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is the continuous updating estimator (CUE) of {{cite:88c075fdd7c3967bc2c9635ccb7aee6be81e93aa}} which results from a non-convex optimization problem and can exhibit unfavorable convergence properties if {{formula:90b035bc-c12b-4dfe-b895-900f4555e528}} is ill-conditioned {{cite:3000911e7f8badc09ea06f22de3f117ce296e798}}.
Therefore, one often resorts to a 2-step procedure: first, an inefficient but consistent estimate {{formula:99666efa-f0dc-4095-b8bf-98c6c1ecb164}} of {{formula:7991c248-6b63-45f1-8db9-b45c58bdda8a}} is obtained, e.g., by setting {{formula:6ddebd23-cfd4-4de0-9101-3b2873919754}} . Second, this estimate is used to compute {{formula:19b3ffa3-e9fb-4c56-9c38-beae801f811a}} which is kept fixed during the second optimization step.
This yields the so-called optimally weighted GMM estimator {{cite:d9743e16eb951bb155a84cae6d0110a4cbdce039}}:
{{formula:512334d1-2665-4de7-8cbf-80bf4f434cec}}
| m | 5b3a22f3b17fdcc32d5bd1215a1a0b69 |
for any {{formula:123d01ae-3828-46b7-87f2-87e85114ed7a}} (c.f., {{cite:478c7217df237ffce5ad18ac51774d66c864c86e}}).
Let {{formula:9694f08a-ed77-443d-a958-1189109ca030}} be bounded vector valued functions, i.e., {{formula:6ba382dc-fb16-40b4-9cfc-1602168b2a56}} . Then, for any {{formula:cda5b337-9104-4d6f-8279-a639ce9632f1}} , we have
{{formula:81d06508-f1b8-4700-9bbc-5b2120966e43}}
| r | 886df43937dafb13da9028763f3361e5 |
Image retrieval benchmarks. To test the generalizability of our approach, our method is trained only on Pitts30k{{cite:053ac0fde14472f2562e0656a7e9146a60efbb20}} without any fine-tuning on the image retrieval datasets. For Oxford 5k{{cite:1a4ec7dc9cf688840adb4e7c7cea5dd251b78672}} and Paris 6k {{cite:b309e1a77e0d20474f9c7b5527fad52b87dd1515}}, we use both the full and cropped images; for Holidays{{cite:cb535dc8cd5ec156e48768a361952018521d7298}}, we use original and rotated images. The results are displayed in Table REF . Our results set the state-of-the-art for compact image representations (256-D) on all three benchmarks. On all metrics, our margins consistently exceed the mAP of other methods by 1 to 5%. For example, there are a 3.86% improvements on Oxford 5k (full) than the next best method; and there are a 4% improvements on Oxford 5k (crop) than the next best method. Our methods can be further improved by fine-tuning using the three image retrieval datasets.
{{table:87c25f90-c906-4c8f-8d7b-73b55edbea07}} | r | ce69c81bd3f9f148a9eaa03e8b54fef5 |
We compare GROC against two other self-supervised methods, GRACE {{cite:5c5b7033d48036b76697fadba9d37a56ef0cafb3}} and GCA {{cite:4c9a3854d67442771f950c86f9e93856e87203fb}}. We show comparisons with the degree-based variant of GCA (GCA-DE), as we did not observe significant differences compared to other variants. Furthermore, we evaluate GRACE-ADV, an extension of GRACE that, instead of removing edges randomly, uses gradient signals as in GROC. Finally, we include a fully supervised baseline GCN, where we train the entire network with the supervision from node labels.
{{table:87b74006-da3f-44a2-b94b-911fb0b57850}}{{table:8c1f99b9-3e85-45c1-94f5-e5433e499259}} | m | 6a8f504536fbb8201dc107ffb2f6cbcb |
In this work, we aim at understanding the extent to which MMS fairness, as well as PROPX/PROP1, can be satisfied when the valuations are not additive.
First, it is easy to see that allocating all items to a single agent achieves {{formula:f777b43a-451d-42dd-be06-c7dbfdd374b9}} -approximate proportionality and thus achieves {{formula:948bf192-55bb-40ff-8a92-ff7501cd1b85}} -approximate MMS fairness.
Surprisingly, we show that {{formula:8ee4fabc-03dd-453f-b38f-6cd935fc586a}} -approximation is the best possible even when the valuations are submodular.
This result exhibits a significant difference between the allocations of chores and goods, since for goods with submodular (even XoS) valuations, we always have constant-approximate MMS fair allocations {{cite:3b9e72db629522fc631965813474a6706565ee10}}, {{cite:cf2b0753fea36e1936c179ec849d2cad778942bc}}.
| r | 4f9e095f1f354f5209e9c735d09f9931 |
We assume that each client's training data {{formula:36e409a1-3025-4b7a-af09-d1f8bcb8747f}} is
IID (Section REF ), and based this assumption on state-of-the-art papers {{cite:28e1753c713ada33a476ca2d460615352b30a79a}}, {{cite:960a9ffadc2d040c6f7e21443ee407124b9ddffe}}, {{cite:9ff4ebeb97a5d5d5f5b93204e8786795cd9f4364}} Although IID assumption leads to a better setting to study the impact of model utility requirement REF , in real world federated learning applications, {{formula:b623abcf-8f0a-4f8d-b207-f37a92dbbdab}} 's are typically unbalanced and non-IID. Therefore, we evaluated the performance of Waffle and WafflePattern in non-IID scenarios, and concluded that we met requirements REF and REF with a slight increase in communication and computational overhead. Detailed experimental results can be found in Appendix REF .
| d | d6c3ebb89a615277576c9491d80cbcc0 |
From the experimental perspective, we note that timescale separation is generally
induced in laboratory experiments by preparing the reaction so that the ratio
of initial enzyme concentration to reactant concentration is small (i.e., with
{{formula:1d58c1da-64ad-4658-89df-424e2dbd8fd5}} ); see {{cite:b34d573f8694e4db6f898830851504225c7542d0}}, {{cite:9c985754af17d148dafbc7f7af896c1dd917623b}}, {{cite:c597d5f7d776bb08d07af728d1311afd419de9d8}}. However,
the condition {{formula:a96b9a29-bd34-4dfd-967c-e8ebd46e28b6}} does not ensure that the spectral
gap of the Jacobian is wide enough to validate (REF ) or (REF ). This
result differs from non-autocatalytic Michaelis Menten-type reactions, where a
disparity in initial enzyme and substrate concentration is some times enough to ensure
the validity of the standard QSS reduction {{cite:aea0f6224035fdd19d0aaeabb04f8753fe5304de}}, {{cite:4b978e369ef0c1337dfc4353403943569a062a32}}. We also
note that the IAZA reaction mechanism analyzed in the work was comparatively simple,
and more complicated mechanisms have been proposed {{cite:b34d573f8694e4db6f898830851504225c7542d0}}.
Moreover, most reactions can be controlled with
inhibitors or activators. In the the presence of these modifiers, the determination
of singular perturbation parameters for the reaction mechanism is much more difficult.
This is because experimentally practical QSS reductions of three- and
four-dimensional systems will generally result from projecting onto a one-dimensional
slow manifold.Generally, time course data is extracted from a single chemical
species in a laboratory assay, which makes one-dimensional QSS reductions particularly
favorable. Thus, while it may be that only one eigenvalue vanishes in the singular
limit, the accuracy of the QSS reduction can require more than one dimensionless
singular perturbation parameter to be small since there can be multiple fast timescales
in higher dimensional systems; see {{cite:b12165471c1e9cd3b4cc9565724f888ee829d864}} as an example.
Understanding the qualifiers that ensure the accuracy of QSS reductions in
higher-dimensional systems is critical if we are to make progress in metabolic engineering
and drug development. And, as we have illustrated here, there is room for
mathematics.
| d | e3f7d1a411529578968526a1a1d42bf6 |
We chose two different structured pruning methods: Slimming {{cite:50992ea3d97781a86e4d9c676f4ad45668595a54}}, an influential method in the literature, and SWD {{cite:8d99afb464620470f489984c8573e290378b5825}}, that is more recent and has shown a certain ability to give competitive results on multiple networks or tasks with different kinds of pruning structures.
| m | c8cab52529f7496210be9ce746023fd7 |
In conclusion, models of neural circuits are complex dynamical systems capable of a large repertoire of behaviors. Mean field theory, in his diverse incarnations, is one of the few tools at our disposal (and arguably the most successful) at predicting the collective behavior of such models. As we learn more about the potential link between neural dynamics and brain function, these methods are being rediscovered and sharpened to deal with increasingly more sophisticated applications. We hope that this elementary introduction can be useful as a first exposure to the ideas and methods of this approach as applied to networks of spiking neurons, while referring e.g. to {{cite:45ac1591e5213a706214957c08c34e74537a3843}}, {{cite:910afac6a9858f27e744fd19114212f823d4a78a}} for comprehensive treatments in the field of neural computation, and to {{cite:db1c832f050132e3d1319fe874bae0782b98cf69}}, {{cite:b4298c6cda23c07f6c63127db35b888ebe256bf4}}, {{cite:17e676d1a5ea56145c3c3f271e2c271e39a0558d}}, {{cite:d665d9f1ec6500d746f262219d0cf01539342394}} for applications to spiking neurons and related topics.
| d | 6ef8a65e88b86cc26ad84b709679a259 |
Pose estimation aims to determine a six degrees-of-freedom (6DoF) transformation between viewpoints.
One way to determine this transformation is to compute point-to-point correspondences of 2D features tracked over time {{cite:f00fae9432724f7978d8de208f4220bff5fb7c33}}, {{cite:17df33c571f00eb175789b80972f070046cba052}}.
However, features may be wrongly associated or lost during tracking, due to sudden camera motion or viewpoint variations.
Alternatively, the 6DoF transformation can be determined by processing point clouds, i.e. through 3D point-to-point (or to-plane) associations {{cite:96e95744c8681ccfd9725feefbfd127ac5734f5f}}, local descriptors {{cite:b91239a9a190275139730262c3082899fc993d53}} or direct pose regression {{cite:ba765d6e4518a09836e22ec9b6c6e0c00da36aca}}.
Iterative Closest Points (ICP) {{cite:96e95744c8681ccfd9725feefbfd127ac5734f5f}} is the gold standard for point-to-point registration, however ICP is prone to failure when point clouds are significantly mis-aligned.
In the case of significant mis-alignments, local 3D descriptors can be used to register a pair of points through RANSAC {{cite:b91239a9a190275139730262c3082899fc993d53}}, {{cite:9ab9f0121c35ba3d6364b9eac1d5c897ed71b8ce}}, {{cite:59acda808339e1a38e269ced34ea82207810957e}}.
Recent deep-learning-based 3D descriptors {{cite:8f248c6b2e32b618e1372fa0535140724c5d5246}}, {{cite:9ab9f0121c35ba3d6364b9eac1d5c897ed71b8ce}}, {{cite:59acda808339e1a38e269ced34ea82207810957e}} have outperformed the handcrafted descriptors {{cite:3791a9bde182764ef3dbb00e1b4d5e6cdbf46a56}}, achieving state-of-the-art point cloud registration accuracy with a promising generalisation capability.
Poses can also be directly estimated through regression with a Siamese deep network that operates on the whole point cloud, however it requires a certain overlap between pairs to function properly: to estimate the 1DoF transformation between a pair, the minimum overlap should be about 30% {{cite:ba765d6e4518a09836e22ec9b6c6e0c00da36aca}}, while for the 6DoF transformation, the overlap should be greater than 70% {{cite:62fb0c58f0dfc123bf11bb0793e1b5293346296b}}.
| i | d23d5288b3b4b2b63ff95823fa3badb7 |
In this work, we use adversarial robustness to probe ideas regarding the `dimensionality' of neural representations.
The neuroscience community has advanced several normative theories, which include optimal coding {{cite:a3eaea2f29fe04492295ad37ad4f099435e75554}}, sparse coding {{cite:8e961b694fb01530a3a12f049b3bf436f929ce97}}, {{cite:42b6869018bb82e805630cc0c357cd1a9858cbe8}}, as well a host of experimental data and statistical models {{cite:dae05c13b5ce5cfe07393f9dfff89ccf1a9e3b1b}}, {{cite:f0fc2f951a5f1eec45b9cdcdd5e277cd6f3535ad}}, {{cite:e2b0a7b52163db61a22466c951e119e5792a546b}}, {{cite:1a80860794adce7a6a5f2ff47c9fbf48d66ad576}}, {{cite:c1aa5ea21874c22c323925f0f5aa6631b3dfaace}} – resulting in, often conflicting, arguments in support of the prevalence of both low-dimensional and high-dimensional neural codes.
By comparison, the machine learning community inspected the properties of hidden unit representations through the lens of statistical learning theory {{cite:d6e735fd49128dafef4797cdf51f4133b0e12794}}, {{cite:4ad4a618e321df44988c3ec06980c3b2d6227dd8}}, {{cite:163b3962527ebb9e10c864f4d38cc89babf2061d}}, information theory {{cite:219c210958cd8d51532c20250832b3b71453b4e5}}, {{cite:d99bece9e0a9028ad46b2f913e15273dde0baeaf}}, and mean-field and kernel methods {{cite:547411e0be0ad0cb8041375da3e382136ceb8fca}}, {{cite:ba491756996bb0eab4a9c5fd617864a64baa988e}}, {{cite:31913bc9cde3f0d13aa158dc35739414185e7715}}.
The last two, by considering the limiting behavior as the number of neurons per layer goes to infinity, have been particularly successful, allowing analytical treatment of optimization, and generalization {{cite:547411e0be0ad0cb8041375da3e382136ceb8fca}}, {{cite:cd4ce25117ed1004fe7a2c333afcc8337852f5af}}, {{cite:375810edf17ab493eb72f2d78fd2ceeb66afc8c8}}, {{cite:c8411676aaae679907fb306916acaa82a618df10}}.
| i | 64f2ab28d0bdbddfd3e0f22d59499d55 |
The results from both the SED and the two-filter method imply that the global and peak temperature for the observed TRAPPIST-1 flares are lower than expected from the empirical flare temperatures used in modeling the energy budget of a flare {{cite:d8277025f82be6ca9b92b557ae6d2f6fe84f1ffd}}, {{cite:e6cbc9322f7f31c389a8a85451bc53c99d61e2f1}}, {{cite:ed9c4e29bef9eef08dde2b0d040b34f6fed9cbe0}}, {{cite:656843b809623ea7449a3d5b0e501ec6a8e76151}}, except for the peak temperature of Flare 1, where the temperature from both applied methods is consistent with the literature. The two methods are consistent within a {{formula:6ed63af9-f20a-44d4-aad8-e84fc35ad6f4}} confidence interval; see Table REF for Details.
The color temperature evolutions are shown in Figure REF and Figure REF . For both flares, the different ratio functions are consistent within the uncertainties.
Comparing both methods, the clear advantage of the SED method is the simultaneous use of all filter fluxes and the simultaneous fit of the area parameter. As a consequence, the SED method is not affected by the disadvantage that we do not have a blue filter in our data set.
The uncertainties on the two-filter methods could be improved by MCMC sampling of the theoretical black body flux values rather than using a simple {{formula:46d1f259-9f68-460a-aeb6-c12f52876c02}} reduction. However, this is beyond the scope of this paper as the two-filter method was only meant to prove the temperature consistency of our SED method.
| m | 66beee417369ec1ee8eed467c413d50c |
Deep neural networks (DNNs) have established themselves as the first-choice tool for a wide range of applications, including computer vision and natural language processing. However, their impressive performance comes at a price of extensive infrastructure costs — as state-of-the-art DNNs may contain trillions of parameters {{cite:244e9f68278e377fc191405ad837964b7a27cb1d}} and require thousands of petaflops {{cite:d24865d21adfd7348ae5bbac47c5e8a47745724b}} for the training process. For this reason, compression of DNNs training and inference process is a research topic of paramount importance in both academia and industry. The main techniques of compression include quantization {{cite:4a9d1d974c0983496e0798ed9f0831853eb3c0c3}}, {{cite:d7c554c74ed3f226fc35df127d743df1a4e18fd1}}, knowledge distillation {{cite:66fa2d9bbd9195dd83a20b0a6462a1a95ed98411}}, and pruning {{cite:a5687cd46ca8e0ba1f784bc5499180dde374bde7}}, {{cite:c89c8119307be0b3a83ba0e6ca93d006bfd4a730}}.
| i | 4b7785ec21e0ad488549df7005ba43b3 |
The hot-film voltage {{formula:99ca8a39-e78b-450a-81f9-8a99ed365f9b}} is measured over time. We remove parts of the signal where bubbles interact with the sensor using a threshold method on the time derivative of the measured voltage across the hot-film (see {{cite:2a6788fe43fdc55316b5653762aac5f41297208c}} and the references therein) or the time derivative of the liquid velocity ({{cite:b9bfddd3fe761132a4fcfd4765c9ebdc3e26b7f0}}). During a bubble collision with a probe, there is rapid changes of {{formula:c324b9bb-360c-4dff-83da-91ed84183bab}} , and the typical shapes of {{formula:7341b84e-5bff-48f3-85b0-6faff06bb08d}} when bubbles colliding with a hot-film can be found in, for example, {{cite:2a6788fe43fdc55316b5653762aac5f41297208c}} and {{cite:78c888e473a8f374d6a1447731811edb0532d538}}. In this work, by inspection of the derivative {{formula:c65a550f-6819-4bf2-b404-8396d5efbb28}} over time, a fixed threshold {{formula:140eabf1-4a73-4398-9211-3f6a3413cf1c}} is used to detect the moments when bubbles are colliding the probe. We find that the findings and the conclusions of this work are robust against the threshold values within a reasonable range. Apart from the said threshold, we also set the minimal time between two successive bubble collisions (5) in order to determine the moments when bubbles impinging and leaving the probe and to capture the entire bubble interaction events. We check the latter threshold by examining the distributions of the bubble residence time and any unphysical bumps present in the energy spectra due to many unphysically short bubble collisions. To calculate the velocity power spectra, we use the Bartlett Method ({{cite:7bebf60fee792a7b82d707a6c135b076e8400139}}) with linear interpolations between the `gaps' of the liquid phase velocity over time for each {{formula:7bb0a619-7556-4645-8d33-ec1ed8d721e0}} . Each partition segment (20) cover at least one turnover time by inspecting the auto-correlation function of the signal. Linear interpolation between the gaps of the liquid signal to calculate the power spectra was also used in {{cite:cbbc256cc04d8d75a5f60a2a043bc0e3c628d727}}, {{cite:b9bfddd3fe761132a4fcfd4765c9ebdc3e26b7f0}}. The discussion on the effects of using linear interpolation can be found in {{cite:2a6788fe43fdc55316b5653762aac5f41297208c}} and {{cite:cbbc256cc04d8d75a5f60a2a043bc0e3c628d727}}.
| m | 4e8be5431763a4bef0175cf9e1fc28e2 |
We evaluated the perceptual quality of the synthesized speech produced
by our ultra-low bitrate codecs, operating at {{formula:55402c21-f90f-4ca4-9853-0dfe42541cc0}} and
{{formula:86ee4109-b117-479c-96f8-437808b38bbf}} , by comparing to Speex
wideband {{cite:ca93338f336c4e1d7b965d783afdfbfec10955d9}}, MELP
narrowband {{cite:ede626eb2b7ee2e9116f3967ca0a87c570ff42e2}}, and
LPCNet {{cite:093f65ed2ff0d464835b438bad0cd673ecf8590f}}, operating at {{formula:64409c1c-ac72-45d3-95de-710a02f47744}} ,
{{formula:bf6a0364-2a37-4c3a-869e-9ba6b2bae2c1}} , and {{formula:a59dfe63-023d-45b7-8a05-b243bde05d72}} , respectively. We
performed MUSHRA {{cite:eb3b04d08d841002d281831c3e9c00b9b4369414}} subjective evaluations of
our proposed codec by human raters in order to evaluate its performance. The test used 24 raters per utterance (78 raters in total) over 32 clean speech male and female utterances.
We further post-screened the raters by removing the ones that did not rate the hidden reference above 90 at least 80 percent of the time.
We did not include the codecs utilizing only one of CNN features or
Transformer embeddings in this subjective test as their perceptual
quality was clearly worse than that of the proposed codec.
Figure REF plots the mean MUSHRA score and {{formula:850f55e3-6162-4393-9b76-27cd1b9fc1bd}}
confidence intervals as a function of codec bitrate, where higher values
indicate better quality. We observe that our {{formula:d466e07f-94a3-4015-b9b8-f7512fa3cb9b}}
codec clearly outperforms all the other codecs. The {{formula:4387766c-ef70-4836-ac0a-eebbc035f04b}}
codec performs as well as the LPCnet codec while outperforming MELP and
Speex.
| r | 44f86519770a82bac4a54689c469ec02 |
We study the correspondence theory of intuitionistic modal logic in the modal version of Fairtlough-Mendler semantics, using algorithmic correspondence theory methods, as explained in {{cite:fe0fc9b27cf56bc25c6cf985d2ed2410f491261e}}, {{cite:1df29c62974dd5d53e8ad00db58c65e4a0fb5c35}}. We define the class of inductive formulas for this semantics as well as the Ackermann Lemma Based Algorithm {{formula:e652abfa-c512-4553-81fa-856c597458ff}} which computes the first-order correspondents of inductive formulas.
| m | 0ccd38aa4417134600a18701e0fa1a1b |
The suggestions in {{cite:e8cff6739a33df07f0af2a9f6602b2c42b59a437}} are applied to create the segmentation model. As illustrated in Fig.REF , the input image is passed to a feature extractor CNN which generates feature maps initially. Next, the PSPNet {{cite:e8cff6739a33df07f0af2a9f6602b2c42b59a437}} which uses various pooling kernels is applied to capture different receptive fields from the preceding output. Besides, the dilated convolution with various dilation rates such as 2, 4, 6 are appended to the pooling pyramid while summing their outputs after the convolution operations to remain the feature map size. Then commonly used feature extractors such as ResNet-50 {{cite:b3e06c658d1901a473e61370e9ade0bd39f0f9f7}} and ResNet-101 are employed for backbone architecture (Fig.REF ).
| m | 7667cb27ce6ffc1adc78d732e877e9aa |
Assuming the form of {{formula:21e414ac-285b-4cc0-96ff-df36ff7323ad}} we are able to
solve the field equation with/without an unknown rotating
function. Our solutions cannot coincide with the 3D solutions of
GR because the constant {{formula:88f1e429-ad89-44d9-8c4b-51a40d591e64}} is not equal to zero. Although our
field equation do not involve the cosmological constant term,
however the study of the asymptote of these BH solutions showed
that they behave as AdS/dS. In fact, the constant {{formula:9f0c7558-3c31-46e6-b1e9-7d37ae923cf1}} plays the
role of the cosmological constant which indeed means that this
constant cannot be vanished. We also showed that the invariants of
these BHs have a true singularity at the origin and a strong one
as compared to the 3D solutions of GR. The source of the strong
singularity comes from the non-trivial forms of the Ricci scalar
of the two BHs. We calculated the form of {{formula:fd4ab227-07dc-4d0b-b7cf-0d024e71fabd}} of the BHs and
showed that both of them behave as a polynomial one. Moreover, we
calculated the second derivative of {{formula:3817fc67-cae7-4e50-89c5-34f4bfe90354}} , i.e., {{formula:36661270-ae69-4a34-8461-52b13bbff9a6}} of the
two BHs and showed analytically and graphically that they have
positive values, which means that the Dolgov-Kawasaki stability
criterion is satisfied {{cite:5042618b101eecc88c52b04176ff9bc279c172ed}} and this ensures that
our BHs avoid tachyonic instabilities
{{cite:65b06945663bff7162f3a869a0539beee698ab4c}}, {{cite:969b1e0d056087f82ddad035204fba836c091133}}, {{cite:91734b5d23d13ea77c7d5d1a6f1afbb87b86923e}}, {{cite:1202b315e67ed2d9a7610723ee6d6f0aff0b9af1}}.
| d | 69129b6e51990015aa6b699c284f594f |
We observe that these convex loss functions have some limitations.
For example, {{formula:7dd1a7f6-6434-4200-8b1b-e1802669029f}} is a convex upper bound to {{formula:584ddddb-b1ef-4fc8-addf-24a73017e188}} provided {{formula:2f8f6016-cbf4-422d-a623-64475f7c0844}} and {{formula:8056d767-198f-472f-a32b-ae496d71a756}} forms an upper bound to {{formula:1dd5420d-68a4-434f-bbf2-bd3d70f59cdd}} provided {{formula:1e95884a-9725-4e50-9b00-3afb4ea43487}} (see Fig. REF ).
Also, both {{formula:93a7f5d4-f62c-48b2-838b-c0555cd4bce9}} and {{formula:c50c138e-13ef-4a52-b5c5-dea495536dce}} increase linearly in the rejection region
instead of remaining constant. These convex losses can become unbounded for misclassified examples with the scaling of parameters of {{formula:8f01bd2b-94c6-405a-88a2-5a4e84383562}} .
Moreover, limited experimental results are shown to validate the practical significance of these losses {{cite:979c4de375b2d757ac3d21cb80f5f8efc3433834}}, {{cite:04d4eaa88d6e4f721898231369d8f25b1acf26bf}}, {{cite:9d37a758d14175dde46f2bb85363f89d2cb7d952}}, {{cite:9edb9b6a4fbcd1a5f6d1d29d7c4fdf4e7eee3338}}.
A non-convex formulation for learning reject option classifier is proposed in {{cite:c05171e93837b013900a270f7fa9e0c8511a4eb8}}. However, theoretical guarantees for the approach proposed in {{cite:c05171e93837b013900a270f7fa9e0c8511a4eb8}} are not known. While learning a reject option classifier, one has to deal with the overlapping class regions as well as the presence of outliers.
SVM and other convex loss based approaches are less robust to label noise and outliers in the data {{cite:44e173a81f4e637c03251ec3141773e92594d555}}.
It is shown that ramp loss based risk minimization is more robust to noise {{cite:379c1bee1879f9274d1f9275408d8f52bc190192}}.
{{figure:b2e160f1-1289-4b6a-8cda-8513844f943d}} | i | 8b1c7310cb78aa391cb182a7f92f2d86 |
Leveraging ML/AI frameworks to discover (as opposed to merely fit) the governing equations of physical systems from large amounts of data offers intriguing possibilities and remains an open field of research. Recent efforts in this direction include physics-informed discovery strategies {{cite:00f98acd289e058578ccac5348129bde290b0ffb}}, combining first principles arguments with ML models such as Gaussian processes {{cite:b9d9424808cfcf7d4b93a175a500334758ad804f}} and deep neural networks {{cite:a93c7e0a5310506685e9506fe2392db1701e7b5c}}, {{cite:84c43bb0d6c8e3399e5f54285fc75861d44692aa}}. While the predictive capabilities of such physics-informed strategies are good, even when trained on coarse and noisy measurements, their reliance on significant (if not complete) structural knowledge of the equations governing the system dynamics constitutes a significant disadvantage when it comes to discovering they governing equations of new and unknown systems. Further, as is inherent to most (deep) machine learning architectures, such models can suffer from lack of interpretability, hence failing to provide insights on the selection process of the functional terms that dictate a system's dynamic behavior.
| i | 98e5d876d70be27af4214b30778a9fa4 |
We report results on the production of {{formula:7d8a9337-a4bf-4bad-80a2-4c6a327e4814}} , {{formula:45eaf56a-5197-4ac4-94df-166b959b625e}} , {{formula:33eec4bc-b726-4673-8241-34f0f84c14e2}} and {{formula:b344f0e4-b203-4db7-884b-5826a9d01854}} measured in {{formula:43461590-3b74-442f-8d5d-b6cee21cad6f}} collisions at {{formula:216aaa58-4e54-4628-8baf-dd3dfe7e481e}} as a function of centrality, as discussed in {{cite:a6fb0e205dbd1c7d0336532ff84d071fdcf49abf}}.
The data sample was recorded with a minimum-bias trigger.
The total charge collected in the V0 detectors, a set of two scintillator detectors located in the pseudorapidity region {{formula:c1643e12-60fd-4322-ade5-44ef710d8e78}} (V0A) and {{formula:c7d48293-10a6-40d8-a4de-5c78527d0854}} (V0C) and covering the full azimuth, was used to determine the centrality of each {{formula:e7715d77-cf23-47ec-adb8-b79359ee1d09}} collision defined as percentiles of the total hadronic cross section.
Further details are given in {{cite:9a9d3abd13f0cb8587f8b3e0c880d90ea28b07ae}}.
Contributions from weak decays of strange particles and from particle knock-out in the material were removed with the data driven approach described in {{cite:a6fb0e205dbd1c7d0336532ff84d071fdcf49abf}}.
Systematic uncertainties were estimated by varying the PID technique and the selection criteria used to define the track sample.
The amount of pile-up per event was reduced by selecting runs with low interaction rate and by rejecting events with more than one reconstructed vertex, resulting in a negligible effect.
The evaluation of the efficiency and acceptance corrections was performed using events simulated with the HIJING {{cite:3c79429ea36357161836e4733eb4096f1a11592a}} event generator and embedded into a detailed description of the ALICE detector through which tracks are propagated with the GEANT3 {{cite:72f0545cc6d412bbb13554b9f3eb3eab03882b57}} transport code.
{{figure:169a97ab-57b3-4e82-920f-c199681cec88}}{{figure:79fcf4b9-4051-442d-a6b8-dd860916399e}}{{figure:7e1ebb4e-93c4-4686-93b9-823c127c7ac0}}{{figure:d38b4988-1e88-4751-b03b-6d11727938cc}} | r | a31aab8bfd0eb3bc9cf2747cdaa9e9e1 |
We first emphasize Theorem REF is not perturbative of {{cite:331788da1ffe99f46b1910e4daa93616e27dfc9e}}, as will be shown shortly; the non-integrable feature of the particle system of interest is manifest in some quantity which does not vanish as {{formula:a8a9d966-4876-4396-9dcb-a4557262d09a}} uniformly in {{formula:8e8a3271-5cdf-4952-9b9d-dac23311a157}} , so that the model herein is "genuinely non-integrable".
Similarly to {{cite:af95277aff83863214fc43e665bfc7a3cc7c694d}}, we specialize to the regime of near-stationary initial data, as the regime of narrow-wedge initial data follows from the adaptation performed in detail in {{cite:fb3fedf9e09851c665b3a049aced1ccc14afe5ba}} almost identically; the extension to the latter singular initial data therefore effectively constitutes an exercise provided our analysis for near-stationary initial data.
We reemphasize the specialization of our model to a single slow bond supported at a fixed point is the KPZ-related content of {{cite:e96a0097e846faadb40ebc5a7082c7a945091589}} with a larger set bond-strengths considered in that article but restricting to the stationary models.
Courtesy of Theorem REF , under appropriate "double-limit" procedure, statistics of the height function {{formula:165979a5-f34c-4dc2-b641-2c3c5c634407}} converge to those of the so-called KPZ fixed point, as a consequence of the main result within {{cite:56af3c4d166b4bda0a4c809ed1d99399fb0a75fb}}.
Understanding the invariant measures will not play a substantial role in our analysis. Thus, we allow small though microscopically detectable perturbations of the slow bonds, and our analysis would be almost entirely unaffected.
In addition to the slow bond problems in {{cite:e96a0097e846faadb40ebc5a7082c7a945091589}}, there is recent interest in hydrodynamics theory and corresponding fluctuations for generalizations of ASEP though with a slow-boundary dynamic; see {{cite:6d50b960c07f9ea06be95510d687e477331940bf}}, {{cite:a3c5a90c3c3544a795ffab61e41623084989ff7f}}, {{cite:118824396edfd80ec303e2693830dea250ed95fe}}, and {{cite:6d51f8b1bb52203afaaf131bf95a62ab6656c223}}. We believe that large-scale KPZ statistics are within reach with the methods developed herein for appropriate weakly-asymmetric versions of at least some of these models in the non-integrable and non-stationary regimes as well.
| r | 0938ab8d45772797336b4f5409720083 |
In addition to the corresponding query strategy, some researchers have also considered the impact of batch query size on query performance. For example, {{cite:1828fd1ade1733391dfeefdf442d1695827c5303}}, {{cite:456c37e025a0f0e935caf6ab6c22311d47f2bf23}}, {{cite:ff1e96613f30cf4fefd075aee72ae0215f0c7e67}}, {{cite:87631ff5829fe514f9616c6b45eedda58fc0ee61}} focus primarily on the optimization of query strategies in smaller batches, while {{cite:1ba120994b7db93f352dfc7a90fbe62324a7c76c}} recommended expanding the query scale of AL for large-scale sampling (10k or 500k samples at a time). Moreover, by integrating hundreds of models and reusing intermediate checkpoints, the distributed searching of training data on large-scale labeled datasets can be efficiently realized with a small computational cost. {{cite:1ba120994b7db93f352dfc7a90fbe62324a7c76c}} also proved that the performance of using the entire dataset for training is not the upper limit of performance, as well as that AL based on subsets specifically may yield better performance.
| m | 376c5a8d83c107d7591ed49c0c269342 |
For fully-connected layers, it suffices to ensure that the weight matrices themselves are orthogonal.
The GroupSort {{cite:84856027d422b7222500620f6b002a4e9eeb822a}} architecture
achieves this using classic results from numeric analysis {{cite:ec21a67f674665fad30d0930b3aa695ff40fc5cf}}. The authors parameterize an orthogonal weight matrix as a
specific matrix power series, which they embed
in truncated form into the network architecture.
Orthogonalization by Newton's Iterations (ONI) {{cite:6024aae4fba14776cfd688ea0c3a17885617b791}} parameterizes
orthogonal weight matrices as {{formula:dbcaf651-a7d6-4e22-a898-553462c3f1a7}} for a general parameter matrix {{formula:6a373ba6-d369-4d59-a20e-4ba5020bbe5d}} .
As an approximate representation of the inverse operation the authors embed a number of steps of Newton's method into the network.
Both methods, GroupSort and ONI, have the shortcoming that their orthogonalization schemes require the application of iterative computation schemes which incur a trade-off between the approximation quality and the computational cost.
| m | c46d202bd86481a576548bffdee3093f |
where {{formula:65f36a59-e587-4371-8d23-87e2ef43ef70}} is the intrinsic kinetic energy and V is either V{{formula:219beaba-5210-4db7-b1ee-d5ba664ce997}} {{cite:fbb044cea3e4cc7a48093d1245b25c7f5028156c}} or V{{formula:85ddd16a-f9d7-42a0-9610-10ccab1d4298}} {{cite:7b3adfaa50487b8296394a91f8359321b509e8ca}}.
V{{formula:6949fab5-f702-4508-9b6c-75c61dedd4d4}} is obtained by optimizing simultaneously the two-body and three-body components of the {{formula:ecb54fe4-5a38-4eb0-a5f0-52757aac9522}} EFT potential at N2LO with a cutoff parameter {{formula:8622aba8-cc7e-4d17-af30-bb6724ce0372}} MeV. In the present calculation the full three-body force is used to generate the HF basis and is truncated at the normal ordered two-body level in solving the multiphonon eigenvalue problem.
V{{formula:01d75e8a-59cb-44c6-b08c-e945caa6726f}} is derived from the {{formula:2a3d1010-6875-45b2-bb4a-42ae5aa7e2a9}} component of the N3LO potential {{cite:c607bd0d086470abcdce38987e74da69be21492f}} in two steps. The {{formula:cf68eafe-1249-4991-a241-bc76297aa0b1}} potential is first softened by a SRG method {{cite:afeab00c2a2f67933e8162cb5fe27769a24327e4}} with flow parameter {{formula:cf0df3f7-fd88-41f8-bbf5-123533567561}} fm{{formula:21a719a3-4f29-4c45-9a7f-47c9cbea5987}} and then subjected to a phase equivalent transformation which determines an optimal set of parameters of the {{formula:d5ac9448-802f-4669-8eee-ea5fbc37fa02}} force. The absence of three-body forces reduces considerably the computational effort.
| r | 6e1f9a06ba06de1fc799ab7581a2e6c5 |
In this section we record a number of properties of certain boundary extensions of holomorphic maps between simply connected domains and the relationship of these boundary extensions to the harmonic measure of sets on the boundaries of these domains. In doing so, we use a number of classical results on the boundary behaviour of holomorphic maps, which can mostly be found in {{cite:d77d95b0524ab5e664c1c774c2b3a515d925db19}}.
| r | 9f462eb2a321f7c6a3429b4a3d11a741 |
The Pitman-Yor process is a particular case of a Gibbs process {{cite:40b2c8d452a3c11dd4a7e269dd18c3a162b8fcae}}, which itself is a special case of species sampling processes.
| r | ac98cc9732cc106e8e047124477e7e38 |
To address the above problems, we propose a complex hyperbolic KG embedding approach with the fast Fourier transform. Our approach can utilize the representation capacity of the complex hyperbolic geometry as well as the well-developed attention-based geometric transformations as relation parameterization, while we borrow the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) to provide the conversion between the real and complex hyperbolic space.
We regard the complex hyperbolic embeddings in the unit ball model (a projective geometry-based model to identify the complex hyperbolic space) {{cite:255c98af47b2df79dcdaa6c51ebe4117ea004f28}} and the hyperbolic embeddings in the Poincaré ball model (a model of the real hyperbolic space) {{cite:ca7ed44ffc0e39f5a9cf8b188ff83bf4e5481e30}} as frequency domain and spatial domain respectively. Then FFT and IFFT enable us to convert the embeddings between the two geometric spaces, accomplishing the leverage of real hyperbolic transformations to the complex hyperbolic model.
The framework is simple and effective in learning the complex hyperbolic KG representations.
| i | cf1b047523d1fcb527498d28fac98d93 |
The maximization problem (REF ) can be handled one matrix {{formula:0d53e518-d3d4-49b3-8431-c530ff4253ab}} at a time ({{formula:6cfcc6d3-1c7f-4a85-9605-ba3052f71924}} ), that is, by block coordinate ascent {{cite:b820a726313557091e9dceb4f15d3d463e9ad317}}.
Given a current solution {{formula:1b7096fe-181f-4613-b4f0-c6b5c2b2041b}} and an index {{formula:91a1c8aa-aa47-405d-ae4f-bb85c8247426}} ,
all matrices {{formula:9cf7cca3-947c-4187-989f-8eb1d7986b62}} are fixed and the task at hand is
{{formula:6357cdb4-ce9a-435b-ac0a-9f8548003188}}
| m | cb119dc3664b6ae8ddce214a7f401be4 |
An RW on a two dimensional square lattice also returns to the initial
site with probability {{formula:29b246f7-98fd-4890-927f-65955d086218}} .
In contrast, for RWs on hypercubic lattices of dimensions {{formula:ae8a55a8-7e9c-4eac-b0a3-d113d8ea68de}} the
probability to return to the initial site is {{formula:59c7a617-7b84-4daa-a850-2ae30dfa537c}}
{{cite:b1d5fad4b8919ea601266958151d62444c7f4a8b}}.
As shown above, an RW on an RRG of degree {{formula:1e7d0b2a-b3dd-4b2c-a1e6-88b8123e4021}} and infinite size
returns to the initial node with probability {{formula:545ca8c5-08c3-4d4c-910d-a8496f1f6c50}} .
This means that RWs on RRGs behave qualitatively like RWs on
regular lattices of dimension {{formula:ca7b3bcf-7da8-4b35-a602-9d5f2760c072}} .
For an RW on a hypercubic lattice of dimension {{formula:5900d133-70fc-4273-a8b3-1a4fccd1d677}} , the probability of return
to the initial site is given by
{{cite:38696ecde24b49ff419178f8cf7ba7bc6a91ab56}}, {{cite:a884d4fd6a7796183293de574536451a0ca950f4}}, {{cite:e2cfd9daa4afe47592ffdd7c18f2809cd0d159a0}}
{{formula:ae909a5d-4018-4803-8ea1-e89dcf1fccd1}}
| d | 08d931048664b424fa9b160913cb0c33 |
In this paper, it is assumed that CSI is not available at the transmitter. In some scenarios it is essential to obtain CSI at the transmitter. The impact of total CSI or partial CSI at the transmitter on the behaviour of multidimensional constellations can be investigated. For example, it is likely that the user-specific 2-dimensional rotations pointed out in Section are useful when CSI is available at the transmitter.
It is assumed that each user and the receiver are accompanied with a single transmit and a single receive antenna, i.e., SISO-SCMA. Alternatively, employing multiple transmit and receive (MIMO) antennas can improve the system performance by exploiting the spatial domain. As such, the effect of MIMO antennas, i.e., MIMO-SCMA (e.g., {{cite:e565a340acb183c9bb55f561439f46b025802d7e}}, {{cite:d75f3df91887e81d412269e331f13bfd08e15cea}}) on the performance multidimensional constellations can be studied.
For the coded scenarios, only the LTE turbo code has been considered here. It can be verified whether the KPIs provided in designing multidimensional constellations depend on the channel coding techniques or not. Therefore, the behavior of multidimensional constellations in conjunction with other channel coding techniques such as LDPC codes ({{cite:f6bd3de680111ed8c1f871f104d18af2164b453f}}, {{cite:d48f2a98b3fe21435d5c8f476a7e106ca5626ba9}}) or polar codes (e.g., {{cite:057b8a8ccbb545b0dd4341ef6a9bbfd2fe42b2a4}}, {{cite:fb92bccb3cd0f3614a6e65dff3ee6091cb4bc1c0}}, {{cite:7aa8c8206fbd07ac38b6bc5ef587dffc9164df6d}}, {{cite:5a4c069e001a087fa6f3192be6d0d979e7121050}}) can be further examined.
All the comparisons are made for BICM. It is shown in the literature that for some applications (e.g., {{cite:524adadf0e4844a47e917e9ed46a6775930734bc}}) multilevel coding (MLC) {{cite:1201dbb2e3318f992ad54eb6e3f23d79b2b21e58}} exhibits some gain over its BICM counterpart. Studying the KPIs for MLC is a possible research direction.
It is assumed that the detection and decoding are performed separately in a non-iterative manner. It is shown in e.g., {{cite:a1ccf39d13e37c67926304e8953df44c5e59d5ee}} that an iterative multiuser receiver improves the SCMA system performance. The effect of iterative decoding and detection, i.e., BICM with iterative decoding (BICM-ID), (e.g., {{cite:a1ccf39d13e37c67926304e8953df44c5e59d5ee}}, {{cite:71c2d024e614fdb6c8733817553ed134e2cb18c5}}, {{cite:f72e57501dc6f254bb3c2d97a8147317c37301c2}}) can be investigated.
One of the main challenges in SCMA systems is the receiver complexity that inherits from the detection of all active users {{cite:58334497624bd95393bba12e346f6a5a06cca4c1}}. In this paper, the widely-used non-binary MPA is used as the multi-user detection. The impact of the choice of constellation when other lower complexity detectors (e.g., {{cite:10e0bacede771893c169eb3ef5f11dce34288d60}}, {{cite:ea7ffa06ef764fa8c2a722f65cfa46c514cd27ee}}, {{cite:3c71f944970d151aa5c45fd37dc811c76ed854e1}}, {{cite:517998e856b516e60bbc135308ec49ffd009173b}}, {{cite:d0a5eb4ca2cef68c3a9fcf2770aeb1a8995356e0}}, {{cite:787584c8e83d02635a6ac1edde96c9a56fd98181}}, {{cite:5b3934c35e0f1b4bd01e11d86e6539ad26abfa16}}, {{cite:e91f7b0e3f9a47458068099321a0742bab639879}}, {{cite:d85daf8acf8ce14214eac0e4a5a42ddaf5d303de}}, {{cite:6911839775209e23600334198c1c45a655c42e09}}, {{cite:413d25519c4acee9e9189ac9688d6ef50e378b8c}}, {{cite:739475144d6075563ee33cc98e6f75d5e6c27ba5}})
are used, should be further studied.
All the comparisons in this paper have performed for a regular user-to-RE mapping matrix. It was also shown in {{cite:71b5adb82c9d38d761f006762e8e4302cdced82f}}, that a regular user-to-RE allocation is advantageous. Nevertheless, in a regular SCMA structure, it is not possible to serve different users with various requirements. Thus, studying the effect of an irregular SCMA structure, whereby users are not forced to occupy only a fixed number of REs, e.g., {{cite:cf294b4ccfc4971b67b49dd3ee6d62ffb96726de}}, {{cite:ea56a4a1d59d10b3469538b85e04f0898e5f9879}}, {{cite:f77d5e0d727b2c84a4b9cbcce17ca724f15c3daa}}, is a possible research direction.
Mathematical analysis of the error performance of constellations provides more indication on their performance in different SNR regions. In {{cite:559e726ccef9b1d132148597d15c385598f6384e}}, {{cite:f90c84531d00062b39a4c2264362203be9682f24}}, {{cite:7cd41ab70d0f47ae4938671b2a2d98ce2431b415}}, {{cite:9512af27c8057a17bac55d2f1b7564da7cef4844}}, {{cite:8f1eaa27983347e90a8de24bdd4d8fa8795392d5}}, {{cite:1e62ed396b13fdaee6bc750cc7ecad95f358603a}}, the performance of some of the constellations has been analyzed. The performance analysis of different constellations under different scenarios is a possible research direction.
One of the problems with multi-carrier systems is their high peak-to-power-average-ratio (PAPR). Since SCMA can be regarded as a type of multi-carrier NOMA {{cite:e6b2392495f3cbc9fffbc14718a1ee06100be0bf}}, the behavior of different multidimensional constellations from PAPR perspective can be studied along with PAPR reduction techniques, e.g., {{cite:9c63b187622f098400c6b65af59ec1be380df71d}}.
The KPIs of designing multidimensional constellations for other channel models that are out of the scope of the current work can be explored.
Obtaining the relationship between the KPIs that we have obtained for SCMA systems with the KPIs of single-user systems over different scenarios can be considered.
The KPIs that are given for each specific scenario can be considered in the design process of new multidimensional constellations over each scenario.
| d | e5dadb37b356e440382ddeab06c5021d |
A very different behavior is found for quantum walkers {{cite:06d0acffd1084dd99ae461fb9c6ae6ce4f69b661}}, {{cite:afe434401aa279dbb19247a8286615ecb40fee6d}}, {{cite:9765ce63f359eb70695f7470aa3a3d9bc1c37f48}}, {{cite:0f8928e6a445daf13ba6dbb5c8a3d87f6a4579d6}}
on finite graphs that start localized
on a node of the graph. Firstly the concept of quantum arrival is not well defined, and instead we discuss
the first detection, see below. Secondly, destructive interference may divide
the Hilbert space into two components called dark and bright, and this yields an effect similar
to classical non-ergodicity, {{formula:09d45a74-b533-4432-972a-8de72cb39bdc}} . More specifically, an observer performs
repeated strong measurements, made on another node, in an attempt to detect the particle {{cite:fa69edd72f205ad4b865bf7e52c3443da8fda5e5}}, {{cite:ca04b7c78d07bf898f54545a9f1870349bba2f74}}, {{cite:7d7a9a4c43584fbc52a3c014c9aaa4d1c8fcf261}}, {{cite:e375c369074b0e0b8c26c819a8aaf5c628dedbbd}}, {{cite:dc7b3cbef0e9a7bc09b8a517375397abe772f1c9}}, {{cite:e3b0acab04bb44799b0d3de7e97c743102b92d84}}, {{cite:70d532c2e0cb71245b96633f6c776b6311d59295}}, {{cite:290d4a89547f2bb5f4424401702bbdea078fe222}}, {{cite:51404c18c5d25323138bccf66ec7abecfaeb10ec}}, {{cite:9ae86a8558f14269c59ed396165086bc6a0f3ee8}}, {{cite:6c4d535549ffa8a0402e92bcbaa7edfa5bd798ba}}, {{cite:aac0ed7a3ac7207f7711e1c4ab20c2ebd86004aa}}, {{cite:2a1bc582df6ac7c6fcfcc2e406d6686bf743b7cb}}, {{cite:d1e4dc13f5bb0a28575c8cb7dc8cef9705226881}}, {{cite:778a70b0554d5d30129d5a97d0fc009eb5f33e2c}}. In the time intervals between the measurements the dynamics is unitary.
The rate of measurement attempts is {{formula:7bbdb963-ba95-4cc5-84b3-cbbf80181316}} where
{{formula:c116513a-caf1-43d3-b445-6e18ed173ac0}} is a parameter of choice (see details below).
Due to destructive interference, there might
exist certain initial states whose amplitude vanishes at the detected
node at all times and this renders them non-detectable.
Such initial conditions are called dark states and they are
widely encountered {{cite:c7cbcb01c86ddfaebccdcf5727660a43eaf3e199}}.
In this case the mean hitting time, i.e. the mean time for detection,
is infinite {{cite:7d7a9a4c43584fbc52a3c014c9aaa4d1c8fcf261}} and this can be found for simple models like
a quantum walk on a hyper-cube {{cite:ca04b7c78d07bf898f54545a9f1870349bba2f74}} or a ring {{cite:9ae86a8558f14269c59ed396165086bc6a0f3ee8}}.
More precisely to get non-classical behavior
for {{formula:d59494d0-061d-476c-88fb-8e7b0352879d}}
the system has to have some
symmetry built into it {{cite:7d7a9a4c43584fbc52a3c014c9aaa4d1c8fcf261}}, {{cite:12dc51ab570e0a31412a3a049bff537a1299d389}}.
Generic initial states {{formula:4b153d65-0d5f-4615-8854-fa1a8ac01042}} are linear combinations
of dark and bright states, the latter are detected with probability one.
It follows that a system starting in state {{formula:75fc7c1e-8daa-4b86-ac75-8733937301db}}
has a probability to be detected that lies somewhere between
zero and unity.
The question remains is to quantify this
probability {{formula:28bffbfb-796b-451c-908a-329d0c3f7b20}} ?
| i | a2f0116becd374697d55ccc1dc8889ea |
The knowledge graphs are important for many applicative use cases like social networks, web-based collaborative knowledge bases like DBpedia {{cite:3060157e721ddff4dbb9bdbb93646befef222518}}, and in healthcare when trying to model protein-protein interaction networks or genetic information {{cite:272b613d755d41084d26e44222c746b6785d6401}}. They are also useful for Natural Language Processing (NLP) applications like entity recognition {{cite:75f158977d699c0b3e523291fdc294ade0066813}}, entity linking {{cite:721684c9e09b141a4893b2560c7d4747185d9fbb}}, dialogue systems {{cite:93c1f833597b69ad93d74b42a33d0b9fbc7c90fb}}, semantic parsing {{cite:f8b91273072c09caf873f8297395b7bf0e1cb79c}}, information retrieval {{cite:9d35739a790428cca8838b6f52a740859460f586}} and question answering systems {{cite:4bb7811bc1e3489165b8d7a6aa1975b793a0a356}}. Most KG's are available online and open sourced ranging from domain specific KG's such as GeneOntology {{cite:a81f1e21a40cef2fc8e56740b8bdd7a803c86183}} and for general purposes such as YAGO {{cite:95e03089e108cae32698b8c2bc8bfa76080d6c63}}, FreeBase {{cite:60ad2603706739ac745aa6e7e6691f2228ee6ac8}}, DBpedia {{cite:3060157e721ddff4dbb9bdbb93646befef222518}}, WordNet {{cite:6f968fa4ee9566afbe3dc5a44ad2ad2f65f249e7}}, NELL {{cite:4b69f1b466b0d79864fba51cd09808e035875bd6}}. Knowledge Graphs are the result of automatic generation, in some cases from mining web pages like GDELT {{cite:bdb92353f324626e67682d4851e2b846228e8a44}} and craft source operations like WIKIDATA {{cite:8546d150b157bbbdf57e58282eaa7e0a6f343305}}. Commercial KG's are pretty common in applications like search engines. Examples of commercial KG include Facebook Open Graph, Microsoft Satori, Yahoo Spark and Google Knowledge Graph {{cite:6c93d3adbfb79d7b782a3eb636eb7e6ba8974d34}}.
{{figure:fccbc698-65ac-40e7-b815-6660fee507fd}} | i | c01f050560e202afd47b091ac5eb6de0 |
The Deep Learning Toolbox was used to design network architectures and perform backpropogation training. A Scaled Conjugate Gradient (SCG) algorithm was chosen as the training function to deal with the large AUV datasets effectively. The SCG algorithm {{cite:28425df004bdcb522d192cf8c8ffeac6dc22d8ad}} abolish the need for line-searches as presented in its predecessor {{cite:73b9e1808dc11048a03706382c0b3f6c03a817a0}} which reduces the computational load. To improve the generalization of the neural networks, early-stopping was introduced. Early-stopping divides the AUV dataset into training and validation batches. The training dataset is fed into the SCG algorithm to tune the weights and biases, while the validation data is used to monitor and detect if occurrences of overfitting is evident {{cite:db13ff6fa1a2eb9398f82f1e2e765a10cda19187}}. If the network starts to overfit the dataset, the training is aborted, hence the name early-stopping.
| r | 7f21b497e642682b893ecb2951fc74a5 |
For comparing the ResNet+TCN network with other works, we took reported results from the following methods: video-level and frame-level InceptionNet {{cite:ea6b59f45238ceddf0833087c68a5a92e989b58e}}, C3D {{cite:ea6b59f45238ceddf0833087c68a5a92e989b58e}}, I3D {{cite:e3881dc528c0a71a760340a771066e759965fd50}}, DERN {{cite:e609363dceb224130f3a76e55740d6df4f85ad6d}}, and DFSTN {{cite:ed54221059ffe6d7c715a49ef96aecec89470467}}. In addition, we implemented the combination of the ResNet with LSTM, and C3D (up to the layer pool-5) {{cite:d4abd2172e12d748bb8aac941c51ea6cc33bc5e6}} with LSTM (one-layer unidirectional with 128 hidden neurons) to investigate their performance compared to the ResNet+TCN method. Figure. REF shows the results of applying different end-to-end methods to the four-class engagement level detection problem in the DAiSEE dataset. In this figure, the accuracy is shown for the previous works and the methods we implemented to evaluate on the DAiSEE dataset. Figure. REF shows that the ResNet+TCN method achieves the highest accuracy of 63.9%, which is 2.75% higher than the best performing method of Resnet with LSTM (61.15%) and 3.9% higher than the state-of-the-art DERN method (60%), and higher than other previous methods. These results show the superiority of the ResNet+TCN in modeling students' engagement level as a spatio-temporal classification problem.
| r | 9d70370224ce5dc6c487c9965e9c4bb7 |
Sparsification of neural networks is becoming increasingly important with the increased deployments of deep network models to resource-limited devices. The most straightforward way to sparsify neural networks is by removing weights with small magnitude {{cite:bc3e12755c8d70aba7ccf7637f3b02d5f2d286d4}}, {{cite:4756deae75f4b32ccca0446bf7265a562be0e12e}}; however, such heuristics-based pruning often degenerates accuracy, and {{cite:f6dbfbb53762f956a5ebe4a42b961ed0cde89cf9}} proposed an iterative retraining and pruning approach to recover from the damage from pruning.
Using sparsity-inducing regularization (e.g. {{formula:2ba23dfe-6e9b-4d8a-86b4-1f8b3dc8c62d}} ) is another popular approach for network sparsification. However elementwise sparsity does not yield practical speed-ups and {{cite:79cd2a42ff255e4549276b80ed2e557f13b97cd5}} proposed to use group sparsity to drop a neuron or a filter as a whole, that will reduce the actual network size. {{cite:bb5eea1f738f90bf4dc043573c73161fd29b14bb}} proposed to learn the individual dropout rates per weight with sparsity-inducing priors to completely drop out unnecessary weights, and {{cite:ff700a58be282d1a97e963a8ee25a51801ac32e3}} proposed to exploit structured sparsity by learning masks for each neuron or filter. {{cite:f238bcfa3d7b8234fa74b21c6354603505012178}} proposed a variational dropout whose dropout probabilities are drawn from sparsity-inducing beta-Bernoulli prior. Information-theoretic approaches have been also shown to be effective, such as {{cite:576c52ecfeeaa9deffafc2f52efbff421a8719bc}} which minimizes the information theoretic bound to reduce the redundancy between layers.
| m | aa3c582287b9a797e7e7a69928941eb5 |
Finally, in Table REF , we summarise the results from using our stacked neural network and compare them with results from using simple methods (persistence and climatology), other neural networks {{cite:53c9c56d901b84d4a4107b3f0cbf8ac43e5fefff}}, {{cite:963c62e425a2cd64c515cb7ed276135a946e378e}} and numerical models (IFS T42 and operational IFS) where the numerical model results have been taken from {{cite:db1990283cff88642f23bd78c5c7223fc2c83ccf}}. The key finding shown in this table is that our approach is approximately as accurate as that in {{cite:53c9c56d901b84d4a4107b3f0cbf8ac43e5fefff}} despite the fact that our neural network has a simpler setup than the U-Net approach used in {{cite:53c9c56d901b84d4a4107b3f0cbf8ac43e5fefff}} and we are using categorical data rather than continuous data which adds an inbuilt error to our results. This highlights the advantages we gain from the data exploration and good choice of neural network architecture described in Section . The table also shows that our approach is more accurate than the coarse numerical IFS T42 model and the simple methods of persistence and climatology, but less accurate than the neural network approach in {{cite:963c62e425a2cd64c515cb7ed276135a946e378e}} and the operational IFS model. It is likely that our neural network's lower skill compared to {{cite:963c62e425a2cd64c515cb7ed276135a946e378e}} is due to the fact that the {{cite:963c62e425a2cd64c515cb7ed276135a946e378e}} model is trained on a much larger dataset of the WeatherBench data (117 data variables compared to our training dataset of 34 data variables for Z500 and 33 data variables for T850) and is also pretrained on extra data from the Climate Model Inter-comparison Project (CMIP) {{cite:fb9e89c6e7bc44ab2ba20337afae023ead224525}}. Thus the approach in {{cite:963c62e425a2cd64c515cb7ed276135a946e378e}} is both much more computationally expensive and much more memory intensive than our approach. Furthermore, our approach has introduced improvements which combine dropout based ensembles with the ability to predict probability density functions instead of single values. In the next section, we show how this enables us to make a more informed weather forecast.
{{table:d9a55684-6e65-4f83-973c-227259c71502}} | r | 6a8ed107b78f73f02a06f068d956ab70 |
The video sequence is high dimensional data that contains plenty of visual information. Thus, preserving important cues yet filtering out the redundancy is important to learn effective anomaly detection models. To learn robust global spatiotemporal contextual cues, we feed the extracted local contextual features of {{formula:1a8f5706-3204-43e2-9cee-fda56151a56b}} consecutive clips into the global context-aware stream to learn high-level features. As shown in Fig. REF , we adopt a two-layer Convolutional LSTM (ConvLSTM) network {{cite:6ba2f27583c7f8de7f5cf5aa77ca83dc3ba9e5b0}} to learn global spatiotemporal features of a video segment. Unlike LSTM, ConvLSTM {{cite:6ba2f27583c7f8de7f5cf5aa77ca83dc3ba9e5b0}} is designed by using three-dimensional data as the input and uses convolutional operation, which can obtain temporal information and extract spatial features. At the same time, it provides good generalization by reducing the number of parameters and the computational complexity. Specifically, we show the formula for ConvLSTM as follows.
{{formula:64924b7c-e38e-4a9c-add5-49bde4a3fbae}}
{{formula:bc7b4816-4682-4d2e-978f-f3436716ed19}}
{{formula:4278d4f9-e309-4d72-b708-5b8189c042ad}}
{{formula:a3cacb7f-1661-4ee5-bf8c-623d42d63c5d}}
{{formula:60148e89-4612-4c7c-aee2-9e1e4356ad0f}}
| m | 10b82457cb8e845d2f8ad8227069ce6d |
In this work we numerically explored optical nonlinear and nonlocal interaction between thin liquid film to channel WG modes in integrated photonics platforms, and employed it to perform digital and analog RC tasks.
Our 3D simulation results which take into account optical propagation with losses, heat transport, fluid dynamics as well as the underlying surface tension physics,
indicate that the magnitude of the self-induced phase change due to the TC effect in the liquid film, is approximately three orders of magnitude higher compared to the more common heat-based TO effect.
Importantly, TC-based interaction can be implemented in a variety of optical components; for instance the self-induced transmittance effect can be employed to modify the bandstructure and transmittance through the 1D periodic structures, thus opening a way for future studies of bandstructure tuning in photonic crystals and its topological properties {{cite:1a177f6c48ca06093c25060d7d6acc8c5b39920a}}, {{cite:45dd3d20a5fe1a51e6c6a0029be3ec28bc0ed7cd}}.
We then employ the self-induced phase change together with the finite relaxation time, acting simultaneously both as an optical nonlinear actuator and memory elements, to demonstrate physical RC capable to perform digital nonlinear XOR task as well as the more complex analog handwritten 'zero' and 'one' classification.
While in this work the input data used for the analog task was not subject to any preprocessing, we expect that common methods such as edge detection should improve the accuracy.
Our analysis of thin liquid film deformation predicts nonlocal interaction between WGs even if their separation exceeds the optical evanescent scale, providing nonlocal scale with significantly larger values compared to other known optical nonlocality scales stemming from other optical nonlinearities, thus potentially providing additional memory resource useful for optofluidic RC systems.
Importantly, our modality is capable to induce additional nonlinearity beyond the commonly employed square-law detection, without utilizing optical resonant structures, and operates under wide range of conditions which do not require phase matching conditions.
Notably, our work demonstrates for the first time that liquids can operate as RNN computing media, and further provides design principles of compact optofluidic and complementary metal-oxide-semiconductor (CMOS) compatible RC systems.
In particular, our design of optofluidic-based RC system is capable to lead to four-five orders of magnitude reduction in size compared to previous liquid-based RC {{cite:8ae576d2a0e24d1b6a07337546644f83fe8e4cc5}}, {{cite:3066a59f3cb57a7bb21b9bb34b7ef59a9a9ac092}} systems, and also to few orders of magnitude faster computation compared to the surface waves dynamics and reaction-diffusion processes which were employed in {{cite:8ae576d2a0e24d1b6a07337546644f83fe8e4cc5}} and {{cite:3066a59f3cb57a7bb21b9bb34b7ef59a9a9ac092}}, respectively.
Furthermore, our identification of a liquid cell with a WG which together operate as an artificial optofluidic neuron, motivates further exploration where numerous optofluidic neurons form more complex RNNs capable to perform more advanced computational tasks.
Interestingly, thin liquid film which introduces gas and liquid phases in dynamically evolving spatial regions, fits into the paradigm of phase change materials, which were recently employed for NC applications {{cite:fe937f4aa2679b686d6d23fc6fa62c5e89939dba}}, {{cite:554c3c319b428c543454b64b68d0296aafff6dd6}}, thus potentially stimulating more fundamental material science oriented studies of liquids on a nanoscale.
To summarize, we believe that our results open a way for future experimental realizations of the described light-liquid interaction effects and employ them for new types of compact optical devices such as phase shifters and threshold elements with RC applications which can tolerate ms response times.
| d | 7bb211e5e4648562feacf2b6581b5489 |
Consequently, nonparametric methods may be expected to have an
advantage when an accurate model is important to obtain an unbiased
estimate, e.g., in the presence of significant, complex confounding or
censoring, especially when response and/or treatment assignment surfaces are
nonlinear {{cite:4e8dea729aa7ec9b53d9ba60f075be9f02eac106}}. In real data analyses, this may happen with observational study data with strong, complex confounding of the exposure-outcome relationship, or in observational study data and randomized control trial data with significant, differential dropout, mediation questions, estimation of heterogeneous treatment effects {{cite:ce6d9e5c33f33f8a4526670c4623ccf45ec62cec}}.
| i | 91128ddafa52bedb5a5adbaef5334307 |
Since the theoretical results in Table REF can agree well with the data,
our approach can be feasible,
which is based on the factorization, pQCD counting rules, and baryonic form factors.
In particular, several {{formula:edca8755-e709-484c-b9a5-8f53ce4b4955}} asymmetries predicted as large as 10-20% can be
promising to be measured by LHCb and Belle II {{cite:cdc3c2b3964c4cbd3d48d4a07425467b763ae477}}, {{cite:a7014ce35e1fae8d9f45277f4017a0069d36309e}}.
| d | 05f233b8179edf8e480fd3a325fc3d56 |
The algorithm that we use to fit the suggested model has been described earlier in the statistical literature {{cite:9246d591c213e73c3a9a7ff1a8d9012f90be783e}} and its use illustrated in various simulation settings. Moreover, there does not seem to be a general agreement on how to simulate the data resembling the true RNA-seq data in an optimal way. Due to this, we do not include a simulation study in this manuscript. Instead, we simply demonstrate the behavior of our method on two real datasets: a mouse tissue dataset and a human prostate cancer cell line dataset. The results are compared to those obtained by applying the Poisson method of {{cite:3e9a8c99035476ff37cc9ca03dc1b41dd8609468}} and a transformation method of {{cite:fcb55750475f3e18861e3a13aed040af8c6302b4}} to those same datasets. In both cases, the npMSL method seems to identify a number of biologically meaningful clusters that is at least comparable to the number produced by other methods; in the human prostate cancer cell-line dataset case, it outperforms both alternative methods. For both datasets, the performance of the methods has also been compared using the adjusted Rand index (ARI) {{cite:e87c374ffdf4692e8597e6c8b15ccda93db3c45a}}.
The results are summarized in Tables (REF ) and (REF ). The most salient feature of this summaries is that the clustering produced by the nonparametric npMSL method is very different from those produced by either Poisson method or a transformation-based method. In other words, these seem to represent different solutions of a problem. We would like to note here that in the only case we are aware of where a researcher tried to applied a nonparametric method to clustering of the RNA-seq data the conclusion was a rather similar one - the clustering produced has been quite different from those produced by parametric methods {{cite:b7bc3b2ce39fbc819c29bd095fc1b1158e8830be}}.
{{table:7187a52a-39c1-4f19-aa8d-fc00e6afc039}}{{table:881ca0c9-1bb3-4017-b10e-17aafa417d6f}} | d | 7230bd208137fa67b699f8855e6b3ac0 |
This leaves the question whether the long-range spin-spin correlations might be used to witness the phase transition. In a large, yet finite system the long-range correlations can be build up in finite time {{formula:6a1d2a5b-db5b-48b8-a68e-cb268b9630c4}} , where {{formula:ff223928-f26a-424a-8e76-8879fe4e2a5e}} is the Lieb-Robinson velocity {{cite:40c47042acc8251c073bd1d72b9b7806d8dbdc50}} of the system. We conjecture that this is also not the case.
{{figure:063367a4-31f9-4f44-b849-3746bdff11e9}} | r | 46cb24956b51ef6d501fd5608e6341e1 |
Datasets We evaluated our method on a few standard image classification datasets, including Cifar10 and Cifar100 {{cite:be6ffda37a333514e590b9babfe9df9ac30f6dcf}} and Tiny imagenet {{cite:12c23423be7ff9f25c5f424188bca2650c442340}}. Cifar10/100 consist of 60k {{formula:fe838afe-e363-4105-b6b6-9bbc963b1eb1}} color images of 10 and 100 classes respectivaly. Tiny ImageNet consists of 100,000 images from 200 classes of ImageNet {{cite:f40c2166bddf2d8cd9b9aa42db8be9b04617d337}}, downsampled to size {{formula:0b0181de-3609-488a-b46b-c79341a06241}} . Animal10N dataset contains 5 pairs of confusing animals with a total of 55,000 64x64 images. Clothing1M {{cite:37f6448d3139240c11d2d7593b14bf26523b8fb9}} contains 1M clothing images in 14 classes. These datasets were used in earlier work to evaluate the success of noise estimation {{cite:b48aa63f4ffda4491d92cada2ec84c5183d3854d}}, {{cite:8d5d07f63297e9418229cf19fd723ce7e56db0ca}}, {{cite:da653f7e5c5c2b599ed067091a661b86f016ffed}}, {{cite:24ba90e9168a4d1e82ee95f8ea3af68d9b8e169d}}.
| m | 27c8dd244fc6cef8792bd368e702b3b4 |
In this work, we firstly calculate the {{formula:92e66eb7-e849-422e-b4cd-10489c8587bb}} radioactivity half-lives of nuclei with 4{{formula:3a3b8f4c-39d9-41de-99cf-6d7dc614654a}} Z{{formula:4fc644e5-1922-46b7-8a3d-0cd2fec8f11a}} 36 using the TPA while the nuclear potential is obtained by SHF and compare our calculated results with the experimental data and theoretical results calculated by GLDM{{cite:64097c3415a26e2dd3fbefdb34a2d1d6d783e2e6}}, ELDM{{cite:367cde2a79f14c61f18f3d34bbde57698f4ac038}} and Gamow-like models{{cite:90b47c086dff591b2095db2b81142fbf3ede3214}}. For Skyrme effective interaction, there are about 120 sets current Skyrme parameters. The SLy series parameters are widely used to describe the different nuclear reactions in various studies and the {{formula:3f4e98d2-8458-4353-94a0-7bf98ba7d19c}} decay since spin-gradient term or a more refined two-body cent of mass correction is considered{{cite:5038403e43a04f77b9274e7d75eccaac0cbb844d}}, {{cite:04f8f33b5dd323db4a5b1b0dc6f0a2c2f058fe2f}}, {{cite:1c5fbf008b3022853c21a373851ccfffa0074e3e}}, {{cite:b794c3daf19a6952df0c14c5af0677270a9ff57c}}, {{cite:23e9a4502c15d2aced8278d47cdcedf5579fc507}}. These parameters are listed in Table 1. As an example, we choose the Skyrme parameters of SLy8 in this work. The detailed calculation results are listed in Table 2. In this table, the first two columns represent the two-proton emitter and the experimental released energy of {{formula:a0a63ebc-0f64-433a-831b-a4e7c8bd624c}} radioactivity {{formula:458dac67-a431-40cf-b4d8-45c5859a14ec}} .
The experimental data of {{formula:05f26100-785b-42b2-b134-b942fd4dd41c}} radioactivity half-lives, the theoretical ones obtained by GLDM, ELDM, Gamow-like and our model in logarithmic form are shown in 3{{formula:19fad377-b69c-4bc7-ae0b-4d735c2e466c}} 7 columns, respectively. From Table 2, we can see that the theoretical {{formula:92bdfc3d-12e8-406b-b26a-ee50933ba7f6}} radioactivity half-lives calculated by our work can reproduce experimental data well. In order to intuitively survey their deviations, we plot the difference of {{formula:ec5b1ffe-7080-450f-bc7f-e5c24d8d118b}} radioactivity logarithmic half-lives between the experimental data and the ones calculated by these four models (our model, GLDM, ELDM and Gamow-like) in Fig. 1. From this figure, we can clearly see that all the points representing difference are basically within {{formula:d9883395-4379-42dc-837d-8ff08a9424e2}} 1. Especially for {{formula:b6b60072-3717-47b4-9ebf-fd1fc0bc375c}} Ni of {{formula:e205dcbb-8359-4e71-bc9e-d95fbc49c7a3}} = 1.350 MeV and {{formula:95d70b02-6e5f-48f8-ace9-dc865de41a2d}} Zn of {{formula:b904a36a-035e-4fba-9894-337f6856f1a8}} = 1.280 MeV,
our calculated results can better reproduce the experimental data than the other models.
| r | 1f79633d6648588ef289eba29adc9a23 |
From Table REF we can see that the our method has a higher advantage compared with the baseline and the source-only accuracy, a little lower than the target-only accuracy from both adaptation directions. In comparison with other models, our model has a better performance for most of tasks. The CDLM has a higher adaptation accuracy for the scenarios with seemingly larger domain gap, such as MNIST{{formula:ee27b8be-986f-4b71-8b93-1334ad89f20b}} MNISTM and Fashion{{formula:c11b94f1-69ae-4846-a4b0-7a14b39b532e}} FashionM. For the 3D scenario, the performance of our model is a little lower than PixelDA {{cite:c18921bb7523924f8f72a9e8745c2fe4f0859195}}, but outperforms all the other compared methods. In PixelDA, the input is not only source image but also depth image pairs. It might be helpful for the generation. Besides, we visualize the t-SNE {{cite:4a1345db2047b26433de5c782c43a235bdc97b0e}} for latent encodings ({{formula:0d896cb3-41e4-48ae-b7d1-f971d238f7e0}} ) w.r.t the source and the target, respectively. Fig. REF is the visualization for task MNISTM{{formula:ed1051eb-4701-4aa5-a27c-3d1166fcc5e0}} MNIST and MNIST{{formula:b2baf756-d517-463e-bc6f-eb2e82ea5188}} USPS, and it shows that both are aligned well.
| r | 06a369a58ad142b59815086589a8b093 |
We have used the dataset from Surface Layer Turbulence and Environmental Science Test (SLTEST) experiment. The SLTEST experiment was conducted over a flat and homogeneous terrain at the Great Salt Lake desert in Utah, USA (40.14{{formula:d86bfe47-c5bb-4462-94fa-14a7b7cf7aba}} N, 113.5{{formula:9a837cb7-fdf9-44bd-be22-b581dec248f7}} W), with the aerodynamic roughness length ({{formula:1cd42c79-40a0-4b81-b2a4-7a4984fee34c}} ) being {{formula:fb83dfad-a98e-4e33-9a5c-3d417bb2b734}} 5 mm {{cite:8c803257633c38af6a98abc8e61ebcb1cf0318d1}}. The SLTEST site characteristics and the high quality of the dataset have been documented in details in many previous studies {{cite:2ca6d03be449ac4930972b25afccfe81693722c6}}, {{cite:8ca0d6af2983253e1eec68817af0dadae0c1654e}}, {{cite:cf19f25b15a6f9dfb1e147639f702210c86607ee}}, {{cite:7bcaa7cf3ea2f8bb9f247642defcf5f7daf050e7}}. In this experiment, nine north-facing sonic anemometers (CSAT3, Campbell Scientific, Logan, USA) were installed on a 30-m tower approximately logarithmically at {{formula:b11c86f7-35ee-4bed-bb8d-6d3ed01c189b}} 1.4, 2.1, 3, 4.3, 6.1, 8.7, 12.5, 17.9, 25.7 m, levelled to within {{formula:25c48ab5-b23c-4676-9a25-aea959a136e7}} 0.5{{formula:3a374c90-5b99-4863-b8ed-9fb32ac5ba12}} from the true vertical. All CSAT3 sonic anemometers were synchronized in time and the sampling frequency was set at 20 Hz. The experiment ran continuously for nine days from 26 May 2005 to 03 June 2005.
| m | 2da684c0014f67dfbf46aabf6969ebcf |
{{formula:f521c43d-a463-4d86-b3e6-6fdeb8e15779}} can be ascribed to {{formula:af0c0b69-9d4c-4ca5-8e8d-eb6b7e237f52}} , the SUSY contributions to
{{formula:bdab1101-ac34-46ba-8d83-fa7b2b56adaf}} in order to constrain our model.
With further results to come from the Fermilab in the near future and
the data from upcoming experiment JPARC{{cite:b3f107f6f29ec0f40426d4393af09e34e6451ed9}}, muon {{formula:8e3dceef-8093-4f0d-91e3-848713c5bfcb}} can
shed light on various BSM physics models.
In this context, we must point out the
recent Lattice result{{cite:5a4ac5269def2a51f663aad6b0c8eda45fb9dc58}}
for the hadronic vacuum polarization. This has
effectively shifted {{formula:24f899fe-1c57-4b61-b405-b1115beb962c}} to move toward {{formula:5b0741f2-26d3-44db-9160-b939b414d96d}} rather
closely. This has created tension between the two modes of
evaluations of the hadronic uncertainty amount. The issue will be transparent
in future,
but at this point like many BSM physics analyses performed over the last
few months
we will use Eq.REF for
{{formula:775f4e8b-b35a-4e0c-9601-2ea649b53b88}} .
| i | 7b75a1d07715d8fcb278b3dc3074fa4f |
We calculated the performance of our models by training them 5 times with different seeds. Table REF shows the average recall over all emotion classes obtained using the different features extracted from wav2vec 2.0 models. We also show two systems based on eGeMAPS and spectrogram features, which can be considered as baselines. In all cases, features are normalized by speaker and the Dense model architecture in Figure REF is used as downstream model. We can see that features for both wav2vec 2.0 models, the one finetuned in 960 hours of Librispeech (wav2vec2-FT) and the one that is not finetuned (wav2vec2-PT), the local encoder representations lead to better results than both of the baseline features. It is worth noting that eGeMAPS, spectrograms and the wav2vec 2.0 local encoder representations contain information restricted only to a local window around each frame, of 60 ms for eGeMAPS, and 25 ms for the others. Also, the downstream model combines information from consecutive frames using just global average, which is a very simple approach that might be suboptimal because it cannot take into account temporal patterns in the features. In spite of that, the local encoder representations, particularly the ones obtained from the PT model, reach a performance comparable to much more complex models like the one proposed in {{cite:9a1065980f816ebcebec3c6c40b905afe047a047}}, which is a CNN with Bi-LSTM layers trained in a fully supervised setting with spectrograms as input.
| r | afbdc8da22be8e190c414c04200f6b6a |
We have generalized the mean-field Hartree Fock description {{cite:3bdb8642860b1bb9fa130e63f6261fd05f86bc88}}, {{cite:45029e275707f143eb89588b51d3f25a7ba24784}}, {{cite:7721fc79e61edd1fec6a635e5dfa27e2e06d43e7}}, {{cite:a4f25c578898d8ec3980eb9240aaf5891cc335f3}}, {{cite:f7a49931bffe68ed1604398bc1993210a8208b92}} to provide a comprehensive qualitative description of broken symmetry ground states in RMG, including the effects of defects including random disorder and stacking faults.
The non-trivial topology of the low-energy bands is reflected in large Berry curvature and Chern numbers per spin-valley flavor.
An obvious generalization is to a number of stacking faults separating rhombohedral sections with different numbers of layers {{formula:1325e9c3-9570-4216-8cc3-0cad54a305aa}} , each section contributing a pair of low-energy flat bands and a peak in the Berry curvature at a characteristic {{formula:40131ddb-5474-48bb-8cbc-961d542fdf6f}} -dependent wave vector.
In RMG, each stacking fault contributes a pair of low-energy flat bands because they are more complicated than the domain walls usually considered in the SSH model which consist of isolated monomers or trimers {{cite:8f193a675960471705afdaacd04f73055515b14f}}. The Bernal fault corresponds to two monomers (and a 4-mer), the twin boundary fault is a monomer plus a trimer.
| d | af7981a4aecd169f107509e3061f7a0d |
Finally, we also consider a supermassive black hole binary (SMBHB) system to explain the long-term periodic temporal signals.
{{cite:b31c9434e5b6965d1b35001f12b1841e3754898c}} ascribed the optical QPO in the blazar OJ 287 to this mechanism.
Several other discovered candidate QPOs sources are also discussed in this model, such as {{formula:b5ebf821-fb39-4b50-bd85-228681e57fc4}} 2.18 yr in PG 1553+113 {{cite:be85b79f5300796f444c9a7d61717e06b9a624e6}}, {{formula:535f8417-3bc3-4eb2-a222-200ecc48db27}} 2.1 yr in PKS 0301-243 {{cite:6d2d9788d4e859da7e028022e1fb93283e7c56ad}}, {{formula:594f9e54-e7ab-48bd-a10b-e3046b984446}} 3.0 yr in 3C 66A {{cite:6dde842ab53152b895ba9de44f9d0c083f658901}}, and {{formula:96396311-06b7-469e-918c-53def6adf71a}} 4.69 yr in PKS J2134-0153 {{cite:af77e19471ef350532f6f1765628181948253bdc}}.
The Keplerian orbital motion of an SMBHB would trigger periodic accretion perturbations, or the gravitational torque from a
companion would induce the jet-precessional and nutational motions in misaligned disc orbits
and yield periodic timescales in the range of {{formula:b8062e97-8dca-4b01-81ce-c880ca27c165}} 1 to {{formula:e6867e49-017c-44de-b11c-3574a768c731}} 25 years {{cite:0d9e30d09dba9c3296dac84c5681298392e9c602}}, {{cite:1183097d049eb5df1b536725c371ac238b0e26f4}}, {{cite:834d7e70419ed15dc9473deb1889f82cfc3c354c}}, {{cite:2905c72ba606fd04dc16fce04598a662ddda65bf}}.
The observed period {{formula:b78aa764-2317-4b20-af93-1f02d439039a}} of {{formula:0f8d488c-13e6-4543-a2a7-00d2c55662a1}} 2.8 yr is corrected to the intrinsic orbital period {{formula:3061b43e-04d8-482b-ad69-fd1042814531}} days for the cosmological redshift.
According to {{cite:5b4f97eafd95ad4342410bbf4980c3147602edfb}}, the mass of the primary black hole can be estimated via the relation {{formula:0c07da05-2d92-4b01-b749-c1bea5bc330b}} , where {{formula:83e9a63e-d5bf-45ac-ab5c-f01fbc221599}} is the mass ratio between the primary and secondary components and {{formula:9efccfa8-e6ad-404d-9c6c-3831253691cc}} is {{formula:1e64bd50-0c10-4440-a64b-7af62b88e219}} .
The value range of R is generally 0.01-0.1, where R = 0.1 is used to calculate the mass of the primary black hole {{formula:3f2f109e-6374-46da-85e7-1a069ec81d0f}} {{cite:923fdd4c0fca845f576ce759008a889dbefc2d87}}.
Based on the value of {{formula:abbe53c1-4007-4193-88f6-6f0a5f3f3cb0}} , we can calculate the separation between two black holes as {{formula:d53f16cb-a1f0-42c0-adb6-a312710a1842}} parsec, where {{formula:b67434a5-f81f-4f58-835d-a1a9e0532f2a}} represents the Schwarzschild radius of the primary black hole {{cite:6ed0572c6b9b10d0707a0c73aa6149e38ce176f9}}. Such a milliparsec separation might be too small to yield an observable orbital decay time-scale in the evolution of SMBHB systems.
The orbital decay timescale in the gravitational waves (GW) driven regime can be estimated with {{formula:1c16a71a-ff9a-4562-80d8-d272a9720237}} yr {{cite:3303a855c7c15724146b5fda2fa67a129acf7338}}.
If the quasi-periodic behavior originates from such a system, we may predict that the system will experience gravitational coalescence within 56 centuries accompanied with the emission of GW. Therefore, this object may be one of the future potential targets of GW detector observation.
| d | 3adb0a54158316ef91cbe79b84379984 |
To tackle the aforementioned issues, we propose to leverage the Marchuk-Yanenko method {{cite:b980b6af3aa13029320e1e14fa88e6137a359145}} and the {{formula:57019c4c-8d10-492e-9545-dce1a5e26e4e}} –projection {{cite:a562dcbecd90769fdb3401c2f42e2fffe0cd9988}} to implement the time discretization of equation (REF )-(REF ). The Marchuk-Yanenko method is chosen because it does not lead to coupled terms at different time intervals and hence does not introduce any complication in deriving the corresponding adjoint equation. We are motivated to consider the {{formula:65ab263a-e09a-4fa1-8d73-a03cc1704946}} -projection method by its popular application for unsteady incompressible Navier-Stokes equations, see {{cite:20a5c7ef2c46fd215e02d3c08378b6b46bcfa667}} and the survey paper {{cite:6db34c195eb339aa97c0ffbf10aa375da4b0a66c}} for a thorough discussion. Inspired by {{cite:6db34c195eb339aa97c0ffbf10aa375da4b0a66c}}, we advocate the {{formula:e9899a9a-7199-4c8b-96fb-b523b6193e6c}} -projection with an incremental term of the pressure {{formula:8ddc85d0-e06a-4215-b3c6-c6f00a423771}} (see (REF )) to increase numerical accuracy and stability. Consequently, a scheme combining the Marchuk-Yanenko method with the incremental {{formula:05d60d76-604f-46bd-862c-f59b643a0841}} -projection is proposed for the time discretization of (REF )-(REF ). The resulting scheme only needs to solve a sequence of decoupled linear time-independent equations for {{formula:58991cf0-1920-4547-991f-ddc47e83a974}} , {{formula:366e733b-cdac-48bf-803e-439a2f2bde17}} , and {{formula:2933422d-9884-4f1a-8a17-090d6d36cf34}} at each time step. Computing time can thus be substantially lowered for large-scale cases. With the proposed time-discretization scheme, the gradient is relatively easier to compute when a gradient-type method is applied. More precisely, we only need to solve four linear advection-diffusion equations and two degenerated Stokes equations at each time step to compute the gradient. All these equations can be easily solved by some well-developed numerical methods in the literature, e.g., the fixed-point iterative schemes in {{cite:1c3e797db76faf0a5cdfd10f20bdb075a4911b0c}} for advection-diffusion equations and the preconditioned conjugate gradient methods (e.g., {{cite:20a5c7ef2c46fd215e02d3c08378b6b46bcfa667}}) for degenerated Stokes equations, respectively.
| m | b34f539706f7cac45bed6d554aa5ffa5 |
The explosive growth and increasing complexity of the data have raised huge difficulties as well as challenges to the traditional centralized machine learning schemes due to their heavy dependency on the local high-quality computing and storage resources. In this context, the distributed learning {{cite:5c57fde01f6e585a1952e80eeee432c5cc25bf3e}} has emerged as an effective solution to utilize the ubiquitous but low-quality resources to tackle the large-scale data problem, especially in the era of the Internet of things and edge computing.
One realistic application of distributed learning is federated learning (FL) {{cite:dc233f951307bc8482eaae4b2ad6a242ac41b35b}}, which intends to keep clients' training data locally rather than transmitting them to others to protect the privacy of each client. Specifically, during the training process, all clients train their models locally using their own private data, calculate the model updating information (such as model weights and model gradients) and then upload them to the parameter server, who will aggregate this information to update the global model. Thanks to its privacy protection capability, FL has been successfully applied in the financial and medical fields {{cite:96064f3dea67297dc80cd9bb57063d4a5b4fd5d7}}.
| i | 2c0a1661152f0880947239571c0f07d1 |
We propose a framework for processing unstructured information into a knowledge graph.
The framework consists of three distinct modules, namely an information retrieval module, an information extraction module and finally a module for risk measurement and graph analysis.
Even though the source material consists of written news and reports, the framework implementation does not reuse the text or otherwise infringe the copyright of the authors. The first module aims to gather and process relevant unstructured information from unspecified online sources.
It begins by collecting a list of urls of news reports of cyber attacks that are of interest to the analyst.
We used Python libraries for requesting the page from the given url, if the source allowed scraping, and cleaning the text by removing irrelevant content such as html-tags, other urls or embedded content.
This cleaned text is then processed by removing stop words and extracting the relevant entities and their relationships in the information extraction module.
The relationships between the target and the attacking entities are extracted as a triple in the form of “target - attackedBy - attacker”.
The extracted entities are compared to the results of DBpedia Spotlight {{cite:348b7e0a7a5d0a643b4f11f3c2dcf395431a0e6d}}, which finds related records in DBpedia {{cite:f9c04a923c71ce8dc82106ff384ff710eb6bc623}} as linked data, which we then use to complete the fields in the ontology.
DBpedia Spotlight annotates the entities found in the text and performs disambiguation using the context of the phrases.
In an ideal situation, these entities are correctly resolved and found in DBpedia, but in a situation where this additional information is not found, we omit the information while keeping the entity as it was recognized by the Spacy NER {{cite:033b1e73b3e78d82452e70abcaa0295a3e2da7d8}} and adding the triple of attacker-victim relationship.
In a complete system one could also crawl other sources for additional information, such as software vulnerabilities.
Lastly, we use the generated knowledge graph for constructing a naive measure for risk.
The risk level in this study is based on the frequency of attacks in connected entities in the resulting knowledge graph.
| m | 02eda1f7db6719b19d447ead0c70ede6 |
In closing, we comment on the possible relationship between the superconductivity reported here and that observed in moiré systems.
In RTG aligned to hexagonal boron nitride, the moire potential only weakly perturbs the underlying isospin symmetry breaking{{cite:937ae0b82973b14ab0236d0583a6b3727a10def8}}. The {{formula:6b42fd34-a8e8-44fc-ad7d-e488b5723f34}} and {{formula:30fd8169-8a41-45bc-90f9-b030996c8258}} dependence of the signatures of superconductivity observed in that system{{cite:18b1cf41d8e8b1f215ca6017b181cc6e1762ed0e}} would appear to be most consistent with SC2.
Twisted bilayer{{cite:c6772f89b4f0ef4055781a7a17fbf79bff69f22b}} and twisted trilayer{{cite:19fb349a8c20d2ed5f42d7088c838dae2d8c3d6d}}, {{cite:7ee192a3f65a740104573304b38e1e7098df4a31}} have different microscopic symmetries; however, they share several features with RTG including enhanced density of states and isospin symmetry breaking. We conjecture that the superconductivity observed in all graphene systems has the same basic origin.
| d | bcbcabddf198edede28b84c816b5d304 |
By using the isotopic IBD yields from Eq. (REF ) and the correlation matrix of Eq. (REF ), we can estimate the predicted IBD yields of a future experiment with ({{formula:43572dfd-5ae8-4878-9db4-8befc083f654}} ) {{cite:a4aa9bafb327785d9f83dd7fb4f084a6069b9799}}:
{{formula:6a3ecbcf-1e0c-4e91-9db1-0050bf74be97}}
| d | 0d2ccb63c5e3acf6b2428775cda5e4e0 |
These results shed light on the question of why higher-order interactions may be important in various applications that exhibit collective behavior. In particular, by modifying one's balance between dyadic and higher-order interactions, a system may self-regulate not only to modify (improve or worsen) its current collective state, but also broaden or contract the set of possible collective states that the system may support under further modification of the individual unit's local dynamics (here given by the oscillators' natural frequencies). This observation may be particularly useful for generating hypotheses for systems that exhibit a strong tendency for re-organization and self-regulation such as the brain where empirical evidence suggests that higher-order interactions play a role in collective behavior {{cite:c10cb9fce028dbdcc42323a37cca34243dc65b8c}}, {{cite:2dd07fc913e58bf76e3a6432be0513ac24e911e1}}, {{cite:c7eb1c479e8460032b851f2317af48a6dec00f69}}, {{cite:e9733d9593bec446d3f1c3050499b7c7962a7eea}}, {{cite:22165d466d07bf161256405c8c034d9b4bf13ee2}} and an optimal range of dynamic behavior is crucial for function {{cite:02d47dc94b0255ec464d56c909a3c285a4a31c39}}, {{cite:0e1b4f72fed45ecce371793a6941f340bf9ab2e8}}.
| d | 2ee887a407d5bc3c3204880c073006fd |
In this section, we detail each part of our proposed SAFF, which aims to develop a solution that can both improve the transferability of cross-domain features and exploit class-discriminative information to generate labeled cross-domain representations that implicitly preserve class-discriminative information, thereby further narrowing the domain gap in UDA.
Fig. REF illustrates our proposed SAFF. {{formula:0eb98519-de35-4aa5-930e-dad5bb3927ad}} , {{formula:dca47608-b3ad-4f50-aad7-b33e639595f2}} and {{formula:70385f9e-51e8-4e98-ada3-c058f16ab495}} are samples from source domain {{formula:17e9e01a-707d-41f5-8a33-979316728903}} , SSID {{formula:faf2e80e-cf57-4e98-9085-f40372a9705e}} and target domain {{formula:c4fe29af-abcd-427e-8e13-75feedea44a2}} respectively, which are fed into the feature extractor in parallel, and {{formula:8c209b08-59a6-4e10-96df-68d43fbce72f}} is initialized by {{formula:42e3a50e-26a3-426b-bf39-cada9d4b00bf}} . Where {{formula:9af97cf2-0a7c-473c-822d-22114a9c96e9}} is the label of {{formula:7dafffb7-7a69-400d-8d70-776f344ed6ee}} , {{formula:efa1d06b-9527-40de-97fc-2abbb4caaa4e}} and {{formula:7bbdb7cb-9801-4024-9bc8-a157e861efbc}} denote the number of sample and class respectively. The Vision Transformer (ViT) {{cite:3190b003505f7293a7effc600c89c50307cfbb4b}}, {{cite:a56ee4d1a75d8906a9f87eae9c7a9ac91bd3449f}} is used as the feature extractor to extract more general representations as its outstanding performance in many computer vision tasks {{cite:ccde780180de1c0d746350320c5af261650f05cc}}, {{cite:504b82cff94e5864a3acb70b39a5348cf482f0d9}}. Our feature extractor consists of {{formula:ee1d29df-db58-4e35-aeca-8088906c6ef2}} feature extractor blocks followed by SSID learning strategy, which we described in detail in Section III. A. Then there is the max-pooling layer, the bottleneck layer, and the classifier head layer for classification. The specified output of the feature extractor and bottleneck layer are stored and updated in the external memory bank for subsequent loss function computation. The memory bank and loss functions are introduced in Sections III. B and III. C, respectively.
| m | 2e41910c5a273edb53dcb769e5e59bd5 |
The generalization of the RT formula to geodesics with non-zero winding number found in this publication considerably strengthens the “entanglement builds geometry” proposal in the AdS/CFT correspondence.
Due to the fact that the BTZ black hole is given as a quotient of pure AdS{{formula:ce4bcd39-4f0b-44a8-aad2-288624ab8f0c}} , the winding geodesics whose field theory dual we have found cover the entire black hole geometry up to the horizon in the one-sided case.
Moreover, in the two-sided case the non-minimal geodesics also include the wormhole geometry behind the horizon.
The correspondence between entanglement entropy and geodesic lengths then allows explicitly reconstructing the full bulk geometry from boundary data (for instance from integral geometry techniques which naturally incorporate winding geodesics {{cite:1284c7ec2446e1a9e1f04181a20f2bcfba5a631b}}, {{cite:b67eee6c3fa15bf05e4b2cb071e8b0f8b4264b45}}, {{cite:f21d360dd618e31b040b6c7245cc86915c91adc7}}, {{cite:c7c9279ee9105da1c8d49eb5c1618baa748b2a4d}}, {{cite:2cb694b31aca562102b2d2120d8a3cda36a384d6}}, {{cite:957c15729e4d5f14e180fb86bd83ac9706867b18}}, {{cite:090b90dc68b9b65c376db06a5b38ed13df003f61}}).
It is likely that the correspondence will also extend to other asymptotically AdS{{formula:79cfb1aa-840d-46f1-a38d-0c4247717bb3}} spaces, since these geometries are all obtained as quotients of pure AdS{{formula:e6cc523b-54cd-4955-b1b5-48ae3a81ff70}} that naturally include winding geodesics.
This includes in particular conical defects, for which the correspondence between the entanglement entropy of non-spatial degrees of freedom and the length of winding geodesics has already been worked out under the catchphrase of “entwinement” {{cite:a28cca0896a91c9663e73aeb7e58ea1e390a0247}}, {{cite:c25bf14b53b64779c15a5234ea00b4a11add8622}}, {{cite:08d536324d7968c3b0b044d3c8def6a4afc27ece}}, {{cite:884dc2f507f9fc81de01940bab6bb54dd8a02772}}.
| d | c0f9a94edb60ae68eebafa566d7cdbef |
Section 6 is devoted to a proof of Theorem B.
By virtue of the identities (i) (ii), the proof of Theorems B boils down to establishing the level-1 Large Deviation Principle (LDP) for the map {{formula:2b3d85ef-a8fc-4d37-958a-a3abcb608c69}} and the function {{formula:2dc48dbd-8327-4449-aaaa-d2711df31d52}} .
If {{formula:e814cf59-d3bb-4f0e-8eb2-166c32955b82}} has no parabolic element, the Markov partition
constructed in {{cite:8e386ad2306f81f7837291605c25d377a192e992}} is a finite partition, which semi-conjugates {{formula:12cc02bb-cfd0-465b-821d-cb275ad9c505}}
to a finite Markov shift.
There is
a unique Gibbs-equilibrium state on the associated finite shift space, and the level-2 LDP holds by works of Kifer {{cite:cb67fc1038e574e00cccddfdc8a00255ab21a3d0}} and Takahashi {{cite:ba82290aa60a9e7b92e8146453c56585892b3bff}}.
Even if {{formula:2959ab1c-cddf-4781-bbef-4e133b7b3070}} has a parabolic element,
one can extend
arguments in {{cite:ba82290aa60a9e7b92e8146453c56585892b3bff}} to establish
the level-2 LDP
using the finite Markov partition constructed in Section 3.
Via the contraction principle we obtain the desired level-1 LDP.
We then relate the level-1 rate function to the function in (REF ) using a dimension formula for {{formula:f4431490-add6-453f-95a8-dd0f81c3a0f9}} obtained in the proof of Theorem A.
For a general account on large deviations,
including the precise meanings of level-2 and level-1
we refer the reader to the book of Ellis {{cite:882d64aa9f4b0b853278a0e102429b8d53f8d679}}.
| m | 2a503022589ede1c5b08201320885361 |
{{cite:adfbfd6bee5287ecd0bed2227aa53b8b2b8efe5b}} discuss transparent models that automatically incorporate explainability such as Logistic regression, decision trees, and nearest neighbour models, as well as post-hoc models, that are explainable with the aid of an additional technique.
| m | d8eb06f5f41fb125f48d399eeb527d55 |
However what is interesting in the present calculation is the simplicity by which one can deduce the main features of these cross section calculations for these interesting processes using the leading order diagrams, {{formula:b0cfbdbf-7759-4382-9493-42d129262d97}} in QCD in the framework of BSE, namely the consistent treatment of internal motion of quarks in hadrons in BSE framework, which we feel is the single most important reason for obtaining theoretical values of cross sections of the same order of magnitude as the lower bound set by BABAR and Belle{{cite:8e678b749f7c0d3828b1d4779e48ea39890c34fd}}, {{cite:5b39fb8cfbf61a65fd1fb3c0ee5f823c169f0806}}, {{cite:715b2f8153bf671904b50985f877d23ac38d7950}}. We wish to point out this is further validated by a recent calculation {{cite:581afb36216513a1cfe80a0ebf897099a81dc740}} on {{formula:37cd0a1e-997b-46e3-ae56-681e49851d55}} using Light cone, where the authors had shown that by taking intrinsic motion of quarks inside the hadrons, one can significantly increase the value of cross section.
| d | 19a83f1977bf2971f9d5bf749db50662 |
If {{formula:16c82ff7-e868-45cf-963a-82e0f1ec4c77}} is slice, the notion of slice regularity coincides with Cullen regularity (see {{cite:ebddee9c8579c8df456d31d9c9617d9a7a4c1019}}). A useful result for slice-regular functions is the following
| r | 45e57fc856f235639c9c4c976a9a738f |
Edge detection is a task and a method of feature extraction. In this paper, instead of producing edge-maps such as in {{cite:9077caa3b78301d8a621b5af64ad44d17de3a017}}, {{cite:a8be79107d423db7f27fd725f4cc182ebe4c2be3}}, we will focus on how to extract robust features for image recognition.
To the best of our knowledge, we are the first to design artificial neurons specifically to capture edges.
In image recognition, alternative convolutional layers have been proposed such as local binary convolution {{cite:3c859f4dce03c6d2494729c0ba6289661c0c80a7}}
and quadratic convolution {{cite:b84ab4acdcf991cc88a5d3e29735ad176e4dfa3c}}.
Gabor filters were used in {{cite:de2a809418c6d97a022cb729f6fcff5d0aed6b51}} to replace the first convolutional layer to reduce sample complexity.
In the broader literature on neural networks, {{cite:57ab3cea1bc7222c428761a0f5c92b3ba427ab08}} proposes specialized units to perform arithmetic operations.
| i | c82fa11c9b15a0622ce07a4d565d8ee5 |
{{cite:000cbd7adf4ebe6829271d2005324b28af95d3d6}} also find that SNe Ia with early flux excess originate from younger stellar populations. This, and the early flux excess in some super-Chandrasekhar SNe Ia (e.g., SN 2020hvf; {{cite:31a01c6857751f33b999671cf83e8f8a029ea0c0}}), might suggest that some early flux excess SNe Ia come from the CD scenario. The CD scenario can account for super-Chandrasekhar SNe Ia and can explain a short CEE to explosion delay time ({{formula:3d5c4193-9a28-4343-9349-3a20fa1d3ca3}} ; {{cite:d24f9933dd92ccbb806898a83ecff612ceacd5dd}}). Therefore, it is possible that the CD scenario might account for early flux excess in some SNe Ia, but not by LTP/VLTP. Either the early flux excess results from ejecta-CSM collision like in other SN Ia scenarios (e.g., {{cite:720c8232f452f7479b86fe6bba45c95d018a9c8b}}, {{cite:5167c2b34aef587de946fa4f70580e111ed58c2a}}, {{cite:546202f283d1a28dd65295384fcbd09b3cc1cc40}}, {{cite:b28f8e0a5cac6407d84a2366578ddd328888cc0a}}), or the explosion mixes {{formula:587e6246-9c0d-4400-8409-30008a31ec56}} Ni to the outer regions of the SN ejecta as in some other SN Ia scenarios (e.g., {{cite:b28f8e0a5cac6407d84a2366578ddd328888cc0a}}, {{cite:9db7cfe17d605da982253d6c3a647802ba257143}}). The CSM might be gas from the planetary nebula that falls back towards the remnant. The fallback process requires further study.
| d | c1e29ffba9b3da8eb594ccc3a21bf3e4 |
Point-based methods aim to use deep learning architectures to directly process 3D geometric data.
For example, PointNet {{cite:b07f5e8d93117c8e9916f049c842c611fba5bfdb}} applied successive multi-layer perceptrons (MLPs) and a symmetric function (e.g., global max-pooling) to learn translation-invariant geometric features from irregular point clouds.
Although PointNet has achieved promising results in multiple tasks, it tends to ignore local spatial relationships on 3D shapes as its architecture learns features for each cell independently.
To address this limitation, PointNet++ {{cite:cd5f315c6e755cc4c0d322866e6ac3fe374c6b8a}} constructed a hierarchical architecture that recursively applies PointNet to exploit local spatial relationships on 3D shapes.
To learn more detailed local geometric information, other works further extended PointNet++ by integrating attention modules {{cite:cbca32ac69c2767cfef144086a44c39626a29c05}}, geometry sharing modules {{cite:963ae5b4bdeda728ed065c53e7a0d53f56f76e88}} and edge branches {{cite:25dcf35605abc48703eb73f6d0abb810a3e842ce}}.
Similarly, PointCNN {{cite:e205eb19662891626628c069a964e3fcc6773c51}} adopted an encoder-decoder architecture with {{formula:ad5c7e1a-0ed6-45fc-a2ac-6d6bf98fc90e}} -transformations of unordered points to perform general convolutional operations.
| m | 0647e32aebc40d2f3d2a9099e97e590e |
Next we turn to the strain dependence of the in-plane upper critical field, {{formula:9c9f68c3-c968-4f86-af2f-bace7d6ae739}} , which was measured by ac susceptibility at 20 mK.
Experimental details can be found in Ref. {{cite:0673bdcfb8630f49728a69d026d4f672a406381c}}.
Figure REF (a) shows {{formula:4f5a0eb7-e83e-4e9d-ab10-e0cf676b0cda}} against {{formula:3caa0808-c98e-4ab4-bceb-23dbb9db0a72}} .
The in-plane upper critical field is approximately proportional to {{formula:f76f4312-ddde-4c64-8b86-26ce5a5f8eff}} and deviates from proportionality only very close to the Lifshitz transition.
The linear dependence of {{formula:742b68f5-1768-4cc8-949c-ed9fbc94c64f}} on {{formula:e3ff56df-a6ea-4eff-a57a-b88f5f4de422}} , and therefore on the {{formula:0834cb08-e632-4959-ad18-ba7034ba7af1}} -averaged value of {{formula:3131a591-44d3-4879-a590-3cfe99216979}} , is expected for a Pauli limited critical field {{cite:c51f2ae5b427206fffee863b581f954874604cca}}.
Pauli limiting is associated with spin-singlet superconductivity, so this observation is consistent with an even-parity state {{cite:0673bdcfb8630f49728a69d026d4f672a406381c}}, {{cite:b6fa2d4f4ebda3a0a8d93f836b561423c677e3bb}}, {{cite:c6c136b241ef225f51bfb7ce17eb7ad8c46b0a5a}}, {{cite:0ffc2adafa5efda35ae4dcda217223718913c904}}, and results in a first-order transition, which has been observed both at zero strain {{cite:10502471afd935b91e4a6848d4742106f29ed48e}}, {{cite:92b487de6b138c9aa8007b08cd41ee13381827d6}} and at the Van Hove strain {{cite:dc514fd264c31e89f2dabf7b348ef81d575b20b9}}.
| r | 9e53ebeba793d01078488dc729b980c5 |
The characteristics of unperturbed density of states {{formula:f8a523da-79db-4bdb-9d33-f520a19b0913}} for pure Heisenberg ferromagnet in the simple cubic lattice shown in Fig. REF is well known; see e.g. {{cite:4b440e71de2ad057bdab2f7f395da45295195431}}, {{cite:98c65a95a05f1e84fe1efc138e14406083453917}}. The plot of {{formula:ff985e81-3a32-4686-8bdb-06db7cd3ace6}} given by Eq. (REF ) in the domain {{formula:6c058809-797c-4cde-a6d7-f4f26dc20a08}} , Fig. REF , displays the van Hove singularities (for {{formula:6d1a4358-14ac-4cef-9820-1c6d14abfe06}} ) at {{formula:4eadb961-0514-499f-a7a9-2ce5e7003223}} , and at its minima {{formula:14fed0fc-c30a-4647-b829-16c587bffc21}} , where {{formula:28245b3f-36ea-45b3-8541-1b28fef1e378}} . These singularities can be understood from Eq. (REF ) of ; see e.g. {{cite:70b0fbcd61befae161f10b475430afa750f58ac1}}. Perhaps less well known is the behavior of the Hilbert transform of {{formula:b77b4722-b822-4a01-92ff-27e4c3b9da9a}} , i.e. {{formula:be8c3d7b-2395-4185-8e07-352695883e32}} , as calculated by Eq. (REF ), also shown in Fig. REF , which exhibits the van Hove of singularities at {{formula:09d19a48-568e-4c0f-8859-1b3fc9047b47}} . This plot shows that {{formula:c8ff213b-8e30-40ea-92f7-719d0409f652}} tends slowly to zero as {{formula:8f94a082-73c0-458b-b00b-56c86c86390a}} increases beyond the value 3.
| d | 6adf5d25e485d9d755551352f3a7f18c |
Recently, {{cite:cbbc17991871109997ea1ceec524939ebf1c0f5d}} took a significant step forward in this direction by developing a semi-analytic Monte Carlo-based model for the dynamical evolution of binaries that is analogous to a first-order diffusion-based model.
They compared the results to direct {{formula:e4976273-4c46-4ed4-be20-3b5a9f18978d}} -body and Monte Carlo models for GC evolution with very similar initial conditions, and found excellent agreement over several Gyr of cluster evolution. This model was subsequently applied in {{cite:7fcf0b62b3068e213752a6a5883c0a6cf777adba}} to quantify the impact of binary-binary scatterings on the results, since the authors considered only single-binary interactions. As illustrated in this paper, adopting the higher-order diffusion-based model presented herein only serves to improve the agreement between the analytic theory and computational simulations.
| m | e0ab241ab9c05921dabcc1889854f73e |
Weakly-supervised segmentation methods {{cite:e7922b71ca7ff938ecd433ebd241b949c2820051}}, {{cite:2eccfe840ffd83e6619f40c1672a333f734d360b}} rely on weakly annotated data to produce annotations for the unlabeled portion of the data. The newly produced annotations along with the original existing ones are then used in a supervised manner for the task of interest. However, due to the need for weak labels in such methods, recently, semi-supervised segmentation methods have gained more attention. Many semi-supervised segmentation methods have been developed mainly based on
producing pseudo-labels for existing unlabeled images {{cite:8e5c282c6bdcd50685db5411cb44edc32d1cf314}}, {{cite:53a6836a968c35c172439ad1ee33b7b402ba1992}}, {{cite:7fffa871733c0f9e78c98fefe37be1c0abab93bd}} or through consistency-based methods utilizing augmentations {{cite:43e373fa8114eb23a9ea670918af94b5b66ce1af}}, {{cite:2e40c1e5b2d8d21db3f07d673062c9ca729e8559}}, {{cite:519c1e420ff1c21e966b75566cf9fa82deb9b3ac}}, perturbations {{cite:43e373fa8114eb23a9ea670918af94b5b66ce1af}}, and multi-model collaborations {{cite:6816e6f1eb9fc0c02475b6823af88a48ccb4754c}}.
| i | 177c366247729e8f293e276665a6a91c |
such that {{formula:afa5288c-85f0-4318-87b5-b97a25860651}} , is finite. In analogous way is defined Noetherian ring; a ring {{formula:4f7f1052-af01-4c2e-8175-109e2f0964fe}} is Noetherian if it is Noetherian as a left module over itself. One can see equivalent definitions and properties e.g. in {{cite:ebb3cd358d7cc68aa8dac5b2e8d00473ad09ad95}}. In particular, every finitely generated module over a Noetherian ring is Noetherian. Since the ring of integers {{formula:b993f877-85f1-4d09-9ece-0958e001166a}} is an integral domain, as it is well known, it is Noetherian, and therefore, every finitely generated abelian group as a {{formula:374147df-a7a1-4ca7-90fa-e01a54348942}} module is Noetherian.
| r | 44ec21d77ddcfebaea32b07e7fd858e7 |
where {{formula:51945e21-e23c-4cc7-a788-2cbd6e62d983}} is node representation, {{formula:60c3a5dd-f332-4121-81c6-604b6d122a0e}} is also the node representation, but it's not used in the downstream tasks. This setup is similar to {{cite:44a96b963ff2d46844d3be5b8cab78141308993d}}. {{formula:e6575008-7a6b-4401-8e14-8269f36cbf4b}} is the window size of window centred at {{formula:0142ba82-b591-44a4-9376-715567e1a59f}} .
{{formula:c5b9fde9-f8c9-4f86-b26f-43d420ecb6c9}} is often re-written using negative sampling method {{cite:4d100e5d3dedb282ff0f1fa8769b4ed246e38cd5}} to avoid the computationally expensive operation in denominator of softmax as follows-
{{formula:91e58663-86ff-4390-8c71-74b3274bb349}}
| m | 2df87ce8d84d2cc6e756872b763e9aa9 |
Here, {{formula:998f64ff-86f1-4da9-b9fe-3dce354164ae}} is the quantum of conductance {{formula:0391114a-33a2-4695-a1fe-7e797048955d}} . The transmission is computed using the NEGF method {{cite:72ce11dbac2fbf69ebeb8bda87aca05279c90ac4}}, where we employ Wannier tight-binding Hamiltonians constructed using DFT as described in the Methods section.
| r | 49f53666aa04084fcb00014698785e44 |
The longest common prefix (LCP) array is a commonly used data structure alongside the suffix array (SA). The LCP array stores the length of the longest common prefix between two adjacent suffixes of a given string as they are stored (in lexicographical order) in the SA {{cite:174424f3ca42484cd22cfd07cd51ccf4eb260371}}. A typical use combining the SA and the LCP array is to simulate the suffix tree functionality using less space {{cite:78b4e84676c48b3a3d8156ade0ce2208325aa178}}.
| i | 6ce26802d83743f3567ad4f402f78597 |
Adjustable latency. Figure REF shows how the performance of our online approach evolves as we decrease the allowed latency from {{formula:79b7b6f8-add0-4a29-a8af-8509cdc46a79}} s to {{formula:71160c5d-8737-455e-a26c-9fbfc735e88b}} ms.
Speaker confusion error rate consistently increases as the latency decreases – while false alarm and missed detection remain constant. This can be explained by the ensemble-like aggregation process described in Section REF that combines more views of the same problem as the allowed latency increases. Note that we kept the hyper-parameters ({{formula:186c971b-0a1c-46c6-ac6f-c0689b2d5103}} , {{formula:50bc1940-4f56-4a70-b41f-663a37ae8af6}} , {{formula:9b563d44-f9b9-4e82-b9bf-bbc5e6f3712d}} ) optimized for latency {{formula:0ff08204-3e93-44ee-aa93-e6aa5c072b16}} s and still get reasonable performance for lower latencies. However, it is also possible to re-optimize the hyper-parameters for a specific latency. This is what we did for the {{formula:626ac924-96c9-4013-9f7c-d79c517badc4}} s setting marked with {{formula:d622a9c4-a8e1-4555-b51a-bc70323fd83d}} in Table REF for comparison with FlexSTB {{cite:fc25f23728dd0746338d11859daae56862b7e9b3}}. Not only do we get better overall performance, but our approach also has the advantage of a lower memory footprint, as it never ingests nor runs inference on more than 5s of audio at a time (compared to 100s of FlexSTB) and keeps a single vector per speaker in memory (compared to 100s of acoustic features and per-speaker scores in FlexSTB). Furthermore, our approach with {{formula:39bf62b4-0ee8-415b-a9f4-02f5581f8e8a}} s reaches the same performance as the official offline baseline {{cite:5fe3088190ddbe5c60c8c808c8e1c8497c3636ef}} of the DIHARD III challenge ({{formula:ca84c5fe-db8d-49ac-b4a8-d656452897fa}} vs {{formula:487c0362-14cc-498c-8623-3cf38c4afafa}} ).
{{figure:8cdf2214-c6f9-4cba-afb6-5c0ac70a80d3}} | r | af543274ab12e26f8d7772b0448fe0dd |
Our work is also related to a large body of literature on dialogue policies
in negotiation {{cite:0e7fa5aca281c980206686e1b5fba2e6c52b39cb}}, {{cite:c96fa6d47b62c05ac69a95b35a6df1b5080c02a7}}, {{cite:47323373bfd4ee3c0a9ac40fb56af776f239384b}}, {{cite:48be0c87713fcb28f35aa35d86219c458cfe8a2f}}.
These work mostly focus on learning good negotiation policies in a domain-specific action space,
whereas our model operates in an open-ended space of natural language. An interesting future direction is to connect with
game theory {{cite:e1753ab304e79c4f5b818077da0d9367c5bc4eb8}} for complex multi-issue bargaining.
Another direction is learning to generate persuasive utterances,
e.g., through framing {{cite:523d49a8d729639e8715c7d92593b2cbea88a241}} or
accounting for the social and cultural context {{cite:330b2d482093bc57191593e1f1c2858ed95f5ac6}}.
| d | 3ef66b92e6b009a6cff53a1e2cfdb9e5 |
In this section we present a summary of the two-level PR-RBC method and its extension to systems with moving loads. The two-level PR-RBC method can be applied to any linear time-domain PDE which admits an affine representation of the parameter. The latter can be recovered by means of empirical quadrature procedure (EQP) {{cite:a9796b2f960abfc411614500451ede25eb817123}} or empirical interpolation method EIM {{cite:4a33f457a06251b174c06ee48e5e1269be37bc33}}, {{cite:01caf10a8d35ff49708749a9834b6c170d1a2e40}} if needed. Within our context of SBC, we restrict ourselves to the PDE of linear elastodynamics in this work.
| m | 6baee192e99023482032e92541120d49 |
Let {{formula:a2978224-efd7-4f59-b76c-893ea6774081}} be the uniform Cayley tree, where each vertex has {{formula:d3334009-105d-4143-995e-f06a0537082e}} neighbors with {{formula:c799c006-e849-41e4-a4c7-48a64bba5811}} being the set of vertices and {{formula:a46d8530-8e15-49d3-ba12-3a3f4ac30c23}} the set of edges ({{cite:819335665960d7ec55be80bf0f6ac9fefb31e419}}).
| r | 0657ce7d891bdd83f1e37e63b1c788a7 |
Little is known for extrasolar planets, comparing with those residing in the solar system. Theoretical estimates on the obliquity variations of planets have been done for those residing in the habitable region, motivated since obliquity determines the latitudinal distribution of stellar radiation and is important for snowball transition of planets {{cite:41d72850428e0b582522aba833113f226f2b728a}}, {{cite:3e904af866c8a67f017a2ae0aea4ac32e974c072}}, {{cite:4a5abe290b746e80ae74ff6d20cfc4b00e78f8b5}}, {{cite:1f28e351d857a796afaa3eaa28b7ec7d1d7125f3}}, {{cite:be77b7ea3dc1068586c68312cd6b7137c4d97166}}. For instance, it is shown that Kepler 62f and Kepler 186f do not require a massive moon to stabilize their obliquity, different from Earth. In addition, different mechanisms have been proposed to tilt the spin-axes of exoplanets during planet formation, such as via planet-disk interactions {{cite:a990581c751ac13078512e4797aafbfa011ec75c}}, {{cite:9de63d138e11c7900ec6e4039e4e88ff1228e3a1}}, {{cite:3e4c4e711ce730a56f90ef4769bc1557bbc512b9}}, planet-planet interactions {{cite:54ec5c2ea1258ab7a7ab33ef35b1f92b3acfa31f}}, {{cite:afaaef47b75c435a7949541269310d9246abc436}}, {{cite:5b23c7409da1dca17a3517ce617d2cac7507bdea}}, {{cite:839bfaaa92e257f0d0c945f417127e68d8b12f94}}, planet collisions {{cite:8d1f363afcc188ba5c510fbc90bc2d9d6771cca3}} and satellite migration {{cite:5423d9afe643b0a24feecbbb6b80af035748ad64}}.
| i | 86991db9030036facde68e29031e1d3c |
In this paper, we generalize the gradient norm minimization to the composite optimization based on improving a pivotal inequality in {{cite:04247494ad01ffd1c64951b1beec9cc4aa66d7cb}} and {{cite:2df0561ec84d6b5ef316cccd93659d7ea3024d07}}. With the well-constructed Lyapunov function, we use the phase-space representation, whatever gradient-correction or implicit-velocity, to obtain that the squared proximal subgradient norm of ISTA converges at an inverse square rate and the squared proximal subgradient norm of FISTA is accelerated to converge at an inverse cubic rate. Furthermore, we highlight some merits of the proximal subgradient norm minimization in practice. Meanwhile, we also find that the model used to characterize the linear inverse problem with sparse representation is the composite objective function, a smooth convex function plus a continuous convex function. However, the symmetric matrix {{formula:dd2bbc1e-d1b7-4377-a253-ed84085e553d}} in the least square part is invertible, even ill-conditioned. In other words, there always exists a maximum and a minimum in the spectrum of the symmetric matrix {{formula:dbcb5541-7893-436e-a74f-17f9eef6e7d8}} . Furthermore, it is more reasonable to use a model with a quadratic function plus a continuous convex function to characterize the linear inverse problem with sparse representation, to say the least, a model with a strongly-convex function plus a continuous convex function. In further works, we will continue to investigate the convergence rate of ISTA and FISTA.
| d | fc84ad16ecb0100242f625f28ec70a76 |
For our approach we chose a recently developed spiking neural network {{cite:75536e327d5d1aef0a99d7b91592e2217c48fce6}} with an inhomogeneous weight structure.
In a first step we successfully transferred the main principles of this network to the Loihi research chip from Intel {{cite:6e1a92b4b9f2b792c3816ea8a618f3d8166f39e1}}, a neuromorphic hardware architecture implementing spiking neurons.
In a second step we tested the stability of the anisotropic network implementation and compared its stability to a classical randomly connected network, similar to echo state networks {{cite:a20864595dbae9d14b9ecdf60f4bd4ac97a887fd}}, {{cite:6e88bd0289f1b6fb16ccdefed89f77815c1673e5}} or liquid state machines {{cite:a96d05c3d0cbce5d1e362a443a7484aca138756b}}.
We finally used a pooling layer (Figure REF ) to efficiently read out spiking data from the chip.
Using these spiking data we were able to learn 3D trajectories in a noise-robust way (Figure REF C).
The pooling layer successfully increased the simulation speed to faster than real-time.
It was also intended to make the spiking activity more invariant to small changes in the network, which is the exact purpose of using pooling layers in deep neural networks ({{cite:ddbf09d7e210b3cfc067d534d89c4cadf0b998f1}}; {{cite:4888c3b7bd9b62fbe0498aa33f94845d18860fd0}}).
A pooling layer has been applied to spiking neural networks before {{cite:3f00e6eb7e98ef9c0f23bcc859e5ece5e0b48339}}, {{cite:4c62e189f63550cbf4ae60291adee6ed8d4d2be6}}, but – to the best of our knowledge – such a structure has never been applied to enhance the performance of read-outs from recurrent network architectures.
The fact that the pooling layer improved performance for the anisotropic network in our study indicates that implementing pooling layers in reservoir computing architectures could be useful in other cases, for example when the reservoir has spatially-dependent connectivity {{cite:a96d05c3d0cbce5d1e362a443a7484aca138756b}}, and especially for reducing parameters on algorithms running on neuromorphic hardware.
| d | 74ce09ee6fa6c6a5d6a232824b2a44e0 |
with {{formula:befcee19-6731-42e7-a2ef-7e34ea7c02ac}} a classical weight, and {{formula:5844413f-0f0c-4b48-aadd-07699f10fbcc}} or 4, are prominent
in classical random matrix theory. For example, with the choice
of {{formula:f2a8242c-3d67-4d3a-b9ac-789eb0aa3e70}} as a Gaussian, (REF ) is the eigenvalue PDF
for the GOE when {{formula:44c2713e-22d2-4dd5-9f37-689954ad8375}} , the GUE when {{formula:320306f0-b14d-440a-bc1b-36c257e2451f}} and
the GSE when {{formula:d0ae2a26-6498-4b07-b978-945cca230ffc}} . Thus the exponent {{formula:49398537-8e23-4ab6-aee1-9eb32c316cba}} — often referred
to as the Dyson index after the pioneering work {{cite:8fb79fcf94a101cb8674d14ee448e0d685cc1b57}} — corresponds
to the number of independent real parts in the corresponding number field.
Beyond these three special values of {{formula:991dd757-668c-49fe-99a6-c9798b2eabb9}} ,
for the classical weights there are constructions of random matrices with
eigenvalue PDF (REF ) for general {{formula:69e47f7c-dc30-4a4c-b79b-e7f298e9ffd4}} . In the case of the Jacobi
weight as written in (REF ), this was first obtained in {{cite:a380f0c638dff26cfdc821d78f2ff469e3ee52a3}}, while
for the Cauchy weight it was obtained in {{cite:9440a3880b4504928717a415bdcd38e433f8461c}}; for a text
book treatment see {{cite:ad9463ab9cc2914f4962d047bf1cf59ae34c254c}}.
For the Gaussian, Laguerre and Jacobi weights, the theory of Selberg
correlation integrals as applied in {{cite:eb55e012161a4bc464e485503cafd39e26af15e4}} tells us that there are integrable
structures by way of linear differential equations
for the density of degree {{formula:dd4be47b-71f9-431b-8d4f-1685f185798d}} for all {{formula:3a8769a4-4ee1-4655-b8ce-eac71574ddfe}} even, and that duality
formulas extend this characterisation when {{formula:8778446b-30d0-4d6d-8912-2d5813aa9668}} is replaced by {{formula:51ae0e9f-23d7-4677-85b2-53b32148c486}} .
From the differential equations, difference equations for the moments can be determined.
In the Jacobi case these are of the same degree, but in the Gaussian and
Laguerre cases their degree reduces by one to now be equal to {{formula:bbea5197-66a3-4e63-984f-b430b3a0fd83}} . In practice, beyond
the classical value {{formula:afd9a31d-10d1-4c7d-b254-f67b4b8490c7}} (and by the duality, {{formula:9bc7aeae-3b2f-409e-94a6-3576b40a8422}} ) it was not
feasible to make these differential or difference equations explicit. An exception
was {{formula:62e1ea55-6905-4ac0-82e3-76759112243d}} in the Gaussian case (and by duality {{formula:0a428f72-885b-46dc-98e7-fc9d80c06ed8}} ), where the
seventh order differential equation, and sixth order difference equation were presented
explicity.
| i | 89f14d661395536aaff08e5148b77b46 |
In follow-up work, Wang et al. {{cite:efdd50251c0a431df66d4c42706b12f1365beb2f}} presented an improved
verification tool named Neurify
(https://github.com/tcwangshiqi-columbia/Neurify), which supports
feed-forward and convolutional neural networks with ReLU activations.
Specifically, they improve the underlying over-approximating analysis by
partially retaining dependencies with the input neurons even when the
activation status of a ReLU activation is undetermined. Instead of using
the naive convex approximation of Figure REF , they use the
symbolic approximation shown in Figure REF , where {{formula:32a725dc-89e0-405c-9999-98e8e950226c}}
is the symbolic lower and upper bound representation of {{formula:f973a227-4d87-410c-9c4a-fb00e66cfa69}} .
Additionally, Neurify iteratively minimizes the errors introduced by the
approximations by splitting on the over-approximated ReLU activations with
the larger output gradient.
On the ACAS Xu neural networks, Neurify is on average 20 times faster
than ReluVal and 5000 times faster than Reluplex.
The experimental evaluation also shows that Neurify is able to verify
safety properties of neural networks with over ten thousands hidden neurons
such as the self-driving car convolutional neural network Dave {{cite:ce9aecf2977c0a7b82e2de3c5b8ea7a77e9d47e7}}.
| m | 7889001d3ebf730fb919cb3be58143fb |
In Fig. 1 we show the typical stress vs strain curve obtained from the AQS simulation. The system yields at around {{formula:b00cae2a-19cf-4158-b489-7662187f16aa}} and after that steady-state plastic flow sets in. The mechanical response comprises a series of plastic events involving the rearrangement of cluster of particles that produces long-range displacement fields. To investigate the heterogeneous response, we resort to the microscopic analysis involving spatial configurations of atoms with large relative non-affine displacements associated with the deformation events. More precisely, we compute the non-affine displacements of the local shear transformations in deformed solids originally proposed by Falk and Langer {{cite:031be0a2383c6970d65606d1005d48d546a9cc10}} with some important modifications involving the strain {{formula:3f2f1e27-521c-4876-bd2a-ffa54f3528ae}} , defined as
{{formula:6c6da15f-b9e1-436f-a8ab-ec1a2c399ff7}}
| r | 0677c1383f90859cbd698caf1ca9a931 |
As a prevailing approach to AI, DL is an efficient method to analyze data by identifying patterns and learning underlying structures, denoting an effective approach to problems faced in various scientific fields. DL algorithms have been integrated into the physical layer of wireless communications systems {{cite:1984a248498388231037444f9fb626a1b4e49c82}}, {{cite:536267e83bac29bef19f8b88f6a2965bf776ee37}}, {{cite:03086ccb16c3a2525c7788a5c98f4e3b57e884ed}}, including channel estimation {{cite:00ebed6e389a24f225ba9dd7ece228bb659081db}}, {{cite:d4aabd124d748abe3fdd8ada74e9d5d67d73c87a}}, {{cite:0465e6133726f8d8230aae3824bd423eb597518e}}, {{cite:43b7c0bd7d7dca78837d9e9ef03dc186d3ae1169}}, {{cite:761bfbb554eaaddd2403f6700f188f42d59ce77f}}, {{cite:960d30d72a6493a796428645339ad715f8b61abf}}. In turn, this is attributable to the great success in enhancing the overall system performance, particularly when used in addition to conventional estimators, where coarse channel estimation is derived from conventional estimators, following which DL is employed to achieve a fine estimation. Therefore, DL-based channel estimators are capable of significantly enhancing the performance while preserving low computational complexity.
In addition, the GPU-based distributed processing allows the DL employment in real-time applications, as a result of which DL can overcome the limitations of traditional channel estimation through robust, low-complexity, and generalized solutions that improve the performance of wireless systems.
| i | e3419b7769cd32f7ade3ed771c2f1e60 |
Video Generation Module:
Our video generation component takes inspiration from the idea of decomposing videos into a separate motion and content part {{cite:f19d3eb7162be156db41c85062f3f93ea06cf313}}. Our video clips {{formula:5163840a-4a61-4915-b348-57218a6142bf}} are composed of {{formula:5af2eda9-2fdd-4287-ab96-d0eba3edb4ae}} frames.
The temporal relationship between the video frames is obtained by modeling the latent space vector {{formula:8c29c0c0-6b68-4f4b-adfc-89a26dd6ca93}} . The content of the video clips is encapsulated by introducing a context vector {{formula:de348ce4-df27-450d-a9d0-6c1ca4792cc4}} and is combined with every motion vector. Each input to the video generator is a combination of the latent motion vector and the latent content vector.
Each {{formula:b696c990-7088-4a62-9f5c-ed73a7d2bbcc}} is an input to the image generator to generate each frame in the video clip. We use individual image discriminator {{formula:bdb9ff15-bef5-44db-afec-3f2128b09eb9}} and a video discriminator {{formula:b908dccc-8d15-4f9e-b7ff-420cc5a43f85}} to play the role of a judge to provide criticism to video (image) generator {{formula:fdfb792a-fcf4-4d0c-bf06-89442b42a115}} .
The learning problem is formulated as:
| m | eb454364af622508ca044cc3e5c97e2d |
We visualize the multi-head attention maps of the [CLASS] token to all the other segment tokens in our vision transformer. As the [CLASS] token is optimized for image-wise discrimination, such attention maps indicate the most informative groupings of segments that will induce the most discriminative image-wise representations. We visualize the same attention maps used to generate the figure-ground segmentation, which are the ones in the 9th transformer encoder block. The layer takes 32 coarsened segment tokens as inputs, resulting in 12 heads of {{formula:a746eceb-1cc6-4014-b911-4dff555d4c70}} attention maps. We follow the same procedure as DINO {{cite:ff7e90e326eddcb9b39ca0685074dba9d9abe2db}} to display the binarized attention maps. The threshold is adjusted to keep {{formula:835a1abd-4304-42fa-bbc2-dc02e67a4c85}} of the mass. See {{cite:ff7e90e326eddcb9b39ca0685074dba9d9abe2db}} for more details.
| r | 1753634a6379bb112fdc2d58a9531159 |
The {{formula:724a182a-ff14-4c60-bd0e-e5dd4fd18be9}} theories were mainly introduced in cosmology in an attempt to describe the early and late cosmological history of our Universe {{cite:d0bf9462cfdc646b9c9ebd86a849c020a60965f5}}, {{cite:725d78a172120d01faf1d1fe70ab0ac1599b3152}}. The consistency with GR imposed constraints on the choices of the {{formula:0938d420-5862-4a14-b90d-f4005767caa5}} models {{cite:2c8df8386b0d143cdc91b0e07e7942b32688ed27}}. In these theories black hole solutions were found, that deviate from the GR black holes or they possess new properties that are distinguishable from the known GR solutions. Static and spherically symmetric black hole solutions were derived in {{formula:13ea9084-203b-4ccb-bdb8-384abd38ed58}} -dimensions and {{formula:3d79d439-0bbe-4168-bda4-8035d5143ba5}} -dimensions {{cite:eb0954717155690f24edfba0527a370ebca4174f}}, {{cite:8aa59a26f8fab2f84f3e167037f4e926985e5e8c}}, {{cite:9626968cae62b3d3c7e4b66c55d7d7c560a060ed}}, {{cite:b8accd152ac64731276cc0e4d7603f8217bdfbed}}, {{cite:de218888e3f73f86d71bc635994fac26606420c8}}, while in {{cite:afdf4b9a586d22e66952e9295fb710ece21aa526}}, {{cite:2857e57268e93eb705cf9bba17bd91c2b57da9fa}}, {{cite:fc1c17783b42c74ed74819963cac3d4592140ad9}}, {{cite:a949bc04ac4c526f3eb108cb261929e8277a2ece}}, {{cite:9a9c9347e073c0ec504add46ea65bf307a5620ac}}, {{cite:c016c53601e3e9ba5333b11f20fe9ec4c3bdf40a}}, {{cite:3fca8aa0f638f19c92f1db24b328b7c0d45f5be8}}, {{cite:62592bd70a45179bb516df8731521bb9894c4b50}}, {{cite:33efac58a99caa7379464506c81e2be8eb04c6f3}}, {{cite:ef202ba7f5d4a124e9c8c7445c072bfd5f11b477}} charged and rotating solutions were found and thin-shells surrounding {{formula:f9b1435b-19fc-43fc-a826-520d3eb4c3b8}} black holes with dynamical scalar curvature were discussed {{cite:dc3e36707eb910f240dc060b7e23eeb233a27655}}. Static and spherically symmetric black hole solutions were investigated with constant curvature, with and without electric charge and cosmological constant in {{cite:dc1c1d190d84e709cc328597a07c5101678286fa}}, {{cite:790e67d807fd76e7779a235e4bd728135272f7e3}}, {{cite:99e4157875b2a34e1ba0b58e12858c4af15c79e9}}. Scalar fields have been recently introduced as matter fields in the context of {{formula:95a52e0d-0875-46f7-8c02-90431039841e}} , exact black hole solutions have been found and the corresponding physical properties have been investigated in {{cite:6e3c9481d9100b85509b2f1a2401582b285e9ab0}}, {{cite:f56a51ffbac398fc9b95baace9ec5a8e733f2d42}}, {{cite:0f9d6ec19f66ce752d950824b06dc4f66cfeaebe}}, while the stability of {{formula:18dd6e56-8b77-4d47-90fa-26997f9448fe}} black holes was also considered in {{cite:0464a226f39c67c8c90267629b1c6a360859d8d4}}. The possibility of dressing the black hole with a gravitational hair has also been discussed in {{cite:1c0a7a1d79787ebb2bd9c73428d54ccad5e5c9e8}}, {{cite:5df3b2ecc5784748f54b564f9f85338683d9cbc0}}.
| i | 34b9e86e9f2fa3d497850552d040adb2 |
Table REF presents the detailed results of OOD detection performance on long-tailed CIFAR-10 with imbalanced rate 100 with various OOD test datasets. From the results, we show that our method can outperform OE {{cite:1cda6fa1d109e11eac9ce4fba673aca9525c941f}} in OOD detection tasks when training dataset is class-imbalanced.
{{table:833f52b2-ab9d-4dea-bbe2-ec21b9bdbc58}} | r | 0da56f3308a1bf784ac1757fb860bbf0 |
All models are trained for 1 million steps with a batch size of 32 using the AdamW optimizer {{cite:cbec1620f79eeac91215a451654b38c93568939c}} with a weight decay of 0.04.
For EfficientNets, the learning rate is set to 5e-4, and for XCiT networks the learning rate is set to 2.5e-4.
Because our data is natively complex-valued, we convert them into real signals of 2 channels, using the full Sig53 input sequences of length 4096.
EfficientNet inputs are downsampled by a factor of 32 internally while the inputs to the XCiT networks are downsampled by a factor of 2 before the body of the network.
Both of these networks were natively built for images, so 2D elements are converted to 1D for the temporal signals.
For the initial experiments, we do not use any data augmentations, training directly on the static Sig53 impaired training set.
Data augmentations, which are used later, are explained in the next section.
After the full training session is completed, the best model checkpoint is loaded and evaluated against the Sig53 impaired validation set, yielding the results seen in tab:sig53-results and fig:sig53-results.
| r | 07784feb4084ad7195bcf91e398a596d |
Learning Without Forgetting (LWF). LWF {{cite:531aab452bf03c0185252556d0eab3eed36ecbba}}, when learning task {{formula:dafb183a-e1c2-466b-a403-85ddac171949}} , uses knowledge distillation {{cite:702379a7223810df0b84e59edfaa15caadba89dc}} between the old model (with parameters {{formula:da319fc6-c88e-4a5b-b77c-65bc9a190e4a}} ) as teacher and the current model (with trainable parameters {{formula:a64effb7-4d3c-4aa1-b50d-cd8abaf5b1ad}} ) as student, on the new task's data:
{{formula:a787f5eb-19d4-4519-8a30-76e1132664e8}}
| m | 8aae8ac0e7ef081f5fef34e885f8c62f |
As shown in Figure REF (a), existing dynamic speaker-specific modeling methods {{cite:dca931958f84d995d1626a5aa1a18c514ce5415a}}, {{cite:442a1a3345781f3e28888f3ced0685a3d6c7cd4f}} design speaker-specific recurrent neural networks (RNNs) to capture self-dependencies between adjacent utterances of the same speaker. In this scheme, utterances are classified based on speaker identity. However, sequences composed of separate utterances attaching to the same speaker are disjunctive and incomplete, which hinder the comprehension of the context. Moreover, overreliance on the speaker identity hinders the modeling of dynamic inter-speaker dependency. In this way, the model can't explore dynamic interactions between different speakers, which greatly affects the psychology of speakers, and then results in different emotional expressions. Nonetheless, how to explore intra- and inter-speaker dependencies that change dynamically is still unresolved.
| i | e0eee7929db71b6b3461436f16d10edc |
Human Motion Prediction (HMP) has a wide range of applications in autonomous driving, human-robot interaction, and animation creation. Most previous works {{cite:3e02507909ba8f101428ee8e2f12c7656e4c697a}}, {{cite:3702421d20b58dddcc000f2b221cc83fa3545af5}}, {{cite:244513a183811f28d0328110582b17a1e9fd7f0a}}, {{cite:dba382f82292ffb1f6bce88f6434446b29351067}}, {{cite:dd78f00bf95e7585cfdca30eb0040b1d4a4eaeb7}}, {{cite:7cb478ffe421d081458f9492d9b177f631bc5698}}, {{cite:7800f321c77578a174b032d25ebcc7eda61938a7}}, {{cite:2b09e152120c84dd0f232d92281578ef7d98af71}}, {{cite:6e8aadeaab3be2be1920b801de12302ad0cba354}}, {{cite:a3b7958d4face6e3bed99ba89b1c7b85b00b2900}}, {{cite:fc2510b06230451804010d059dc1894497eff9e5}}, {{cite:27488fb4e799e05dc99c58973998b18e99c1813b}}, {{cite:2d422bb63743385194757ac4c218a2787c9fe2e4}}, {{cite:85b7a7cb7f9224d52c4d2d323937c16d71f2578f}}, {{cite:3faaad9c3b54471b62d2ec07b1be190e3d0f16bd}}, {{cite:fd9c44e8736b812e76c06c47defad05657d0609f}}, {{cite:2ecb59e5eacd5165c671e62ea8b873ce688dcdf6}}, {{cite:ec424aa7016b45a6fd1c3801fcb5dc5e3e67dd9f}}, {{cite:c39b844f68b3d5c1427ef1a6de25f4433da0f92a}}, {{cite:8a294706e9b7c981fdf3425dddfce4e46ba1973d}}, {{cite:95211a1094f8f09308960c8124d778c0c6e59c40}}, {{cite:e5a5ca57c237d5a2dbdc093dbfe3b9f5282bef7a}}, {{cite:808b174d3c1c68ccbe6c62d024fa9dc6c8f14072}}, {{cite:0730b92e596de56ac980ce180e40c4904c009f56}} perform deterministic HMP that only generates one result in the future. Recently, many diverse HMP approaches can predict multiple possible future motions. Due to the stochasticity of human motion, multiple solutions naturally exist, and forecasting them is of great importance in practice. For example, it would be better for a vehicle to know that a pedestrian in front of it may not only walk ahead but also turn left suddenly.
| i | 67d5a3418bc19ad8721c7fef376bb1a4 |
Following, {{cite:72e5e965b460e1fec2a15601b391801422077ff6}}, {{cite:656843b809623ea7449a3d5b0e501ec6a8e76151}}, {{cite:0629ce3e9e029917bd0095dda546a97d468e3e15}} we calculated the wavelength-specific flux {{formula:e655f376-e844-473e-a69f-336bf73fa6fd}} ,
| m | 46564b84e9741523d97c4f0d86a05d4b |
As for other methods for the estimation of the mass of the primary particle based on air-shower observable, the use of hadronic interaction models comes with unavoidable systematic uncertainties.
As studied by several experiments {{cite:0f64f9e70c4789967ca7a97d48423116ef0d3582}}, all available hadronic interactions models have a deficit in the prediction of muons, which is largest at the highest energies {{cite:c8c832d03e48afadec99a225f3f73341f5b93617}}.
We do not expect that this discrepancy in the muon number will have a significant influence on the mass separation power investigated in this work, which relies on relative differences in the muon content of proton and iron showers.
However, the absolute scale of the muon density is shifted, that has to be taken into account when comparing simulations to measured data and when interpreting data based on simulations.
| d | 6bcc3a28675e3f41a67450f1ce356018 |
where {{formula:eebd0f64-cd12-4584-b88d-7a62b0315817}} is the evaluation at {{formula:da0f3b8d-b7f5-45d0-8144-105af110e547}} of the degree-{{formula:e2339948-4034-4bb3-be6f-c9c35362f7bf}} (binary) Krawtchouk polynomial {{formula:ab980ea2-33bf-4b63-8497-22373ced4d9d}} defined as (REF ).
This program is equal to the well-known Delsarte's linear program {{cite:583fe82a47ff4e65016dcf00ac146c3df14225c3}}.
| r | 93a361bd89c124902deb571f4e00fa74 |
It has been realized that KL property in the sense of Attouch et al., and hence the one from Definition REF , is satisfied in broad settings. In particular, it holds at every nonstationary point of {{formula:4e46c2e0-1e2a-403a-a114-fb329047e5a8}} ; see {{cite:ac4589560f6b60fb00f4c5b408c06712ee866312}}. Furthermore, it is proved at the original paper by Łojasiewicz {{cite:4172226677915272be285e44dc3b832f85230a32}} that any analytic function {{formula:07350a04-1f96-4aad-926e-4198d8012756}} satisfies the KL property at every point {{formula:2806e14b-a6e1-472b-ac71-8e44e4e42ffd}} with {{formula:4c9969dd-1c3f-4275-b0b5-f9f5e1abe4d1}} for some {{formula:ea6ded48-5834-4f63-b0aa-bd32d98152be}} . Typical smooth functions satisfying this property are semialgebraic functions and also those from the more general class of functions definable in o-minimal structures; see {{cite:7c4944c41bcea59543a5931c7cab4427e1ed853a}}, {{cite:74cebc4069ca811e7a62bf733aed38597e4b470f}}, {{cite:1df2377d6799180d2b3e699255eafebd7702fe8d}}, {{cite:21847f40e6bc63d29e6b8814d8fa2aecf91d4b09}}, {{cite:5f5eceeac81f9e41942116307b4ea21987ec402b}}. For other examples of functions satisfying the KL property, we refer the reader to {{cite:ac4589560f6b60fb00f4c5b408c06712ee866312}}, {{cite:e37fb4ef42d0d8d8f45619dcd8d933acb3bd3e89}}, {{cite:3be2e2d04c24f34d0636019f8b1c041ce78da2be}}.
| m | d91fb1d6bab9ddb6585288176593db5c |
Our brane correlator {{formula:e1585d6b-fd20-4870-86c5-17d3070d7a6f}} is similar in spirit to the two-boundary component of the baby-universe wavefunction in {{cite:e79c521f5d7bca1b48c98c860b92c3e91b030ee8}}, and to the linked half-wormhole {{cite:678134adceb8a73354fb1dcb2086e05ded2e3349}}, but for one key difference. Namely that we have an exponential of this correlator (REF ). The exponential enables us to resolve factorization and discreteness to all orders in the genus expansion, and non-perturbatively, where the mechanisms proposed in {{cite:678134adceb8a73354fb1dcb2086e05ded2e3349}}, {{cite:e79c521f5d7bca1b48c98c860b92c3e91b030ee8}} were designed to resolve factorization to leading order.
| d | 26d37769292326d2bbdb3c852408a6fe |
In 2011, Harko et al. {{cite:ad482c9db58e10ea5e6b728471413a824f0b244c}} introduced another alternative gravitation theory known as {{formula:a5ff5a71-cef6-4f04-9621-bc48d7dc6f2f}} gravity. This is also a generalization of {{formula:dd49b7c6-46f5-450b-a698-ae0630ccddee}} gravity where {{formula:8c5527f8-79b6-460b-886f-569d15ac4007}} is the trace of stress-energy tensor. Because of the consideration of stress-energy tensor as a source, the
motion of the particles does not follow the geodesic path as there comes
an extra force perpendicular to the four-velocity which acts on the test particle. The precession of the perihelion of
the planet Mercury has been used to obtain a general constraint on the
magnitude of the extra acceleration. Actually in {{cite:ad482c9db58e10ea5e6b728471413a824f0b244c}}, the authors derived the field equations of their model using Hilbert-Einstein type variational principle and also obtained the covariance divergence of the stress-energy tensor. This model depends on a source term which is basically the matter Lagrangian ({{formula:2221e9e3-3149-4626-a3dc-4a63b06675e4}} ) and obviously one can obtain different field equation for different Lagrangian. The authors also have investigated some of the popular models for different choices of {{formula:d5ce6add-2f17-44d3-bde4-bd5b5687772d}} including the scalar field model {{formula:dcd26f58-70cb-4e4a-beba-f2e540ea40c4}} . This
theory also relates the cosmic acceleration, not only due to the contribution of geometrical terms, but
also to the matter contents {{cite:ad482c9db58e10ea5e6b728471413a824f0b244c}}. In {{cite:88ad5cec6ab6b0af47ca4b04d0fff4f8bdf562a0}}, it has been discussed
that due to the conservation of stress-energy tensor, {{formula:be8e6221-6d14-4c13-bc86-212139c393b0}} cannot
be chosen arbitrarily but it has a special form. The thermodynamics of this model
has been studied in {{cite:b8bc5b13b73ce048c9a00c9440ce9cf6fa5db59f}}. In {{cite:a6435099efd36989636f756d342e91efd31ce6db}}, the cosmological
re-formation of {{formula:9a6dca0d-34e0-4fee-8b22-88c52a4bc155}} describing the transition from matter dominated epoch to the late-time accelerated
era of the universe is carried out. Also in the same way to pursue cosmological implications based on
this theory, {{formula:0467ae89-858c-4bdb-aaf7-bdd4de952d1c}} function has been analytically reproduced according to holographic dark energy {{cite:a43b632a1e1205f0795e4d4df4e2a7f6e2ef0a52}}.
Jamil et. al. {{cite:4ad34a25c4ee5076c6870254ebc7d39557bfe57c}}, has been shown that for considering dust universe, it generates {{formula:f055b53b-bf6b-423b-a360-011fb9e4a784}} with phantom, non-phantom and the {{formula:df09fe3e-f736-4898-a659-d9f31e459fd2}} with phantom theory. The general procedure to perform this re-production {{cite:4ad34a25c4ee5076c6870254ebc7d39557bfe57c}} of the {{formula:5274f644-3066-40fc-8f20-6f3549d156dd}} model in Friedmann-Robertson-Walker (FRW) cosmological evolution is thoroughly developed in {{cite:c05bd32727abb38d9babd419171a063336ff00b4}}, {{cite:6772aea347a294db18eed6be3f4ce44626252b7e}}. The {{formula:ec132e9d-f4d7-45ca-b9b2-9bcaa9d71417}} models that are capable
to simulate the fourth known types of future finite-time singularities have been investigated {{cite:4a1a5411b129a3c5531c3d334debb425fd7123dc}}. The authors found that, the divergence of the curvature singularity time, quantum effects can be introduced.
Sahoo et. al. {{cite:06b7518af66607752e8b8de7e343046b60ec9716}} have studied Bianchi-III and Bianchi{{formula:ec603d3b-1378-4d62-97ec-77cd66261e89}} cosmological models with string fluid source in {{formula:6458c75b-1d65-4507-9834-5ad621e09a6b}} gravity. They have established the field equations using a time varying deceleration parameter and investigated some of the dynamical and physical behaviours of their model. Singh and Bishi {{cite:30de0018f5d393e77ac5aed2a9ed9e09c77c89a9}}, {{cite:341559933c3bd015fb8d809ad3463c70035cd3a4}} have investigated the first and second class
of {{formula:16b80c6e-7d08-45fb-a4a5-3cbcdee12d8f}} gravity applicable for the anisotropic Bianchi type-I space time. They also have discussed the power law expansion (polynomial and exponential) and generalized form of scale factor to solve the field equations.
After them Harko {{cite:ad482c9db58e10ea5e6b728471413a824f0b244c}} and other researchers investigated {{formula:5cb9a1ca-940e-4e26-bc67-fb2a5084eddb}} theory for different matter distributions {{cite:bdaaeceac0aafd70bf1d1dc7e5d5653072e06206}}, {{cite:41b48eb0f2eb489190b810b1cddd358b9cc96c0a}}, {{cite:e4d353d48e2dd49323fb2d0ec8614b5dee21e128}}, {{cite:82bbe7ecf35062b10a3fb0c0bd5db3b51dbf7a50}}. In this context, Mirza et. al. {{cite:cf5a92945c879a5cb73692f3af4082a7ae71d335}} have been studied the dynamical system of the {{formula:766d4b4f-4ad0-4105-9a91-9c8b05df64de}} gravity. They have discussed equations of motion and future singularities for a barotropic perfect fluid and a dark energy like fluid assuming conservation of energy. In this paper, they have also found that for the barotropic fluid, there exists no future singularity while some kinds of singularity possibly exist for the dark energy such as
fluid due to the new degrees of freedom in some choices of the
equation of state.
Moraes et. al. {{cite:27c9727ef697a1f2c443ac9aff5bf80037ca3b12}} and Sahoo et al. {{cite:06b7518af66607752e8b8de7e343046b60ec9716}} have been studied the Wormholes and a Bianchi type universe model in the context of string theory using {{formula:07c3a14d-2b63-4c0d-9f99-17ecf455891d}} gravity respectively. Zubair et al. {{cite:6043bd9670a82cde729ed81382d7ce4adbed45b1}} also have studied {{formula:d51a0f88-d6d3-4edb-a8a8-d04aa1154145}} gravity admitting conformal Killing vectors and Bianchi type III universe model with a cosmological constant in {{formula:26e4ba87-653f-45f0-816e-d9046b8cbb1b}} theory has been studied by Singh et. al. {{cite:03fe052b920ca67f8c98efd38636c1d713056281}}.
| i | 6c1b213c7323619a9690bcea5c0d5da7 |
The {{formula:0737d676-71b4-44ad-90cd-a3814b49ad88}} torus simulations of the CMB temperature anisotropies were computed by
implementing the following effects of the Boltzmann physics and the influence of the discrete spectrum of vibrational modes dictated by the topology:
the roster of physical ingredients of the {{formula:f9d54ed2-e1b7-4395-bcec-68cec033a009}} torus simulations includes the ordinary and integrated Sachs-Wolfe effects,
the Doppler effect, Silk damping, reionization, photon polarization and neutrinos. The computation of the CMB anisotropies (CMB power spectrum) is carried out along the lines presented in {{cite:737054ee0a96a60e2ff5f68575d6504d0d876867}}.
We use as in {{cite:f04b35d362551cb6b985294f0a28359af26383b4}} the definition of low-{{formula:4f394421-cdb6-4f4e-a78a-3503ae410502}} values {{formula:e413abff-7026-42b9-8e82-8a065df4e7d7}} (see e.g. their figures 2 and 3 on page 6 of {{cite:f04b35d362551cb6b985294f0a28359af26383b4}}) and high-{{formula:e4f33d9c-9c9a-4ccc-acb4-1c4bfad59c51}} values for {{formula:d7d491c4-6729-4fee-b42e-e72309c8d4e3}} . At high-{{formula:c9b94b6d-5ed8-43f4-a710-8aa05d9b072b}} values, the angular power spectrum
{{formula:6c6d20d6-c5f4-4bdc-935d-3edab80bae14}} gets smoother and smoother and approaches for instance, near the first acoustic peak at {{formula:5a372393-9a84-425f-88b9-333ded12c845}} and for all the different {{formula:e312840a-d578-440a-a654-aa2c4baa6a75}} torus side lengths, the
{{formula:abeffc9d-965a-493d-a455-9fe38d9131a6}} CDM result (shown in {{cite:f04b35d362551cb6b985294f0a28359af26383b4}}, figure 57).
| d | 4d4dde6377a3f090a5ee641806e24afe |
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