {{cite:f12ffa17eb1f7db9be99910a5a9255d044f23358}}, {{cite:8ac110b21afadd32d3c1bd02b3b8e898ed937fc8}}, {{cite:3f44a9d27d7b344a86afdc2badbfe5ef5a40ad5e}}) should be included in the numerical response of predator only, whereas collective exploitation of a resource such as cooperating hunting should be included in both functional and the numerical responses. It is rather surprising that this fact has not been largely explored in the literature yet.
| d | ad0676d40a30e0741e7491a8ae72fb60 |
Once again the performance of the inflated (I3D) version of our model is much better than that of the 2D backbone version, showing that by simply switching backbone one can improve on performance or other desirable properties, such as speed (as in SlowFast {{cite:f2083dba1a00289f6853ff1c424b6c5c4eea3546}} or X3D {{cite:9698dde3bc1de2bfb0df31b054f99aa836c07fd7}}), or make the 3D CNN encoding intrinsically online, as in RCN {{cite:89d89f584082137cd10af4ec01d2c1018428a450}}.
{{table:54bd4080-8f00-4a92-9c4e-58e67cd7c859}} | r | b93f02277f00e2a2c187fb630de9fc1a |
Both for black hole (BH)-LMXBs and NS-LMXBs, around the soft-to-hard state transition, the luminosity shows a fast decay stage, which is the `knee' feature {{cite:b19b196b1139e4326de4dbeb3b5ddca038c313fc}}.
For the NS-LMXBs, it could be related to the propeller effect. However, for BH-LMXBs, the propeller effect is not expected in absence of magnetic field, another scenario–the thermal disk instability could be related to the `knee' feature, which could be also related to the hard-to-soft transition
{{cite:33c89c0bc7679c6a4947b45b8d8ad71a6734e260}}. In the rising phase of the outburst in 2021 from 4U 1730–22, we notice that at the same luminosity of the soft-to-hard state transition, the transition of the hard-to-soft state did not happen, but could have occurred at a higher luminosity and not observed due to the observation gap, i.e., the hysteresis {{cite:9a29c977107135d858e09fa6dced6631ef6db490}}. {{cite:33c89c0bc7679c6a4947b45b8d8ad71a6734e260}} proposed that the transitions between the optically thick and optically thin corona are related to the hard-to-soft and soft-to-hard transitions, and thus the propeller effect is not the sole cause of the state transitions.
| d | 895352b86c41ff236165e9a8e37a9900 |
More generally, superconducting circuit QED is a particularly promising platform for experiments in quantum optics and quantum physics generally due to its flexibility and readily available set of microwave tools. Possible applications include exploring the ultra/deep-strong coupling regimes of light-matter interaction {{cite:091dec11e803542649d7a41b85c8128576a7ca76}}, {{cite:bcbe4ad187d192f8b4dfa2e864fe9ef8291b6a4d}}, {{cite:87a0631913ceefbf591f5798a9c977dcffa7c69e}}, interaction with non-Ohmic environments {{cite:d33942b5eb12d8c1ab3631aed4d9152f6d0a804f}}, {{cite:3470091163124a14abbda1b413dc057d93efab53}}, {{cite:8c9ce36ea3b5e5b24db55f374d8a1ea8ee6bc6eb}} and cooperative effects {{cite:26ddff05fc2cf52eb302798662ab03b4de0ca221}}, {{cite:153445bf15d63bfbe0da8d5ddb65cdf1620263f6}}, see also review {{cite:c1b46bd0e55b287586758fd813d605c39c2ee40a}}.
Furthermore, by using the superconducting circuit QED platform we are taking advantage of quantum limited parametric amplifiers. These, or similar devices, have become a standard part of any experimental circuit QED setup. In particular they add very little noise to the amplified signal: reduced to the input noise can be as low as half of a photon in terms of added noise number {{cite:7b4e214ba157bfc1a94909220ecc0d71b76b18ae}}. In our setup we are using an amplifier known as Josephson Parametric Converter (JPC){{cite:5c6b809ef7690104e06cbf65217769c83b15a051}}. The limited amplification bandwidth of a JPC ({{formula:657c9141-5f0e-4f22-9d40-6e92b0c1dd40}} 5 MHz), which in many cases can be considered as a drawback, allows to effectively Fourier filter the single photon signal.
| r | 85fc515057e0b8e788ba502289588ae1 |
For example, video-paragraph shown in Figure REF (b) is clearly more coherent than Figure REF (a). This can be attributed to the ordering of the discourse relations among the sentences. In Figure REF (a), the sentence S1 is the cause for sentence S3; S2 is the cause for S4. In Figure REF (a), the sentence S1 is the cause for sentence S2; S3 is the cause for S4. The discourse relation `cause' is more localized in Figure REF (b) and is therefore more coherent compared to Figure REF (a). Existing video captioning methods fail to perform such discourse based analysis to assess the coherence of generated video-paragraphs. Instead they rely on metrics such as BLEU, METEOR, ROUGE, CIDEr, etc which merely compare the generated video-paragraphs with human paragraph annotations {{cite:68e37e1f68d74d37a669aea349f3c2a480ad5897}}, {{cite:a072ca9ad8f37870407cc79618bd2e1ada1e8e70}}, {{cite:1cd8718aa6a727b77469fb4403507e58f5a08010}}, {{cite:ee47a21d3bd5a9786c34a3773a1a1709fd59cdf4}}, {{cite:72cc784819a820e499074d72613b602a76e116f6}}, {{cite:0c08d52eafba4594339e18add972708ef1884162}}, {{cite:01317d637c183852e114f53cc69c7959fd4193b5}}, {{cite:418b5790b44dfee7787623c3c0651c20ada2e280}}, {{cite:9304ed1d81cf9fd9765d0134dbe067dd8551140b}}, {{cite:8d40594865bf695151a630914c4ed6e048ad3971}}.
| i | a882b0bd820d79ef0268112a9bce10f5 |
Phenomenological studies of high multiplicity final states at collider
experiments present a substantial theoretical challenge and are increasingly
important ingredients in experimental measurements. During the last 15 years, a
dramatic improvement in computational algorithms for one-loop amplitudes has
led to a number of highly automated codes capable of predictions at
next-to-leading order (NLO) accuracy in the Standard Model (SM) {{cite:4c861a7e37fc974268bdb00c2e199d01820cf804}}, {{cite:0a5b20d75f0cdd0eb73992b7d8166ac33164a32b}}, {{cite:f404d25347133cb360db699e363b01447eb8e8fc}}, {{cite:689f5bb77b53822fd2e9e864f305e0af8a15c1b6}}, {{cite:ac97ba5aa4216768c08cb5b7f6f8a0b03efcaa4a}}.
| i | 8112926eac8fcfe37d339c2214eb6354 |
The family {{formula:ba36feca-f5f0-4c5c-962a-e3e4ae3af95c}} in Ref. {{cite:09b39929f5e6bbe83b6f8133f612425bb104a1c7}} was defined as
{{formula:b167f3d0-4f02-4409-9903-2e0303dd5243}}
| d | 0a053b2ffd410adedec624851621b80f |
It is natural to ask if the effects that were uncovered by our analysis are specific to gravity or if they would also arise in electromagnetism.I thank Norbert Straumann for raising this question. The calculation I summarize below resulted from that inquiry.
Are there interesting quantum effects on the non-radiative, Coulombic aspects of the Maxwell field by charged
quantum fields that sources them? Now, as we saw, in 2+1 dimensions, Maxwell fields are dual to scalar fields and even with the axis-symmetric restriction, they carry radiative degrees of freedom. Therefore, in the 2+1 dimensional electromagnetic analog of our model the Maxwell field would not be determined entirely by charged sources; it would have its own radiative degree of freedom. A better candidate is provided by the spherically symmetric sector of 3+1 dimensional system consisting of Maxwell and charged Klein Gordon fields. In this sector, there are no photons, just as in our 2+1 dimensional model there are no gravitons. Therefore, if we use a charged Klein-Gordon quantum field {{formula:c5aba3c8-c138-43c5-a56b-99c410db62fc}} as the source, the quantum Maxwell field {{formula:a651ffb0-eba2-405c-8ad8-b5c66594dc91}} is represented as an operator on the Hilbert space of {{formula:5b492615-ba1d-4d9b-b9c4-a785a97930a9}} . Thus, any quantum features we find in the Maxwell field {{formula:b73a7abd-a049-41dd-bf04-1ac42ae59937}} are induced by the quantum Klein-Gordon field via Coulomb interaction. It turns out that this model is also exactly soluble in Minkowski space-time. Spherical symmetry singles out a time-translation Killing field {{formula:9b5651a2-5e0e-47b8-951b-dc1fbdbd5d95}} which one can use to decompose {{formula:f2ef653d-3bfc-4aae-9eee-aafad2650884}} into its electric and magnetic parts and introduce a canonical notion of frequency for the Klein-Gordon field. In the asymptotic region, we can express the only non-trivial component {{formula:c3aa0bf0-7b82-4401-acac-2879bc1fb39b}} of the electric field in terms of the total charge {{formula:db67dbd4-68b6-40bd-9425-662d21e78853}} of the Klein-Gordon field, just as we could express {{formula:adfbace4-0488-4c2e-91af-d7de3972cb16}} in terms of the total (Minkowski) energy {{formula:a5a884b3-4307-409d-9e0b-f22c8ef10940}} of matter sources in the gravitational case. We can again construct coherent states {{formula:2cfe5e71-2c3e-40a0-a865-37ba027005a0}} in the charged Klein-Gordon sector where (for simplicity) {{formula:f675e57a-3f13-4503-950f-fd0b12e0bc4a}} has compact support on every Cauchy slice and calculate expectation values and fluctuations of {{formula:e4322cc7-c603-434e-9459-a1f3e50f37d2}} in the asymptotic region. They are non-zero. However, whereas the sophisticated non-linearities of Einstein dynamics in the 2+1 theory imply the relation {{formula:63739a31-a93c-4a95-8872-4a3d6f8a739b}} , the 3+1 Maxwell theory implies that the relation between {{formula:2f525ae8-3fda-4b7b-9f73-8036e877c7b0}} and {{formula:19b2055c-8e9b-430f-b639-f792a0367ca3}} is linear, {{formula:b7aea9a9-3c5b-48ff-842d-ed27f93921af}} . Therefore, while quantum fluctuations in the Klein-Gordon sector do induce quantum effects in the Maxwell sector even in absence of photons, they are not exponentially magnified as in the gravitational case. Indeed, the expressions one obtains in the Maxwell case resemble those in the weak field approximation of our 2+1 gravitational analysis.In general relativity, the gravitational interaction `dresses' the bare mass to yield surprising results also in 3+1 dimensions. These are genuinely non-perturbative effects that are lost if one expands the result in powers of Newton's constant. For a discussion of this phenomenon, see, e.g., Chapter 1 of {{cite:aa3b9ce9e7c8d09f468dedef9e96fd54e6d80437}}.
| d | c4be088be39628a67435214c6eb89399 |
Sequence labeling is one of the most fundamental NLP models, which is used for many tasks such as named entity recognition (NER), chunking, word segmentation and part-of-speech (POS) tagging. It has been traditionally investigated using statistical approaches {{cite:4c664ae89bb633f6ca47e75c33d308e8fb7df995}}, where conditional random fields (CRF) {{cite:4c664ae89bb633f6ca47e75c33d308e8fb7df995}} has been proven to be an effective framework, by taking discrete features as the representation of input sequence {{cite:1e088cbb1635c081e90dd0223f280025f871a46f}}. With the advances of deep learning, neural sequence labeling models have achieved state-of the-art results for many tasks {{cite:974d19c7a22464a5f1caf1d000f12c827300a9df}}.
| i | 54ec392ff715ab0335a503e84ff47d76 |
We run the algorithm using AlexNet {{cite:ddeb0be1d93e32b7c376167428e069d776f63e3f}} and ResNet-18 {{cite:e4bef8fac5b0dab92296669594a8b67fd55a6f25}} with EMNIST dataset {{cite:9761cc5ea8cd8640b2de04a06dcbad6d095a9b95}} and Cifar-10 dataset {{cite:7112206ac1532f625e49ba996b9cb42a0e8013e0}} for comparison. We split the dataset in two different ways: 1) IID Data setting, where the samples are uniformly distributed to each client; 2) Non-IID Data setting, where the clients have unbalanced samples. Details are described below. For EMNIST digit classification dataset, each client has 500 samples without overlapping. In the IID case, each client has around 50 samples of each class and in the Non-IID case, there are 8 classes each has around 5 samples and 2 classes each has 230 samples on each client. For the Cifar-10 dataset, in the IID case (resp. Non-IID case), each client also has 500 samples (resp. 50 samples); these samples can overlap with those on the other clients and the samples on each client are uniformly distributed in 10 classes, i.e., each client has 50 samples (resp. 5 samples) from each class.
| r | 586ff45f16a0804335210fa941387553 |
We test our speech dereverberation models on reverberant speech generated using RIRs from four RIR datasets: BUT Reverb dataset {{cite:0c508e25d008d112d7b838a61992155d99db67bb}}, MIT IR dataset {{cite:71e64b393d3bcb8cf00a7b76f181c3e700cbe8c7}}, RWCP Aachen + REVERB RIRs {{cite:118684d820f59ee08cc11faee2cd10a50cd9f11b}}, and VOiCES IR dataset {{cite:cf3a392469330c0f6ab4e09d969b7647901b5b62}}. The number of RIRs and the {{formula:75627842-1207-4458-907b-1d19af46cdd0}} distribution of each of these datasets is shown in Table REF .
The main results in terms of accuracy of the speech dereverberation model trained using different sets of RIRs are present in Table REF . We compute the speech-to-reverberation modulation energy ratio (SRMR) {{cite:6b20ea43abba88ff8726513c66469410216ccec9}} as a measure of reverberation. We compute SRMR for two baselines: (a) the reverberant signal without any enhancement applied and (b) the enhanced signal obtained by the Weighted Prediction Error (WPE) {{cite:94c0ba272a016de89843cacb1672570b530a5b07}} dereverberation algorithm. We obtain the best performance for the hybrid RIR generation approach for the following cases: (a) when training data consists of synthetic RIRs only and (b) when training data consists of synthetic and real RIRs. The addition of real RIRs to the training data significantly improves the SRMR of the enhanced signal. This suggests that there still exists a domain gap between synthetically generated RIRs and real RIRs. However, we observe that across all RIR datasets and for both real and real+synthetic training runs, the hybrid approach performs better than traditional geometric-based RIR generation methods. The FDTD approach frequently performs worse than the no enhancement baseline, but this is to be expected as the wave solver only simulates frequencies up to 1400 Hz and all higher frequencies in the speech are lost after convolution. In most cases, we observe that both hybrid and geometric approaches perform better than the WPE baseline. For the real+synthetic training run, the hybrid approach shows a relative improvement in the range of {{formula:9195b79d-4d94-4cbd-9192-5f0a95a48cb1}} - {{formula:77121a0e-82ea-436f-bbc5-d45e5ea96575}} across all four test sets when compared to the WPE method. The best improvement in SRMR is observed for the BUTReverb and VOiCES datasets, which consist of RIRs with the largest {{formula:113841d7-d7df-4636-b916-0a1815882463}} values. Our hybrid approach also results in an average improvement (computed over the four test datasets) of {{formula:6827da4d-4876-472a-8562-cd225ec1d56d}} for the real+synthetic case and {{formula:e54a7723-a950-44eb-ac60-1e31f92a4b63}} for the synthetic only case, as compared to using RIRs generated using only GA methods.
| r | d75340864f61ff7cb56295f41bb7b781 |
This work was supported by Grant-in-Aid for JSPS Research Fellow 22J01501 and
MEXT Quantum Leap Flagship Program Grants No. JPMXS0118067285 and No. JPMXS0120319794.
Review of the random Fourier feature
Machine learning with random Fourier features {{cite:d14ee9b8eae5eb562f54d3145dea1adb6b2cbd32}} is a widely used technique to solve the scalability issue of the kernel method. Random Fourier features technique is available when the kernel function {{formula:3c46a705-b379-40b1-a682-ef0787f56437}} with {{formula:2c295139-1a94-40d2-9060-e3a6d3269168}} is written in the form of {{formula:52826d30-d4ba-4af7-84b9-83b77ebf6b38}} . The theoretical foundation of random Fourier features is given by Bochner's theorem {{cite:086970b4c02f005f9726c774a4733166728edc2e}}, which states that a positive definite distance kernel on {{formula:26a98bd4-e201-40fe-96da-483e991a91b1}} can be written in the form of the Fourier transform of a non-negative measure. Particularly, if the kernel is properly scaled as {{formula:bc5f7443-850d-41da-912f-9bc447adc46e}} ,
the kernel is written as
{{formula:521942c8-7790-4586-85e9-42198d3adc68}}
with {{formula:0aecaf47-884b-4b7e-9eec-c48b94316e13}} as a probability distribution on {{formula:5f31d304-4169-4bc8-924e-75c50b641dc1}} defined by the Fourier transform of {{formula:03d96d3f-1989-4508-a62c-fabb6895bfe0}} as
{{formula:8e136e47-c9d4-4737-8c16-a28996933331}}
Note that the kernel is a real-valued function, and therefore, the imaginary part of (REF ) disappears; namely,
{{formula:e2cac9d2-42ea-4d9f-96fe-076cdf18ef98}} .
Thus by properly choosing a probability distribution {{formula:66f881cc-7586-4247-8b2d-595cacea3d73}} ,
{{formula:28e190c4-a0e4-4b67-8f2d-8b5ec891ec83}}
holds.
Sampling {{formula:42ad2eb2-35fa-4820-9204-9b208b7dd6a6}} from {{formula:a8078007-c068-420b-92b9-f542c6f819ca}} , we can build the random Fourier features as follows:
{{formula:92a7505d-60e3-48ba-b4da-58be119d84ac}}
Then,
{{formula:9a49a2d1-1044-4918-8e56-49e648f19eea}}
In {{cite:2bb9db0a4cdb65f11820971559b932abe5da4473}}, it is shown that the probability of the error of the kernel approximation is bounded as
{{formula:c7b3a83d-8e30-4ed2-b954-5ca378cfe577}}
where {{formula:813a3847-b9dc-4c99-b2ad-ee92ccf78524}} and {{formula:f628266a-a4e3-4860-81be-dbad85f1f56e}} is the diameter of the space {{formula:b8497553-fdff-4d54-b50b-9fd19bb1b51f}} . Namely, the error scales as {{formula:a38e096a-2364-4d4a-a900-eaaa36afa465}} .
See also literature {{cite:d24a1e4509e5639e10d896c4b9873cec45361230}}, {{cite:48bd94a2cf26cda8ee1a8f95f649bf1f5e5abe42}}, {{cite:6a51a21eb3d0e47662537879b7031e05cde7f5ba}}, {{cite:e18c965a60d5d10024efdc1955131577f9645a2f}}, {{cite:66c98bca910d2b00e4f492062792d24b2da9a239}} for the updated bounds.
A merit of the data reuploading model
In this Section, we show the merit of using the data reuploading model according to the literature {{cite:a2c1620ca4dbd790836d396bf151d39b62ec95aa}}.
For simplicity, let us consider the case where the dimension of the data is one and
{{formula:27321410-7d74-4903-957b-3ec2ab8820b4}}
with {{formula:04021594-c097-417a-9d95-94841cd2941d}} as a Hermitian operator with two eigenvalues {{formula:b4268e88-fc05-4103-a5c7-82d32dbd45f5}} . Then the model function constructed by {{formula:02392404-f35b-46e6-82df-af027232512c}} with (REF ), is limited to the form of
{{formula:605de024-661d-422c-a7b6-93feec2fa380}}
where {{formula:af24a4a0-f239-49d8-973f-29fc9200494c}} and {{formula:d90cd737-877e-44bd-ad1f-5b90b5779346}} are the function only dependent on {{formula:2c6e65ea-8db7-4419-a7c8-7fc2013c587b}} {{cite:a2c1620ca4dbd790836d396bf151d39b62ec95aa}}.
To the contrary, if we use the data reuploading model function constructed by setting {{formula:e2ca5e36-85c5-4f15-8f18-5b43c30329d6}} in (REF ), we obtain
{{formula:31aa8204-2ae7-4498-945a-1f78a558bb7f}}
where the set {{formula:3950dd98-61f7-416f-92c5-c0d9c2a8a32f}} is defined by
{{formula:cfaccfca-5810-4a6e-aee9-677595715264}}
Namely, the expressibility of the QNN model is limited because the number of Fourier components is small; the data reuploading model gives the solution to the problem {{cite:a2c1620ca4dbd790836d396bf151d39b62ec95aa}}.
Analysis regarding QKGC with RO
Let us define
{{formula:c8b64fc6-cfe6-41f9-8bd0-5443c9d5bc23}}
We show that {{formula:70cfb7d1-a18e-4a11-bcde-35906efb3a91}} vanishes if {{formula:6e031469-b563-46a5-bdff-46ff1f68b4cb}} for almost all of {{formula:d71659c4-36b3-41e3-8484-a485cbc20511}} . For the purpose, we investigate the behavior of {{formula:1c6d3b32-c1ab-4421-aa13-e81827908391}} when {{formula:9742aa51-1c2d-4781-941e-5369bd748afe}} is distributed according to the Haar measure.
More specifically, we compute the first two moments of {{formula:3015a94f-34dd-4a1b-8afc-aecc2239b90c}} :
{{formula:6abe20ba-11a4-4ffc-859a-37dd577446eb}}
For the first moment (REF ), we can use the element-wise integration formula {{cite:a034b7e6d2b51f235105ed316acefa494ce0e3d4}}
{{formula:3924bd1e-0205-4be1-ae51-6e94c946d000}}
where {{formula:7f2c76ad-9cef-4074-b4c8-5476dfa13f4d}} is the number of qubits in {{formula:20874f3c-46f5-42c2-97f1-f79fa16eba9e}} . A direct calculation shows
{{formula:914ea0e2-a0fa-4755-97c1-24a0b06518ff}}
where {{formula:463ca97f-94b5-4d94-b35b-8ee197a3a97e}} is the number of qubits in {{formula:09fd4af8-99bc-434e-a0b0-acdc769aa0b8}} .
For the second moment (), we use the Weingarten calculus {{cite:ffc25bd7fd9e8b2794b6a6b9a0c0d3e8a3726ba4}},
{{formula:e90d2e67-55ad-43e2-baee-11eed4b73d15}}
where {{formula:63202efc-01e3-4239-9c95-6ed43c2c9634}} is the set of the symmetric group with degree four and {{formula:8a6b660b-c408-4c86-82e5-79bb7e001402}} is the Weingarten function {{cite:ffc25bd7fd9e8b2794b6a6b9a0c0d3e8a3726ba4}} that takes an element of the symmetric group as its input. A direct but complicated calculation shows
{{formula:69058152-794b-4cc3-b5ff-e7ea3123d21c}}
where
{{formula:ab7e2302-467d-4767-bb7e-9cf36ced9d1e}}
in our notation.
The above computation of the first moment (REF ) and the second moment (REF ) shows that if {{formula:b3c4a0b2-5465-4b48-acc1-1e280f09e2ea}} , the first and the second moment of {{formula:0cf8285b-c875-406e-ba6b-41ba76cc4d81}} is exponentially suppressed by the factor {{formula:d708bc58-2123-45db-9b07-7f252a5522d6}} , meaning that for almost all {{formula:2046d4cf-2680-4cb0-8016-5aa4cbdf075f}} , {{formula:2293179e-909e-4373-b368-c995567da44a}} . Note that as far as {{formula:1de9dd6e-9845-48ec-a057-ad44d20723bb}} is taken to be small, the first and the second moment of {{formula:a1db8b3d-3519-4b27-9007-54bf6973dd6f}} with {{formula:9692ad0f-1a71-4cf2-8a4d-096e8d15e5ca}} is not exponentially suppressed, which is the effect of reducing the dimension of the observable.
Other possible QKGC
One naive approach to realizing QKGC without using RDM is embedding each data with a tiny coefficient. More concretely, given the dimension of data as {{formula:3bdd38e1-e07e-4b42-a917-1ea5142a5398}} , and {{formula:21a0c382-62d2-46a7-8cc9-bcf1e1df0d66}} as a {{formula:294b109e-2dce-4e0f-9a06-e0a652a8eeab}} -th component of {{formula:a812e9f2-eb57-472f-aaa8-833795fa0acb}} , let us define
{{formula:2b71a6c6-d2ba-466a-9e7f-59b48d5a9070}}
where {{formula:c08aa1c0-9b4a-4033-8f7b-1d063f427c31}} are unitary operators, {{formula:bd8fbb61-b3e4-4732-aad0-90730d6bfc09}} are Hermitian operators, and {{formula:d60812f0-6292-4d2e-a2cd-e9566b3cc641}} is a tiny coefficient.
If we define {{formula:9f683e76-07a5-454b-bfa9-b4e18170a3c4}} , we can readily show that
{{formula:a3f735cd-5e12-478e-9fd0-eabc1795c387}}
with {{formula:c3f6f218-5072-4cf4-8b2b-1dceb097c60a}} as real {{formula:567d46b1-3b92-4d04-a76a-ec8495a3ea8c}} coefficients. As long as {{formula:4d0c7d58-eb15-4fbe-839c-ee1fbf7914b4}} is tiny, the quantum kernel defined by (REF ) has a value large value even if {{formula:e8b238a8-08f8-43c0-a08a-9d8e312b4850}} and {{formula:6ed66f15-af90-4def-a8a0-152b79f0ce4c}} are different, and therefore, the QKM with (REF ) may have the generalization capability.
Another approach to realizing QKGC is embedding each data so that the number of Fourier components of the quantum kernel is small. In general, {{formula:aaa13e56-6b72-479d-b215-53cd359430a4}} can be written as
{{formula:7242df99-6eae-4490-83c5-947acf41d482}}
where {{formula:73683c1a-b85f-4b2c-b8f8-818ae5635464}}
{{formula:079c56c5-850e-4727-b9a5-d86a2fedf530}} as a set of vectors with the dimension of the data and {{formula:56cb98e5-8fd6-45d4-a429-8875f6c3eab1}} are complex coefficients. If the dimension of data and the number of vectors in {{formula:8f9fb34c-51d2-4e78-9564-96cf4642bfdc}} are small, {{formula:3a02ab63-5f3c-4ffe-b980-122a8b25316e}} tends to be large and may have the generalization capability even if the dimension of the Hilbert space is exponentially large.
For example, if the dimension of data is one and {{formula:29dc7e93-01ef-4717-8758-de7f195584e6}} = {{formula:20fe2e7e-2171-4d44-b7c9-d36d9e422f72}} , the kernel is given by
{{formula:85fd591d-645f-4969-81c1-496afbe9aabe}}
where {{formula:73402ae4-7d46-4f4e-b969-273d8f9d43f2}} and {{formula:b71d29ed-6aeb-4dc1-8969-13e4a29d9f60}} are real numbers. Obviously, {{formula:348870f7-9804-4494-a683-63bcac3e374e}} can take a value close to one even if {{formula:f8c2e8cd-75bf-43bc-8490-6199edd3afd7}} and {{formula:30f67489-1c48-4732-8100-9883392c350e}} is different.
We can naturally construct quantum kernels with a small number of Fourier components as long as the dimension of data is small and we do not encode data repeatedly.
However, in utilizing the above-introduced QKGCs, the role of the quantum device is quite limited. In the case of the kernel with tiny coefficients, once we determine the values of {{formula:6bd38aa7-36b9-4f8a-9aa0-af5c855fd7d8}} by a quantum device, we can execute all the other processes by a classical computer. In the case of the kernel where the number of Fourier components is small, we can classically pre-determine the set of frequencies {{formula:eb0480ee-95d6-4a40-be06-c1847504483e}} , and determine the values of
{{formula:7fcab0c3-a27e-445c-b502-6e5a32bf09c3}} according to the procedure proposed in {{cite:fb47e6f87665092795d249744204e7d632b97851}}. Then, once they are determined, no quantum computation is necessary. From these observations, we contend that the above QKGCs do not have a quantum advantage, and we do not discuss them further in the main text.
Proof of theorems for the feature representation of the projected quantum kernel
Proof of Theorem REF
Let us expand each density matrix as
{{formula:c5634fa4-c3f1-4c7b-8f72-517d453e8d57}}
with {{formula:9726b9b9-59d1-4c2c-841f-1576ef2ed716}} as coefficients dependent on {{formula:7c373743-9a32-4b81-b34a-6f1274a92243}} .
Then, the left-hand side of (REF ) becomes,
{{formula:350bda8b-beda-4921-a165-d2ff7df040f2}}
The right-hand side becomes
{{formula:dc353af1-556d-4ee6-80b3-0004f15075f9}}
which is equal to the left hand side (REF ).
Proof of the bound for {{formula:a5bd6485-ee66-4244-89c8-2e1281b1db43}}
Let {{formula:eea72686-54fa-4811-aaf5-8c8639b6bfb7}} be an unbiased estimator of {{formula:c37ef28f-c19e-41b1-9eb3-6e23a9343eda}} , whose value is determined by {{formula:8fa64f16-135b-4917-aed3-6d861e388d77}} measurements (each element of feature {{formula:8d7de813-e9de-48d6-b6fe-82815eabe840}} is directly constructed as {{formula:04670976-e406-4017-8060-7863d4713d7b}} ).
Then we can readily show that if at least
{{formula:4031a45b-db42-4ca5-94d0-e0a3851dae37}}
for all {{formula:9fac10bd-b11a-4fb7-87e4-d34b8f61c635}} with {{formula:9eb50299-4301-47c2-ab57-11f42b1b9959}} ,
{{formula:f5ea5d11-610a-49f4-90a3-3037e171bb04}}
is satisfied.
From Hoeffding's inequality, the probability that (REF ) is not satisfied is bounded as
{{formula:3aa18945-9d37-4f77-86d1-c2e2a8af4080}}
Thus, the probability {{formula:7e5a52f9-0c55-4254-be27-d26ac66dce26}} that
at least one of the inequality (REF ) is not satisfied in the training data is bounded as
{{formula:45fc73f3-b0ea-454c-8a54-ed8f90fdf74a}}
Conversely, if
{{formula:df027f5d-bc6a-4e7c-a98d-a127cda6a4ad}}
is satisfied,
{{formula:b3d88983-e45a-46f2-850c-07b0c36cd659}}
holds for all data.
Proof of theorems for the feature representation of the distance kernel with RDM
Proof of theorem REF
With the expansion (REF ),
{{formula:5a4325e6-f6e4-4af5-b812-3b9ba7059b31}}
where {{formula:0cd3f5bd-cdb9-4692-a386-e6c8bca7d588}} .
Therefore, {{formula:c1b3134b-3eca-4e08-a20f-6ffd0b0e1f40}} is a shift-invariant function in the sense that
{{formula:ce8ea014-5b59-4805-b42f-8b14ddaeb923}}
where {{formula:89816355-6e54-4bb5-ace0-4402d8e4849f}} is defined by
{{formula:0833927b-9cbe-4357-b637-89f581920eb5}} .
Then, from (REF ),
{{formula:11e4505e-2fa1-4fdb-bc94-f03908886a91}}
where
{{formula:52f8530b-fc11-43e3-a980-3f488830022b}}
Eq. (REF ) is equivalent to (REF ) in Theorem REF .
Proof of Theorem REF
We write
{{formula:ce8a4e41-210f-4acb-889a-7ce953ec045c}}
From the triangle inequality, it holds
{{formula:12386a1e-4cda-4bc4-b2ca-edd8d8f41d28}}
where
{{formula:46c774ec-cfe0-43c6-995b-4fa8a5e41ff5}}
with {{formula:d41b7a91-eebf-427c-a225-0d2b59a2543f}} as an unbiased estimator of {{formula:7c12daca-5bc6-41f8-9410-b2258dea9a0e}} , where each element is determined by {{formula:d1daad18-9b6d-4efa-845d-0a7f7cf051ad}} measurements.
We see that the first term on the right-hand side of (REF ) corresponds to the sampling error due to the limited number of samples {{formula:7864fb65-8e47-41f4-85bd-95ea8c08526a}} , and the second term corresponds to the error due to the shot noise.
For the first term,
{{formula:abc04f37-2111-422e-8593-ee52be8927a0}}
where in the second line, we use that the Lifshitz constant of {{formula:6fe2acfb-5cce-454e-929a-38a9cf1a0bb0}} with respect to the {{formula:520ee68d-8090-4899-8a7b-35c2c4213545}} norm is {{formula:c988b5d3-caf2-4dee-bd51-8174cef1f960}} . Thus, if
{{formula:7ea679a6-7ff7-4bbd-a8f8-62f0f5722789}}
for all {{formula:c89a45e6-255c-40f6-bfcb-188cbc53b56f}} ,
{{formula:aeec1d59-363f-4dd5-a644-2dc177a81d08}}
The probability that (REF ) does not hold is bounded from Hoeffding's inequality as
{{formula:3430e666-ef95-4581-9ac3-45da1878da37}}
where we use
{{formula:90b520ac-a1cc-42ed-8f71-a478e06bfcb2}}
Thus,
{{formula:bc9b7456-1b85-43e8-aec7-49f2bb625ba7}}
Next, we bound the second term in (REF ). Given the space where {{formula:b410cf63-a669-4cea-b225-0e24c7d69ef5}} is located as {{formula:e286d778-4751-46a4-8252-49c0df393d9c}} , using (REF ) with {{formula:71373951-ee26-4cab-9247-c716406712de}} , {{formula:bdc40204-63ad-47ea-9c7b-4447bb52a6b2}} , and {{formula:16b8ca76-795f-4550-bf32-5b693e952ac3}} , we obtain
{{formula:83ea966a-6adc-4705-80e4-d0ed0fe8f18d}}
Since {{formula:f9ecd72c-6359-403e-a51d-e78883e20aab}} , it holds {{formula:e9db275c-59e6-46d2-8c88-7c85f5d7c084}} .
Therefore,
{{formula:7dca05fe-1ec7-4ff4-aecd-d6db63a5b304}}
From the above, we observe the followings:
(a) From (REF ), with probability less than or equal to {{formula:48803344-fa11-421d-82f3-e3c017a43077}} ,
{{formula:a57cf5a2-9618-4fa7-98f4-67a96a4112be}}
if {{formula:f1a20c89-f6a2-4c43-9dd4-6023e54f136a}} is bounded as
{{formula:2dc71d15-093a-46aa-a956-cd67ec7be607}}
(b) From (REF ), with probability less than or equal to {{formula:bf211579-aa5c-438d-b66a-be17348ccf56}} ,
{{formula:bbf4cb9e-7792-497f-8fcd-0c213ee0181c}}
if {{formula:051f3b61-724d-4d5a-8a22-cf67052d3d84}} is bounded as
{{formula:d628b510-cf2a-420c-adf2-3a70d48036a5}}
Combining (a) and (b) with Eq. (REF ), we conclude that
{{formula:72312dae-5486-45d0-8fad-7b42017047b4}}
if (REF ) and (REF ) are both satisfied.
Detail of the numerical experiment
Data encoding circuit
Here let us show the data encoding circuit in the numerical experiment in Section . Suppose that the dimension of the data is {{formula:e7fc66a9-f704-47a8-a7db-a58e93db81d1}} . The number of qubits is also {{formula:5d5b287b-72c0-4a80-89a7-36595f4456d8}} (recall that the dimension of the data is equal to the number of qubits in our numerical experiment).
Then, as the data encoding circuit, we use the following unitary operator
{{formula:99dca7a8-47c6-406f-83fc-6a24a0c28444}}
and build the density operator before the reduction of qubits as {{formula:bb1f9d8e-31aa-47c4-adfe-2bc2998ce9a3}} .
Here, we define
{{formula:28ca5600-42c0-4e40-a6d3-d495a113fb1a}}
Also, we define
{{formula:00d6f947-9b52-4ff0-b11d-7cec5757c187}}
with
{{formula:91113a0a-63bd-4fd2-bc92-7b4bac3c452e}}
where {{formula:3a74c46f-02f1-4fca-bf9d-371046439b1c}} is the CNOT operator with {{formula:1a1da2d2-7939-4743-bcf7-e5e4adb6004e}} as the control qubits and {{formula:94b7f52e-f837-403a-a8db-957f3cebce42}} as the target qubits. We show the data encoding circuit when {{formula:f4638d63-bdae-4b0c-a10d-cd385328b79a}} as an example in Fig. REF .
{{figure:d555be2e-5038-4ac9-bf73-d83b60721e33}}
Nystrom method
The Nystrom method, which we demonstrate in Section is another algorithm to construct features that approximates the kernel. The procedure for approximating a kernel {{formula:aec3669d-50a3-495c-9493-eb334c898ce5}} is as follows.
We first sample {{formula:f543119e-6782-444a-a941-38035f738fef}} data, where we write them as {{formula:85be7cce-d9df-4fc3-8941-097d236b6fa9}} .
By using the sampled data, we construct the following matrix {{formula:61f9264e-951e-42b7-a5ce-26a5dfaf5ac3}} defined by {{formula:6b0cab5d-66bc-4e45-adc9-635d70557704}} , where the indices {{formula:838ad41d-01b9-44ed-8f61-c610718c31a9}} run from 1 to {{formula:aaf1b7fb-a096-4a7b-a7d1-e669fec79f96}} .
Suppose that the non-zero eigenvalues of {{formula:665139f0-6e71-4efe-9bb8-134210df68c2}} as {{formula:edebfd13-fcb8-4e4c-8580-b9006e9c0e8e}} and the corresponding eigenvectors as {{formula:7bd29a04-28c6-4fab-87eb-c08e4e002c69}} , where {{formula:07824efc-c78d-43a8-8392-c9e9ec9a78e0}} .
Given matrices
{{formula:1f30b713-7bc4-4a7a-958b-de30cc128415}}
we build the features as
{{formula:19c4a811-38e8-48a4-a3cb-e6c5337e8fe0}}
Note that the kernel {{formula:a68c9243-352a-46bb-8299-3439238212f0}} is the approximate of the original kernel {{formula:dc9b4043-3e69-40be-86cb-04464d243b49}} .
| d | 061563e4ef19c8817a32e83a85ebc321 |
The Standard Model (SM) of Particle Physics has relished a lot of success owing to a multitude of very precise predictions about the features of the subatomic world and their excellent agreement with experiments. The discovery of the Higgs boson {{cite:3fa127619d785eadd69190a91efbfde381eefafc}}, {{cite:1e0a9c57c189a72a8b8691b21a2b3939c2842994}} elevated the SM from merely a model to a bona fide theory of fundamental particles. Despite all these triumphs, SM fails to account for not only the dark sector but also several aspects of the visible universe. The most glaring issues have been the observed non-zero masses of neutrinos, the matter-antimatter asymmetry, along with the inexplicable dark matter and dark energy that constitute ninety-five percent of the entire universe.
| i | 6a4180d97034c9a23a80a2224bd73ee0 |
Although we have focused on the donation game as a well established model for a social dilemma {{cite:d47c5b7144c53f1db287a684e7af985b9cae6e22}}, our method of analysis provides general conditions for the evolution of cooperation for arbitrary asymmetric pairwise games (see Supporting Information).
| d | 0415c4faccb2f57d1fc1f7386028a4e7 |
To understand the difference between our approach, UBaPP, and the Laplace mechanism LBaPP, notice from Fig. REF that, for low values of {{formula:87652c72-8418-4d5f-8715-0986b70bb1c9}} , UBaPP outputs a deterministic estimate around {{formula:b99c4b86-c639-43b8-abd4-f53c6d3c46cf}} (which corresponds to the mean of the prior distribution on {{formula:410c07b5-4d40-4589-9c09-c290b68d0578}} ) for every {{formula:0b48e76a-f75d-4c06-b261-a984e4318cd8}} ; since low values of {{formula:1712231b-73b3-4806-ad01-3e466d7a87c8}} imply high privacy, no valid inference about the data (input) {{formula:8cdcb4b7-c943-4205-89ba-e5feaff36d41}} can be made based on the estimate of {{formula:5ca9ab73-c817-4a42-8d22-4338dda51663}} , so the estimator becomes independent of the data by outputting the same deterministic estimate for all {{formula:b95da049-34a6-4aca-805d-f0d57b0a2b6d}} .
Also, as seen in Figs. REF -REF , when {{formula:7c263bc7-34ad-4675-b924-fb026668ccab}} is increased (which implies a shift from high to moderate levels of privacy), UBaPP introduces some level of randomization, because for a given value of {{formula:9718f3bd-f845-4804-8870-b7947f8ccfa7}} the probability distribution {{formula:2d523497-1b60-435c-b851-fbb0da5a960a}} is not concentrated at a single value of {{formula:21adb33c-c681-481e-b989-295050b401aa}} . Finally, as {{formula:d337ff87-ea5e-41ef-b46f-19dde6774949}} is further increased to very low privacy levels, Fig. REF shows that UBaPP becomes deterministic again, as it tends to the standard (non-private) Bayes point estimator of {{formula:b0437f2a-9d01-4b02-8d5a-807400afbc4d}} , which is known to be deterministic for convex loss functions {{cite:04b31f38e5a6f8aaf346f6f233d2aff6794348dd}}. Also, note from Fig. REF that the deterministic estimate varies with {{formula:c988255f-4e04-4cca-9cf4-17b6ff628ab6}} , which suggests that UBaPP estimator becomes strongly dependent of the data, and hence it becomes non-private.
| d | 87169f741a6e91cd4334dfc20be6b11a |
One potential limitation of the current system is the scalability of the parallel coordinate view.
As for more complex datasets, such as Imagenet (1000 classes), visualizing all class direction at the same is not practical.
However, practically speaking, it is important to note that even with a more scalable visual encoding, there is a limit to how many classes a user can meaningfully examine at the same time. Accordingly, a pre-selection, or ranking, can be adopted to greatly mitigate this challenge.
In the future, we plan to develop an easy-to-use interface to help users select a subset of the interesting classes with different criteria, e.g., classes mostly influenced by network pruning or data perturbation.
Another potential improvement of the current system for future work comes from additional introspection ability, i.e., can we combine other model explanation tools such as saliency map {{cite:84e50a3e80dc38d1762f5b1a3cdaa1b6232c72b7}} or concept-based explanation {{cite:d6a88ef2736c0dfe4c559078337da0a855b2850a}} with the proposed geometry metric, to better articulate the exact semantics changes induced by pruning.
| d | 29e2520fedc1a2286d15d826b2948239 |
Perhaps the most striking result from these calculations is that for efficient shocks near 1000
{{formula:de359da5-c946-4cb2-b783-f5d6c878979f}} a substantial number of H{{formula:24a76924-3dc0-4495-99aa-be615411b9fe}} photons will be produced in the precursor. These
will usually be included in the narrow component, potentially affecting the electron temperature
estimate based on the broad-to-narrow intensity ratio {{cite:57b63f4b6974976c28c72c9c7138bd6ba481b7ae}}. Narrow component
emission from the precursor could explain the broad-to-narrow intensity ratios that
cannot be fit by models of post-shock emission {{cite:65a2cb41ca98c713dbd93be9308a811983e9137f}}, {{cite:20b1a1a8f789834fb2a8bd3a11dd57d6c7521603}}. In extreme cases,
emission from the precursor might also contribute to the broad component, possibly accounting for the
non-Maxwellian profile seen in Tycho's SNR {{cite:23cc3ba84566783f2db1830fd1ffe6a56edeb53b}} and generally leading to an underestimate
of the shock speed. Both of these conclusions depend on the diffusion coefficient and the electron
heating, however.
| d | 2366ceb354eb870575ef78583c87d180 |
Results also show that our use of a z-buffer outperforms the consistency-driven heuristic method of Gordon et al. {{cite:3f1866ed8beee02049da2a894ffa75b3276ad3bf}}, even when inserted to the training pipeline with the same timing.
Their method excludes every transformed point that is “behind" the predicted depth of the target image (cf. Section REF ).
Experimental results imply that even when the depth predictions are roughly reliable (around epoch 11), we should not expect points from original frame and target frame to agree precisely.
Some tiny amount of error can make a valid rotated point fall behind the target depth image, masking it from the loss calculation.
With so many extra points excluded from training, the model does not learn as well.
| r | 9ba89a8e30661d627c2c7939fabd9d76 |
We simulate our experiments using Raspberry Pi 2 as our user device with Google Speech Commands (GKWS) {{cite:76c9e37448353ffe2a7c71a1e00192d4d6ee181a}} and UrbanSound8K (US8K) {{cite:a67374a7e1f3b6eca56f02610be4148e7dfd2237}} datasets across 10 FL iterations/communication rounds using our proposed framework. In GKWS, we choose the keywords: Yes, No, Up, Down, Left, Right, On, Off, Stop and Go, and perform regular Mel-frequency Cepstral Coefficients (MFCC) extraction as performed in {{cite:28251235348c046e654d1d2ec26778c961e34ae5}}, with sampling frequency of 14400 HZ. The MFCC data is divided into 20 windows and each window is of size 50 ms. US8K, an environmental sound dataset, consists of 10 classes of sound events: air conditioner, car horn, children playing, dog bark, drilling, engine idling, gun shot, jackhammer, siren and street music. We perform similar preprocessing as performed in GKWS for US8K as well.
| r | 3625c0632ed50b365d5aa5fdc3e8dfa9 |
Of course, with the benefits of GPs we also inherit their limitations. GPs are typically slow, naively requiring {{formula:fc244933-b382-4a0a-91e2-88811d2bc59f}} operations in the number of context observations, and our model inherits this complexity. While this was a non-issue on the time series data used in our work, GP-ConCNP was noticably slower than ConvCNP (roughly 1.5x) in the image experiments, which we included for a more complete comparison with ConvCNP. Our model still outperformed ConvCNP, but for larger images the improved performance will likely not be worth the additional cost. Making GPs faster is a very active research area, as outlined above. For our model specifically it seems reasonable to leverage work on deep kernels {{cite:49bec1489a45aad0520b900bc3fd1ec8cf0f8849}} or to learn mappings before the GP prediction like in {{cite:6036157971b1605115b2d090e5ade3d94ba5124b}} in order to learn more meaningful GP posteriors that capture information about the training distribution. We do expect that our model is well suited to also work with these approximate methods, as we modify the prediction from the GP with a powerful neural network that should be able to correct minor approximation errors. For example, KISS-GP {{cite:cf345f9762669b0c8e629c71edd7d63939d3799c}} only has linear complexity, so incorporating it or one of the many other efficient approximate methods into our model should allow it to scale to much larger datasets. We leave a verification of this for future work.
| d | d6503c8edc13cfc02022bd832cc49af4 |
In order to challenge the generalization capabilities of MonoNHR, we also train and test it on the HUMBI dataset {{cite:7fd8013ee7e870ddd55af92bf5b4768a879ce3be}}, which has a high diversity of human subjects in terms of body shape, age, race, clothing and accessories. We train our method on 9822 frames, taken from 334 subjects, with various poses. Qualitative results on diverse test subjects and poses are included in the attached video. They demonstrate that our method generalizes well to new people, unseen during training.
Also, some interesting effects can be noted in the attached video.
For example, our method learns to correctly reconstruct long hair in the back, given only a single frontal view of a person.
| r | 3e204ce17696ad32a932b753290a83cb |
The existing methods {{cite:bb1b2d3c8aab1cd26aa300caf0431649b0b75f92}}, {{cite:a3026ce507c498d37283e2d9132d8d791d0c9df8}}, {{cite:d4890222b3f0f39e66151e5367c6711e314e2751}} formulates the GEBD task as binary classification, which predict the boundary label of each frame by considering the temporal context information. However, it is inefficient because the redundant computation is conducted while generating the representations of consecutive frames. To remedy this, we propose an end-to-end efficient and straightforward method for GEBD, which regards each video clip as a whole. Specifically, given a video clip of arbitrary length, we first use conventional CNN backbone to extract the 2D feature representation for each frame and get the frame sequence, i.e., {{formula:cb1d225b-f148-4714-acca-3d5780a86b9f}} , where {{formula:0e0878f3-53f8-4eff-90b6-52c557bf75bf}} and {{formula:bb45adf8-feb9-4502-bbeb-1a3727753352}} is the length of the video clip. Then the structured partition of sequence (SPoS) mechanism is employed to re-partition input frame sequence {{formula:3fd851b2-286c-4513-9fb1-d1f71cf24eee}} and provide structured context for each candidate frame. The Transformer encoder blocks {{cite:b7cae221b8f7493db6d5d75213f29b6079a09da0}} are then used to learn the high level representation of each local sequence. After that, we compute the group similarities to capture temporal changes and a following lightweight fully convolutional network {{cite:5f66bf43f311c06080ddfdd15b262be6f4c18c3b}} (FCN) is used to recognize different patterns of the grouped 2D similarity maps. We will introduce the details of each module in the following sections. The overall architecture of proposed method is presented in Figure REF .
| m | d25de418c0727ffcd85a2794f271cff6 |
Recent advances in Artificial Intelligence (AI) and Machine Learning (ML) techniques are massively revolutionising healthcare as new capabilities of automation are being applied in electronic patient record analysis, radical personalization, medical image analysis, drug discovery, etc. {{cite:94a219cf9f7dad1aeb15a1bc1cc6a12ab7ee3cae}}. The application AI and ML in different sectors of Healthcare is impacting its outcomes in new and profound ways. One of these outcomes is observed in Magnetic Resonance Imaging analysis {{cite:e7d0afafa2f5084348d69de70f91a123a7c44dcf}}.
| i | f5debef86f2fa8c0f571a60ba58ad69e |
Existing methods have a clear limitation in that they directly use pretrained features to predict boundary points.
The features are extracted from the classification-pretrained networks like ResNet-50 {{cite:882757728976d76f558842d1ebfe88c2d728593a}}, so that they inevitably contain class-specific or object-centric information.
For capturing generic event boundaries, such aspects of the features can act like noise, not providing meaningful cues for finding event boundaries.
| i | 3707bc9e2fbe7878dd92696ef5600978 |
Lemma 4 (Schwartz–Zippel lemma {{cite:04e090cd2ae90d50b669e2e787fd0d0a232a411d}})
Let {{formula:ab7bbde7-1d4a-440a-bc06-2236e743d135}} be a non-zero polynomial of degree {{formula:80f2a48b-3925-4e63-92ea-007b8745f9d2}} over a field {{formula:402d41a6-2642-4ea7-aa96-7b1232d4a501}} .
Let {{formula:d2048653-4883-4e4e-b3cc-9f7e59b6f6b3}} be a finite subset of {{formula:648634de-f557-45ea-b829-aed814021a6e}} . If {{formula:c11bb23e-3b12-4f5a-abd2-beeddf93384c}} are chosen at random independently
and uniformly, then the probability of {{formula:52f9762a-2e7f-48aa-afba-79eca7d0e46a}} is at most {{formula:203e1cfb-7998-4078-b0ea-67837b89ebbc}} .
| r | f7e257ce7fee9e579e891b3c7801e4cd |
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