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As discussed above, past works have established universal consistency for the set of all processes {{formula:7e57ea6a-a807-4d3d-bed5-4d68ac406cce}} that are stationary and ergodic
{{cite:5e2d2ddf2015e35ad6d4a862d80544b57768c779}}, {{cite:4d314566a5ad909c671061691d9c4ff46641274a}}, {{cite:dd6a65c9e9920542d8f54415e11d4ed7ae0f69d8}}, or otherwise satisfy a law of large numbers {{cite:5e2d2ddf2015e35ad6d4a862d80544b57768c779}}, {{cite:27d18986a935586f25a6bb164fdb3f234b7f4931}}.
The work of {{cite:ddbf616a94443c61abf19777889de1a1665c2ac0}} established universal consistency of certain learning rules for classification,
under a family of processes that allow the {{formula:f4c9fd11-bf38-41f4-8edf-4dcac1da43d6}} sequence to be arbitrary, but restrict the {{formula:601f666c-448f-4345-949a-b1b95f75d6da}} sequence to be
conditionally i.i.d. given a {{formula:44d68be5-55be-4e20-839d-ab8c9590fb08}} value, and respecting that {{formula:bd90a756-1f9e-42de-b284-1890508de947}} is determined by {{formula:0828b930-555b-4096-9440-5ccbbce93e74}} .
{{cite:151ed9f6256b87a1dd2dcafcf6d0836448d5555b}} has shown that any process {{formula:1c18d51c-ce69-483f-a1c5-efc4e7185b9b}} satisfying the condition from {{cite:ddbf616a94443c61abf19777889de1a1665c2ac0}}
also satisfies Condition REF .
{{cite:151ed9f6256b87a1dd2dcafcf6d0836448d5555b}} established universal consistency for {{formula:8801cc27-079c-4203-a99e-abd9d06523dc}} satisfying Condition REF ,
when {{formula:7abbc137-2735-420b-9f1a-3b1a502c6600}} for a fixed (arbitrary, unknown) measurable function {{formula:8dd47d6e-8b83-45e9-96a2-f1c409c4cc82}}
(or more-generally, when {{formula:a938e7bd-8769-4595-960a-42050ed05399}} is minimal, and the {{formula:15d9edc4-662d-4111-88bb-274246d83772}} variables are conditionally independent
given their respective {{formula:077f33dd-6d1a-4800-a9da-68abc1cd944d}} variables).
We note that Theorem unifies and generalizes all of these prior results on families of processes admitting universally consistent learners.
Another interesting work is that of {{cite:073c883907dd281bb42cb621497cb4bea7f30427}},
which restricts the {{formula:45c46146-c891-42fe-9803-26623f6f4d0b}} sequence to be conditionally independent with continuous conditional mean {{formula:23af3db8-5c33-434b-a7ba-4d6117d88bb3}} ,
but allows the {{formula:da19fafa-4dda-4b98-9222-361b24e66652}} sequence to be arbitrary. They establish consistency of certain learning rules under these conditions.
That work is, in a certain sense, dual to the present work, as we seek restrictions on the {{formula:db5a643e-e1a3-47b5-936a-77885b427f55}} sequence while allowing the {{formula:b3a14957-b52c-4b0b-aa26-3a693e8cec9a}}
sequence to be arbitrary. As such, the results cannot be directly compared.
See {{cite:151ed9f6256b87a1dd2dcafcf6d0836448d5555b}} for a thorough summary of past work on universal consistency for general families of stochastic processes.
| r | 3697c3954545b72b36c5461829d2a1ce |
The NEGF formalism {{cite:b929ef282c45a0715502ca4be72e506adde1a0ca}}, {{cite:aaa2476c8652a59e090df6f14eaac1f469f97904}} is a sophisticated framework for obtaining the transmission and other quantities in realistic devices.
The retarded Green's function in the atomic orbital basis is given by
{{formula:01230398-ff9c-4bad-8c5d-6b01a6c686cb}}
| m | e0d7b0da74c6a6a76db41d18ad5f4432 |
First of all, we divide each image pair {{formula:76e8a087-72e6-4b6a-8b12-c70d27b6442f}} that is captured by the same device from RealSR {{cite:3510f454aba2ec73b89ab0afa01d6e48efe44412}} into {{formula:56c962da-8d8a-4713-9599-679dd2d24516}} pairs of overlapping patches {{formula:d3364e06-cfa4-428d-9a49-b8f158a7a099}} , where {{formula:50500340-4f64-4c65-8861-69717c1c8118}} .
For every pair of patches, we follow the procedure described in Fig. REF to obtain the cutoff frequency {{formula:e4f27a6a-28c9-4532-822a-d24750032508}} . More detailed process can be found in supplementary material Algorithm 1.
{{table:1d79c270-80e1-403b-9148-3dae029f189c}} | m | 0388cddffb1d2ffca98f8011e7f23b20 |
Where {{formula:a76585fd-2078-4768-8857-db5607c04e71}} and {{formula:d719c6b8-2726-45f1-a756-e563d9063544}} are the rms radii for the neutron and proton distribution respectively. The addition of {{formula:8b6b0a2c-5197-4ece-9023-48181144099b}} cross-coupling into the Lagrangian density constrains the NST of finite nuclei. Fig.REF (a) shows the NST {{formula:1822c0bf-3068-496c-8e4a-c08aaaf27489}} for {{formula:1d2232e6-5ee6-42b4-9eba-40858d7433d0}} Ca to {{formula:b8ccd83e-d746-45cf-a48c-530de7949abe}} U nuclei as a function of proton-neutron asymmetry {{formula:9a6779d2-7687-47fc-91b9-7cb056641f0c}} . The calculated results of {{formula:95436c29-bf93-4eed-bd0e-b46f835bac5a}} for NL3, FSUGarnet, G3, and IOPB-I parameter sets compared with the experimental results deduced from the antiprotons at CERN {{cite:0315fa6cc0caddacb62044641d7b5015b3ea8c53}}. The experimental data with the error bars shown for 26 stable nuclei ranging from {{formula:9ee00baa-3131-42e6-9a7f-33d19f6a845d}} Ca to {{formula:545908fc-0784-458c-b227-30314da9db0c}} U. The shaded region (orange) is the fitted experimental data which shows an approximately linear dependence of NST on the relative neutron excess of a nucleus. The results of the parameter set G3 and IOPB-I are also shown in Fig. REF (a). The values of the NST of IOPB-I set for some of the nuclei slightly deviate from the shaded region, because IOPB-I has a smaller strength of {{formula:8a1fbbe0-1291-40a2-a333-8a557195ba1d}} cross-coupling as compared to the FSUGarnet set. However, the G3 set is almost compatible with the experimental data. The calculated values of NST for the {{formula:19069c71-bee6-4581-b3ad-1f534097861d}} Pb nucleus are 0.283, 0.162, 0.180, and 0.221 fm for the NL3, FSUGarnet, G3, and IOPB-I parameter sets, respectively. The calculated values of {{formula:7dfc8177-e850-4947-8cb0-690eb6002cd0}} for G3 and IOPB-I are consistent with the upper limit of {{formula:cdf5da33-65bc-4517-9b8f-c46a22899fb3}} fm, which obtained with the help of correlation between the NST and with canonical tidal deformability of the neutron star {{cite:7b514ab5c34d28222be6dd6913f4612e7559987d}}.
{{figure:fdf3d2be-b7ce-43e5-8b75-ee06565f606e}} | r | 0b675fccc4c30a5d88c1eecc88d8073f |
Notice that for the limiting case {{formula:3eccdcec-ccc8-4a6a-ad01-58b140efc868}} , Eq. (REF ) recovers the result {{formula:36138716-4b07-4382-9664-57e54a2bd335}} obtained in Ref. {{cite:2429b62754b6414a5b01b571e54136053699227d}}. The behavior of Eq. (REF ) is typical of first-order phase transitions, as observed for example in opinion dynamics models {{cite:04dddf6e6605efa66eba5027f30b8d1ef2e2f027}}, ecological dynamics {{cite:6b54d283e3257553e65a9cd9e6001d1a0eb6e6a7}}, {{cite:30bdfc7adeba0b6d69b67904dbd435b62a773cf0}} and quantum spin system with long-range interaction {{cite:eccfa102c8aedf1bb8f9a9d96eb469c1ea4340fc}}. Thus, taking into account the solutions given by {{formula:f825ab88-c177-4c18-b1ca-96a6c057844a}} and Eq. (REF ), we expect that the fraction of honests {{formula:fe465520-5d5b-4acd-9a9a-bd316f0bc389}} presents a jump at the critical points {{formula:3ce828af-7c23-4025-8603-86931ad2a330}} given by Eq. (REF ). In such a case, the order parameter {{formula:ea3c0824-0339-4fba-bdc4-bc33c380c0b9}} also presents a discontinuity at {{formula:f2a27d99-0e4a-4e43-8e14-41989aa4954d}} . Taking into account the two solutions for the order parameter {{formula:67545cc2-93fc-414f-acf9-ae3261d4a52c}} , namely {{formula:965bd9a2-5df1-4b92-a728-4dcde38fb8d6}} and the other given by Eq. (REF ), we expect to observe nonequilibrium first-order phase transitions in the model at the critical points {{formula:22138610-411f-4490-b406-e3433a031116}} , obtained in the terms of the models' parameters and given by Eq. (REF ). For {{formula:01467b10-36c3-4719-aeee-f740750ec8a0}} we have a phase where the three fractions {{formula:de72a60d-49dd-400a-b507-5adf24b1dd6c}} and {{formula:3659ab62-7f6c-424c-9bb1-5f155af90c40}} coexist. On the other hand, for {{formula:1fa5c79f-28e3-4d4f-95ae-ab18874923ca}} , the valid solution is given by {{formula:f442709a-6b8b-401e-85e1-e8ad5a7ef54f}} . In this case, we are talking about a first-order active-absorbing transition {{cite:e5c76ac18a5d577435bb77dce978b0e13f27d5b9}}, {{cite:f42318565a067296037488f3424688a554f324db}} that separates a phase where the tax evaders disappear of the population in the long-time limit and the population is formed only by honests, from a phase where there is a finite fraction of evaders in the long time. The susceptible agents also survive in the active phase, and they disappear in the absorbing phase. To the best of our knowledge, it is the first time that an active-absorbing nonequilibrium phase transition is observed in models of tax evasion. However, such kind of transition was observed in a wide range of systems, for example coupled opinion-epidemic dynamics {{cite:609b51c69893e977950c8bc3ae227a2b321b5a7d}}, one-dimensional long-range contact processes {{cite:6180587d0261530b46e0188c415a7d62e8861726}}, Ziff-Gulari-Barshad (ZGB) model {{cite:83b759a39383d6e1b94ce2d335471c91d3895536}}, {{cite:17490b30d47408f9d05261f8bb5333d4cab101b4}}, granular systems {{cite:1c089d8014a5d908669c009a2ab8da8d7b025bb3}}, opinion dynamics {{cite:74b7f5b2fe3a641c1fc8f9705524f92752431147}}, {{cite:57b857f91628d3422b6e1085470c021839a4a5d4}}, naming games {{cite:a69416e1b819a89ad786b640c4b53bab25797d6e}}, {{cite:6076a31723770453c0234ced888428debb84fa5e}}, symbiotic contact process {{cite:c46a68b324c26fc0594adb0c28590d1549be49b5}} and majority-vote model {{cite:df2d604a733b5fc579e9f388353024ed6926b9c4}}, among others.
| r | 05ebeafa94e82d44d18e739124dc5322 |
where {{formula:24456b7a-61f4-46e4-ad7d-ba0ebe8511a7}} is the blur kernel applied on {{formula:b450ad06-81fc-4d21-859f-cad760641cab}} , {{formula:88a4a744-ff29-474b-b8c6-c4ffb5df156f}} denotes convolution operation and {{formula:8eb4a12d-eee1-4ca0-b3d4-fd084cd3b4fe}} denotes downsampling with scale factor {{formula:7bcdc2cc-e2e4-4b87-9632-42af64118a42}} .
Previous blind SR approaches {{cite:fe77bca8665e80d2452d589d7db075ed84e53179}}, {{cite:c967de1a9f1ee60050ba0e5927dac7daf5c3af71}} generally solve this problem with a two-stage framework: kernel estimation from LR image and kernel based HR image restoration.
| i | dc59de0f4843f03a91b9d0d6342ebb66 |
Recently, the study of network science has proliferated in research fields such as social science, biology, and data science, where it has offered new insights through studying network data from a graph's perspective. A popular subject is to identify central nodes through the node centrality {{cite:9fb51b8c23bcf51b3c2dd762a64d84934e457e55}}. Node centrality ranks the relative importance of nodes with respect to the graph topology, and it is useful for identifying influential people in a social network, frequently visited webpages on the Internet, stocks that are important driving forces in the market, etc. {{cite:715f879dcdc38f7077e77b432c76796caf9b1a0d}}.
A number of centrality measures such as degree centrality, betweenness centrality, eigen-centrality, etc., have been studied {{cite:e587e00b8588352e9bcba3e8962ff3d65bc7a2f9}}. Among others, the eigen-centrality measure, defined as the top eigenvector of the graph adjacency matrix, is popular as it takes into account the importance of the node's neighbors as well as the node's own degree.
These appealing features have led to the wide adoption of the eigen-centrality measure, for instance, the PageRank model {{cite:442c6fc5e055721c320c7d9de59900d259904b59}}.
| i | 2a3eb61f205f213d33038ef11c0f8e11 |
Observe the world to form beliefs about it:
We typically observe the world in an unsystematic and unstructured way, so that the observations have a sampling bias.
Applying the scientific method helps reduce this bias.
Exploratory and assessment studies are conducted to form these beliefs.
Explain causes and effects by forming a scientific theory:
The scientific theory underlying the example is that deep neural networks are models of the brain, although simple ones, and as such intelligence could emerge from them {{cite:5f9e9d91aa92e22b4cd3d23d95fd17a6005279c6}}, {{cite:25ea8dbbc3b0565640422ba62021c01097c5795f}}.
Formulate a genuine test of the scientific theory as a hypothesis:
The hypothesis that is tested in the example is that the performance of biological inspired deep convolutional neural networks is competitive with human performance on computer vision benchmark tasks.
Design an experiment to test the hypothesis and document the experiment in a research protocol:
Ideally, research protocols documenting the experiments should be written ahead of them being conducted {{cite:09fecab418215ba763d27b72bb2a74f8e1df81e7}}.
Experiment design has traditionally not been a very structured process in computer science.
Often, making the research protocol and the experiment is an iterative process in which the experiment design, implementation and execution are done interchangeably.
This could be considered HARKing or hypothesizing after results are known {{cite:02502e3f308e77d3e1711f9561358c5339452804}}, which is not good practice.
Implement the experiment so that it is ready to be conducted:
The target of research in a machine learning experiment is often a system or an algorithm such as the biologically inspired deep neural network architecture of the example.
In figure REF this is called the target system, and it is a piece of code that is written by the researchers themselves that has some potential properties that they want to test.
The experiment has many more components, many of them are also code written by the researchers.
Often, the collected data requires pre-processing.
In the example, the raw images are translated, scaled, rotated and distorted.
Hyperparameters, random seeds, the learning rate, the number of epochs and so on are configured in the experiment setup.
Another piece of code could define the experiment workflow.
Figure 1a in the example {{cite:7994723d61f0f5d6f5e07e31903e18cb597dec94}} illustrates the pre-processing workflow.
Also, data must be gathered.
In this case the data is compiled from six different computer vision benchmarking data-sets.
Furthermore, the experiment must be run on some hardware, which in the example is a graphical processing units (GPU).
Most experiments relies on ancillary software to run the experiment .
Ancillary software includes but are not limited to the operating system and software libraries that simplifies the execution of the experiment.
Conduct the experiment to produce outcomes:
Conducting a machine learning experiment typically requires executing software on a computer without any input from the outside world except for the training and test data.
The outcomes that are produced in the example are class labels for the images in the test data from the benchmarking data-sets.
Analyse the outcomes to make an analysis:
The analysis typically consists of visualisations of the outcomes and metrics that are computed based on the outcomes.
In example, the analysis is to compute error rates and display them in tables.
Interpret the analysis:
The analysis has to be interpreted.
In the example, the analysis of the outcomes show that computers have lower errors than humans on these tasks, which leads to the interpretation that deep convolutional neural networks are competitive with humans on widely used computer vision benchmark tasks.
This interpretation is the result of the experiment.
Update beliefs according to the interpretation:
Scientists update their beliefs based on trusted results and interpretations even if they are the exact opposite of previous beliefs.
Surprising and counter-intuitive results might not be trusted immediately, but they could spur new and different experiments to increase the trust.
Although the analysis (low errors by deep learning methods on visual benchmarking tasks) have been reproduced many times {{cite:5f2ed485c33bb168b6bef24a96aa61b5907521c5}}, the claim that deep learning achieves super-human performance is still debated {{cite:fdd017df84184e2b766f95e7076c4bbe616aae10}}.
Observe the world systematically:
To be a trusted source of knowledge, experiments must be designed to remove biases.
As many data-sets are biased {{cite:14e350a96a402acb3701c7e2d06ace4e4ceb6e00}}, the bias can be reduced by conducting the experiment on several data-sets, similar to what is done in the example.
| m | efeed316ba52aac0c96a0cdee3664e29 |
By Hilbert's Nullstellensatz {{cite:3b93c6fbf8c7c953601ae6d73412ace75a39b693}}, a polynomial {{formula:04b397f3-811b-4125-822e-1f484855e4a9}} belongs to {{formula:f49bd710-693a-44e2-979b-236dba01aa0d}} if and only if {{formula:9ebca9e4-60cc-46dd-97fd-12c997f88e7d}} . In other words, the map {{formula:d743944f-6994-4940-844a-89c81bda7ee0}} is injective. It is also surjective: there exist Lagrange polynomials {{formula:3cb7754e-e256-4789-b58e-fd2d0fc9e340}} satisfying {{formula:7ab74950-e287-4d20-bd28-a42a5a950a12}} if {{formula:278a35ab-e8e0-4cac-9ad0-218f7e2d83ca}} and {{formula:e3dd6931-1f35-4594-9c69-a036cc5fed6e}} for {{formula:f7e86aae-6314-420d-a469-4b76576d1e98}} {{cite:ecb564181eeff18e84b04e693ec1b4973fd5ee12}}. We conclude that {{formula:042ca469-5cb9-4f08-a09d-ae333ef549be}} establishes the {{formula:29d1ee0c-bbdc-4204-8437-7c9bb330a729}} -vector space isomorphism {{formula:c70dd229-704e-48d1-b6a9-f03803f1caac}} .
| m | f52adfe7aaacf8f34355d7385701aefc |
The adversarial MAB {{cite:c5c886262f432516c8dd1b2f27e494131056359b}} is a paradigmatic nonstationary problem. In this model, the bounded reward sequence at each arm is arbitrary.
The performance of an policy is evaluated using the weak regret, which is the difference in the cumulated reward of a policy compared against the best single action policy. A {{formula:70986d37-1c8d-434a-ad13-8de005a34d26}} lower bound on the weak regret and a near-optimal policy Exp3 is also presented in {{cite:c5c886262f432516c8dd1b2f27e494131056359b}}. While being able to capture nonstationarity, the generality of the reward model in adversarial MAB makes the investigation of globally optimal policies very challenging.
| i | e9c523f1ed32470521574bbe9cb75754 |
As shown in Eq. (REF ), the modifications in the spectrum of the primordial GWs at particular frequency ranges can be related to cosmological events occurring at corresponding temperatures.
In this sense, the GW spectrum represents not only a snapshot of the early universe but also a movie looking deep into the very early universe, cf. Fig. REF .
Different GW detectors sensitive to different frequency ranges can give snapshots of different epochs,
providing us with a possibility to reconstruct this “cosmic movie" by combining the results of various GW observations.
The SMASH model can be seen as a benchmark model for such a strategy, as it is a minimal model of particle cosmology,
allowing us to describe the whole thermal history of the universe from inflation until today in a decisive way as explicitly worked out in this paper.
Furthermore, one can also think of other minimal models of particle cosmology, such as for example the
Neutrino Minimal SM ({{formula:7553be9f-e0a1-4b05-bbf3-0d0f85578b6b}} MSM) {{cite:e4cb032c20745745a95c92699d50d459bf7a4dc3}}, {{cite:e780b730ff2de50c424db1fabbfae3993be398f1}},
a model based on a {{formula:3b42753a-5a93-43a9-a335-22a95144f237}} symmetry {{cite:5e462380385249e4be78a6e4301aff3d9cf64a23}}Attempts to
estimate the spectrum of GWs predicted in the model proposed in Ref. {{cite:5e462380385249e4be78a6e4301aff3d9cf64a23}} were made in Refs. {{cite:67c9570897a3bcc0784cdfca9876174ee97ab8bd}}, {{cite:361d3c9f94c0a6abdbe2cfbe3b1917159f3d4b1f}}., and a model based on a flavour-dependent global {{formula:f17144c8-a2a2-4675-9c12-bebada6938ce}} symmetry {{cite:adb818b2be13b749c54516d6f9aa558cf09a52a6}}, and study the spectrum of GWs predicted in such models.
The formalism developed in this paper may also be used for such endeavors.
| d | 4bed950fbf92cd07d0488f3f1bb7a4a5 |
There is also evidence {{cite:5d7fa9d215ce6f3d675e42de56fefe1facc142d4}} that multi-task learning can improve the performance of each individual task . Rich Caruana's PhD thesis {{cite:9dd1307d3ce84315bc0bb134c7db3edaef5f370a}} was one of the first to study this topic, and his work found that performance improvements in multi-task learning come from extra information in the training signals of the additional tasks. There are different mechanisms that produce this effect: statistical data amplification, attribute selection, eavesdropping, and representation bias. Caruana also mentions that backpropagation automatically discovers how the tasks are related in a partially unsupervised way.
| m | cf64a6a46e2c1e009dac3c153ad98a96 |
One of these areas is exactly solved models, where the elliptic beta integral {{cite:c353bed5f35a17f63aef23149ec5ab8e2cb46595}}, a central identity for the theory of elliptic hypergeometric functions, is known to be equivalent to a Yang–Baxter equation {{cite:b0b5152b12e8175d14487e2c374c986640f4b8b6}} (more specifically a star-triangle relation), which is a fundamental identity for integrability of two-dimensional lattice models of statistical mechanics {{cite:5e0a4b763c96a919c985ef529a1b337fbbefe765}}. Specifically, the Yang–Baxter equation implies that the row-to-row transfer matrices of the lattice model commute, and following the method of Baxter {{cite:03665671a0636576c4d1b5735e3683384ef001bc}}, this can be used to solve for the partition function in the thermodynamic limit. Such lattice models related to elliptic hypergeometric integrals are quite general {{cite:6e1859291a859e0331b1fcfe0d915c23e86e167e}}, {{cite:2d77d11cbafe283ee2b0da037b7be326dae0794f}}, {{cite:5fd66afc88131d149b47592005b972183f0d7507}}, {{cite:b0b5152b12e8175d14487e2c374c986640f4b8b6}}, {{cite:c0c73d1571974578a80bbb2b3c54a69ecfc2af41}}, {{cite:59c9d1d05dc1f5215191146ebf46df97e741e9ee}}, {{cite:00d781b9bcdfc385c7cd638b89c1e491a7d14791}}, {{cite:432b7a5cead040b23bc6ac554be43857a82322a6}}, {{cite:294653df51cba6d53fbee941f9359c59775713cd}}, and reduce to many important integrable lattice models of “Ising type” (e.g., {{cite:7cceb411ed9eba6d254caf3988e7df3d0e1db54f}}, {{cite:819f79a000cadb05b4c5dc6d6a18f3a95199bfef}}, {{cite:805abf481f6544a3fe985811277f7224ad05c28f}}, {{cite:0c7d900bb46f5fee690641e64619f4e117846364}}, {{cite:ea58712c7202e3c78823b1be0d4632d11baf5410}}, {{cite:a819992f9662bdbf268800c66b5c42671a57cf45}}) as special limiting cases.
| i | e16eb86556b14eeb492c7e67289a2e7f |
Table REF shows the results of the proposed models on the ETIS-Larib Polyp DB. In this case, we do not compare the results with UNet and ResUNet, but compare the models directly with ResUNet++ as it already showed superior performance on Kvasir-SEG and CVC-ClinicDB {{cite:ba6765f6ec181067da79f60c43b4e6f324c9c6bb}}. Here, there are only marginal differences in the results of ResUNet++, “ResUNet++ + CRF", “ResUNet++ + TTA", and “ResUNet++ + CRF + TTA". However, ResUNet++ achieves maximum DSC of 0.6364, which is 0.84% improvement over SOTA {{cite:dd203b5b61438d08bfb07ceb136591be1852fac0}} and mIoU of 0.7534 which is 18.64% improvement over {{cite:dd203b5b61438d08bfb07ceb136591be1852fac0}}. The recall of ResUNet++ is 0.6346, which is slightly higher than the proposed methods. However, the precision of combining ResUNet++ and TTA is higher as compared to ResUNet++.
| r | 669c0da887fd67bf8f1663ca82460326 |
Most existing sensor fusion methods focus on the LiDAR
and camera fusion problem. MV3D {{cite:36a769590a64495a7f7d0e817939b2343bc4ef31}} extracts features from the
front view and Bird's Eye View (BEV) representations of the LiDAR data,
in addition to the RGB image. The features obtained from the LiDAR's BEV are then used
to generate 3D object proposals, and a deep fusion network is used to combine
features from each view and predict the object class and box orientations.
PointFusion {{cite:261162bfba5d1f98880a975c83c3ecb897d1d4f4}} processes the image and LiDAR
data using a CNN and a PointNet model respectively, and then generate 3D object
proposals using the extracted features. Frustum PointNet {{cite:e59270ab6c7420b0c9fa38561b5de5329d7a919e}}
directly operates on the raw point clouds obtained from an RGB-D camera
and uses the RGB image and a 2D object detector to localize objects in the point cloud.
| m | ca0c1a37ea43d3e3a43536ef9efb4f85 |
In traditional sociolinguistics, weak ties within a social network have been linked to innovation and language change.
Yet most studies only use indirect evidence to infer the underlying network types {{cite:7320cce3a33112a7107be9bd5553195a56b45478}}, {{cite:fcfb62bc650ed0e27a65000ab0e145224889919e}}, {{cite:0cdf85f98beafd0686766768393535778de50694}}.
Our quantitative analysis suggests that multiple structural properties play a role in lexical change. The overall network size is the most prominent factor in lexical innovation and survival, as large communities provide the base population to create and use those neologisms. The effect of network size has also been emphasized in other network studies of language {{cite:641d6c42ec8aac5301506b5953284923319648fa}}, {{cite:b25401b60b92fc6c82b377c50d3a8e04af6b497a}}, {{cite:66c5e4889f915c119aec892b8a3da1fbf550b4af}}. However, sheer size is only part of the story, as dense edges between users, the lack of separate local clusters, and rich external connections also promote both lexical innovation and survival. Dense connections within and across communities increase the visibility of neologisms so that they can be imitated by other users, as exposure alone predicts users' information spreading behavior {{cite:900eb8e46477a4dbafd94c47e77e7477762942d9}}. In contrast, local clustering tends to separate networks into disconnected parts, slowing the spread of new words. These structural attributes are found to facilitate information spread in online social networks {{cite:5478d422043ef964e1c809014ba1a10e2a8c14d8}}. On a broader scale, our results suggest that the lexical change process in online social networks may be similar to other information spread processes {{cite:f29910d338086b00ea44f986e9a2b5fad7874f10}}.
| d | 3e17a6cc7f0c1492872ae7c516440fc6 |
Professional politicians and political organizations use Facebook to share announcements and information about what they believe to be interesting events in order to reduce distance from their constituencies. News organizations also rely on Facebook pages to encourage and support interactions with their audiences. Compared to ego networks, Facebook discussion groups are thought to resonate better with users who have weak ties with other users {{cite:567e4657d2af4e0cd1b03e8fd76ddde3166decd6}}. According to Granovetter et al. {{cite:1636fb3215feb4f882bc117c4d1188057ff0757e}}, individuals with few or weak ties tend to be deprived of information from distant social system locations, and are therefore confined to news from local sources and the views of close friends.
From attacker perspectives, the interpersonal networks that exist within and between Facebook discussion groups are more suitable than personal walls for launching attacks. The diffusion of rumors and other bits of information tend to be moderated by friend relationships, meaning that they are more likely to flow through groups of individuals with weak ties. Facebook discussion groups are much more popular than personal walls — three examples are CNN, Fox News, and The White House. Since these and similar groups do not have privacy setting concerns, they are invaluable for researchers interested in conducting communication and cyber security studies.
{{table:7108f830-29f2-47c6-b27a-818eb15d91ca}} | d | 75484e2b4bdc30f1117d457135132233 |
This experiment investigated the utility of automatically extracted word level prosodic features from child-directed speech as predictors of age of acquisition of words. We utilized a generic set of 88 prosodic features which have been previously proposed in the literature {{cite:daa4a13447a62423374e1abaf1c8b5b232c1aa64}}.
| d | 4e4b1c1792f18a32a01422a2b76e8122 |
Figure REF shows the deformed images and the velocity fields obtained in the 2D simulated dataset
by diffeomorphic Demons {{cite:c1c31a324274c255286d382530b6f69e8a535a76}}, a stationary version of LDDMM (St. LDDMM) {{cite:a16e2c01cf93fb4e4059bdc766eb9c4c9206eb33}},
the spatial version of Flash {{cite:4e9c337fb994441535c71c9333dd2549d42ba73a}}, and our proposed SVF and EPDiff GANs.
Apart from diffeomorphic Demons that uses Gaussian smoothing for regularization, all the considered methods
use the same parameters for operator {{formula:f399c4ad-9968-4e52-b675-17f80fb59274}} . Therefore, St. LDDMM and SVF-GAN can be seen as a model-based and
a data-based approach for the minimization of the same variational problem.
The same happens with Flash and EPDiff-GAN.
| r | 0a8efc9673baef39328687e9b2c93877 |
Although great improvements have been achieved by existing lightweight SR methods, they still suffer from several limitations.
First, hand-crafted lightweight SR models like IMDN {{cite:48e5ee3aed2d6b5eab0f9aab17c05e435a080a45}} and RFDN {{cite:817a4ab17d140a9dddb99d68995a726442e3897a}} adopted several {{formula:2474f546-6eb9-4de2-af57-fe05ed1e7803}} convolution layers with large amount of parameters and Multi-Adds.
The building blocks designed by these methods with the same three {{formula:7d0bea96-e6a3-475c-a699-905c474d1e12}} convolution layers can also be suboptimal and lack flexibility for SISR tasks.
Second, the network-level architecture of these methods only considered concatenating the output features of the blocks at the end of the model while omitting intermediate information flows among the blocks, which have been demonstrated to enlarge the reception field {{cite:928078719f21d22911e941d0efd572260b5524f6}} and could be useful for improving SR performance {{cite:a085a0e6f50566efb857ffb0f85c28a0098aca8b}}, {{cite:16a17f9878f9d09b58f19c5ecf3f9bcc1275f1e4}}, {{cite:07e599586c0d1db10c37f1128f024a966300391d}}, {{cite:c705c12fcc697f17cafe1afcb432d8ce77164e8d}}.
However, the network cannot be connected too densely in order to achieve an efficient lightweight SR model.
Therefore, it's important to find which connection benefits the cell most to improve the performance of lightweight SR models while keeping a slightly low model complexity.
Finally, Most Neural Architecture Search (NAS) based methods for SR tasks were based on reinforcement learning and evolutionary methods which are time-consuming and require a large number of computing resources to search for appropriate models. Furthermore, they failed to achieve better peak signal-to-noise ratio (PSNR) or structural similarity index measure (SSIM) {{cite:f14193a4869a1aef431ac5c12fcb4487943290c8}} results with searched lightweight SR models comparing with the existing state-of-the-art (SOTA) hand-crafted SR models.
| i | 1fd2ee38e23a4406d5a2718bf9c70055 |
Finally, as we have emphasized connections to the {{formula:c94ec145-286d-4ff7-9456-a62cc5370521}} case in this work, it is worth noting that for {{formula:27d76746-5291-4721-a3a0-c355f38d0c51}} the Euclidean boundary conditions with an interval of Euclidean time between two brane boundaries can be filled in in two different ways: we can have a piece of the bulk BTZ black hole bounded by a connected ETW brane, or a piece of vacuum AdS bounded by disconnected ETW branes {{cite:979bfc5f4103ccd711e680d496e53ba0b42ace9f}}. We have discussed the analogue of the connected solution; is there an analogue of the disconnected one? This requires an analogue of thermal AdS for the hyperbolic black hole. No such solution is known, but in the appendix I suggest such solutions may exist. They are more difficult to construct analytically; it might be interesting to study them numerically.
| d | c275fe881a8803da4800b286eb0742af |
Lower bounds: Proposition REF is a worst case result for worst case type, adversarial errors. It would be highly interesting to derive lower bounds for minimum norm interpolated estimators that hold in more optimistic scenarios, for instance when the {{formula:f65fda25-5ae1-47b7-9425-6814a08437de}} 's are independent Gaussians with mean zero. In {{cite:0adbf327d249c057d1f2d79b1c765fb18bcb848e}}, the authors consider sparse linear regression with minimum {{formula:8ed2ca2c-b43b-411b-86a2-3676d2d5b949}} -norm interpolation, basis pursuit. They show that when {{formula:25631664-824d-4413-8f7f-1c411cb0023e}} , {{formula:14540946-c8d2-4efa-97bd-909f9395c2e8}} and {{formula:cf7cb454-f725-4d71-b502-c8784d3ad3ee}} , basis pursuit fulfills with high probability
{{formula:66e15c1c-0a39-419d-a05c-f04bf91d4530}}
| d | dd5ce9b0868384bee5eb38fed7069da7 |
Note that PPGM focuses on privacy protection after being deployed in distributed computing environments, but not during the model training (e.g., usually achieved by federated learning {{cite:a867ccd69455ab64952ad1943acdc3d4d577b999}}, {{cite:15d29e85032bc1d0fbd7f827c618ce2a1d80dee0}}, {{cite:2d047818c66f0433cfa25fcb9ae503103c0f5771}}, {{cite:d716047aabdac8147b083aaf87391ac73571ccdd}}).
However, in real scenarios of graph similarity learning, the privacy issues for deploying are more important than those for training.
Most similarity labels in the training set are generated directly from raw data of the given pairs of graphs, making it unrealistic to consider privacy protection while training neural GSL models.
| d | 508048742979ac21523afc61fad1f1af |
Discussion: Huang {{cite:1f7577f4773056c8fe74e3983f6120f189bb7906}} uses the interpretability technique to design a heatmap to explain the DNNs output, facilitating a more accurate detection for the poisoned model. However, their method requires a clean dataset encompassing all classes. Different from their method, our scheme only needs a generated random matrix, and it directly uses the probability distribution of the {{formula:21b91ea1-8dd8-49fc-a1b6-74a05b301c85}} layer's output to judge the quality of a model. Kolouri{{cite:0e0eccc7736a086ded080619389ade060084123d}} feeds a group of Universal Litmus Patterns (ULPs) through a model and pools the logit layer's output to classify it as poisoned or clean. Nevertheless, optimizing the classifier and ULPs requires hundreds of pre-trained clean and poisoned models, which is impractical in FL because the server has no dataset. Huang{{cite:6f0748b92ce654f6787a7e17fa37a7264bdc8800}} proposes One-Pixel Signature for backdoor detection. As in {{cite:0e0eccc7736a086ded080619389ade060084123d}}, One-Pixel Signature also demands pre-trained clean and poisoned models.
| d | 771c90e08abc1d1b8be09edac8594aa1 |
More recently, Bakshy et al. investigated the nature of political echo chambers on Facebook, where left and right-leaning users not only tend to connect with those who share their perspectives, but also, tend to share different news and other media URLs {{cite:7deb73ab557c2404092a11a5f17eff0d24407687}}. While the exact impact of the Internet on mass polarization in America is still up for debate {{cite:89c9a325dd4211294ec0c042df9257b7319ef674}}, {{cite:ab5582adb1b6502b1ecc6336f485fc3473831a35}}, it appears that on platforms like Twitter, users are increasingly following accounts that share their own political views {{cite:c45a3d0c6713a2122b79d515ce624531a00c4a80}}.
| i | 127e74ceec7cdc411ae868797d115943 |
The major motivation is that, by substituting a vulnerable word with its synonyms or sememes, we expect that the adversarial text with small perturbation can have large semantic preservation. We model the word-level attacks as a combinatorial optimization problem {{cite:cba71acd2ac9b0670d47450cd961380840af168d}}. We then develop a two-step heuristic for solving this problem. In the first step search space reduction, we first build candidate lists for all the content words by combining synonyms from WordNet {{cite:0ab4fa0290dc465fe29b13939ec909af80f5dfce}} and sememes from HowNet {{cite:fb9d25c48f0ba8fc027343ab7d249579e94b37aa}} similar to other word level attack strategies {{cite:9e4b0909fb0d8ab55d0c8bf8ee8b6e100e22e912}}, {{cite:cba71acd2ac9b0670d47450cd961380840af168d}}. To avoid searching in a huge search space, instead of searching through all content words to generate adversarial texts, we reduce the search space by finding a small set of vulnerable words that are sufficient to fool the neural network using a greedy algorithm. Then, in the second step iterative search, we further minimize the perturbation by iteratively restoring the substituted words back to the original words while keeping the classifier making the wrong prediction. Each time we restore a word, we adopt the genetic algorithm (GA) to search adversarial texts over the remaining substituted words.
In this way, we expect to find an adversarial example with the least perturbation on the original text.
| i | eb9bb4f1c91b94ecab274e2ab58a1e73 |
Most of the current research shows exciting and promising developments of AI algorithms in image reconstruction for cardiac imaging. These are mostly attributed to their strong ability in recovering high quality images with fast reconstruction speed, which therefore can further increase the acceleration capability. Current DL-based approaches, especially models learning an unrolled optimisation {{cite:f7ab4c768f51a7b49c2c25beca162cce2bc8301a}}, {{cite:4b359479ae85cdd51751f1e83277728ccaef5e3d}}, {{cite:29eaa34583586db7deb1beb452e2a0d317fbf33c}}, {{cite:64c804cecb8b8c6444c2cd652f8673a8f69b19ba}}, {{cite:3996b7092b706f630ff82f93b0d33fe2b7632922}}, {{cite:2480ad95b11ea8437fa9881a4867cac4fe3af715}}, have shown to outperform conventional CS-based methods for CMR reconstruction, and their application in PI also indicates their potentiality in facilitating fast single-breath-hold 2D cardiac cine imaging. Though promising results have been achieved in recent developments, there are still some challenges yet to be solved for their use in clinical applications.
One of the limitations of current studies for CMR image reconstruction is their limited validation in clinical practice. Most of the existing DL-based works focus on reconstructing images with retrospectively undersampling based on models trained on simulated undersampled data. Though such retrospective study can provide useful insights and initial validation of employed methods, it still remains unclear how well these methods can perform on prospectively undersampled data, which is a more clinically practical scenario. In addition, majority of current DL research for dynamic CMR image reconstruction works on simulated single-coil acquisition setting, whereas only a handful of works propose to address the more practical and commonly used multi-coil acquisitions. This is mainly due to the increased computational and model complexities introduced by the multi-coil data as well as the extra temporal dimension. Thus, efficient DL models for PI-based dynamic CMR image reconstruction are also highly desirable. Besides, as most work investigates reconstruction with Cartesian undersampling patterns, efforts towards non-uniform undersampling strategies such as radial sampling and golden angle sampling are also necessary, which represent the commonly used sampling strategies in acceleration of 2D cardiac MR imaging in practice.
| d | 12f5acf925cfcfebc71ffd1a714a259b |
To our best knowledge, MGPSN is the first work to jointly train motion and image into a unified CNN network in head detection. This work aims to solve the above part problems, such as similar static objects and diverse head samples. The contributions of this paper include: 1) We propose a pixel-level motion-guided pseudo siamese network method to learn the more robust head features. 2) MGPSN is employed among different backbone networks (VGG16, Mobilenetv2, Resnet18) and detectors (RPN, transformer) to verify the generalization ability. 3) Due to extracting effective motion features, we demonstrate the MGPSN on the crowd Brainwash dataset {{cite:6373aa4433636f7a6278d79356b709422207cb70}} with state-of-the-art performance.
| i | c1b28df950a30c93285332d45fd4d987 |
The last effect which breaks {{formula:66a72deb-342a-4da3-bdc8-c3ffc112a83e}} scaling is transverse flow.
The transverse fluid velocity is proportional to {{formula:71324eaf-ca68-42d7-9cb9-c9c44b9027c0}} at early times {{cite:9b7b12ddbbe70df69174346391fea010d4d49c39}}, {{cite:00aef70aacc97860f00e5e1fa4a7ef8a703fad95}}, {{cite:305399430f243bb166941208490f3a884bbdc7ca}}.
Therefore, transverse flow becomes more and more important as time goes by.
Since the time of dilepton production decreases with {{formula:d78e9224-63fb-4d73-958c-363beacd8c6c}} like {{formula:06f115d7-889e-45d5-b5e3-7983e461ce14}} , one expects that effects of transverse flow become negligible if {{formula:7df80c2e-aa68-43e1-9511-0a864f1b6bb4}} is large enough {{cite:8b94029d0e488547bdec32c39c0a5b0ed45cf006}}.
The qualitative effect of transverse flow on {{formula:bef0c3dc-bc50-4399-9ef4-0a79bb8bbe6d}} scaling is the following {{cite:0555fd05d1f8b0bb838ccfd06534b5dc656304e6}}:
For a given {{formula:261bbcf3-1872-44ad-8e7b-315d87823321}} , the transverse boost enhances dilepton production for larger {{formula:c567185a-9cc9-4a32-a0ee-ade97b24ceff}} or, equivalently, smaller values of {{formula:7cc46237-a106-47d6-a2e0-03221148f8b0}} .
Note that this effect is qualitatively similar to the effect of pre-equilibrium dynamics discussed above.
It has been seen experimentally by the NA60 Collaboration {{cite:8f86566feebcce1f1b56b52f3059f8d97f922e8c}}.
We do not model transverse flow, therefore, we cannot assess quantitatively the breaking of {{formula:a3f0c723-4a9d-43e4-bb00-8420c1b69fb0}} scaling resulting from it.
However, we will estimate in Sec. the range of {{formula:aa7bd9a1-53ce-4edc-817d-3ff48ea125bd}} for which transverse flow is likely to be important.
| d | 21776ed3900ae2ce7f148d430ba09890 |
Line-search methods determine a search direction {{formula:e4eaadda-545d-4930-991c-fe1ff53b0a3d}} first and then identify a good step size {{formula:f1ff51f2-c907-429c-9b06-d319f892eb7d}} . Trust region methods do the converse, by specifying a maximum step-size first and then identifing a good search direction {{cite:5d6043fa774eeebf0136263dd32fcafec3e259b2}}, {{cite:2c5cbcfcdc2a0c5df8b8af3d8523015962d217d9}}, {{cite:52d25b8eb245f9752313b91a28b831e4e3eb57fa}}. This allows trust region methods to make large steps close to saddle points and always yield descent directions. Within the trust-region, {{formula:b207386b-c113-4004-9f3d-5678307d00f2}} is replaced by a local approximation, giving rise to the trust-region subproblem. Most trust-region algorithms use the objective function derivatives to construct a quadratic trust-region subproblem
{{formula:71ea0b10-5414-437e-b0e8-c1a829a69ffc}}
| m | 9e6aa430a5447343d787b51e480f7789 |
Despite the existence of outstanding initiatives such as MLS dataset {{cite:26b4f7e0db1b081447b51747b305fe182495688d}}, there is a lack of manually annotated large scale speech corpora in Russian that would be freely available and suitable for training and testing speech recognition systems.
| i | 7435ac653210367fded5f93d631df12a |
Siamese architecture is widely applied in SOT where various designs focus on improving the discriminative representation of objects {{cite:69aa191293adb275bb078eac46d19751d57dd392}}, {{cite:d455663f2611f1d181ef4a8bba9c0faba26f6ca6}}, {{cite:af7926b88567a7765a0015c534eebd237077ddd2}}, {{cite:ecb3830c35bcfab3cddf4760ae3e4ff82198f715}}.
For MOT, tracking by detection is the most popular paradigm and achieves highest tracking performance on several benchmarks {{cite:da69c2346708278a988f874bf8dcddb6619b669b}}, {{cite:cc765f9d62c001d25fd1bba80d314bc538d69609}}, {{cite:3686215fe0dbc819f229675ec9a7a7111df2679b}}.
This paradigm is not applicable for SOT as the model would fail to detect objects of unseen categories in SOT.
Some MOT methods {{cite:2debafbdd1ba9386c08487a31c01ff800f3f4ba3}}, {{cite:a3e0a6dbf221a21b34f714df639e5f748eb2c4de}} use the Siamese tracker in SOT {{cite:6f35a1ac8af731d6a9971247a8312d546f191e3f}} to predict the location of the targets in tracking frames and fuse the predicted boxes with the detection boxes to enhance the detection results.
However, these methods are not competitive to the tracking-by-detection methods in MOT.
Albeit the Siamese trackers have been applied in both tracking tasks, none of these works are able to address two tracking tasks with a unified paradigm.
In practice, a unified tracking system is significant in many fields.
For the AR/VR applications, tracking specific or unseen instances like personal cups is related to SOT while perceiving the environment of general classes like people is related to MOT. It is expensive and inefficient to maintain two separate tracking systems. The unified tracking system, which can easily switch tracking mode by demands, becomes more essential in real world deployment.
| i | cbff21e09b2093e047101bc09cc45da9 |
Evaluation on ImageNet Subsets: Following {{cite:8ff24fa6b3520e973832a17c28178b4922246744}}, {{cite:3fb3f9872746e5f69029be9ada060bad85929822}}, we evaluate the pre-trained models on the ImageNet classification task with limited labels.
We report results with 1% and 10% labeled subsets of ImageNet (table REF ).
CMSF-2Q and CMSF-KM outperform MSF and are comparable to existing approaches requiring significantly higher training time.
{{table:205d933c-8986-4a6c-9952-e9b8f694f531}} | r | f831cc781c591356b33c1ca975b04d8a |
Semi-global alignment score is a compromise between global and local alignments
{{cite:edd3768b2589283449f9ae1a09b29aeb26318d16}}.The global, local, and alignment scores were computed using
LingPy library {{cite:9be3b2f4b83a5777a1d662bedaccd60d41815257}}.
| m | 3c4d83aa93cd2f3e5039788622df1288 |
Overall, our method adopts a similar message passing layer as in GraphMeshNets {{cite:80a650c7b0c632c90145a8b6b5635dc788a8aa13}}. Compared to {{cite:4a0a9a880fe5e508dc38453a9a6ca93a53a27e02}}, {{cite:b8bcd0eb50561ceb5323c6bd371697a77b976f9c}}, our advantage is that no mesh generators is needed for the coarser-level graphs. Compared to {{cite:3bfcf76ce3eba230983d9058c0e8226b0a18dcf9}}, {{cite:cb8c24afdca78f2ec3630b59cf25a48033cb8f0d}}, {{cite:a2bf9aba53bb04bd9643fd4b8052bd632924d7a6}}, our advantage is that no spatial proximity is necessary.
Together, we eliminate the need for building connections via spatial proximity nor using learnable MLP for aggregation and returning. Note that the work of {{cite:d6b0b7dd9cb88bfc0ffbaa78919790bc8c4864d3}} shares similar advantages to some extent, but it focuses on generalization with PDE parameters, while ours focuses on a systematic pooling strategy for arbitrary complex geometries.
| m | eab1b6b6e11e6ebbf7820563526f2c3d |
A manifold is a lower dimensional basis for describing a high dimensional data. Images can have a complicated and highly non-linear manifold {{cite:169e8424d5b963e075adfd2946a51885bb089044}}, {{cite:60dc670921de2bfe044dbfad531e9ddaaf4ce29c}}, {{cite:710c891fd23aba18fc5306b1f1173ea77c69569c}}. we attempt to approximately learn this manifold using the noisy instances of the images, since noisy instances will waver around this manifold, with the more noisy instances obviously straying farther from this manifold. we use this intuition to learn a function {{formula:5dae1373-f438-41a7-a9dd-17d8f5c6f9e9}} that tries to push the noisy instances in the direction of the manifold, so as to recover the clean images {{formula:7bfef97f-f543-4f96-9df7-8c7efd478a05}} . Since the noise is random, we can assume it to be around the manifold, shown in Figure REF . One way to have a manifold learning is to have training pairs consisting of clean images with generated synthetic degraded images from the set of clean images, and use a supervised learning approach to learn a mapping from noisy to clean examples. Although that approach works very well in practice, in certain applications, especially medical imaging, one may not have access to a huge dataset of clean training images. In such a scenario, we try to learn the direction to move within the lower dimensional space without actually knowing the line but rather the normal direction towards the line. For each noisy example {{formula:0f42f8b4-8414-4ee0-b338-aa5512c80055}} lying somewhere in the lower-dimensional space, we apply the degradation model to the image yielding a more noisy instance {{formula:c401ba49-d398-425d-9f8e-ce61df18cb8a}} where the choice of {{formula:d014b35b-2ebb-4c44-8e29-1c4a66977463}} will be made clear in later sections. The image {{formula:d73a750d-2c75-4ae0-a4ee-1a095faabf62}} is closer to the manifold than {{formula:220a43a9-b7b3-40da-9d54-5a13f139ac2e}} because the function {{formula:0f4c4f59-7405-4568-9f56-fe6b85c85578}} cannot recover the original pixel information in the image. For example, for a Gaussian degradation model
{{formula:5ba61741-bcc6-45b1-92d9-df3bf2f80848}}
| m | b19892372f37acf67dd9407f62c48731 |
The problem of pattern avoidance has been an ongoing object of research in combinatorics over the past few decades. We refer the reader to the text {{cite:bef716af0006274fc492f42646f3038ca70a3328}} and references contained therein. Considered originally on permutations {{cite:d70f434407842731393c9d8aa1b989ea788c1506}}, {{cite:9d03d1d8a7d6b752c8cae7d2da4aa9001421e532}}, the problem has been studied on several other finite discrete structures including compositions, set partitions and words (see, e.g., the texts {{cite:2b467bc08202d242845968399cf0f917f673b968}}, {{cite:c4ab46d687ccb2f4e728c62eb06e96c87bf4b1e8}}). Further, various extensions of the basic avoidance problem have been obtained by stipulating that an occurrence of a pattern must meet certain requirements. In this paper, we consider the avoidance of a particular pattern of length four by circular permutations wherein the first two entries in an occurrence of the pattern satisfy an adjacency condition.
| i | 05e9bb54c539795824619c8e98037389 |
In summary, our contributions are threefold. First, we formulate and highlight program-guided tasks, which are generalized from program-guided visual reasoning {{cite:929e63e4d3ff959965f965fe1f067172b5472016}}, {{cite:f782f1e0af1f9d82ecd1cecfa9f8b2f6fadf8e80}} and program-guided policy learning {{cite:481b31e3d8d650342355c535ed8777c92c2fe255}}. Second, we propose the program-guided transformer for program-guided tasks. Third, we conduct extensive experiments on two domains and show promising results towards solving program-guided tasks.
| i | 770c8179a010a3d34448957ed437a1c9 |
{{formula:7d70fc01-2f63-4982-b7cf-3cf5cebf82e8}} -{{formula:3553d4e1-4d09-4028-9e0e-4a6a0604c244}} phase diagrams are established from the above-discussed features of {{formula:f533a964-7cfd-468d-9db2-fc1f088dcd89}} and the field-dependent fit parameters of the Cole-Cole relation on the polycrystalline samples Mn{{formula:3757d97f-948e-472f-8d84-c4cbb70c82a8}} Pt{{formula:3ecc8014-30cc-4b54-ad54-ca75909033f7}} Pd{{formula:8b2b06cf-0b36-496c-b5d8-5e3bb45b1188}} Sn and Mn{{formula:84c7d2d8-9aa7-40b6-a224-09ceb0fa624f}} PtSn as shown in Fig. REF . It may be noted here that the {{formula:32e8513f-570a-49e0-93ba-3decdd0d420e}} ({{formula:a11d7638-fe30-49e0-bd35-7ef0e97e10f6}} ) and {{formula:66269b44-18ab-42bc-a887-718a8837a6ae}} ({{formula:f9b5d7ba-cfb0-4fc8-9f0d-91c161da39aa}} ) are the lower and upper phase boundaries of the antiskyrmion phase which describe the crossover from the helical state to the antiskyrmion region and the antiskyrmion region to the field-polarized state, respectively. The phase boundaries obtained from the Cole-Cole analysis in the present system broadly matches with that estimated from the magnetic entropy study {{cite:03f357999762a15f8ed88767a157c59b84aaf6fe}} and the Lorentz transmission electron microscopy imaging (LTEM) technique {{cite:e1fdb7082b23be5601cd10a44e2c76d2ef04fa3b}}. The discrepancy seen in the variation of the upper critical fields at low temperature regime mostly originates from the non-identical orientations of the crystallites in the polycrystalline samples used for different measurements. This is due to the fact that the angle between the applied magnetic field and the crystallographic orientation of the crystallites determines the critical field required for the stabilization of antiskyrmions {{cite:e1fdb7082b23be5601cd10a44e2c76d2ef04fa3b}}. Hence, depending upon the orientation of the crystallites the critical field for the nucleation of antiskyrmions may vary for different pieces cut from the same sample. The discrepancy found for the lower critical fields in the present study to that of LTEM investigation {{cite:e1fdb7082b23be5601cd10a44e2c76d2ef04fa3b}} can be understood as follows. In the phase diagram inferred from the LTEM studies, typically magnetic field was applied at room temperature to stabilize the antiskyrmion lattice and then `field-cooled' the sample to the required temperatures. Subsequently, the magnetic field was slowly varied in different steps, i.e., either reduced to zero or increased to obtain a field-polarized state and simultaneously monitored the emergence of different magnetic phases. Whereas, in the present case, the sample was `zero-field-cooled' from 400 K to the required temperature and the magnetic field strength is continuously raised starting from a zero value to see the field evolution of helical, antiskyrmion and field-polarized phases. In addition, the Mn-Pt(Pd)-Sn samples used in the LTEM study {{cite:e1fdb7082b23be5601cd10a44e2c76d2ef04fa3b}} are [001] oriented 100 nm thin-crystalline films prepared by the Focused Ion Beam (FIB) technique. Whereas, the present ac-susceptibility measurements are carried out on the polycrystalline bulk samples. Therefore, it is expected that the phase diagram for the bulk polycrystalline samples may differ slightly in comparison to the single grain thin-crystalline-film sample.
| r | 0de80a6ae3e6cf247ff3fd2edde88db6 |
In the past two decades, a completely different line of investigation has dealt with the angular momentum carried by the electromagnetic field. Beth {{cite:ed7687d02064c67b079a3361f58b19323ac70762}} made the first experimental observation that light carries angular momentum. Beth demonstrated that if a beam of right-hand circularly polarized light passed through a birefringent plate, and the beam was converted into a left-hand polarized beam, the plate experienced a torque of {{formula:35ff46c6-2961-4e5a-9ef1-a0403853e8b5}} for each photon in the beam. This experiment is cited as a demonstration that a light beam carries spin angular momentum. Years later, in 1992, Allen et al. showed that laser light with a Laguerre-Gaussian amplitude distribution has well-defined orbital angular momentum {{cite:0495b4c105486c8109252888ec69e995cdcf7f29}}. Many theoretical and experimental investigations followed, see Ref. {{cite:8d2048c8b252dede841e7bb11bbfec9645b2f8cc}}. For paraxial beams, i.e., in the paraxial approximation, it has been demonstrated that the total angular momentum can be separated into a sum of spin angular momentum and orbital angular momentum {{cite:dcce51cca5c35fe27f9fdeefe5ee31b5401ef3c0}}. However, for a general electromagnetic radiation field, spin and orbital angular momentum cannot be separately defined, and only the total angular momentum is a well-defined quantity {{cite:62d2dd60dae0b2f2a8bef5031e4cca80585417e9}}, {{cite:0788da927b5788540ad064179c9d3d4a6d07e2c2}}, {{cite:0f5b58f6fc9b0b15024009066db3fd8ea5b5fc24}}. The interaction of atoms with light carrying angular momentum were explored theoretically in a number of works {{cite:3ed624d5e24aaa84474a871630360cf922d48d60}}, {{cite:25869c33f45104fa72c17227bb4eae9b4c4a6e4a}}, {{cite:6ab26e94d05ece789907ee6fc4c952e54759a389}}.
| i | 421b27a98f30b721828930e3a1192e0e |
In the left panel, we show the DM-proton cross-section bounds for a light mediator of
mass {{formula:09bbeaea-45c2-40f3-bf4b-cb5650a1e90d}} while in the right panel, the mass is {{formula:24732777-cd28-4b1b-97da-2662ac09b14f}} .
For comparison, we also show the bounds from the latest results given by PandaX-II for the two light mediator masses (red) {{cite:a671718bbcf2f699e970504e9db88333788d1f1c}}.
The areas shaded in green, and red corresponds to the excluded parameter space by WD in M4 and PandaX-II, respectively.Here, we have not included the updated and strongest limits given by LZ {{cite:985fa0e8b8257ceadd39f43fb2e4cfc2745e00fd}} since it excludes the same parameter space regime, above {{formula:7f1b182d-3c1e-4cba-9162-9ac22b9bad6e}} , as PandaX-II {{cite:0607418fc44064569fb7e53954b947e663d2006d}}, {{cite:a671718bbcf2f699e970504e9db88333788d1f1c}}. We observe that the limit given by PandaX-II is stronger than that provided by the M4 WD for the two possible mediator masses in the DM mass region above a few GeV. The dashed grey line corresponds to the threshold cross-section.
| r | 29bc297fbf0449aae9560d03af7d7447 |
Pixel Query Initialiser (PQI):
The Pixel Query Initialiser (PQI) module aggregates the global information of the scene into each pixel-level embedding. The image feature map with the coarsest resolution, which contains the most essential details in the scene, is fed as an input to the PQI module. Given an input feature map of size {{formula:8559999a-25d9-4cd4-b4be-78a593924ff6}} , the PQI module uses pyramid spatial pooling (PSP) {{cite:f8cfbeb0fb42ccb66049532397a28e1c2fb70fa8}} with an adaptive global pooling at scales 1, 2, 3, and 6. The feature maps are then upsampled to {{formula:8d41cbbc-f4c5-4a39-84f2-985ae9480b76}} scale and concatenated. A convolution operation is then performed to integrate the global information effectively, as in {{cite:66a7384e36487b3e68ada22d556b9f0d03986b75}}, to get initial pixel queries {{formula:23f49c47-a911-42cd-bde4-e19ab1eec452}} of size {{formula:d10f5915-b00c-4ba5-bb1d-78b364fbdd20}} , where {{formula:cf88676b-efe2-4119-aac4-d3eac4330d11}} = 512.
| m | 26a0bc36c0a801281e5303e0dc2e9aac |
Observations of our Universe across cosmological distances offer us an ideal grounds for testing the behavior of long-standing physical theories, alongside new ones, ranging from signatures of new primordial phenomena {{cite:10b850f7d63c1983e7d9abb3266e7de2a00f1411}}, {{cite:1d906929ab511efafc65bd8b4981f673ecb55a0c}}, {{cite:83f9c7701f25d9b4fd81e9c7334a6c8c43edce3c}}, {{cite:17179a66d08057285ff5bbd3a4f16c150b6e3473}}, {{cite:96ce79cad6c525d612cf1daa4ca0c12a6d57881e}}, to models of dark energy {{cite:c5e562d653807f910f5424935b85d3f1d07818cd}}, {{cite:895abb8964298a3ca006ecade270fdb0b43c48d9}}, {{cite:33957e5a9ee51621800705456992c7e4f658a83d}}, {{cite:4e35f95bf76c13fcf4e1def4917398be46c90843}}, {{cite:c01f2295b288897123d776fe15d2f7c950d068b4}}, to general relativity (GR) itself {{cite:85ba613dc33046cd7a169d23ad67ef4cb7eb764f}}, {{cite:fac1fcad9361a0d928a8ac71569da838d364c43d}}.
On the other hand, it is often on small scales—the distances considerably smaller than our cosmological horizon on which nonlinear growth of structure occurs—that we have been able to perform our most precise measurements.
Upcoming experiments, such as CMB-S4 {{cite:0dcb92867055775eaeba47b9de2355913386ebb7}} and the Vera Rubin Observatory (VRO, formerly LSST) {{cite:4360dc2cb2e708629cfbf9b99f28bbe8e245b4e9}} will begin to provide us with a view of the Universe that encompasses both of these regimes.
Together, maps of the cosmic microwave background (CMB), of the large-scale galaxy distribution, and of other tracers of matter in the Universe, are expected to be of sufficient sensitivity and volume that we can measure or constrain a variety of the subtle effects that leave an imprint on ultra-large scales {{cite:b461cd05ee38cae0d69daf74771c95ebf44e3a06}}.
| i | 459b1bf529f4e2b35d01636370f04d18 |
In this work we have used the DIRAC {{cite:c3739b7380b079ac1bff801539eb55cd4163535d}} program and the Dyall-DZ {{cite:1ccaae7dac5a35943ed4769e85de20884a8de6f8}} basis set to perform DHF calculations with the {{formula:296a6d0d-c124-4b13-ab58-245109509c88}} interaction. This basis was also employed in PSI4 {{cite:715490d6c7e8131d1c78b7ce7943a77893277859}} program to run the corresponding non-relativistic Restricted Hartree–Fock calculations. Furthermore, this basis was used in Gaussian 03 {{cite:339ea623d5b8e949a5c017c37baaff774947999e}} package to run calculations including scalar relativistic effects by means of the DKH and including electronic correlation effects by using the CISD approximation. The correlated 2-RDMs for the CISD wavefunctions were computed with the DMn code {{cite:7c6520e93f0c4c6a224fd9a42bcdb548293d9c93}}. IPDs and EPDs were computed using a modified version of RHO2_OPS {{cite:2659e7168b8a4e37085f668a1d5844439bc7c02c}} code that uses the algorithm of Cioslowski and Liu {{cite:91cf7c25b6775749ad56456c1fe27c6eb918384c}}. The integral {{formula:a9bc50cb-e51b-4533-b311-08e8392b545a}} was computed with a modified version of RHO_OPS {{cite:bd38d6450594f1c167c4a6aa5aad87b551bd3fe3}}. Python scripts were used for plotting the data including the make_interp_spline option from the scipy.interpolate library to construct cubic interpolations for certain rough plots. For diatomic systems (i.e. H{{formula:525528e0-b389-4643-b002-53d430e35f75}} , LiH, NaH, and RbH) the heaviest element was placed at the origin of coordinates for the computation of the rEPD; the experimental equilibrium geometries were employed {{cite:3c9f693e188901822ad52a65fc218d6c1f1c0ee9}}, {{cite:15e175c476c226e89e63931590ce51f0d8013f59}}. Finally, let us comment that the PSI4, Gaussian, and DIRAC programs employ Gaussian basis sets to represent the atomic orbitals. The use of Gaussian basis sets leads to a poor description of the electron-electron cusp condition {{cite:de8a00d43edaf79b830c6906dc993817acfb9388}}, {{cite:5f54993006156a20d55e2547bf13ca90980f2005}}. Nevertheless, we may consider that the poor description of that cusp is similar in our non-relativistic and relativistic calculations; thus, we could expect that some error cancellation may take place in the description of {{formula:dfb2e18b-8cc2-4089-ad6a-df5fccb4f3a6}} . Also, it is worth to mention that in the DIRAC program we have employed the default finite size distribution for the nuclei {{cite:d2b505a2b6b1efaab1b948c70d6869ebd54830e9}}, while in PSI4 and Gaussian 03 we used a point charge model for the nuclei. Our results indicate (see below) that using a different model for the nuclei does not have a large effect on the differences in the rIPD and rEPD due to relativistic effects.
{{figure:17e13ee2-ceff-43a0-9cbc-aa5c40e581df}} | r | 9f66153c47fd602c305be35f7f390bd6 |
In this paper, we argue that there is an additional, previously unexplored mechanism that governs
where future citations end up. We posit that recent citations strongly influence the short-term impact, in that the level of attention papers currently enjoy will not change significantly in the very
near future. We investigate this hypothesis and find that
it holds to a certain degree across different citation networks.
Hence, we introduce an attention-based mechanism, reminiscent of a
time-restricted version of preferential
attachment {{cite:4b5a2980152048b24dcfbb3a76d408617fab9fbc}},
that models the fact that recently
cited papers continue getting cited in the short-term.
| i | 65d82186d0b71f681a22f031cd20447f |
black
In this section, we briefly describe the numerical model employed, namely an extended color-gradient lattice Boltzmann approach with repulsive near-contact interactions, previously introduced in {{cite:49870e476ff5f0decf99010f9f48a6003457913c}}. In the multicomponent LB model, two sets of distribution functions evolve, according to the usual streaming-collision algorithm (see {{cite:6444631bef6eb11f4ff67af932176ce7b021ff53}}, {{cite:e60e4df8f9dcf9803a90480f1f52814f426b68b4}}), to track the evolution of the two fluid components:
{{formula:e6fc2439-d4e8-4e0d-bc35-245ef56c114a}}
| m | 860f5dbd5a85d82a13a3e5dc141af9fb |
The unusual dependence of magnetization on temperature and the finite difference between {{formula:f0754256-5228-4ae2-b80e-b665467892b0}} and {{formula:9c5184d5-dbb5-49b4-9b88-58156b51799b}} curves much above {{formula:43c14d02-dbd2-43e8-93d2-7b191fc307c9}} clearly highlight an unconventional paramagnetic state at high temperatures. Therefore, to further understand the magnetic property of UO{{formula:f4c48488-73aa-4197-a370-421c7ec4da79}} at high temperatures, {{formula:5b9ecacc-b94d-42df-8852-3f570e6bec2c}} versus {{formula:76120f26-bca4-40bf-b9db-cca196e962c3}} at {{formula:d1f86cef-30d5-401c-8173-ef850e897691}} = 100 Oe measured in ZFC mode is plotted in Fig. 4. The {{formula:8dab2c76-7ac9-448c-92df-2fec62ab5920}} versus T data appears to be grossly linear in the temperature range from {{formula:d54e344f-cfc9-4c2a-b516-6e161e8010dc}} = 300 K to 70 K. We tried to fit the results in this temperature regime by using Curie-Weiss (CW) law, given by {{formula:d8155b06-dab3-4429-b01a-ad34f5837bd5}} , where {{formula:4b3144ea-1431-4d50-b95e-12d08734f820}} . However, when looked carefully, the CW law does not fit the experimental data in the entire temperature regime. In fact, it deviates from linearity below around {{formula:f16ce62f-9673-4407-93ed-2e9f35d252fe}} = 280 K (see the inset of Fig. 4). The effective magnetic moment {{formula:aea29c09-1008-43a6-b2ee-e3e400b74500}} obtained to be 2.82 {{formula:3bd6c844-cb12-4352-9b6b-a7e36ca27d26}} /f.u., which is smaller than the expected value of 3.57 {{formula:4078b25c-41b1-4407-8177-006171b6e9a5}} /f.u. for {{formula:df3e79fc-60b1-4066-b28b-4b32b590bf47}} = 4 (L =5 and S= 1). However, it matches extremely well with value of effective moment expected for the threefold degenerate ground state in UO{{formula:470edb96-755d-4329-95dc-399124503c84}} in a cubic crystal field {{cite:2f60ee19783ec28794f587ee4ca56190ccbc5c84}}. {{formula:2711d74e-48b3-48e4-824d-5bb666e31a12}} is obtained to be around 171 K, which is around 5.6 times higher than the transition temperature. The deviation of the susceptibility from CW law, the presence of irreversibility much above {{formula:4aabcfd6-4cd7-4e50-bce6-a729f773b8f4}} , higher value of {{formula:3430bac6-9b34-4ac7-af02-3f3863653667}} than {{formula:705c2402-7cf5-47ef-bd34-cf563ac5c807}} are interesting. There exist some earlier reports of the unusual characteristics above {{formula:b31e5cd7-36ee-427d-abe9-3e1f92a454a3}} {{cite:211d30a5657926bd9e52448029a0874d862c8cb9}}. In inelastic neutron scattering experiments, magnetic inelastic response has been observed above {{formula:c8f2682c-c8e0-4763-a3b3-eafd2ccf7f8d}} up to as high as {{formula:efea8bd9-b360-4f29-94f4-dc6261eab371}} = 200 K {{cite:bba6ed2b8a8befcd1f9f3bff798181e3b96fb01f}}. It has been suggested that the coherent motion of the neighbouring oxygen cages produces uncorrelated 1-k type dynamical JT distortion in the paramagnetic state of UO{{formula:92e42161-21c4-4891-a93f-3c09018d9a05}} {{cite:bba6ed2b8a8befcd1f9f3bff798181e3b96fb01f}}. With the lowering in temperature correlation builds up and a static 3-k type distortion condenses at {{formula:9507be83-6e30-4c81-92a7-6adb3b2e7f9e}} . The tendency of {{formula:59644c61-b51b-4150-b936-fac9a5a54428}} to saturate as {{formula:f6ea4f83-2f84-4f26-a829-f438cbeea686}} is approached during cooling, the deviation from the CW law, existence of bifurcation between the ZFC and FC curves highlight the unusual paramagnetic state at high temperature, which may arise due to short range 1-k type dynamic JT distortion.
| r | 8d91291d9c6bb644d06eaf0b91b4ca9b |
Although the merger remnant is massive, it is hot and more extended than a WD of the same mass that evolves as a single-star or grows by slow mass accretion {{cite:a5767ff419115ee754376f2810ab3eac4c84e7f8}}. In addition the merger remnant is rapidly rotating and sustains a strong magnetic field. Future studies should determine the helium mass that can drive LTP/VLTP on such complicated WD-core merger remnants. In this study I scaled the required helium mass for an LTP/VLTP as in equation (REF ), but one should keep in mind that the required mass might be much smaller.
| d | 5b9a9045754472e7a135fb589cc11eea |
For communication purposes, RISs are employed to offer coverage enhancement by signal-to-noise ratio (SNR) improvement and interference suppression. Channel estimations for RIS-aided communication were discussed in {{cite:55289dd2ef52288889fafa83608bda449fd9e7f2}}, {{cite:877252c6437b5b399cf67ca8e8394cdc7c5ca78a}}, {{cite:0fd1e2c6acdfade51c133f33a18d95c832c605d6}}, {{cite:c9c98367e51926f90c4351b30c73ca20680cc3aa}}. The authors of {{cite:26403d570aab0e491a01a665591e1af56edebc89}}, {{cite:032b051a71876f99f9f58ebb3cc9be5d5cab3016}}, {{cite:255830b3200d13daa76d2882677f2e89a66a778e}} showed that cooperative active and passive beamforming could significantly improve the coverage and energy consumption. The impact of discrete phase shifting was studied in {{cite:24fd69485e1599c2b1fcfc3c880550499e3ebffb}}, {{cite:833cc16bab2606cc3f762a85e86deb786f082d82}}, {{cite:e2408638de6d27d5286966bafc53f4ebb164d04c}}. On the other hand, for environmental awareness purposes, RISs are expected to offer high-resolution sensing and localization capabilities. RISs can be equipped with embedded sensors or active unit cells {{cite:2487809422431867767abab442876bc20ac890f4}}, {{cite:1e2aa384aba8adf1810b14b8f9db0d2dff26abdd}}, {{cite:e12d246d8f8b02b1687dcff29f4f6e20e28fd090}}, {{cite:47ff931075a6bee2f48fb3a48eab06832792def9}}. A sensing scheme was studied in {{cite:9966c705a4e973e9ae22186a0606f42fa602930f}}, which minimized the Cramér-Rao lower bound for high accuracy direction estimation.
| i | 98d9ab67933cbe7f1be96cbdfd8a06e4 |
Natural image: Three real natural images are
studied in this example.
The results are given and compared with method in {{cite:9d1cb0449c67b9052aea484f68091effc79bdad9}}, {{cite:9d04de1dc85603faf01249912b6f2cf87669ceff}}, {{cite:478f762ae7e8a632bac5c84a84f66fde884ab998}}
in Fig.s REF and REF .
The results for this type of images show the efficiency of
the proposed algorithm in restoring blurred nature images.
{{figure:dff9d50e-a4b4-4eca-9868-45039bc768e2}}{{figure:af6bf4da-e2bb-46ec-92e3-124e049c5e61}} | r | 3e1f753b5b268f5b8a1f0147a061fcf4 |
We address the difference between the commonly used parameters due to Heineken et
al. {{cite:d58318e55d92741ab3469def5381a401ce73dbb3}}, respective to Segel and Slemrod {{cite:58c0fa016736eed5cfdbc27094ed43f7a163613e}}, and the ones derived in the
present paper. The discrepancy is due to Segel's choice of a nonlinear timescale estimate,
and we showed that it may provide incorrect predictions for the existence and the nature of
a reduction over the whole time course. In a way, this is not unexpected: Initial conditions
can be moved along trajectories, and this does not influence the long-term behavior.
| d | a2bd27ebcb2f6a37c85216ddf6640bae |
The third term of Eq. REF denotes the shear induced polarization, where the generalized momentum quadrupole tensor and shear stress tensor are defined as {{formula:35fa180d-6d78-4500-bbb6-82b4ee436053}} and {{formula:32812a20-4dd8-4bbc-b518-5b2d003e8b8c}} . This expression can be obtained from chiral kinetic theory or linear response theory {{cite:d64c4136501e6f4f76947a99169dd8e03b442f12}}, {{cite:9902b345495786da82263b56d9da477d341cc708}}. In {{cite:5669208774f9626d1ca0dd3b94434c53e61e5234}}, {{cite:fdcbe3e34ab96f13c15252411416abfc46321436}}, the statistical method also gives a similar form. Such shear term induces similar differential polarization {{formula:f75b9fbe-3199-4d3d-9f97-487827ed8e26}} and {{formula:025b3f37-7fe3-4de1-96ad-3359349c957c}} {{cite:9902b345495786da82263b56d9da477d341cc708}}, {{cite:fdcbe3e34ab96f13c15252411416abfc46321436}} as observed in experiment, which is essential to solve the “local spin polarization puzzle", see {{cite:2d5e5462893f3ee6c4903106afcc9e5a2f94b06b}}, {{cite:09378ae0a14e4a73607a304daea4301f7db45054}}, {{cite:049ebf51373351e415a649886359c11550309eaa}}, {{cite:4709a22871abdba3a1353638fb8cdbe39b0d9f0c}}, {{cite:f7da2a7ce056aae7bbf5fbc7ef26d0314c701f51}} for recent developments of the phenomenological study. The last term of Eq. REF is the baryon spin Hall effect(SHE), which is induced by the gradients of baryon chemical potential and becomes significant at RHIC BES energies.
| m | ce7c7c93dddd7baccb2a2d6147384686 |
We also discuss knowledge distillation (KD) {{cite:d48c1deeddb80831ee5f9cd04623325e7738792c}} as another line of work that introduces uncertainty. KD is a procedure that trains a student model to fit the outputs of a teacher network, which are also 'soft' labels and introduce uncertainty. However, KD alone has been shown not to improve robustness {{cite:5e1cd3c5c96ddc43644f703c9beaa8262d18f7fd}}. Also, while {{cite:2599fa33d0e1bcfc4a8ff8eca33a168f0195312f}} proposed adversarially robust distillation (ARD), combining AT and KD, ARD primarily aims to build robust models upon robust pre-trained teacher models, while we primarily study uncertainty and do not rely on pre-trained teacher models. Therefore we consider ARD to be orthogonal to our work.
| d | 4bcf7bab503037169171facafd73cbdf |
We recover the well-documented (see e.g. {{cite:cedca2bfa246a68c37c6cec6d69ec1e738ba0bcd}}, {{cite:01b12f21c9180ed12b1ccbdabfd617aa0ce5c9c9}}, {{cite:006aa7dd59ac6851e07102cb9d21d91d697f6295}}, {{cite:97f9b586418ab3652d5d1727d16866af326b153c}}, {{cite:f7c9c210ea36fddbac47473e9615bd2c73382756}}, {{cite:db4a9584db43acb2ab8de5f92c7e1aaa1a9417fa}}, {{cite:df87be5f79468bd0dcf90f5e96693934df9a2cbf}}, {{cite:68c787887912bc0f63700e0daa2b5142af59c81a}}) finding that constraints from Planck alone favor negative {{formula:25d518e2-ecc0-48d8-87fc-6d9cc0cb4596}} at roughly three sigma
and are significantly offset from the low-redshift constraints. That offset is along the direction of the primary CMB anisotropies' geometric degeneracy {{cite:0c67888c65d98d84c189a42f858c8fe8335c58b4}}, indicated in Fig. REF with a gray dashed lineThe line is drawn for constant shift parameter {{formula:4a0412a1-e607-4cbd-a994-a10566c1f3b0}} corresponding to the Planck+BAO constraints reported in Ref. {{cite:cedca2bfa246a68c37c6cec6d69ec1e738ba0bcd}}, where {{formula:cd161ea3-307c-4da3-af99-e3117f06af59}} is the redshift of recombination., and when that degeneracy is broken with low-redshift observables the constraints shift to become consistent with {{formula:6128b70c-e7c1-43b1-a6a5-a249ad8c2ae9}} =0. Quantifying the tension between the Planck-only and 3{{formula:792c1cb1-9631-4696-8b25-1e68f0b08f44}} 2pt +BAO+RSD+SN posteriors, we find the Suspiciousness {{formula:b9c6a6ca-3e62-4f1b-bdec-3442af829436}} -value to be exactly at our threshold of 0.01 for combining data.
Given this, we report constraints for the combination of all the data, but additionally report the constraints from 3{{formula:ece4a278-cf3c-48bf-8f99-6f9b581bc856}} 2pt +BAO+RSD+SN (without Planck). The marginalized constraints on {{formula:70ec7f2e-66de-4f43-b1ea-631e7bab3f9e}} are
{{formula:080fb7fc-eada-4d04-ab48-5c305ac18b8f}}
| r | d77367eaedb3db16fa89a681b4052e44 |
In practice, the g-formula typically depends on high-dimensional nuisance parameters. In this case, many estimators of the g-formula and associated contrasts have been proposed including the density-based parametric g-formula {{cite:01b504ce96ba4220a5894bd8891ea44f3508a62c}}, iterated conditional expectation (ICE) estimators {{cite:767a1620ad0b95bbe2b77263caf4b5067008de85}}, {{cite:b73724adc377f3df34d5fc00332f0a01b16e7c59}}, inverse probability weighted (IPW) estimators {{cite:46072bea5b420b9f3922e06bbe01a3058ae88d74}}, {{cite:2084fa1db68823639b960d50b75f1ae2dbbdbf59}}, and estimators derived from the efficient influence function (EIF) {{cite:10cded4f314fe299b4878af559fa5b8b56a15e5c}}, {{cite:7cd6718c562d7938506744486b14b22ec4c8dec2}}. EIF based estimators (i.e., estimators constructed to evaluate the EIF from an empirical sample) have several theoretical advantages over the other approaches including they may be {{formula:63a752ac-84a6-4cbd-9608-2c8940cbbed2}} -consistent if the nuisance functions are estimated at slower rates through flexible nonparametric or machine learning methods {{cite:915aee210982733980556bf271f475b4cd95669d}}, {{cite:88d8e04676021536589ede6a0d845e46c8954b76}}, {{cite:5d643f6758aa5a7719563ef58c6b5267e0e6d340}}.
| i | bfb418d6d868e99bc95e12f651ed58c0 |
There is a substantial body of literature studying the interplay between freeze-in and freeze-out processes in determining the final relic abundance of DM in hidden sectors with light mediators {{cite:3c55e8424302da11a0823fcb9c0015b8647b9391}}, {{cite:9c06e99f57ea39c2f73b859adf52bfbea7a4bc8f}}, {{cite:aac975962c52a67bd740fd404214ea25aaf90f44}}, {{cite:8fe783294e3a8b4ec4c470648200ccfb72016957}}, {{cite:8c9c8e8771fbfc73e2d27ecf4e5dfc98a393c63f}}, {{cite:4972cb98ec00153b7dffd1776ebdd9c4c28818a3}}, {{cite:fea816d8988e91d48472390a195fcc773a9b2e21}}, {{cite:d5b14ede06c5b983ab2a18fcd272f155e92aa837}}, {{cite:4b7c3bd36bfe9f84eec8605d80aa4df94cc03a50}}. These studies consider the case where the energy density in the dark radiation bath is built up entirely from the energy injected from the SM. The novel point we focus on here is the qualitatively new sensitivity of the final DM relic abundance to the initial dark sector population, which we parameterize through an initial temperature ratio {{formula:da37a98d-aeef-4061-9196-0a690c7e64f8}} ; previous work corresponds to setting {{formula:b33837f1-832d-4521-8f47-d55e03701c0f}} . We call freeze-in into a pre-existing thermal bath “glaciation.”
Taking a Dirac fermion {{formula:8e24dbc5-2d97-46b9-b259-044ee961a4a0}} interacting with a light kinetically-mixed dark photon {{formula:51ebc626-1e7e-4424-9056-e36b6d0f0517}} ({{formula:138e3c0b-8f55-420c-8ec8-a68a26e64ba2}} ) as our benchmark model for the dark sector, we establish the regions of parameter space where both traditional freeze-in and glaciation are self-consistent descriptions of the theory.
We demonstrate that for larger values of the model couplings, the energy injection from the SM overwhelms the initial conditions and predictions are UV-insensitive, while for values near the traditional freeze-in curve, the realized DM abundance can depend sensitively on the initial temperature ratio. Our results substantially clarify the theoretical status of the freeze-in curve as a target for direct detection experiments, and motivate an expanded “glaciation band” which can extend up to an order of magnitude below the freeze-in cross section.
| i | 3366c0802f559f447bf3860e1acc5e57 |
As widely reported {{cite:bdf8dfd8175c7fd2f705e4ee16d3368ee18ef42d}}, {{cite:8ea00601fac581295a9d1c5187412ef170afe3b6}}, {{cite:e7891892939da9dd35ff9f50d219f515c2b5d440}}, using the likelihood alone performs very poorly on a number of dataset pairings, such as FashionMNIST vs MNIST and CIFAR10 vs SVHN. Typicality substantially improves performance on the three dataset pairings that simple likelihood performs the worst on, but offers little improvements on other dataset pairings. In agreement with {{cite:3d75236110042748fb3d8cdb1fb0bd6084c82c94}} we found that WAIC provides little advantage over using just the likelihood, and sometimes degrades performance.
| m | 3f792143bde8b5c56d28ab30b2736e0a |
In the above assumptions, (a) and (c) are standard in the stochastic non-convex optimization literature;
(b) is an expected Lipschitz smoothness condition over the data distribution, which implies the conventional global Lipschitz smoothness {{cite:77a213b3895498abbf4bdd211e9c74b4849b5fa5}} by the Jensen's inequality.
Note that (b) is weaker than the individual Lipschitz smoothness in {{cite:86d466d05291e4811481513ffe4235f7e16e5670}}, {{cite:2e013712bbd19cc2522d5cdc845af3c5ce5acf5c}}, {{cite:e99c772dd102298d9435fab2f1df217825912def}}: if there exists an outlier data sample, then the individual objective function might have a very large smoothness parameter while the average smoothness can still be small;
(d) is equivalent to the Lipschitz continuity assumption, which is also commonly used for non-convex stochastic algorithms {{cite:7d1c29f67ab755e37745e7964dffd5219efda384}}, {{cite:fc3389d637c81b2f7fa287b75c814cde1509f9fc}}, {{cite:4a17b4ad892bd2a6c8b397d37161770c7a99b6f0}} and is essential for analyzing the decentralized gradient descent method {{cite:020a7a9ebd5b70fa2a7878e927feeddd0d0af2f1}}, {{cite:91b3bb9adb2333e56186c78048a534f81c6e1c61}}, {{cite:86b4ac9c7a3a950ecc750bd0ddec0977c5207461}}.Note that under the assumption (b), as long as the parameter {{formula:6f655da2-d9cf-461a-9364-97ee4cf0e72a}} is bounded, (d) is satisfied.
| r | 67abb599c4cf52e20de6c2c6e26d312a |
Topological photonics offers a unique path for manufacturing photonic devices immune to scattering losses and disorder {{cite:5f3c42d19d8cc73343a282e500c3d88cf7091f1f}}, {{cite:67a2f7b2cc247454bb4a4fedd27fb4cb295b403c}}. Since the pioneering theoretical predictions {{cite:480deb56d29d9803d7c8ff3450b12217c326f383}} and experimental demonstrations {{cite:9b033de98b1cc17ee3a19f1d484a6ef91f8abbb5}} of topologically protected electromagnetic edge states, most studies have
focused on linear topological photonic structures {{cite:5f3c42d19d8cc73343a282e500c3d88cf7091f1f}}, {{cite:67a2f7b2cc247454bb4a4fedd27fb4cb295b403c}}. However, by combining topology with nonlinearity {{cite:61dfa95ba1815164ed724d1dd484407a77129006}}, {{cite:5c1d2f2e0f128aa962d827d26696752cc1970ec6}}, {{cite:0b99cd92c2cd66c01315747b13482f4965cfeef6}}, {{cite:b78251b01f0e56fdcc1064c4dd5e6894db49b83b}}, {{cite:ab8587c23fe4d88c83d6c7cc018234dc87ddc872}}, {{cite:426fb5d792667290845f5d97e5fe38f78c59811f}}, {{cite:57df85731605e3a6cc19bc12c8df420e24b306d1}}, {{cite:04b5fd0be11a1573245d825a5bc18c66f0fecd11}}, {{cite:4df4fc770eabfd5671536b3e96db68e95078683d}}, {{cite:daa4a7a437093f22f3f98bc7b7fcd117a47442fd}}, {{cite:07cf5aa8f4919b7db9d171293ef9b686231a4eb9}}, {{cite:bf83aa3e0dd684585b2b3df6e9dffe675c056bec}}, {{cite:9aa0654c0115841995e650be791040196bf7ec6b}}, {{cite:fdbb5317ef9aa2fa29b9270fe9ee3ae65071954a}}, {{cite:226825c6eac505a71c8dcb082217c8dee501dbca}}, {{cite:11c16dbe9aa21056c0194ea36a570f04ded5dd4e}}, many opportunities for fundamental discoveries and new device functionalities arise {{cite:6f8b820a2b61db0292bd9adbc385d06c763314de}}. This is appealing also because nonlinearity inherently exists or is straightforwardly activated in most of the currently used linear topological photonic systems. The studies of nonlinear topological phenomena in photonics include, for example, nonlinear topological edge states and solitons {{cite:61dfa95ba1815164ed724d1dd484407a77129006}}, {{cite:5c1d2f2e0f128aa962d827d26696752cc1970ec6}}, {{cite:0b99cd92c2cd66c01315747b13482f4965cfeef6}}, {{cite:b78251b01f0e56fdcc1064c4dd5e6894db49b83b}}, {{cite:4df4fc770eabfd5671536b3e96db68e95078683d}}, {{cite:daa4a7a437093f22f3f98bc7b7fcd117a47442fd}}, {{cite:07cf5aa8f4919b7db9d171293ef9b686231a4eb9}}, {{cite:bf83aa3e0dd684585b2b3df6e9dffe675c056bec}}, {{cite:9aa0654c0115841995e650be791040196bf7ec6b}}, {{cite:fdbb5317ef9aa2fa29b9270fe9ee3ae65071954a}},
topological phase transitions activated via nonlinearity {{cite:ab8587c23fe4d88c83d6c7cc018234dc87ddc872}}, {{cite:426fb5d792667290845f5d97e5fe38f78c59811f}}, {{cite:57df85731605e3a6cc19bc12c8df420e24b306d1}}, {{cite:04b5fd0be11a1573245d825a5bc18c66f0fecd11}}, nonlinear frequency conversion {{cite:226825c6eac505a71c8dcb082217c8dee501dbca}}, {{cite:11c16dbe9aa21056c0194ea36a570f04ded5dd4e}}, topological lasing {{cite:dc24862be51511fd7066692da476212f7cca7a1b}}, {{cite:e567226c840f090c0128d8e815bde84cbee3154b}}, {{cite:a6ef6da2b03653969c7fa643d757b13cf0a8134f}}, {{cite:5957e2fe28d9edf3d6ba75f8107dc65dee094996}}, {{cite:542ec5ce7dadc5c1379231c5b12c853250267fd8}}, {{cite:a8297957c0e9b7f4c1da3ed7689005877406244e}}, {{cite:adfda9748eb62930d18549e694615a157d757ff4}}, and nonlinear tuning of non-Hermitian topological states {{cite:049ada1db8a7db6c0f858310f2aa13705c68d6dd}}, {{cite:45da7063b04ae07b1a3330d2686d6660864bc053}}.
| i | 7b06cf24a3aa65568a2c8c5cb8035768 |
Fig.3(a) shows the zero-field cooled(ZFC) and field-cooled(FC) magnetization curves for SIO-as prep and SIO-anneal samples at an applied magnetic field of 1T. Both the samples exhibit magnetic transition below around {{formula:262d76f1-bbc1-4904-8266-933b2ade7016}} 238 K as seen from the inflexion point in the derivative of the ZFC magnetization curve, inset of Fig.3(a). The inverse susceptibility shown in Fig.3(c) do not obey Curie-Weiss behaviour in the entire paramagnetic region of both the samples, but in a limited temperature region. The transition temperature (T{{formula:1505fad4-b2a0-441b-a61a-91213a8fa3af}} ) obtained from the fitting are 233.7 K and 233.8 K, respectively for SIO-as prep and SIO-anneal samples. The estimated effective paramagnetic moment {{formula:d6ab83fc-8a17-4adb-a2fa-cba7962d78b2}} value for SIO-as prep is {{formula:4f2c70af-87fd-49c8-a157-1371add7f39b}} 0.58{{formula:a4c7c619-2802-4755-bac4-5aa2f48b1698}} which is close to reported values{{cite:8fb02be1806405f7bd00c18ae133f5231aebfcfe}} while {{formula:f0c87795-d44a-49f9-98d6-9c5b67afbd98}} for SIO-anneal is {{formula:1b7830d5-27f7-4cd9-aed3-152618d24a13}} 0.60{{formula:328db9b9-2142-41c7-8d2e-415701d7e544}} ,higher than SIO-as prep. The transition temperature marks the transition from paramagnetic to canted antiferromagnetic structure. The rise in the dc magnetization below T{{formula:cbfd4a80-90ad-4471-8ca1-fa32efdef536}} suggests weak ferromagnetic behaviour arising due to the canted antiferromagnetic structure. The magnetic structure of Sr{{formula:ba3cc77d-4481-4b48-9829-116ddd789c71}} IrO{{formula:3c719619-3e6f-429f-ad5b-89273d3cd8b7}} compound is shown in Fig.1(d). The J{{formula:d357da3c-5643-46af-96e0-d19cd34c7866}} =1/2 pseudospins are rotated in the ab-plane by about 13{{formula:65351c4e-e22b-4957-a9ec-9083d84909ab}} and are locked to in-plane IrO{{formula:de280685-5370-4a2a-9180-c1c97844cd36}} octahedral rotation due to strong spin orbit coupling.{{cite:b1540b640896bc5c5197f9fe6897814546b1ce8d}} This canting of spins results in a net magnetic moment along b-direction in each Ir-O layer which are arranged in ({{formula:94b1622c-6044-41c1-a70b-735eb1e78775}} )manner along c-direction as shown in Fig.1(d).{{cite:b1540b640896bc5c5197f9fe6897814546b1ce8d}}, {{cite:808b01349206ae5aae6da236703882da7bbb1157}} The intralayer magnetic interaction which is dominated by Heisenberg exchange coupling ({{formula:a3c4e9ec-17d3-4f54-9f76-a5fe8c688c0e}} 60meV) is stronger compared to interlayer interaction.{{cite:7ac11df15d1321bcb3d921690763b1b0e32906d8}} Both these interactions (intra and interlayer) are proposed to be necessary to stabilize the observed canted AFM magnetic structure.{{cite:7c8950ea00609f9f2dc1a4880c6d590b38c3e376}} The canting of moments in the ab-plane arises due to DM-interaction which is responsible for weak ferromagnetic behaviour of the compound.
| r | f455ac7afefc7a532ff79961084ae6ad |
[leftmargin=*]
RCPO ({{cite:70b39d126b2fb9ac19f3c6fd3c45f854801396c7}}) is a general CMDP policy optimization algorithm based on Lagrangian relaxation, which introduces extra learning parameters to control the constraint-objective trade-off. We adapt RCPO to RCB by the proposed POCMDP formulation. While its maximal performance reaches CBRL , its average performance is hampered by high variance. The instability is due to (1) the sensitive initializations of the Lagrangian multipliers for stochastic optimization, especially in the non-convex condition; and (2) the soft combination of constraint violations and delivery with improper weights that leads to ambiguity in rewards. Particularly, we notice that the ambiguity makes instability combinatorially more likely in MC than in SC (wider box in MC than in SC ).
USCB ({{cite:a0e1ab7e1338cbc93d0e15eb00050c864ce706e9}}) is the prior art that formulates an RL framework and uses extra hyper-parameters to non-linearly control the constraint-objective trade-off, which can be treated as a variant of Lagrangian relaxation. For a fair comparison, our method CBRL and USCB use the same input features and network structures. We provide two specific implementations, USCB and USCB-DDPG. USCB aligns with CBRL in entropy regularization {{cite:259b8edae053a50aa2334391d240b7cade24a7ea}} and independent action space, while USCB-DDPG respects the plain Monte Carlo estimation based actor-critic approach and the temporally correlated action space in {{cite:a0e1ab7e1338cbc93d0e15eb00050c864ce706e9}} (check the appendix).
It follows that USCB tends to be more stable than RCPO (narrower box), as the instability caused by non-convex optimization is alleviated. However USCB still suffers from the reward ambiguity. In particular, we remark that while the best USCB model (top-rating in ANS) exhibits the best ANDR performance (at the cost of constraint satisfaction), its trade-off parameter design indeed shows a significant see-saw effect, and requires laborious tuning. By contrast, CBRL adopts a parameter-free solution, which is user-friendly and turns out best-performing in ANS.
CEM {{cite:7acf2e5436729b7f317cc470410b93cbd8d31204}} Cross-Entropy Method is a gradient-free stochastic optimization method. Widely used in the industry, CEM attempts to optimize a greedy sub-problem in each time slot and bears the exploration-exploitation trade-off. Since winning is sparse in the data, more exploration is required to obtain a more accurate estimate, which squeezes the space for exploitation. Consequently, the best CEM model achieves decent constraint satisfaction (around 0.8 in CSR) but lower objective optimization, due to the averaging effect of the dominant exploration traffic.
PID ({{cite:b5a1c96d32c3c85bb3c6815b8044920ad9e78d3e}}) adopts a PID control solution to bidding with CPC constraint and budget constraint. Based on the optimal bidding function (REF ), we adapt PID to control the bid ratio that drives the ROI constraint toward the target in each time slot. We note that PID itself does not handle changing systems well, and the online adjustment of PID parameters to suit the changed systems is non-trivial and beyond the scope of this paper. We find empirically that PID cannot balance constraint-objective trade-off well in highly non-stationary markets presented in our dataset, and hence the best PID model with the best ANS score shows the only moderate status of both constraints satisfaction (CSR) and objective optimization (ANDR).
RM ({{cite:ea75b17fa0a4048db63405f4ed0271ce30977d3b}}) propose to deal with RCB under a static functional optimization framework, which solves the optimal bid ratio over the train set and applies to the test set. The solved bid ratio achieves the best performance on the training problems on average, but does not adapt to each of them. As a result, in the ID test set, the RM model performs far from optimal, although it respects the constraints well (CSR close to 1).
{{figure:83039041-017d-414d-913d-c743ed43ae41}}{{figure:53520ebe-1550-485f-b99b-8acf7df0b6dc}}{{figure:bb9bfbc4-9f06-44c9-bdd3-a5f537f1a12d}} | r | f29e493e852b4368596aabcf30137421 |
Neural dynamics- The system consists of {{formula:2cb04460-8201-4899-a711-6caf26fdca31}} spiking
Izhikevich neurons interacting by transition of chemical synaptic
currents with axonal conduction delays. The dynamics of each
neuron is described by a set of two differential equations
{{cite:b28d44658ac1cf57eb31330adb40fb3c0edb3bb6}}:
{{formula:5cbaab57-3132-4af8-8552-144d8c3cfbb3}}
{{formula:2c681adc-8f5b-4e86-8144-289e4faa0352}}
| m | 150b2460615cdd03dc45230813466ab7 |
In 2016, Gatys et al. proposed the use of a VGG network{{cite:87ddeab52dc647360c63ae9a277d84b8a0d83581}} based method to extract features and to perform art style image transfer. The authors deployed a pre-trained VGG model to obtain deep features of the input image and a style image, and showed that a stylized image with both the target content and the required style can be generated by optimizing a random noise image iteratively. At the same time, their method of expressing style information with Gram matrix has also been widely used. The Gram matrix is composed of the inner product of the two vectors, so the Gram matrix can reflect the internal relationship between the vectors in the group of vectors. The deep feature of an image can represent the structure, texture and other information of the image, so when the Gram of the deep features of two images are similar, they have similar internal connections, that is, they have similar styles.
| m | 6f12f60a87d17e564244436f08442ac1 |
For CDFL {{cite:50f7a244107d55e7ee18458f0c92ef845dd7c96c}} in Table 1 and 2, the alignment acc-bg on the Hollywood dataset is somewhat different than the one mentioned in the referenced paper. Similarly, for TCFPN {{cite:b5219674b491ef65ad67a0c8459ce6f595d2de29}}, in some cases, our reproduced results are not the same as the ones mentioned in {{cite:b5219674b491ef65ad67a0c8459ce6f595d2de29}}. In this case, we reported the results after contacting the authors and having their approval. For a fair comparison in both baselines, we reported the results, that represent the initial pseudo ground-truth in our method.
| r | 2d05830e43ed76456fe069f30af84b30 |
Deep Neural Networks (DNNs) are now widely used for many applications, such as computer vision, speech recognition, and natural language processing. However, their large number of parameters and associated computational complexity makes DNN training expensive. Most prior research on reducing DNN computation costs focus on DNN inference. For instance, quantization {{cite:2d3cfdf89b6a2a993075b4d59f1c3d05dd7f8969}} can reduce the number of bits required to represent model parameters, allowing for more efficient storage and faster execution. Weight pruning {{cite:87c283c77c2ca2d49cad03cad4df9fe27c1eb4bf}} is another technique that can reduce the number of model parameters, by setting some parameters to zero during training. However, while these approaches can lead to more efficient inference, they often make DNN training less efficient. For instance, weight pruning often requires a longer training regime to reach convergence after multiple rounds of pruning {{cite:e1cea35dbcf7156f76122e556287b5a1774e3430}}.
{{figure:a550cb58-feaf-4672-9b63-976ac30e4729}} | i | 6253920becfdc325febde867d3acc5cb |
The choice of activation function in a deep learning architecture can have a significant impact on the training and performance of the trained network. The machine learning community has so far relied on hand-designed activations like ReLU {{cite:52ac7c5348ebf7fa0c523668448fe93d2c9a4c1e}}, Leaky ReLU {{cite:e48a86e5a8654a34cf526ed3968bdffb11991bdc}} or their variants. ReLU, in particular, remains widely popular due to faster training times and decent performance. However, evidence suggests that considerable gains can be made when more sophisticated activation functions are used to design networks. For example, activation functions such as ELU {{cite:fe0344dccd2014a16d8858b2b512966f0c71b968}}, Parametric ReLU {{cite:d19929a7a94914426f1134f0d87cbf1a22044ca7}}, ReLU6 {{cite:5b685511ffa535394666879ae8d04c31d60fcf1f}}, PAU {{cite:c42b1f6b3ec89c94375e53700086db06e5223cf7}}, OPAU {{cite:c86bc3d0cc7f56aad0e0e5edc7b86134efba7299}}, ACON {{cite:f2ddd6116a8fb3178c3bc7266802130383acf185}}, Mish {{cite:827854fa1f45ef19c82e71219e6ffd2d29d4c67c}}, GELU {{cite:4e7b98010bdc852b4676445bd08ae91df309905b}}, Swish {{cite:09176fdf653bef2d7bb8c10b5f1bf11af40a3f7d}}, Serf {{cite:58cdcfce1ff2b7ec7852131bb1b1ac3618b481c3}}, TanhSoft {{cite:bc96f5f6ac0d8c369d786ee3e94e653621bae4b0}}, EIS {{cite:09f663499dfe568a95a8be8babd4d31fce8888df}}, etc have appeared as powerful contenders to the traditional ones. Though ReLU remains a go-to choice in both research and practice, it has certain well-documented shortcomings such as non-zero mean {{cite:fe0344dccd2014a16d8858b2b512966f0c71b968}}, non-differentiability and negative missing, which leads to the infamous vanishing gradients problem (also known as the dying ReLU problem). Worth noting that prior to the introduction of ReLU, Tanh and Sigmoid were popularly used, but performance gains and training time gains achieved by ReLU led to their decline.
| i | a47e9be616ec58a3587050b5a8758faa |
While the EoS of symmetric dense nuclear matter with an equal fraction of neutrons and protons has been reasonably constrained by analyzing the data on kaon production {{cite:e8736c31159a71e416e320c182adc61c330a0228}}, {{cite:c6051538f5381fe437c988f82e45073ddce4e6f1}} and
collective flow {{cite:f5ae347801e76ba822653656f2e965853f2068fe}} in heavy-ion collisions, one still cannot determine the critical density for the phase transition of dense matter from the hadronic phase to the QGP phase. Moreover, the EoS of dense neutron-rich matter (i.e., neutron star matter) remains largely uncertain due to the poorly known high-density behavior of the isospin dependent part of nuclear matter EoS, characterized by the symmetry energy {{cite:7766ab7b85382095f8017d6fdb62483ae9f6eb0d}}, {{cite:5f4e2977097a74b2cb07ac2134fdf75efce5d0df}}. Both of them require a delicate determination of the EoS of dense matter. Therefore, one has to find more sensitive methods to probe the EoS of dense matter created in heavy-ion collisions. Besides searching for more EoS-sensitive observables such as the double strangeness {{formula:0d22b682-79c6-4299-a91d-bf6d0d6a0420}} production {{cite:9dbf25694acf6946fdfd37a8e2fadb1022305d36}}, it may be possible to create high sensitivity to the EoS via the production of long lived dense matter with large volume in heavy-ion collisions.
| i | 65159994cc68ca5776a5d818e5a5e4c6 |
Additionally, using neural networks to learn the kernel function have been proposed {{cite:9695b8fd4dc69736ba8dc69e9c49fd755524e4c1}}.
This model uses a nonlinear transformation with a neural network {{formula:2c563106-8956-423b-88ab-4c27c1beb3b9}} parametrized by weights and biases {{formula:124915e7-155a-403b-a394-86d4c2be333b}}
The data is transformed and the kernel function with parameters {{formula:5e217ceb-0656-4b8a-a5e1-185c4b9ac19f}} is then applied to this latent representation as:
{{formula:8433e31e-1753-443f-9191-59a0ba16ff33}}
| m | 513a144f6aa28c92bfa3ad55b0bc8df2 |
These studies established the choice of single-particle basis as a crucial factor causing major differences between different implementations. For instance, the results from TURBOMOLE, FHI-AIMS and MOLGW,{{cite:610fe4a1ee16c1b9fde0ff1f7552a8dfeb710db0}} but also from the low-scaling implementations by Wilhelm et al.{{cite:b3a1d6f922523093d5df2335fbd5bdae444f3601}} in CP2K{{cite:4ce918dd947b9db07dd9fa0ff32f6d71e33f6496}} and by Duchemin and Blase{{cite:60c1192bd703d8b098b55604358755342d9d7557}}, all using the same def2-GTO type basis sets, agree within a few ten meV on average for GW100, even though these implementations differ in frequency treatment as well as calculation of four-center integrals. The differences between codes using different basis sets are considerably larger. The discrepancy between the TURBOMOLE and BerkeleyGW results of nearly 300 meV on average reported in ref. numbers{{cite:5a56bbdcc6a5a6c35d88d56529f9cc7e668b2f0b}} for the Highest Occupied Molecular Orbital (HOMO) were not necessarily insightful since the BerkeleyGW results were not CBS limit extrapolated. With only around 60 meV on average, the agreement between the CBS limit extrapolated PW results obtained with VASP and TURBOMOLE was found to be significantly better.{{cite:9bfaf8ffc355b63776fa93855e10e138913bf53b}} However, for EAs the disagreement between different codes is considerable larger and differences for systems with a positive LUMO can easily exceed several eV. It has also been pointed out in ref. numbers{{cite:9bfaf8ffc355b63776fa93855e10e138913bf53b}} that the type of GTO-type basis set has a major influence on these EAs and that Dunning's correlation consistent basis sets are more suitable than the def2-series which has been used in ref. numbers{{cite:5a56bbdcc6a5a6c35d88d56529f9cc7e668b2f0b}}. Beside the choice of the basis set, the treatment of core electrons (pseudo-potentials vs. all-electron) also plays a decisive role for many systems.{{cite:e629f67f46917f4c8ed33b01349a8ce61e4055af}}
| i | 3898f76dacd5eae9b27d608b9e827fc2 |
On a technical level, we provided a generic characterization for the bias of gradient descent on linear models parameterized as {{formula:48783aa9-8e96-4b08-b948-890b4ce8ff60}} for a homogeneous polynomial {{formula:55f429c5-3096-480e-8202-8fe273b57f0d}} . The {{formula:f4d4d623-c236-49d3-841d-fd889a473e2f}} bias (in parameter space) we obtained is not surprising, but also should not be taken for granted – e.g., the result does not hold in general for non-homogeneous {{formula:d23da24b-b577-47d0-8550-97a08b260970}} , and even with homogeneous polynomials, the characterization is not as crisp when other loss functions are used, e.g., with a squared loss and matrix factorization (a homogeneous degree two polynomial representation), the implicit bias is much more fragile {{cite:d635fed230891d62783dc039bd8282af18f980ab}}, {{cite:0ea0cbe16858dd5adc27cb7cfee015798bc84217}}. Moreover, Theorem REF only ensures convergence to first order stationary point in the parameter space, which is not sufficient for convergence to stationary points of the implied bias in the model space (eq. (REF )). It is of interest for future work to strengthen this result to show either convergence to higher order stationary points or local minima in parameter space, or to directly show the convergence to stationary points of (REF ).
| d | 6bfb7045641c64f92d9115e4263a5d75 |
The algorithm is implemented in Python by using the machine learning library TensorFlow {{cite:ecb6cda928bcadacc814f79ca378f4e47e883548}}. The code can be found in a public GitHub repositoryhttps://github.com/frankhan91/RNN-ControlwithDelay upon publication, and thus the results presented here can be straightforwardly reproduced and further developed.
{{table:7cf14ab1-5341-4015-8652-a769d49b4820}} | r | 53165988a5886ee2159131d5b87868ed |
Our experiments are conducted on various image and text datasets. The MNIST {{cite:9266612873c67c0db83719d3bb20b7740788f2ae}} contains 60000 training samples of {{formula:51b7a184-8201-437d-a047-335252ae095b}} gray-scale hand-written digits from 10 classes, and 10000 test samples. We train MNIST with a Convolutional Neural Network (CNN), which has two convolutional layers followed by two fully connected layers with ReLu activation. Dropout is applied after the max-pooled convolutional layer with rate 0.5. The CIFAR-10 dataset {{cite:894be6fffba45da969704506360fe604643e3d19}} consists of 50000 {{formula:4cf061c4-b1bc-4bed-976d-9cd313e05995}} RGB natural images from 10 classes for training and 10000 images for testing, which is trained by LeNet-5 {{cite:9266612873c67c0db83719d3bb20b7740788f2ae}}. Moreover, we also implement ResNet-18 {{cite:bb8a17cc33bf05fb9f74153d202c4f191e8f8943}} on this dataset. The IMDB movie review {{cite:83f8293c94347bf10fe20853bb4b0ec9b43e882f}} is a popular binary classification dataset for sentiment analysis. Each movie review is tokenized by top-2000 most frequently appeared words and transformed into integer vectors, which is of maximal length 500. We train a Long-Short Term Memory (LSTM) network with a 32-dimensional embedding layer and 64 LSTM cells, followed by two fully connected layers before output. Cross-entropy loss is used for all the tasks. Following the classical distributed training setting, in each training iteration, data samples are uniformly randomly assigned to the workers.
| m | edddbb3a6cfe2baaaf3bdd915c784418 |
Planets that have strong magnetic fields in their interior region, like Earth, Jupiter, Saturn, and Mercury, are enclosed by invisible magnetosphere {{cite:33769595e9c7fb38e988fb013ee70ebc37a9e1a6}}. The charged particles of the solar wind radiation (electrons and protons) are deflected by their magnetic fields as they stream far away from the Sun. This deflection by the magnetic field creates a magnetic sphere that acts as a protective "bubble" covering the planet {{cite:eea2d626b4b258f86dae38a77997dd993094c2f9}}.
| i | 52bc9736746a742cfd2b54c96d5c81dc |
Building a model that is able to predict the future states of an environment from raw high-dimensional sensory data (e.g., video) has recently emerged as an important research problem in machine learning and computer vision. Models that are able to accurately predict the future can play a vital role in developing intelligent agents that interact with their environment {{cite:9bb85579571c9044490607b66565249e3b02ae09}}, {{cite:a4713c2fe15bf022515f5ad38acb5b0de42dd0ff}}, {{cite:17fab58d42f05a1bf6167d93ac6374be14752275}}.
| i | 34b5f2eb3bf80062ff6b9828e50d4673 |
FedDG re-ID prohibits the transmission of images between different clients, which limits the application of most DG {{cite:e3a074f5fee7a3bc999933e98d69d89919ee534b}}, {{cite:e77651725fcdce2ca00aef8a5167e00626018a9c}}, {{cite:3749669c0adcf8272e63a3e9bfd551d6363b341d}}, {{cite:989c0a51378c4c6d61c5203284220d39bc2a03e8}} algorithms. Generally speaking, the privacy constraint refers to no data transmission. However, recent works state that sharing averaged images {{cite:8b911929bfa9fdccf224a929214295d9fea47b15}}, domain-specific classifiers {{cite:053fdc07fef5d55a374c2890cb51876b9afdf231}} or intermediate feature distributions {{cite:6fd9415c0cf22c90f3683d72a141b780b0927d5f}}, {{cite:95aa5333c9aa7fd5813bfd02711106a58c0e6f7f}} will not bring the leakage of data privacy since such weak information cannot be used to recover the original images. For example, FedMix {{cite:8b911929bfa9fdccf224a929214295d9fea47b15}} weakens the data-privacy constraint by using the averaged images from other clients for optimization. Wu et al. {{cite:053fdc07fef5d55a374c2890cb51876b9afdf231}} attempt to handle the federated learning problem by jointly using the classifiers of each local model for optimization. Luo et al. {{cite:6fd9415c0cf22c90f3683d72a141b780b0927d5f}} propose CCVR to alleviate the heterogeneity in federated learning by sharing the feature statistics of each class for each domain. Despite their effectiveness in closed-set classification problem, most of them are not suitable in FedDG re-ID. This is because each domain has completely different IDs in FedDG re-ID. In this paper, we follow {{cite:6fd9415c0cf22c90f3683d72a141b780b0927d5f}}, {{cite:95aa5333c9aa7fd5813bfd02711106a58c0e6f7f}} and share domain statics between clients. Different from them, our method shares the global statistics in the pooling-5 feature space to synthesize novel features for optimization with re-parameterization trick {{cite:790c134a81020cdedf541e728aeaad4df730ea68}}, offering a plausible way to handle the heterogeneity in the open-set FedDG re-ID.
| d | 49b138e41e5ffb5804ec805ee492cc84 |
We summarize our results in Table REF . For both corpora, both the Subject and Non-Argument Hypothesis Models exhibit significantly greater representational similarity to the Reference Model than the Null Hypothesis Model does. This shows that the contextualized representations of verbs encode both of the noun categories in the sentence. Furthermore, these two syntactic categories are not encoded to the same degree, as the Subject Model reliably exhibits greater representational similarity to the Reference Model than the Non-Argument Model does for both corpora (Figure REF ).
From this, we can infer that BERT's embeddings of these verbs encode the verbs' subjects to a greater degree than they encode the non-argument nouns, despite the fact that the non-argument nouns exhibit much less surface-level distance from the verb.
This result corroborates other evidence—from behavioral evaluations {{cite:0058b577ee8d6504c0e14bd9b3cf178c644e7bcb}}, analyses of attention heads {{cite:ffe49ce63526166a5319b785894074839c5dc072}}, and probing classifier tests {{cite:de9ff6aae825a043de54e21e44b8ee6a7e043a89}}—that BERT is sensitive to subject-verb dependencies.
{{table:e8ed1e94-1421-4c4b-a2d6-b2848114336e}}{{figure:a8ba4098-bc8b-40f8-9dcc-6369ced743e9}} | r | f709b9b5768f46ebd71b2a51c320b91d |
In this paper, two evaluation methods were employed to assess the model’s fidelity and diversity, which are essential parts of this research: precision and recall {{cite:0b9b59aabc808790af4987f1f8bc6c442a4a1efa}} and density and coverage {{cite:bf1c6c3c574a781fdfc00834c33f49d0aa745b79}}. Fidelity is evaluated with the precision and density method, while diversity is evaluated with the recall and coverage method. Since both evaluation metrics compare features of the target images to those of the source images, the choice of feature extractors has a significant effect on the process.
In this paper, VGG19 {{cite:fb59fbe56aba5629d7c1a865dd0ae65883c572ae}} with batch normalization {{cite:d40bb0e9bb1f8b47896ec073f4501c359404db6c}} is adopted as a structure, and its parameters (weights) are defined with three different approaches: random-initialization {{cite:4cd1dd721695c2123babfb8b5bbf79f3430979c4}}, classification with ImageNet {{cite:7fc107884b9568b20784cf595261c8be8ea908e5}}, and classification with CelebA {{cite:7b32decbc4414a6e1675560d71f1e8100f9f1b74}}. Since random-initialization does not limit any condition on the model’s future parameters, it can genuinely reflect the fidelity (diversity) of the outputs. On the other hand, feature extractors pretrained with a classification task are more likely to represent the class-related fidelity (diversity).
| m | c21c0604893589e7b6956326d71eafba |
We will check the performance of the three proposed PANNs (CNN6, CNN10 and CNN14) on the SER training and test datasets. In order to take advantage of the large pretraining done on the AudioSet {{cite:b5414bb3f62214544496c4efce2c4b5e62b27638}} dataset, we will use the pretrained models of CNN6, CNN10 and CNN14 made available by the authors of {{cite:aa273658b66e758da9657a44feb7c1c18141da69}}. These can be found in Zenodo. These pretrained models will be finetuned on the SER training dataset in order to achieve better performance than the baseline.
| r | 59b67ed2508d640c8781d7e408c9b99f |
IL was originally used to train predictive coding models of cortical circuits {{cite:f587d282f06d5eb511093972f4691ce2d2b9aae7}}. The success of subsequent predictive coding models lead some neuroscientists to propose the hypothesis that predictive coding and IL are canonical computations used throughout the brain (e.g., {{cite:b1986b4f0168cec871769fa1986339743cba1e46}}, {{cite:f1d4ce224b52f286feb3d7bc27fb3804b3cc9d90}}, {{cite:31561dec112715e885d6e093768f92fc7042d976}}, {{cite:f671f4aa3c261afabed2cc77bcc8b7d665d40624}}). In this paper, we provided novel mathematical justification for IL by showing it closely approximates a proper optimization method known as implicit SGD, which is distinct from the explicit SGD executed by BP. This finding, in conjunction with the theory IL and predictive coding are canonical computations in the brain, suggests the interesting possibility that implicit SGD, and not explicit SGD, is the central optimization method utilized by biological neural circuits. We observed two performance advantages that fit with this possibility. First, consistent with our theoretical interpretation, IL algorithms are more stable across learning rates than BP. This property is compatible with the fact that synaptic plasticity in the brain can fluctuate rapidly, e.g. due to neuromodulation, yet maintains stable learning properties. The stability of IL is arguably its main advantage over BP, which is consistent with claims that the main advantage of implicit SGD over standard/explicit SGD is its stability across learning rates (e.g., see {{cite:59bc5ab7ff3b81db237a184aa8c306180f2bf47a}}, {{cite:dfa92e180a972f326cd11422b00ac88b8fa5e217}}). Second, we found IL minimized the loss more quickly than BP in the more biologically realistic scenario where single data points, rather than large mini-batches, are presented each training iteration. These simulations provide evidence that IL is more compatible with biologically realistic learning scenarios than BP. Collectively, our findings suggest IL is a promising basis for developing biologically constrained, high performing, local learning algorithms.
| d | 790cf39a0c4341ebb2bbea0457b48fcd |
One of the most important challenges, in the past decades, in
condensed matter physics is finding a justification for the high
temperature superconductors. The well-known
Bardeen-Cooper-Schrieffer (BCS) theory is the first successful
microscopic theory of superconductivity. This theory describes
superconductivity as a microscopic effect caused by a condensation
of Cooper pairs into a boson-like state {{cite:3310c034ce370e2c783b56ce64d3bae01128c35b}}. However, the
BCS theory is unable to explain the mechanism of the high
temperature superconductors in condensed matter physics. The
gauge/gravity duality or Anti de-Sitter (AdS)/Conformal Field
Theory (CFT) correspondence is a powerful tool which provides a
powerful tool for calculating correlation functions in a strongly
interacting field theory using a dual classical gravity
description {{cite:ec1cd46f6df3c6c9439886cd920dd4090c9100c1}}. According to AdS/CFT correspondence,
the gravity theory in a {{formula:260c5fc2-f97f-47a9-ba3b-e6cfff29428d}} -dimensional AdS spacetime can be
related to a strong coupling conformal field theory on the
{{formula:e80c1fba-83b1-4352-9890-bb7a82f6f874}} -dimensional boundary of the spacetime. The application of
this duality to condensed matter physics was suggested by Hartnoll
et.al., {{cite:7fb2255854ae6614a0f53cfa63ca8ebee87d549b}}, {{cite:31fb7ac9345543996c350f0badbfb98dc48b9956}} who suggested that some properties of
strongly coupled superconductors on the horizon of Schwarzschild
AdS black holes can be potentially described by the gravity theory
in the bulk, known as holographic superconductor.
According to this proposal, a charged scalar field coupled to a
Maxwell gauge field is required in the black hole background to
form a scalar hair below the critical temperature. It was argued
that the coupling of the Abelian Higgs model to gravity in the
background of AdS spaces leads to black holes which spontaneously
break the gauge invariance via a charged scalar condensate
slightly outside their horizon {{cite:4fb2dbf9132e63c9bf6f96cd24d2d25eaac4906f}}. This corresponds to a
phase transition from black hole with no hair (normal
phase/conductor phase) to the case with scalar hair at low
temperatures (superconducting phase) {{cite:4fb2dbf9132e63c9bf6f96cd24d2d25eaac4906f}}, {{cite:d04132bddb80f936ad93bcd47aa7603e10cbf569}}, {{cite:96cf6d204d816ddd56c58172e57e4b69a423fea6}}.
| i | f581f681274b810f3ca430e05d57043d |
Our main focus is to study the convergence of the metric {{formula:2791e095-ef71-472d-aa3b-bea6013ce334}} at two different dynamical phases of the LRIM as the convergence of {{formula:982e82fe-0fa2-47b3-8cf0-45c66d78371c}} to zero suggests thermalization in that particular phase. For all the quenches we prepare our initial state as the {{formula:8e8ff8d9-8bd8-4cec-9e51-4ee420a91fc4}} symmetric GHZ state REF which is the ground state of the Hamiltonian REF . We choose this initial state instead of the more common ( and easily prepared in laboratory {{cite:d6874fff507fc46b5fed4c3e13dfbdf57b7b1ba9}}) fully polarized state because the model REF thermally transits from paramagnetic phase, with Gaussian PDF, at high temperature to a ferromagnetic phase with a {{formula:acb4a194-9073-4cec-8cf1-e62535aea0ac}} symmetric bimodal PDF, see appendix . We keep {{formula:5a902593-6e6a-42fb-8bab-4e8c21c91cf4}} as it is a more interesting region that exhibits both finite temperature phase transition {{cite:b96b30a47817613f9d5d055cee71ed71256485ca}}, {{cite:e3d93f00e04ab9635bf48572b803280b65f3a351}} and dynamical phase transitions {{cite:99e9dd78dba06955a9ed410a33025e4e785b74ee}}, {{cite:6252fc26128791d35c690191ef38496e76f8db63}}, {{cite:e94748cc170daa50d4dbc96d6a8357a5c9f13006}}, {{cite:4e1014c189d341654f5f619b7e1fccc0d5f886df}}, {{cite:4626a6080bad997814f6a91cb370e2a2e2bfc051}}, {{cite:755496c1d5b5ade4fe8d311455bc634ab3c55a33}}. We take three different values of interaction strength, {{formula:befb3e77-8fd8-4402-9459-c051bbd04584}} . At {{formula:17a7e498-895f-4178-bcb7-dcee608d08e7}} the system is integrable as it is fully connected and has full permutation symmetry so we don't expect thermalization. The other two values are chosen as {{formula:e37069ef-5842-4384-a881-2d9a262b9e10}} and {{formula:58f6e136-12f5-47ff-8ab3-8ed3f147ba87}} because the system exhibits relatively faster equilibration (and Gaussification of PDF) for these values following a quench to the dynamical paramagnetic phase {{cite:755496c1d5b5ade4fe8d311455bc634ab3c55a33}}.
| r | 1aad8aecc847e2fa58de71c8567a8213 |
Indeed, by collapsing all nodes in {{formula:5839446b-96b9-4534-ab98-d62da3949144}} into a single node and similarly for {{formula:9dbf64fd-41e3-4b14-94c7-935fec0472b5}} , one reduces to the same setting of {{cite:f23ce882680cf4a78ea95185afbd6b38bb22e2ba}} where (REF ) is proved.
| r | fdb05c47b2f0686b01f6d95ccc9bdf60 |
Upon considering common forms of vector presentations of textual content, bag of words, word embedding, and sentence embedding are three of the leading methodologies in the present. Word embeddings have been observed to surpass the performance of bag of words for large enough data sets {{cite:ed5284fa5ed36adfb313266cc1640836b10793db}} because bag of words often met with various problems such as disregarding the grammatical structure of the text, large vocabulary dimension and sparse representation {{cite:7d64b3b0967a7390248f848def9357f468694d68}}, {{cite:d757b2464e58717129435513af1560473a744a4a}}. In order to tackle the above challenges, word embeddings can be used. Since word embeddings capture the similarities among ingrained sentiments in words and represent them in the vector space, word embeddings tend to increase the accuracy of classification models {{cite:a4ebc80f6922b5f06c27f5c63f8cb5aa3715933c}}.
| i | 6535e3bbf9f9575716a4c173c32b80f3 |
Label bias arises when
different output states have very different numbers of outgoing transitions.
In directed generation tasks
such as machine translation and abstractive summarization,
there is a nearly one-to-one mapping between the input and the output.
The transitions between the output states are almost deterministic,
thereby label bias exists but is not a serious issue.
Previous work {{cite:d0516606753a92a8e9fa10ebea08fa2fceadedfe}}, {{cite:d6a410b6d45589dddb08857b24ebcc429716c9a9}}
observes some moderate improvements with globally normalized training.
It remains to be seen how state-of-the-art text generation models
based on BERT and GPT are affected by label bias.
| d | fa0ddbac28063391552283d89d87cbfb |
Both the order in perturbation theory and the treatment of unstable particles that one uses for the calculation can have profound implications for the size and shape of the background.
Thus, one of the primary goals of this paper is to quantify off-shell effects and higher-order corrections in NP-sensitive observables.
As these build the foundation for any Beyond the Standard Model (BSM) analysis, we want to further evaluate the impact of these changes in light of a typical search for a {{formula:f12e6ea4-7540-45bb-babd-3babb434a26b}} signature.
To this end, we compare the different distributions after applying very exclusive selection cuts that are designed to disentangle signal and background.
These cuts are based on the analysis presented in Ref. {{cite:a863f27bcbece253f3f3ccc2bb6a5bad8231cf08}}. We then use the resulting distributions to calculate exclusion limits for the signal strength depending on the mediator mass.
For this, we employ both dimensionless and dimensionful observables and assess which of these yields the most stringent exclusion limits. But here, too, our focus will be on the background modelling and the ramifications of using an inadequate description.
| i | 238264d59b06ff32b8468fad8547e56c |
Related work. Our work is closely related to {{cite:3d0b0ddfc51f2d6ba6bc460b5674f4ce84a9a98e}} which evaluates feature attribution methods by their ability to diagnose different kinds of model errors. Similarly, and {{cite:e27b650a691f26d23c6bf350a091a9a4565e5122}} study whether feature attributions detect spurious features, and {{cite:578650576a10551fb33bb6eaeb40e112fb60c2cc}} shows that model explanations can't uncover unknown spurious correlations.
Compared to these works, our framework is more flexible: given a set of reference models and a distance metric between explanations, it can work for any explanation method, model anomaly, and any modality (vision, language, or other).
This flexibility allows us to broaden our scope to feature visualization methods such as Caricatures, and to consider a greater variety of model anomalies.
| d | bb1855e6a6076257283d84df65a6af40 |
The bipartite approach is broadly used, for example, to model scientific collaboration networks {{cite:e60984ff3faa42ad15fa44b45bdae604611130d8}}, {{cite:379627db80c78543ebe611ae2f122e8745134489}}, product exports in economics {{cite:7d75b6de065f7ba698b111dd9d1fed5f0f0cb9e8}}, relations between different species in ecology {{cite:5aec3a591e30d5d24235357a588a88005443a32b}}, {{cite:c46b27ec262d1bac703ce2e175e49d80dbab15ea}}, relations between diseases in medicine {{cite:a10d50ecb28ea4c749b1a62b74e051f37c728075}}, and the similarity of degree programs in higher education {{cite:a60be75cb6a437e8031eb8caa30f0bbcead03d46}}. More recently, some online education studies have used this approach to capture student interactions on forums {{cite:b7011973cb98bcee84b5aee2c18fc0cc706a5254}}. Here, we adopt the same approach.
| d | 3e03bea84f0eb607b7ecf11bff3d9327 |
One finds that {{formula:e18052f1-97a4-4fe3-9a56-efe515fa2efc}} can be expressed as {{formula:29c3b1b2-dcff-4e0a-b3bb-46f298cf0b08}} , where {{formula:95ac4601-0d08-479e-ad81-00bca920240c}} is an integer.
The results of Sec. REF -REF were obtained for an arbitrary pair of {{formula:766e2337-c666-4331-9da1-eb1f901477ac}} and {{formula:ce9d3f3e-7f1f-43b8-b49e-c24cc7d3eec6}} bands. This means, that using
Eq. (REF ) one finds
{{formula:46d2d649-fe70-4d6d-a9fe-c1d2779d21d9}} .
According to Eq. (REF ), the non-zero matrix elements of {{formula:e9732eac-5a72-4fb2-93d2-ab4a76b3f51a}} are
{{formula:0f926b7e-c3bf-4682-a9e0-944b901a5c52}} .
For {{formula:7567b386-39ff-4941-b827-2226e27e80a8}} one finds that these matrix elements are {{formula:488a9752-439f-4697-b27c-818fa81c1c57}} .
This means that for interlayer twist angles where the {{formula:18d72914-6ff4-40fa-ab9d-57fb1f3348b4}} symmetry of the stack is restored, the Hamiltonian of the induced Rashba SOC simplifies to
{{formula:c18d9bec-9415-4495-93e3-95a77e800dc4}}
which is, apart from the sign {{formula:b71bb58e-b848-4b3e-98ea-e875afe7e0ad}} , the well-known result of Refs. {{cite:279ab0018e49b1e6b921c761c24d80e83d8e6433}}, {{cite:53e45de027af0ddcec579ca4462cf400c16c7efe}}. This shows our results are in agreement with general expectations based on the symmetry of the system.
For twist angles {{formula:8501a63c-3baa-431b-b27b-13b904eeffdd}} , i.e., when the stack has only {{formula:299db7a0-7c91-4b69-b2d0-70a060a83276}} symmetry, {{formula:951f0eea-e2f7-4f54-bee1-56303d35b531}} is a continuous function of
{{formula:4bde0822-ed99-480d-b1de-7ea9d9e84040}} (through the wavenumbers {{formula:fd990104-74af-43df-96cf-86e66feb3609}} ). Therefore the matrix elements {{formula:180831e3-168e-425a-b733-4317bf96a1ab}}
of {{formula:88461760-cbba-4203-a4e9-0a92cf60dfef}} are complex numbers.
One would expect that {{formula:1613189a-d35d-4e1e-87f9-c1a2b5be6cd5}} . As shown in Figs. REF (b) and REF (b) below,
we find that {{formula:1b2b3a64-84d3-408f-a779-3b40619019b0}} .
Note, that Eq.(REF ) gives the lowest order non-vanishing contribution. We expect that higher order contributions in the perturbation series,
albeit small in magnitude, would lead to {{formula:ff42ab81-e6ca-4f65-8d60-eebcf90120de}} periodicity.
| r | bf4358c4dd5e5a8456603b15b2ffa576 |
Thus, Elimination Distance–({{formula:a5c9ec3b-0a70-4500-b163-6da6d18d38ba}} ) to {{formula:f5bd22de-d487-41c6-8235-f54bbc0e0255}} can be stated as follows: given a graph {{formula:12caa363-5fb2-4354-8394-7a3b6755c4bc}} and a nonnegative integer {{formula:f2a3db39-5cc0-4a3c-b6fb-bab84fc5038e}} , is there {{formula:6bf184a7-8cf9-4c8e-90bb-9cffd873c0a6}} whose torso has the tree-depth at most {{formula:5d44e1f3-075e-49d4-b176-a0368853ed6c}} such that {{formula:2c213930-fb1b-4243-b635-1fa9ab2d3085}} ? In other words, we ask whether there is a set of vertices whose torso has bounded tree-depth such that the graph obtained by the deletion of this set models our formula. Then we can consider the variants of Elimination Distance–({{formula:5716d4c5-7cfc-4833-a7f3-fd2af319ccaa}} ) to {{formula:b7474d2a-b7a1-418c-85d0-96d0f6c74b25}} for other “width-measures”. For example, what can be said about parameterized complexity of the variant of Elimination Distance–({{formula:c2b4badb-519a-40eb-b478-c21e88b981f1}} ) to {{formula:5f2670e2-f7c4-47c0-b475-615ed49d9fa9}}, where the tree-width (see, e.g, {{cite:fdcb4defe39009e7c51941a1712cee62dc9f2cae}} for the defintion) of the torso of {{formula:61fc9706-4f70-45f0-8bda-5ef6eb634cac}} should be at most {{formula:129416b4-162e-4028-9239-ec89672f10a8}} ?
| d | 8aace6745e431777171cc67bc4c8249d |
Many other linear bandit algorithms can be accelerated in the same way. As an example, the SupLinUCB algorithm {{cite:727b5ff6ec4bb32c25a38961aa85e3a5f6b4873a}} can be accelerated by alg:mips-adaptive. The regret of SupLinUCB is {{formula:025814a4-61a2-4fb6-88aa-b7e8b4d64884}} , which is favorable when {{formula:9e8a828c-a90d-4db2-bc0f-2182abe7fb7a}} is relatively small.
| d | 5464d6a058617664decece03df4f6a95 |
What we propose is not a specific model, but a general and compatible framework for multi-view gait recognition. As shown in Figure REF , the input is a gait silhouettes sequence {{formula:4afe8432-2838-4d94-bbf7-0939dd166d6b}} and a backbone model {{formula:e6369df7-aa24-4b97-b1f0-201a4c71e1d9}} is used to extract feature map {{formula:39444fbe-edc3-4473-b678-436a3c6d7d81}} . The backbone can be any silhouettes-based network, such as Gaitset {{cite:d887dd7404f03737b249b45370ffca78576c16e9}}, Gaitpart {{cite:ac9a46e6ce247a77cace341625eea72051382d6a}}, MT3D {{cite:226c0ee16d27747cb14b8cb897e572108aa8f74c}} and GaitGL {{cite:d6dd81dfee94cd24d911c85b0e701ede7282fbc5}}.
| m | e39194d53b488f46309959f34ff9f87b |
Since our proposed approach is a method for training a convolutional dictionary, we compare it to two classical model-agnostic CDL-methods, which we refer to as CDL 2D and CDL 3D. For this, we pre-trained the 2D and 3D convolutional filters using {{cite:d852531024a99cda629793cad589758add2fb856}} and {{cite:fd9fb3f7d6cf1f1e08c57e4184fc3ec4448b0b08}} with {{formula:6471e954-c0ed-4469-a751-b0bd918e622e}} and {{formula:be7575eb-9547-46c8-9d63-e7b5c5d4342d}} , respectively. After having obtained the filters, we fixed them in our network and only trained {{formula:e35ee5ee-b831-4ddd-82f1-4dd7837cb02e}} , {{formula:a3c204a4-12eb-4d5f-9210-8d3a81154327}} and {{formula:2d001071-5e51-4e9f-bfcc-36641f933823}} to exclude a possible change of performance which could be attributed to a sub-optimal choice of the regularization parameters. Further, we also compared with the method in {{cite:c3cd14799bfff874815e1438ee393fadfc417086}}, which corresponds to the analysis operator counterpart of this work and which we abbreviate by NN-CAOL 3D. We abbreviate our proposed methods by NN-CDL 3D and NN-CDL 2D, respectively. Last, we also compared our method to an adaptation of the deep cascade of CNNs presented in {{cite:afce1ee7b55e57b5335c84fbdcfc0726a8dc787f}}, which we denote by DnCn3D, see {{cite:c3cd14799bfff874815e1438ee393fadfc417086}} for details.
We trained all CDL-methods for different filter configurations {{formula:3074c863-2337-4e25-97da-7fab353ba1a4}} with filters of shapes {{formula:6aaf9a7d-210e-4728-af12-4b819e707c2a}} for 3D and {{formula:7254ae82-fcc4-435a-917b-d5cce20b7aef}} with {{formula:49ca6f33-3de2-42e6-94cb-21db71c7cdda}} for 2D. Based on a hyper-parameter selection on the validation set, we finally used {{formula:fa971bc5-820a-4e92-80a5-fdf8d47a9636}} and {{formula:efacc23b-24d0-4932-9cf4-7f566eb90824}} for CDL 3D, NN-CDL 3D and CAOL 3D (see {{cite:c3cd14799bfff874815e1438ee393fadfc417086}}), while for CDL 2D and NN-CDL 2D, we used {{formula:9b25c8c1-913f-4388-9c44-0cfd999949d5}} and {{formula:bd7455c0-fac2-4483-96af-e0f0ef683ec6}} . The length of the networks and the number of CG-iterations for solving (REF ) were set to {{formula:77534006-5a01-4357-8ef2-49c7c6075db8}} and {{formula:dbd195f6-616a-421d-a65e-a7a2415b16de}} for all CDL-methods. Because problem (REF ) is separable w.r.t. the temporal dimension, we trained all INNs on images only containing {{formula:798c8a6e-a0b8-4e05-89da-0fea05ba3c16}} and {{formula:22ce05c0-c478-4e10-9aa1-c1cf4e6b2a94}} cardiac phases for NN-CDL 2D and NN-CDL 3D, respectively. The INNs were trained for 16 epochs by minimizing the squared {{formula:31540b37-9340-47fc-8798-09dcc41c36c7}} -error between the target image and the estimated one using ADAM with an initial learning rate of {{formula:04d36cfe-e7e6-4f53-84db-ce0b4bd53835}} .
All reconstructions were evaluated in terms of PSNR, NRMSE and SSIM which were calculated over a central squared ROI of {{formula:14ddcae3-c2f5-46fe-b3ad-fbd6ef21d68a}} pixels.
| m | 6e1193916bb9b7a435748fbc1074f22b |
Once the network features are selected, we use a random forest (RF) classifier, which accounts for correlated features thus allowing for more flexibility with feature space partitioning {{cite:ef384e6ea83e4dfd7cad08835e5d6c1e1a8daccb}}. The network characteristics mentioned above are general and were chosen to cover both local (e.g. degree centrality, clustering coefficient) and global (e.g. betweenness centrality, link diversity) structural information.
The method itself is domain-agnostic, but one could consider more or other domain-specific features including nodal attributes (e.g. the sex or age of a person in a social network) or dynamic state of nodes/edges (e.g. infected or not by an epidemic/rumor).
In each of the tables reporting accuracy values (percentage of correctly classified nodes) in Sec. , we present results for the same experiment but with a lightweight classifier that uses only linear-time complexity network features (i.e., removing betweenness and closeness).
| m | b55b4c3f503c76d3d86382915ccb6084 |
Several strategies for containing the spread of misinformation in
temporal networks have been proposed
{{cite:82e9cba7467d3428d8e829d8fcb017a6ed5310bd}}, {{cite:84b489df6afbba37ef4693818ae141312610ed93}}, {{cite:466585a0cb38a3004b01a8feb9ec88f3da6dd066}}, {{cite:6a6f4c0729942219be3f00b94fabef20435bbe44}}. Liu et
al. {{cite:84b489df6afbba37ef4693818ae141312610ed93}} examined epidemic spreading on activity
driven temporal networks and developed mean-field based theoretical
approaches for three different control strategies, i.e., random,
targeted, and egocentric. The egocentric strategy is most effective. It
immunizes a randomly selected neighbor of a node in the observation
window. Other effective approaches using extensive numerical simulations
have been proposed
{{cite:7579107d900ca18644556e597cb927d846a4caf1}}, {{cite:75d18cb280e0e77647422188142e2ea13b572f62}}, {{cite:4e2a7de321a2854dd39e6ce46cef50041d3cfff2}}. For
example, Holme and Liljeros {{cite:7579107d900ca18644556e597cb927d846a4caf1}} take into
consideration the time variation of nodes and edges and propose a
strategy for containing the outbreak of an epidemic based on the birth
and death of links.
| i | 9ac6f73e31e59246f2f56f68e3eb8839 |
With respect to the manifold learning, we can in fact add more constraints on the reconstruction terms in Eq. REF to enforce it to learn more of the desired properties from the biomechanical simulations, which could potentially facilitate the learning and capture more diverse patterns. For latent space exploration in Eq. REF , different initializations of the latent motion matrix could lead to results converging to different optimum, however, we empirically found that the averaged performance remained similar on the cohort. An example of this is shown in Fig. REF , where different random initializations of the latent motion matrix {{formula:c265e08c-6de0-4949-86c5-592785aa2920}} were performed on a single subject and the results were found to be relatively stable with respect to different random seeds. More advanced optimization and initialization techniques could also be investigated for the manifold traversing, such as spherical optimizer as proposed in {{cite:3b3587f3df77a37138635ea4c0b26ad6107fa852}}. These could possibly further improve the motion tracking performances, and we will leave these for future explorations. In addition, though the present method shows the motion tracking on short axis views, there is also possibility to generalize the method to long axis views and we will investigate this in future work. Besides, one limitation of our current model is that it performs on 2D myocardial motion tracking, where the cardiac deformation is constrained to be in-plane. This is mainly limited by the existing available data where there are only 2D acquisitions of cardiac cine MRI. Nevertheless, this is consistent with the clinical practice in evaluating the cardiac motion and strains on 2D tagged MRI. For future work, we will extend this work to 3D applications, where we will generate 3D simulations and predict deformation fields based on super-resolved 3D cardiac images, to consider more realistic and complex cardiac motion. Possible challenges of extending this work to 3D may include the increased computational burden due to both 3D data and 3D networks, as well as the prior learning in capturing more complicated through-plane cardiac motion. We employed simplified biomechanical simulation scheme in this work and it can be further improved in future work to reflect the in-vivo physiological condition, e.g., more realistic constitutive relations. Besides, it will also be interesting to investigate the applicability of the proposed approach to more general scenarios, such as to other anatomical structures and modalities.
{{figure:8af9241c-552c-4220-b003-3060a1907edb}} | d | ac967c75b420fb3e044cce7cde4e39ba |
In this section, the UAD and channel estimation performance of Algorithm REF and the impact of UAD errors on the throughput of IRSA are studied via Monte Carlo simulations.
In each run, independent realizations of the user activities, user locations, the access pattern matrix, and the fades experienced by the users are generated.
The results in this section are for {{formula:6f3a2208-8b56-432a-81ae-5ceae82618f6}} REs, {{formula:ca8d5061-5c9d-4b5e-99e9-6d54c2ee7f81}} Monte Carlo runs, {{formula:418c0a8f-225e-40f3-bcea-37acc41a61c8}} iterations, {{formula:4c66eb1e-a686-44d9-b51a-bc1e721669ca}} , path loss exponent {{formula:d249591a-c808-4619-9833-cb83458628c5}} , and channel variance {{formula:85d9db1b-eaaf-45f2-bf21-1902c6e5a127}} {{cite:cdb76612e0b5e69d9e2466de129427bfd2cb5285}}.
The pilot sequences are generated as {{formula:6b38d244-0a7b-442b-b633-b2efff4d43eb}} as in {{cite:6b8123116578624980b73ef19364235a4ea7618e}}.
The users are spread uniformly at random locations within a cell of radius {{formula:cb7fc327-911d-407d-a6fc-35ef22c5ca3a}} m, and the path loss is calculated as {{formula:3b015e09-f970-4e5e-8484-88c82c7a39a4}} , where {{formula:2d5b4df2-ef19-495c-861b-d552f0a78c5b}} is the radial distance of the {{formula:db1c4fca-d9d6-45f0-87c2-9111af341965}} th user from the BS and {{formula:cd8bebe1-4044-4d55-bd04-5b900aa10702}} m is the reference distance.
The soliton distribution {{cite:a740c76d35d90d215e2f67962ea170127878deb0}} with {{formula:6b11cd9b-308b-4a71-8620-a7995811bfbc}} and {{formula:1c9e2aa8-fd0b-4f3b-bfac-5b36ca5b47be}} is used to generate the repetition factors.
| r | e68e80b6eca5ffeb2ba363cd579aca4f |
The resulting circuits for executing such models simply involve sequential application of the same unitary process {{formula:0a7838b0-eb6c-46c6-80ac-b2d8c4ddb5e8}} at each time-step.
The dimensionality of this unitary is then bounded by the memory dimension of the quantum model.
As such, a fixed memory dimension guarantees that the simulation of a process for {{formula:275749a1-47d1-4009-868a-e9911921a29b}} time-steps has gate complexity that scales linearly with {{formula:c2cf0a10-f034-4eab-b149-0b4aa11200fb}} .
Moreover, unitarity means such quantum models can generate a quantum superposition of all possible futures if the outputs remain unmeasured.
Thus the quantum model produces a key resource for various quantum data analytics algorithms, such as amplitude estimation, Grover's search, value at risk, and importance sampling {{cite:f99fdbfadbbcc8c560c15bc421d3f65947b36437}}, {{cite:0539e2d6bb8f03df3168c949370d3a8f264bf19b}}, {{cite:dc5174b7d79055e943b497b86e8a0392d772e1e0}}, {{cite:5300e168bb14297433977bfca008e795fa62593f}}.
The capacity for our models to generate data by sequential application of the same unitary makes them particularly amenable to certain contemporary hardware architectures (e.g., loop-based photonics where only a single optical circuit implementing {{formula:50420882-6ca3-4207-99ba-13459803daa4}} needs to be engineered {{cite:60761023dda6708cca8ea09db1cb9e20a4bbc84c}}).
Our techniques thus pave the way for quantum-enhanced tools to analyse time-series data from diverse fields such as financial forecasting {{cite:26a8d6ff98b1f147994e2f95a50ce9f9f2016156}}, {{cite:536d1422be22c769eeb015e9e3e3978ee32e5907}}, neuroscience {{cite:7020eceb5e21f333758d37e63a0a272a7ecb5823}}, {{cite:d064e60be32229b9a82bfb04b6a0d071284d1533}}, seismology {{cite:870f235d30efdb7c32d4f64f0b3c5ad33d61cceb}}, {{cite:607b79a7d7d9948e6b928ab5d04873e850abcd2f}}, and natural language processing {{cite:e313f481f1f2377f1feb5022549f64e351937802}}.
| d | 7c43e44dd9f2eabae50e32fb7ddf4c8f |
The physical process of these two types of SNe can be described as the iron core collapse and electron capture, and the latter is driven by the neutrino {{cite:1c07a45b5f1b3fbc51c2cb947191c84737781c8c}}, {{cite:401d80c5b34510f8a61ed90b782ffbfe08057556}}.
The iron core collapse is the dominant process of high-energy SNe that is generated from high-mass main sequence stars {{cite:2562cb4cbb4a2bd75941af35ed5a5d261af716fa}}.
The electron capture may be an explanation for the low-energy SNe, while the degenerate oxygen-neon core is collapsed to form the
NS{{cite:0889978980a55c587a7efcaf00d4e9180fdf60b4}}, {{cite:5ef8f25900c8d2537091df1263a596b7c60d2d43}}, and the mass range of these progenitor stars is about {{formula:50386432-480e-4f89-9604-1f166e0341ad}} {{cite:710a7a084978c8daf797de3263997f97160e1473}}, {{cite:dab77f15b2797dd5e83d36a588d48d61a24f363d}}.
| d | 70c322c832fabed19c5015e60af9481a |
Second, in the medical literature, FST is arrived at by either self-report or physician accessed direct assessment. Both require access to the physical subject for whom an FST measure is being calculated. All existing computer vision work that has used FST measures has done so by having human raters judge the skin tone of subjects in images {{cite:7df3012e5a33cddc24fca0513d79df81b76170be}}, {{cite:f8c445d5c4ed0442eedc7e9d3b1c72c43ff1d88d}}, {{cite:f0c7a38a0cae4229501dd4afefb5137a75bc12db}}, {{cite:f817a51f66cfd1afccf01cd87888f515a08af058}}, {{cite:2ecab2c37b2905d636f0224e89d6c91576ea60f3}}. However, as this study has shown, the face image lightness of the same subject varies greatly across uncontrolled images. Because of this assessment technique, we believe it is inaccurate to even describe the arrived at quantifications in {{cite:7df3012e5a33cddc24fca0513d79df81b76170be}}, {{cite:f8c445d5c4ed0442eedc7e9d3b1c72c43ff1d88d}}, {{cite:f0c7a38a0cae4229501dd4afefb5137a75bc12db}}, {{cite:f817a51f66cfd1afccf01cd87888f515a08af058}}, {{cite:2ecab2c37b2905d636f0224e89d6c91576ea60f3}} as Fitzpatrick Skin Types. These studies have measured something using an image, but it was unlikely a good estimator of the FST phenotype, and is almost certainly not FST as the term is conceptualized in the medical community.
| d | b6f84579ca821ab5d515606f30ae42c6 |
where {{formula:97e1e3fd-31ae-49f0-8d23-9b484d9596e8}} and {{formula:3cda9057-f810-4122-b361-50ef2714dd6c}} for all {{formula:210e23fd-7ce2-431c-b542-19c957b54f23}} . The interested reader is directed to {{cite:5a175f6952981378488f7fead4c20408ad0ed0a9}} for a Metropolis-adjusted LD algorithm.
Note that all the MCMC methods described so far require computations over the whole dataset at every iteration, resulting in high computational cost for large datasets.
Motivated by SGD, in which at each iteration only a mini-batch of the available data is used, {{cite:ca8bd1a20c82ef2edf9c3be775ca99135f0e3907}} proposed a technique that combines LD and SGD, referred to as stochastic gradient Langevin dynamics (SGLD).
Specifically, the resulting parameter update is computed using only a subset of the data and is the same as the update in SGD (Eq. (REF )), except with added Gaussian noise, i.e.,
{{formula:1fca3e12-718f-40ec-8d84-cf14f00b4e61}}
| m | 35a84f71f26d30cdede58ab63701900c |
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