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In this paper, we exploit the recent advance of interpretable generative models {{cite:bf5d40222743e57f72138dca82eceaaa06e531df}} {{cite:39d52b754e87cc99c4884cd0d34b1b0e881e028c}}, in particular, semantic StyleGAN proposed in {{cite:3a0b19c6c356d88f86a872c9471accfc90289e8f}}, to extract disentangled semantic information from input images and further improve the transmission efficiency. This is achieved by training the network with segmentation labels in a supervised manner. For example, the different parts in latent codes obtained by semantic StyleGAN trained on the human face dataset present different parts of a human face. We also take into account the privacy concern of the image transmission. Note that the straightforward method is to erase the private part and transmit the masked images directly. However, it results in unnatural perception to the viewer because the removal of private parts may make the generated images fall out the distribution of natural images {{cite:81140636a2e5d3c1f2a8707a31df57e08ca9049e}}.
We tackle this issue by ensuring the modified latent code to be within the latent space {{cite:d96d8d50090456a96f098a27bab3e8ded7610f94}}, in order to protect private information while reconstructing the natural image simultaneously.
| i | 6aee630c2c8e80cf4e7b72efc8f00b60 |
Although it gives us the high possibility to estimate the data density, it also contains some drawbacks which can derive some research directions.
For example, when it comes to drawing the samples from the uniform distribution, it can also suffer from the curse of dimensionality because it has to sufficiently cover the region over the domain space evenly.
Some possible ways to resolve include drawing the sample from a smaller space and map evenly to the higher space by means of the deep generative model or generating samples at the boundary of the data distribution as in {{cite:0b9ffda0a7f2b2506bbc3f79d07deb96b7c7c450}}, however, it needs some theoretical foundations.
The performance of the DDDE in this paper is not ultimately optimized, which means that adopting the higher level of the architecture, and scrutinizing the hyperparameters selection can help enhance the performance of the DDDE potentially.
| d | 5608167f88102a0ac5030d4ed61ce5d8 |
We use both all-atom molecular dynamics simulations (where water molecules and graphene are simulated explicitly) and brownian dynamics simulations (where water molecules and graphene are treated implicitly as continuous media). Both are carried out using the LAMMPS software {{cite:af6468056aae80ce53777fd78494cf97178fd253}}.
| m | 4fd835e877226b95780094df7f1255b5 |
In all cases, {{formula:31277c28-c55c-4e19-9bd4-3c59864ff34d}} -EFT and Astro filters
cut off higher ends of the distributions of the
experimental nuclear physics informed AME+R{{formula:2cb86479-5f02-400f-afc5-7517ff762f1f}} distribution.
Coming to the skin measurements, the
CREX filter shows absolute insensitivity to the concerned astrophysical
observables, and the same is true to some extent for PREX-II as far
as the very massive 2.0{{formula:0b5f9168-8894-4fc2-8c0b-f3fdd9744185}} neutron star is concerned. This can be easily
understood from the already discussed effective decoupling between the low and
high density domain that exists even in the conservative hypothesis of purely
nucleonic degrees of freedom in the core of neutron stars, as shown in the
correlation plots above. Concerning the 1.4{{formula:4858c650-a26f-4729-b1c3-b7748ba5d810}} neutron star observables,
however, we can observe some effect of the PREX-II, and hence
PREX-II+CREX filters, shifting towards higher values the
{{formula:7081d845-18ed-4c6d-abd9-defb4108da89}} and {{formula:aad2818b-63a4-48c2-951c-54474b68d114}} distributions, particularly in the correlated sampling of {{formula:e7b21bc7-2bc8-48f4-979e-6dd54e337a29}} .
This directs towards an important impact of skin
measurements on neutron-star observables {{cite:b8dcdef8ba87f567b36df8a8768f2750211396d3}}, and a possible tension
between low density and high density {{formula:b7a4d4f6-8cfa-4cd2-bf7b-89d2c3bee710}} +LVC data that was interpreted as pointing
towards the existence of a phase transition at high density {{cite:8a4128a1cfcf37c74faff6b500b35ffaa83b9276}}, {{cite:4300d9c42a1fd27d1edee14c869762f372e9acee}}.
However, we observe that this tension already appears with respect to the
{{formula:c1d9ef23-3ae6-4efe-8b4d-b4b1bc0ff42e}} -EFT filter that constrains the same density domain as
PREX-II+CREX, and only appears if the surface parameter {{formula:d7a0844c-627e-462e-91b0-738bc223c380}} is robustly
correlated with {{formula:92e19457-68dc-45cf-a87a-b6762078bf90}} . Therefore, these findings do not support the interpretation
of Ref. {{cite:8a4128a1cfcf37c74faff6b500b35ffaa83b9276}}, and we rather associate this tension to the degree of
interdependence between bulk and surface properties obtained by the underlying
nuclear model. Deeper studies, probably beyond the mean-field picture, are needed
to sort this problem out comprehensively {{cite:7511404e78922015dc92341c99272c976b068333}}, {{cite:45a1366ab64ea0c7bf4ba4af1f6cd4342272da29}}, {{cite:27f965adab19c90dd96ecdcb50944abdfc3ff119}}, {{cite:0046471b394e088688164e5c6cbd745a36bc9ca2}}.
| r | 8331e38012c3921c1e84b6e5e401c77e |
We observe that in real Hilbert spaces, the duality mapping {{formula:5662a0b8-9c30-47db-8d6c-b13fd818657f}} becomes the identity mapping and our Algorithm REF reduces to the algorithm proposed by Tseng in {{cite:2c6be0afe4b7bf02dd09992c30886b4fb45cb063}}.
| m | 7f23f20be308a90666412be1ab9aeb04 |
The general theory for the Carleman estimate was designed mostly
for functions with compact supports (e.g., {{cite:37a388beb46c854c2999184f9e5cd7e6c1014f3c}}, {{cite:e72deec5fc6502b796a545739e7cc86c28b45a95}}),
while our Carleman
estimate does not assume that {{formula:5bc6446e-76cc-488a-a5f1-3c310b84648c}} has compact supports, which allows us to
apply a simplified argument by Huang, Imanuvilov and Yamamoto {{cite:30dcc182f22d01dac98f06338f846e7132892899}}.
If we apply Carleman estimates with compact supports, then we need a cut-off
function, which is a quite conventional way.
However, the cut-off procedure makes the total arguments more complicated.
The application of
a general theory for constructing Carleman estimates for functions without
compact supports, is also very complicated and the direct way is more relevant
for the derivation of a Carleman estimate for (1.1).
| i | 9e4f203323622d337453442ded858a7a |
Mixup can be interpreted as a method for convexifying class regions in the input space {{cite:7d1a17544e710a8776fc6aa090becff6b071336f}}. By enforcing that convex combinations of training points are assigned convex combinations of the labels, this augmentation method regularizes class boundaries, and removes small non-convex regions. In particular, we are motivated by the idea of using mixup to promote the removal of small “gerrymandered” regions in input space in which a target/poisoned data instance is assigned an adversarial label while being surrounded by (non-poisoned) instances with different labels.
| m | b7ff987e482380c3dd33e8c89d75e742 |
Our implementation of the OSBGD method is a gradient descent procedure which is based on the Barzilai-Borwein methodology: at each step, the gradient is calculated using finite differences over a fixed sample and the step size is determined by a cheap approximation of the Hessian (see {{cite:decb75d1b48c0c1bb8090fcc7fe680cb4d6813fe}}). The stopping rule is based on the difference between two consecutive values of the objective function in Problem (REF ) and the algorithm is stopped if that difference drops below {{formula:61861fd0-1db5-4436-9e17-6533e481babc}} . The MSBGD method is very similar to the above procedure, but the gradient is calculated using a new sample drawn from the chosen model of asset returns at each iteration. The algorithm is stopped after a fixed number of iterations rather than using a stopping rule because of the stochasticity of gradient approximations. The final estimator is computed by averaging the last iterations.
| m | 4065eca66b19a8343fd9474b89be09de |
In Tables-REF and REF , we present results of different defense methods such as AWP-TRADES {{cite:45acc44b83627b69f87644cb766a7157011d8112}}, TRADES {{cite:96895aaae3dba511d661dd1094333c160eca347c}}, PGD-AT {{cite:537c73d1aa54c322f86c5fe5c3f5d558302ae33c}}, ExAT {{cite:bcb0eb13b7ac1dbd696a2fc0e9751b1b6c505d15}}, ATES {{cite:47f576d766a43c680462470aa7713489e9a36dc8}} and FAT {{cite:ed4fae61678ca80604dff3192db75aabb608dd04}}, evaluated across a wide range of adversarial attacks. We present evaluations on the Black-Box FGSM attack {{cite:6b589081a283dfbdff37b89b3c4636b80d0bada2}} and a suite of White-Box attacks, on {{formula:52e11440-1b95-4278-8768-c42f0d184ea4}} constraint sets of different radii: {{formula:2e63dbeb-19b6-4dfd-93c5-4284ff1ad3aa}} , {{formula:65798b1c-0962-4629-87b5-6c4277dda3ad}} and {{formula:fec74f7d-a296-41d4-9b5e-26c6aadda819}} . The white-box evaluations consist of the single-step Randomized-FGSM (R-FGSM) attack {{cite:305133fdb7a694e701c9b9dd32e30b6fc647fe32}}, the GAMA PGD-100 attack {{cite:24c7738cb6323226d851f4f61e1f68d31da36544}} and AutoAttack {{cite:97329833b0649f15441ffd46639b32aa5e77a859}}, with the latter two being amongst the strongest of attacks known to date. Lastly, we also present evaluations on the Square attack {{cite:c981532167c322a73778264969e18b7a56b1e396}} for {{formula:4e6a3b97-c602-4eec-a83d-b4ab56bdec59}} and {{formula:79f4f2e3-d6fb-45c8-8345-69972c9d5d6f}} in order to evaluate performance on Oracle-Invariant samples at large perturbation bounds.
| r | 1b0382121a019a22cdd1915ec8cf365c |
In order to speed up the training process and to compensate for the overfitting that may occur with modest sized datasets, we rely on transfer learning {{cite:55d64e228effd5887cd697d78a786585a92ca0d5}} using pre-trained state-of-the-art models as a starting point. In particular, we consider four modern architectures known to achieve high accuracy on standard dataset such as ImageNet-1k {{cite:1e642af88e88f384544fd40f0abfe1dbf92c1e9c}}. The models used are VGG {{cite:891d22b44b0583da43060fc4fa9e4f014370381f}}, ResNet {{cite:ef069a13d50331487e1829fbe06dcfd84122138c}}, Vision Transformer (ViT) {{cite:1f707f04b09c6f577d577128bf1e6d61ed149aea}}, and Swin Transformer (Swin) {{cite:c2f59377f79bbf8b5ad9268ccbf9dfdc89a6be2b}}, all pre-trained on the standardized ImageNet-1k dataset.
| m | ce116abd2778b2ee25112c2832a52983 |
Quantitative Comparison on CIFAR-100. As shown in Tab. REF , we compare FFSD with several state-of-the-art methods on ResNet-32 and WRN-16-2. FFSD surpasses most knowledge distillation methods, including traditional knowledge distillation KD {{cite:600685a6be133391740473c24f93d27cd3e532a6}} and AT {{cite:6776e74a5787a697cb4461573dcda166e53d8723}}, mutual learning based DML {{cite:e67060050dacca751d02eb159f0e02ecaf7dd5b5}}, AFD {{cite:257225becd140a4cc287fd0c09fc25e77f51eb28}} and AMLN {{cite:6c0053ac10d3bc87d217af6c771976176ddb9090}}, and ensemble learning based ONE {{cite:89dc5e3dee652f0754a9d009df39d6216915d609}}, FFL {{cite:ca88152a982b2ba863a3754f696c3e22cfec8087}}, KDCL {{cite:54450c387716f975db89657d04e12d68bde4f200}}, and OKDDip {{cite:6e9473e49382d744c0f5a206e492c1e188bba5d3}}. For example, with ResNet-32, FFSD achieves an accuracy of 74.85%, which is higher than AMLN's 74.69%. In addition, with WRN-16-2, FFSD can achieve a 3.84% performance improvement, which is superior to AMLN's 3.59% and KDCL's 3.53%.
Similarly, EnD2 {{cite:7fdf7a141d93c61aaae8ec57a8a680fdece9d3b7}} also distills the prediction distribution from an ensemble into a single model. Following EnD2 {{cite:7fdf7a141d93c61aaae8ec57a8a680fdece9d3b7}}, we compare FFSD with EnD2 on VGG-16 {{cite:a4d8b6347631919952ab51485dd76962b23c6807}}. FFSD achieves an accuracy of 75.87% while End2 has only 73.7%. It is worth noting that EnD2 needs an ensemble of 10 models to capture the diversity of the ensemble, which makes EnD2 hard to be extended to a larger model, like ResNet-34.
| r | 3671302668faf0bd3fee9ec7c79d38e2 |
We have studied the leading correction to the {{formula:c2916256-07f1-4425-b53b-128ff1a63c27}} behavior of a number of physical observables in the large {{formula:479677d8-dfd8-4782-aa69-4ae9d118f683}} limit of the class {{formula:c58160d1-7fa9-4f84-9643-9bcbf66996cc}} 3d {{formula:07ce3acd-5436-4468-a9f4-dc78959e5973}} QFTs. Studying the behavior of more subleading corrections is very interesting but challenging both on the QFT and gravity side. In supergravity one needs to study corrections to the supergravity action that involve six or more derivatives while in the 3d-3d correspondence we need detailed knowledge about the large {{formula:ae219620-c63f-4860-ba71-dc07e779e543}} behavior of the perturbative CS invariants {{formula:98b704c9-5763-4071-bed8-4e862bf96b3b}} for {{formula:3291d6a5-b890-43da-ad61-9cf6c9e8010d}} . Progress on both of these fronts will be very interesting.
As described in the introduction we have studied higher derivative corrections to supergravity by using a 4d approach and thus circumvented the need to work with the higher-derivative corrections to 11d supergravity. Understanding how to uplift our explicit results to 11d and map them to coefficients of the supergravity effective action, along the lines of {{cite:31b7f94868ae8b0afc2ca45c1915635c7d5a1ff8}}, {{cite:842cc51fa2830492c4cd97a80e6f8c35b96cf3dc}}, {{cite:bc733ddf1f491868ffadb493dafaef410a15261d}}, is a very interesting topic for further exploration.
Our supergravity and holographic results have lead to the conjecture in (REF ) for the large {{formula:c36a289d-3185-426f-926c-4d452bb4e067}} behavior of the perturbative invariants of CS theory with a complexified ADE gauge group on a hyperbolic manifold. It will be most interesting to confirm this conjecture with explicit calculations along the lines of {{cite:3afa64778d93f1501a5d4a89f6ef2b6267939930}} or furnish a general proof.
In our analysis we have assumed that the hyperbolic manifold {{formula:3ef5c582-7326-4f67-8562-416ece69a01b}} is smooth and compact. This was necessitated by the use of the supergravity consistent truncation results and the restriction to work in the minimal 4d {{formula:de067313-424b-48d3-bd66-fe67ce427c8c}} gauged supergravity. It should be possible to generalize this setup by including defects and boundaries on {{formula:f0965883-f354-4348-b97e-b1d95ba1ce7f}} which support additional degrees of freedom in M-theory. In the context of 4d {{formula:793af2f7-e488-4d54-8867-2fdef28e3d7d}} gauged supergravity these extra degrees of freedom should be incorporated by the addition of vector and hyper multiplets. The probe brane analysis in {{cite:feb7a25ba50e62d1e18e66a640d90d3188b3d8c2}} may be useful in uncovering the details of this setup.
All QFT results for the 3d {{formula:6a173b7b-c953-49c3-aa1d-97a6925c416b}} theories of class {{formula:411634f8-896a-44e4-98a0-ddd95b828f12}} we have used are obtained by using the 3d-3d correspondence to map the calculation to complexified CS theory on the hyperbolic manifold {{formula:30186c17-aacd-4f4d-9630-d201b8c4706f}} . It will be interesting to understand whether some of these quantities can be computed in a more direct manner using the properties of the 3d {{formula:5382f157-7bf5-4a54-83b3-4754486bccc4}} theory itself.
Here we have focused on twisted compactifications of the {{formula:e45a0b40-fdb2-485c-ba47-9cdf6d3946a2}} theory to three dimensions which preserve 3d {{formula:6c4ce0e0-d91f-497b-89ff-c272b553d5ef}} supersymmetry. Geometrically these twists can be realized by wrapping M5-branes on special Lagrangian submanifolds in non-compact CY 3-folds. There is a generalization of this construction to twisted compactifications preserving only 3d {{formula:1574ef8d-687f-4640-84ad-4069a9f85c53}} supersymmetry which is realized geometrically by M5-branes wrapping associative cycles in non-compact G{{formula:611bb6e8-9d72-4e50-bcef-ac0b97564966}} manifolds. Indeed, this generalization has been studied both on the supergravity and field theory side, see {{cite:0da0a17a02b71f6777b4792113a67c49c9766ffd}} and {{cite:eea6d83564253eb6ccf210f5eb134cc8c8d3380f}}, respectively. It will be very interesting to generalize some of our results to this less supersymmetric setup. We expect this to be non-trivial and plagued by technical difficulties due to the small amount of supersymmetry and the lack of explicit results for the large {{formula:fd646c0d-8967-40ad-9c68-440419e01613}} limit of the {{formula:c9b360a2-92b2-459b-b2a8-a71c07d92779}} 3d-3d correspondence.
It will be interesting to perform a 1-loop supergravity calculation, along the lines of {{cite:213a6b36177213cef68db196552cff8476791fb2}}, and confirm that the logarithmic tem in (REF ) for {{formula:16b1410f-ad7d-4aeb-bd00-ae808649ae1f}} indeed does not behave as {{formula:9a41d6c8-7b5b-4942-9254-ba4f0a72fb66}} .
The 3d-3d results for the superconformal index in (REF ) and the squashed sphere partition function in (REF ) are valid in a Cardy-like limit where the length of an {{formula:99f12573-e1b2-4f59-9a7f-c0c8a53ed41d}} in the geometry is vanishing. On the other hand, the supergravity results in (REF ) are valid for general values of the squashing parameter {{formula:66270cf2-908a-4860-9a5d-5b78c2c1afd6}} and the fugacity {{formula:2b85e51f-ec6c-4467-b583-1b7ec668b1e0}} . It is desirable to extend the range of applicability of the 3d-3d correspondence and calculate these two partition functions for general values of the parameters.
The expression for the partition function in (REF ) bears a strong resemblance to the structure of the anomaly polynomial of a 6d {{formula:19961a0f-8335-40f3-96e3-6da1ce5a56e2}} SCFT of type {{formula:3c6e8e85-8b47-4db3-9017-aa58842cde54}} . It is tempting to speculate that (REF ) may be obtained by a suitable equivariant integration of this anomaly polynomial.
Wrapped M5-branes lead to a rich family of 4d {{formula:8b562e17-5ae1-433a-8eab-6b3e6b9ae71d}} and {{formula:8ba2f915-fa4a-42ed-a98d-dc62334730b7}} as well as 2d {{formula:8716a780-c73f-4620-98a9-846a7bfe8743}} SCFTs which have an explicit holographically dual description, see {{cite:9e9cc10df93362506e1becddcda7806f9c12a8fe}}, {{cite:a9b2a8772b8b8ab961311a2a3a93a815465a31be}}, {{cite:4df5dd69e1d826416c40419b4765543ef06e994a}} and {{cite:8ab11e3a85c5277b72bcf5f37cbc98112a1517ba}}, {{cite:14bf470728b9002f22981fd3612eef91228730cc}}, respectively. It will be very interesting to study these SCFTs using higher-derivative corrections to supergravity. Some concrete results in this spirit were obtained in {{cite:de6222ec8d516f78efd011695f6652a15ac51e31}} and we hope they could be generalized significantly.
| d | 6a70efa01e204a73d62d31f03336c308 |
The structure of this paper is as follows. In § , we recap the main results required to apply the formalism of {{cite:bce9ef904d672e15398e47ac1405e580c74a3571}} to obtain the linear tidal response. We then provide simple estimates to predict when nonlinearity might be expected to be important for tidally-excited gravity waves in § at three particular locations: near the centres of radiative cores, at the radiative interface with a convective core, and at the interface between a radiation zone and a convective envelope. This motivates the more detailed calculations of the generation of super-harmonic gravity waves by weakly nonlinear interactions in a local Cartesian Boussinesq model of the transition region between a radiation zone and a convective envelope in § and . We confirm our analytical results by comparing them with numerical calculations in § . We then derive simple criteria to predict when this new nonlinear effect is likely to become important in § and then apply these to stellar models in . Finally, we present our conclusions and a discussion in § . In the main text we assume that the star is non-rotating. However, we briefly discuss the most important correction to our results if the star rotates slowly (which is the appropriate regime for many stars hosting short-period planets) in Appendix .
| i | 78f4c693e08a81a4e37d04fbd59d5824 |
In the field of heavy-ion physics we are faced with fundamental questions: What are the different particle production mechanisms across different system sizes? Can we find the onset of the QGP in heavy-ion collisions? Is there a QGP droplet formed in small collision systems {{cite:7bcbc4bff71e35befbff0d1e748994773639691a}}?
In proton–proton collisions the particle production mechanism at high {{formula:3e5be08e-83a0-409f-a164-e758bb0eb281}} {{formula:0663a865-ba5d-492b-881b-44b76d8f8caa}} GeV/{{formula:5e953cc0-cc34-4c45-af18-fe96139eeab7}} is expected to be dominated by the fragmentation of high momentum partons in jet-like structures. In collisions of heavy nuclei such as Pb–Pb , the production of particles is expected to be dominated by the hadronisation of the QGP for low {{formula:66f6ab11-b8a4-407a-9033-c29121445958}} {{formula:4d346bf6-c4b0-4e64-b90e-3fc062c48e89}} GeV/{{formula:d5043cb1-ca20-4e00-915d-0b316929ee6f}} , while modification of the hadron production at higher {{formula:d991fcc7-79c8-4349-9c27-4dfd7651ab85}} will also be influenced by parton-QGP interactions. Studying the particle production mechanisms is thus key to understand the physics governing both small and large systems.
| i | 8ad2d5d8ff09ac6400a0f3981559d746 |
{{cite:2f498fa232f33d8eee578a03ea51d13a2408a97f}} propose a neuron alignment method in the context of multi-task model compression. The algorithm leverages layer-wise Hessian approximation to match neurons by computing a similarity measure based on their functional difference. {{cite:dc5eddc89cb8c896e55e55d652bcb5b2c8aff691}} propose a model fusion algorithm which leverages optimal transport to perform neuron alignment in the Wasserstein space {{cite:0805e3c4934df0f7a4da76e9079f50a2f7615c51}}, achieving a barrier of 16% for ResNet18 trained on CIFAR-10; furthermore they show that by finetuning such interpolated networks, the original performance is recovered.
| d | cf5a238b32464f84f344ab8ff6b69e89 |
Machine Learning projects in the past relied on human knowledge and were easily comprehensible by both developers and end-users. For example, decision trees have been widely used for fraud detection {{cite:16719aeb80d58c8b31cd230c6c82089fc09d4f64}}. However, the surge in popularity of Deep Neural Network (DNN) based models in the previous decade, due to their potential to produce more accurate results, has abated this comprehensibility. An example is the Convolutional Neural Network developed by Krizhevsky that was able to achieve “top-1 and top-5 error rates of 39.7% and 18.9%" {{cite:d78c3b6a8edd6cf5d0abddc56e99e3616fb48721}} on Imagenet {{cite:cc7383fda7c278fc638a4eefd2cf233001943704}} comparing that to the second place error rate that was 26.2% on the top-5 error rate. Such superior performance of DNNs has come at the cost of explainability as they can comprise up to millions or even billions of parameters {{cite:8cf5171a34fb0faaf0d814e845d5dca07d72f393}} {{cite:28875e129aac85e6daa6c760b280b85bd2222e5f}} whose synergy in arriving at the final output is often undecipherable. Moreover, these models are considered to be ‘black boxes’, where not only the end-users but also the developers are unaware of their inner workings.
| i | 33119d158ce7e4ea5f76bfa5683bfd13 |
Table REF itself expresses the predictive power of modified formulas and also the use of machine learning methods as the decay modes are anticipated effectively. In fact, not only the decay modes are found in an excellent match with available experimental/estimated decay modes but also the half-lives are found in agreement with experimental half-lives. In addition, we have compared our estimation of half-lives for the experimentally known decay chains {{cite:ae1368933acf9f9fa93f40a962d5719a736745ef}}, {{cite:054b6206a9fdd38a257c1a8f2cff02ae0bfba7e6}}, {{cite:9ae5b27a80985ea3120e8d2c0501c5f8e63b893e}}, {{cite:943b3425a0b780c9f462555b8968749fe2029b9e}}: {{formula:b2227a25-0011-4696-bd08-d657d4dcdb27}} Og, {{formula:b869ddf5-5419-4ecb-8c58-029964ef87cb}} Ts, {{formula:c4e23d05-23d6-4c5e-9e84-354158ee75d8}} Ts, {{formula:52ae0aa1-91fe-42f2-8f69-486ea3782135}} Lv, {{formula:264f8c88-1d9a-4103-b96e-255e76fb06a6}} Mc and {{formula:4845cc8b-b7ab-401c-a75b-7a5bff423b9a}} Mc in Fig. REF . The {{formula:9191a8db-aa90-4c20-be62-ad6c5753bb14}} -decay half-lives are calculated by employing MHF-2020 (set-1 and set-2) and MSF-2020 which are constructed in this present work along with machine learning methods: XGBoost and MLP. Satisfyingly, these half-lives are found in a reasonable match with the experimental decay half-lives mentioned in Fig. REF with error bars.
| r | 2f138df335bbe2bc33ada05487b3a8cd |
It is likely that the semi-analytical method of this paper can be generalized
to study more complex coherence-incoherence patterns in large networks of phase oscillators,
including breathing, pulsating and alternating chimera states {{cite:062837da443ff689adaa91a21dead1cffecf9ae1}}, {{cite:05d985d5443766fb0713d2a318a1a5c0e1ad8a29}}, {{cite:ee676f1dbdbf1b99bd370e4c996b086d757a7b5e}},
as well as moving chimera states on two- and three-dimensional oscillator lattices {{cite:d1bb166ca18602f03be8a56055e7ced184669c98}}, {{cite:971f082a9d77d6c32312d82aa6909e307aa12e25}}, {{cite:b03b4238fd98187d458a60686dad0b38bba4875f}}.
Another class of potential applications is concerned with Proposition REF ,
which can be useful in the study of moving and oscillatory bump states in theta neuron networks {{cite:bb6dafe0645acb19d6028368cf7eeca20fbf16df}}, {{cite:b46032499460c13ed74aa6f3241dfb810cfc9272}}.
Moreover, recalling one of the recent applications of the Ott-Antonsen method
to networks of quadratic integrate-and-fire neurons {{cite:b0ac5a8a29bca06f769a0b3fad0321f289fbef83}}, {{cite:c919176f6133269b1783cce544d004c5995ec083}}, {{cite:0d258dee27b28f1b886e08bbcf9f28800377ecb0}},
we expect that our method can also be adapted for such systems as well.
We plan to report on these issues in future work.
| d | 6f54445d76a3f565b87e261bf3097d85 |
In addition, matrix/tensor completion has attracted significant attention in the recent literature {{cite:62ad58ac2a0e747064084f5d2b43b92e135a1a0a}}, {{cite:35c38017cf5c9d6d10a795621feb0bda46ba11f1}}, {{cite:92e1ec28b6815365e085f7ddca54a419caa2d663}}, {{cite:1ed53325c316d28d220b2afc0794555470c84836}}, {{cite:d7b46ab81000f8d2e546d6e651f37c47a01099c6}}. The central task of matrix/tensor completion is to complete the low-rank matrix/tensor based on a limited number of observable entries. Since each observable entry in matrix/tensor completion can be seen as a special rank-one projection of the original matrix/tensor, the idea behind ISLET can be used to achieve a more efficient algorithm in matrix/tensor completion with theoretical guarantees. It will be an interesting future topic to further investigate the performance of ISLET on other high-dimensional problems.
| d | 3d197fc49e686f0cb945e3067f4525cc |
The band crossing features of the HD bands provide an additional tool
of configuration assignment which can be used more frequently
than in the case of the SD bands because of strong mixing between the
different {{formula:5edefa60-c8ac-4285-86ba-dc62fd2f3428}} -shells at HD. The large peaks in {{formula:0b19070b-134e-4e0b-8a34-9bcce78e0458}} of the {{formula:86056654-47a0-4975-a1b3-22452fb943e5}} and
{{formula:d0cd65a5-d018-45aa-b08d-004aec9dddbe}} configurations in {{formula:fbb07433-8f8a-4d78-959d-1c808a1f4779}} Xe
(Fig. REF d) are due to the band crossings with
a strong interaction. These crossings are also visible in the effective
alignments {{formula:fab869dc-19b9-4437-8966-145f9f590630}} (Fig. REF d)
and relative transition quadrupole moments {{formula:f3f5ef9e-e36c-4c34-9efc-469573bfba9c}} (Fig. REF d).
They originate from the crossing of the same signatures of the {{formula:b07b69b4-75d5-479b-8b89-041eaabedbe5}}
and {{formula:666d7303-9c32-4cd0-b0c2-4eb011925a5b}} orbitals, where {{formula:ecaa56a7-d0e0-4353-8aea-1cc801f70f00}} and {{formula:cc93f654-c583-4154-9fa5-7945fe62a74b}} have signatures {{formula:ecd2928c-0771-4835-8d6a-7b422996222e}}
and {{formula:cd8f1532-8290-472c-b959-4f5755343afc}} , respectively. The former orbital is occupied before band crossing,
the latter after band crossing. An unusual feature of these band
crossings is the fact that they originate from the
interaction of the orbitals, the dominant {{formula:4386c7cc-9eff-49f1-b3c7-cd6dd1dddb73}} -components of which differ by
{{formula:c5e04c77-5e3c-4467-85af-c35791e365e4}} . At SD, the crossings between
the orbitals dominated by different {{formula:cd72c951-b100-46f9-9804-ab11e52bf5eb}} -shells have been characterized by a
weak interaction leading to a sharp jump in {{formula:c53e2f91-965f-46b1-8fe2-63628399f612}} {{cite:b6b09a4188341a53a02aedc62dac7b2f2b4e0d84}}, {{cite:d63623256fcce2eaa2ef7d44ce2775e72d20133c}}, {{cite:050e3244802b51a212e2cfc1f3bd2466f5a91c74}}.
The observed unpaired SD band crossings with strong interaction are between
the orbitals with the same dominant {{formula:b3080693-c67b-447c-a9fb-fbefd5d3832a}} -shells and they were observed in the
nuclei around {{formula:07e72f32-1661-461a-b610-201bedcce582}} Gd {{cite:be51f1b064e16c6c473c965016c1a8102a56a418}}, {{cite:b6b09a4188341a53a02aedc62dac7b2f2b4e0d84}}.
| m | 83bab7c1ce389bfeb04a8de90190fe74 |
We put complete results of GPS+DER, GPS+DER{{formula:0accdd8c-4ef2-4b59-880e-b5e67c031ee7}} , GPS+HAL and baselines in Table REF . Note the A-GEM {{cite:a02b23462d9c45dd295b4aac40f49c8f00653233}}, iCaRL {{cite:898492ede4d63f5064b3f4687c2a34fc66b414d4}} and GSS {{cite:23baa9ccfc33a3231e835acef435b5615c22b81f}} use the same memory size as the ER series for fair comparison. The results stand as a complete empirical support to illustrate that the performance of other ER variants have been improved after using our GPS method.
{{table:b6397de3-5a8c-4ef1-8257-6e4a305ab980}} | r | 5514d742fe348a29f23a7a458c83792d |
The reward conditioning approach (DT) takes an entire trajectory sequence and conditions on it using the sum of the rewards for that given sequence.
Such an approach struggles on tasks requiring stitching {{cite:8e25c9405145d6326f138aee920c6e8974a9adb5}} – the ability to learn optimal policy from sub-optimal trajectories by combining them.
In contrast, the Q-learning approach propagates the value function backwards for each time step separately with the Bellman backup, and pools the information for each state across trajectories. It therefore does not have the same issue.
Our approach tackles the stitching issue faces within the reward conditioning approach by relabelling the RTG values with the learned Q-functions. With the relabelled dataset, the reward conditioning approach (DT) can now utilize optimal sub-trajectories from their respective sub-optimal trajectories.
| m | 7b4158118ae17a2d86f95bd865ef2dd3 |
Four CNN-based methods {{cite:4820b937b17ecaa30a7f22d054e50d8b5a2521f9}}, {{cite:a52a96f7cf880d0be1611b50317b58b91273dd1b}} including the proposed method were used. EEGNet {{cite:a52a96f7cf880d0be1611b50317b58b91273dd1b}} and shallow ConvNet {{cite:4820b937b17ecaa30a7f22d054e50d8b5a2521f9}} showed similar performance in both paradigm and class classification. Although shallow ConvNet was designed to extract band power features, which are known as MI-specific features, it showed the best accuracy in paradigm classification. Compared to paradigm classification, CNN-based methods dropped around 30% in class classification. The teacher model was designed to decode hybrid paradigm induced EEG signals through hierarchical classification and achieved the highest performance (61.27%) although shared module showed only 83.61%. However, student model which was trained through knowledge distillation achieved second highest accuracy. It recorded the best performance among the singular CNN architectures. Through the results, it confirmed that the hierarchical architecture improves the performance of a singular architecture through knowledge distillation. Results are described in Table II.
| r | eb9237f53efd5b2c8823a36b87e8da58 |
The essential idea for domain adaptive semantic segmentation is to effectively transfer the knowledge learned from a distinct source domain to a target domain. Previous methods achieve this goal by bridging the domain gap in the image level {{cite:114a52047518fe05f7d057152a0a2537901593b7}}, {{cite:97ecd8a49edf808c6166bd04bdee40b755e537c7}}, {{cite:265e0a51eaa2b7a8eac6ef8fa9f6c448bf63c5c8}}, {{cite:eab14a224468cb04ea94acf5da41cc98d273c343}}, {{cite:a0ddbefe850b76966820214063879309090b59c8}}, {{cite:378ad5caa1b00661ce7dc4758a2abd45210bf348}}, {{cite:ab8fa6de4394db1ac25c30239311f76ec4d706e8}}, feature level {{cite:ecb94b586c508938618ee3bf68c1de4e7d9d7b50}}, {{cite:c54a71d2a490eec562d99f8dcc722cd8a2c114ef}}, {{cite:afc2acb543a0b76806753fa0326529bcda87ecc9}}, and output level {{cite:3c3e5785965c037c0adcb4b3dec961509f183c46}}, {{cite:304f3d964a34c4481d984fc508045d1c16eabb20}}, {{cite:12269fd8d0708750c27b209bdd8e29d45ec3ed8e}}, {{cite:2c29b5425c5cf7970773ab4489d69140be3ae2cd}}. Although these approaches have made remarkable progress, they usually require access to the labeled source data during the alignment process. However, in some crucial scenarios, the source data is inaccessible due to data protection laws. Thus, this paper addresses a challenging source data-free domain adaptation setting for semantic segmentation, where only the trained source model instead of the source data is provided to the target domain for adaptation.
| i | 7712efbd3107a3ce6d79aad9b1ebc820 |
Given the role of collective behavior in the function of physical, biological, and neurological systems where higher-order interactions may play a critical role in shaping system dynamics, understanding how higher-order interactions balance with dyadic interactions and affect collective behavior is an important question for a wide range of disciplines and applications. In this paper, we have addressed the topic of optimization for collective behavior in networks with higher-order interactions, focusing on clique complexes, and found that as higher-order interactions are equitably strengthened relative to dyadic interactions, optimal collective behavior improves. This phenomenon stems from the broadening of the eigenvalue spectrum of a composite Laplacian matrix that encodes the collective dynamics and network structure at multiple orders and generalizes the Synchrony Alignment Function framework to this important case. In particular, as the spectrum broadens the dominant eigenvalue(s) increase, which leads to this improvement. Moreover, we find that optimal solutions are robust over different balances between the relative strengths of dyadic and triadic interactions and that the broadening of the eigenvalue spectrum also widens the range of possible collective states supported by the network. We also find in more tightly constrained optimization scenarios that an ideal balanced between dyadic and triadic interactions occurs at a nontrivial, critical value of the bias parameter for networks to support the strongest possible collective behavior. Interestingly, the improvement of optimal collective behavior stemming from the broadening of the eigenvalue spectrum for the case of heterogeneous dynamical units lies in contrast to the case of identical units, where optimal networks stem from the concentration of the non-trivial eigenvalue spectrum {{cite:563026a98d47d87b5c02641dd0d6d8ddc46b2283}}.
| d | dc41c7008d6803e58892bb2749e5a769 |
Given unpaired training samples in two image domains {{formula:3d64481a-c7a4-4a14-91fc-e812efd4883b}} and {{formula:ba812e0e-9964-4d1c-bd13-38fc914548c9}} , the CycleGAN model proposed by Zhu et al. {{cite:3dc622f498fa84a019dced4e146f9ec1f9218d87}} learns a mapping (generator) {{formula:2b19bcfc-c99b-4f2b-b653-d5f77ce491cd}} and the reverse mapping {{formula:dc7935bc-a8dd-4165-bcef-42c5e1087ddf}} .
These generators are trained to produce outputs that are indistinguishable from real images in the respective target domains for discriminator networks {{formula:a9407a9e-4037-46ca-89ec-30223b6896fc}} and {{formula:0149b841-63a4-4710-ab10-701a0afd34ea}} .
Additionally, the consistency of the cyclic mappings {{formula:485d7044-7270-4a74-9608-0e22d1434f78}} and {{formula:3ec96093-a23e-4a7a-8e75-10e98194fc0d}} with the respective inputs {{formula:be5bb940-2451-4ad2-bf8b-8cfd25343f9d}} and {{formula:781d9646-aa9c-425e-88ab-6c9d89a0af62}} is enforced by using the {{formula:8ea86515-b6c9-43be-a5ce-0ecf8c0668f2}} -norm.
The proposed method builds upon this idea to learn a style transfer between an image stream from the source domain {{formula:0c4ed400-8fdf-4567-b88f-e02f3d90d94e}} of surgical simulation to a target domain {{formula:aa8b6277-c127-4c5a-84d7-87747ca19f50}} of intraoperative surgeries and vice versa in the absence of paired endoscopic image samples.
| m | ce8b0119dc09afcc2cc4abe1dac1f9b9 |
A finite state-space truncation covering the same area as the initial lumping approximation would contain {{formula:7604687f-e858-4bdd-a394-596b682b9b46}} states.Here, the goal is not treated as a single state. Otherwise, it consists of {{formula:0ede63d6-086d-4402-89e6-c5a285f52cf7}} states.
The standard approach would be to build up the entire state-space for such a model {{cite:164d398af10cceac25900ec5a79d45e64204293e}}.
Even using a conservative truncation threshold {{formula:e62e61bb-8771-4133-81e1-9a1811a26b19}} , our method yields an accurate estimate using only about a fifth (5450) of this accumulated over all intermediate lumped approximations.
| m | 89d6290223bc52a7d3815c1cef15e9b4 |
We can easily find in the first-price bidding function Eq. (REF ), the bid price is jointly determined by utility function {{formula:40579c82-5fe0-480a-a73a-7782752091ec}} , {{formula:b9ac2f8f-290c-4ee9-b172-1f9af23e106d}} and market parameter {{formula:71b71d6f-7c84-4585-82b4-7ea89086c960}} .
Specifically, the bid price is monotonic increasing w.r.t. utility while decreasing w.r.t. {{formula:302e78bc-25c7-4b8a-9ed0-8c394971de9c}} .
Moreover, different value settings for parameter {{formula:c47f9e20-bdda-428c-9390-f879dae43472}} also influence the final bid decision as is shown in {{cite:26573aea673f916fb78cf19a8533176b7efdb4da}}.
As is defined in Eq. (REF ), we can tune the parameter {{formula:0c23c4ae-5d47-4d4c-94b6-246bfb794aa7}} to alter the winning probability so as to fit different market environments.
In fact, we may conclude that: the market consideration influences bid price by tuned {{formula:6cd6bdde-8489-4e2f-91b2-0f5b92ac48dd}} , the budget constraint controls bid function by {{formula:fd1c1b12-1b0f-47da-9a8d-a0e29dda2a8b}} , while advertiser's utility expectation {{formula:dd16f2d4-f751-4063-b13c-ffc4556fddea}} could finally determine the final decision.
| d | 1b2f4b6141a687c9e29f27687475193b |
To better understand the behavior of ContrativeCrop, we discuss several properties that may contribute to its effectiveness. We first investigate the relation between semantic information and positives similarity. We take the class score of a crop as an indicator of richness of categorized semantic information. The similarity of positive pairs is calculated in the latent space as the cosine similarity between positive representations. Both the class score and similarity are average results of a large number of cropping trials from a standard ResNet-50 {{cite:d334ca5847f19c1ea7f4402ec1e5da6917c5057b}} trained with ImageNet {{cite:931e38224722ed3adb6e4a80798693701007fb9a}} labels. Their relation is shown in Fig. REF . One can find that ContrastiveCrop conveys more semantic information than RandomCrop at the same level of variance, showing the effectiveness of semantic-aware localization. Furthermore, with equal semantic information, ContrastiveCrop achieves larger variance than RandomCrop, which can be owed to center-suppressed sampling.
| d | 97af6899ec09be72c7b4a45dc5cb752e |
In this work we present improved numerical results, with extrapolations consistent with, but not definite proof of, the saturation of the {{formula:3540363c-89de-468d-9a8d-ac57c752b8e1}} -bound by the {{formula:a53730bc-2615-4160-af9e-10c840ac3e07}} SCFT.
Moreover, our results seem to imply that, even if there is more than one crossing symmetric four-point function for {{formula:7b321087-9ecc-4ddb-a53d-33b52cd8a861}} and {{formula:422957e9-07c6-4373-9caf-bfa07a591dfc}} , these solutions do not differ by much as far as some observables are concerned, and can be used as an approximation to the low-lying spectrum of the {{formula:e615a7a6-225d-4936-ac25-7a1957dd06b4}} theory.
In particular, we are able to obtain the first
predictions for unprotected OPE coefficients in the form of true upper and lower bounds for OPE coefficients, together with conservative extrapolations for {{formula:39c77f84-7f3e-4cf8-810f-c36edd8ec138}} . In addition, we also estimate the value of the lowest-twist unprotected long multiplets appearing in the non-chiral OPE. In this section we focus on the lowest spin operators, but numerical results for larger spins are presented in section , where we compare them to estimates arising from the Lorentzian inversion formula of {{cite:8a3afb56f46b53ebd8feb654f0e4ed815c2cdfff}} adapted to the supersymmetric case.
| r | 2747d90003db583660e9bb7e8aee5be0 |
We follow the recent study {{cite:971a663e603beff87ea1db9c0483ba2e84d5133d}} to evaluate defences against two optimization-based attacks in FL: the classical optimization-based method named DLG attack {{cite:39f97ab8daf3b712a4b1445b4c86855d681158be}}, an improved version called GS attack {{cite:05332da899f4fa15109697b087c0b75d8acdb22e}} that introduces image prior and uses cosine similarity as distance metric. We also include one model modification attack: the recently proposed Imprint attack {{cite:08cc1672b4cc1b888dd3827584f20f070ed4c1dc}}.
| m | 44a233e626c2f1298ec52f6014227c10 |
The gauge/gravity duality {{cite:ee29a29aba7dc8196a4aeaa1d165686fbf23e098}}-{{cite:00d2ce2f34d13ff3bb1c451259e676b4ac4a0f13}} has been applied to strongly correlated systems as an efficient tool to handle the strong coupling.
In the context of this duality,
a theory of superconductivity was set up {{cite:568fac3b4eb710458781bcf0dfe7e147ed47fba9}} using the spontaneous symmetry breaking of the {{formula:3121f371-fb34-47f3-8f3c-114cdda093f7}} symmetry of an Abelian Higgs model coupled to {{formula:4741689c-20f0-4834-90ff-c09ff12aff50}} the gravity {{cite:8b1653c8437e7ea6ef7d7c411f4f142f8c8b96a0}},{{cite:51ecf4ec21a6a9259cbb130b9848119a91c6fcba}}, after which huge number of investigations on {{formula:ce96737f-2dbb-4823-a310-5ba4b527a270}} -wave holographic superconductors {{cite:99bb728a554b3884708bba2cd26ad3a4d05cb188}}-{{cite:b93ededbfcb6e8719f3b7ac25cacf5cef1887b3f}} has been reported in past decade.
Although the original model {{cite:568fac3b4eb710458781bcf0dfe7e147ed47fba9}} allowed to estimate the gap and the critical temperature of conductivity of isotropic system,
typical high {{formula:d7e13ec7-65fe-4c04-b548-cb6fd3c7ac4c}} superconductors
show the momentum dependent gap structure {{formula:4bedf056-7974-4690-9c5f-3afd3589378f}} {{cite:a9bff756ef17240f730c667b7b8c6448681411f8}}, {{cite:b9faf69c31f29bf38cc77c93e15f2d25f2a17017}}, {{cite:1b4e75ff37930f19c3714856c06986ceef6ecdb5}} which has been
considered as one of the most important finger prints of high {{formula:d770f5dd-da8a-4084-ad67-964f90aa64a5}} superconductors. To address {{formula:102831d3-4966-436a-b62f-ab125cc9dc60}} -wave superconductors, Gubser {{cite:d5581e1d8fadcf7c481e88226586bdfa291708d8}} first introduced the non-Abelian gauge field for holographic superconductor model, which is followed by many investigations on {{formula:233386ed-2e61-4320-9ccc-549ac4c85a67}} -wave {{cite:51c0b6b705717d9ca16199f68d8498903177e694}}-{{cite:ea2bc250f000286d00eff5f20a6f71b2cdb9211a}} or {{formula:7e21d474-9377-4c2c-adc2-689e6dfc981b}} -wave {{cite:fff24be05fc1b2636b2018be900a2b739a5589c7}}-{{cite:fb72b750edb3799887af03109709b907b8c06a1b}} holographic superconductors using abelian vector and tensor fields. However, to our surprise, none of the investigations addressed the momentum {{formula:7da40731-4c65-4cd1-a8ea-f52b5e7fceb2}} dependence of the superconducting gap, because in all the previous works,
non-vanishing components of vector {{formula:e8f7935f-f1f2-45a7-92aa-3f45ca535453}} or tensors {{formula:910d8580-a84b-4ea8-ada4-cab9731d2c16}} were assumed to be isotropic. Although the angle dependence of the gap was introduced in a notably exceptional paper {{cite:fff24be05fc1b2636b2018be900a2b739a5589c7}}, the angle dependence in that work was introduced by considering the `fermion spectrum' explicitly rather than through the gap equation, that is, the equation of motion of the complex scalar function. For more review, see {{cite:86c6c77081429c046d6bdcd8ef58d0bc52776512}}-{{cite:2454e300667f6d2c5cf5285ed46b353991ab4cd2}}.
| i | b934eeb215d3a1ae2ec0d9f200cdddf9 |
Estimation of the covariance matrix is a classic topic. In high-dimensional statistics the role of sample covariance matrices is central to Principal Component Analysis (PCA) and to linear least squares. Most of the existing work focuses on estimation of covariance matrices under different structural assumptions allowing minimax estimation in the high-dimensional setup. We refer to the line of work {{cite:1b3a771db64d184cbe4a637a867ec41468068e12}}, {{cite:9a53b1b96a0ae742010ca6ff459dcc5cd72184b3}}, {{cite:6bba9156accf6808f74bc6b524ea10096d44f82c}}, {{cite:7c4501ff1854190fce2c3170e29286bf84833b9f}}, {{cite:833adbec9a120fa1f5f4f5150cbc44209086f74d}}, {{cite:e8ddb73f6a43cd120ca7867faa4ad58b36a41ceb}} and the recent surveys {{cite:c339076d862865cab6132e09055886a495c3dcdc}}, {{cite:2b7fec79bd683e20e5b5f099c065dad3bb70816a}}.
| i | e459a04ec42c25ec11ad7a52724ffce3 |
In this section, we give a broad overview of the various methods employed in this work for GNN training and accuracy evaluation including: virtual sample generation, CEFEM modeling, HEDM, and GNN surrogate modeling. In addition, details regarding the various training and testing data used are provided. A schematic of the various components of the effort, displaying LSHR data, are given in Fig. REF . Briefly, a transfer learning approach {{cite:87dfc175b6c71d992acc60d1895e731a2dd99eb1}} is taken in which the GNN models for LSHR and Ti-7Al are trained using simulated data from microscale CEFEM modeling (the Source Domain) and then transferred to predict the mechanical response in a microstructure measured experimentally via HEDM (the Target Domain).
{{figure:4e7375bf-cb0c-4ef8-8a42-658f054c2e57}} | m | 9ca45d6a4f0088aa6651bba137a3e5b4 |
Data privacy for deep learning has become a challenging problem for many application domains including Natural Language Processing. For example, healthcare institutions train diagnosis systems on private patients' data {{cite:9721af23070b9bbfe88172acf7ff1388b497b8dd}}, {{cite:457975dfcd2becb288f7b4172383d612fe723626}}. Google trains a deep learning model for next-word prediction to improve its virtual keyboard using users' mobile device data {{cite:8e8ab04cb1024cf6a67d8c4b0f2f489cacc11c3c}}. Such data are decentralized but moving them to a centralized location for training a model may violate regulations such as Health Insurance Portability and Accountability Act (HIPAA) {{cite:1bbf5f20ea693c8010563c94344f66085786e3e4}} and California Consumer Privacy Act (CCPA) {{cite:11eecde269afb4a24d91918e30ba21617ffcb0d5}}.
| i | ecc71f298af6e0f7a14c009dc2bd9f09 |
This work studies the relation between contrastive instance discrimination and feature learning. While we focus specifically on contrastive learning, it would be of interest to also study feature learning for other empirically successful self-supervised methods {{cite:487748d502f3aacf271c69e23a2564dcac5ab2b7}}, {{cite:7d54ed05722b577377534d87096cde41b9d1aa25}}, {{cite:65b836b0f853ffe1b5ec0eb4692547dfb98467e6}}, {{cite:1875bf9cbea4c2d0fa310c6053bf742c2b55efc3}}. Understanding differences in feature learning biases between different methods may inform which methods are best suited for a given task, as well as point the way to further improved self-supervised techniques.
| d | 9d3ad7e38122e6238f76b95bf20709dd |
One of the most common attributes among different organisms in nature is to dwell in groups or move in consensus and mimic the activities of their local neighbors, the reason of which can be traced back to the survival instinct of those organisms. The examples of which can be found in systems as small as bacterial aggregation {{cite:0e5ab543e37834dd3072bdd4f7694c26befea560}}, {{cite:43e7fdc51d635e68663a38b08f5306f865c9305e}} to macro-organisms such as flock of birds, herd of sheep, and school of fish {{cite:938287b9e0cb4a5d610fef0f4e55fd315c3f1830}}, {{cite:f371e70a6cd7f158cc645ac16f0a20f85fc374ba}}, {{cite:db9514cea144fde9d7018742b1d86e783ac20f7c}}, {{cite:8cc95537b7ef5f49489e7ef195ebcec4dbf5268a}}, {{cite:61156816387774c47eb92e15d29482d5344c05c4}}, {{cite:c4883fdcc9ada3d5d4c4e03436179698135cd122}}. In all these systems, the individuals organize their positions in space to aggregate together or move in unison. This phenomenon, commonly known as swarming {{cite:f1ebc65a092e7fb04f5f8846596814b92055c4f5}}, {{cite:bef9d0c5a49b8e2a2a1c7f84d1eecaf4bf93f278}}, {{cite:d6feb552a6db2a6c7765fa4ed3284f72ec1d0176}}, {{cite:adc220393d1e3fa08fd686a952179eb405a9899d}}, is widespread in coordinated movement of a group of animals. Swarming usually means self-organization of entities in space without considering the effect of the internal state. Another such collective behavior is synchronization {{cite:ff15ed1ecb3e635cd1a7fe54a2564786e4081e51}}, {{cite:694401b38fa404e37fe7c4f1fd9efc3589503a25}}, {{cite:07f2177b556e906ed9040a8402b228092a855385}}, {{cite:54526f11f2880289b4ea815db1b3545ca2653ad7}}, {{cite:238e0b189ff61adf75b0ef3336dca0f19280cb2c}}, {{cite:34494e66406b0462494fd40df453d6f645e0628d}}, {{cite:4419ea13a5ea94644189f85e2fa845ba789129a1}}, {{cite:ab6171a96e2461139afa6d06f1f8f9fa7814c407}}, which is more ubiquitous in nature and technology, where the units adjust their internal states to self-organize in time. Flashing of fireflies {{cite:80d900d919ca30ec5775a1aaf97b2b1c0064ad87}}, {{cite:798e969110ec2a1e3ba6cf1a6096f7bc2216179b}}, chorusing frogs {{cite:a3d266e7db73e26a953670698a3f1a4883c19095}}, firing neurons {{cite:0d7d13b634bb948ecee0874cc9532fb3ab32a9b5}}, {{cite:7da26cebadd0761c031cf12027d1dd7ad47856bd}}, phase-locking in Josephson junction {{cite:a369a6d4389d98aa0b1ab3b3b3f6c7e5be399401}}, {{cite:9d7501f00b560e6c4cae6b4641b0d993fa47ff7b}} are some of the well-known instances where synchronization occur. Here, only the oscillator's internal phase dynamics receives the central focus without shedding much light on the spatial motion. Examples are also found in nature where oscillator's spatial and phase dynamics affect each other {{cite:2afe14b73d6e4c8d687875584431e4201b7b3b37}}, {{cite:747d910c2c5e93a2cedbb898e433cd602f42dfd3}}, {{cite:55096d1a3ec0dfb0e488a56b76664ed4fd16d27d}}. Tree frogs, crickets, katydids synchronize their calling rhythms with nearby individuals, and their movements are believed to be influenced by relative phases of their calling {{cite:1341bc0fc86052a1c36136c7a83ccc8804245127}}, {{cite:7f6cd85d67d2aa69096ba8d584f8fc7cdc387852}}, {{cite:fd073dfdc01eb9c14e4c6d3dada541adb9e84326}}. The study of ferromagnetic colloids, sperms, land-based robots, aerial drones, and other active entities involves both dynamics {{cite:4a27e52233533473b1d08441300063410dd2f47b}}, {{cite:dc3f87dc5fdfde2713c1dcf8f20e0158abdeec94}}, {{cite:672e0682c2ac7a197fd7401587818e44d91183a0}}, {{cite:16934213f48cdeb8fb76de8fb3c603fcebc43ba0}}.
| i | 54e66db4f35c1250b1a6d701ebdd13bb |
The first one assumes that the 3D surfaces of point clouds can be computed from the 2D manifold by consecutive mapping(folding-based methods). For example, FoldingNet {{cite:2561f0f2633ee2b768df5f8636e5ea02fa2de8c6}} employed an encoder to extract the global feature of the partial point cloud and then used a 2D grid together with the global feature to reconstruct the complete point cloud by a decoder. However, the FoldingNet cannot fold a 2D grid into a complex shape. Yuan et al. {{cite:eead5ff3b228ba51b565f69f01affd08beeea0c6}} extended this method by first using fully-connected (FC) layers to predict a coarse point cloud and then employing the Folding operation for each coarse point. This method takes full advantage of
both the flexibility of FC layers and the surface-smoothness of Folding operation.
Groueix et al. {{cite:f26cf4252c9f091cf9eb6ceec465530f600ddc58}} used multiple MLPs to deform 2D grids into different local
patches. Although this method can generate more complex shapes than FoldingNet, there are some overlapped regions between patches. In order to solve this problem, Liu et al. {{cite:67dbbcff659f03bdfa7dfe859191d21aa8d83530}} proposed an expansion penalty to reduce the overlap areas. Tang et al. {{cite:4dbb9e3a0c1a5e8ad59007188ef5ffe7ae8aff7d}} used multiple grids to generate a point cloud with shared MLP. They designed a Stitching loss to preserve the uniformity of points.
Wen et al. {{cite:67054db9fad53ae3a4a60db54e38ff119af1e0ae}} proposed a skip-attention module to capture the geometric information of local regions and used the Folding operation to generate the complete point cloud hierarchically.
Rather than utilizing the fixed 2D grid as seeds, Yang et al. {{cite:133321e126ae9c159a020aed76b8bb48629f36b5}} used a network to learn a high-dimension seed to generate point clouds. Similarly, Pang et al. {{cite:e7efda94ef9c229094e602574206181adc7d69dd}} argued that the fixed 2D grid cannot capture the complex topologies of point clouds. They used a network to learn the point cloud topology and tore the grid into patches to fit the object shape.
Yu et al. {{cite:b7b94d34bbaab8f3fcf2e1a43585b2b2f03b82a4}} considered the point cloud completion as a translation task and
employed the Transformer to infer the missing parts based on the given parts.
They first generated coarse missing points and then used the Folding operation to
generate their neighbor points.
| m | c041849caf6583acab711afec1f780aa |
G. Baxter introduced the concept of Rota-Baxter operators on associative algebras
in his study of
fluctuation theory in probability {{cite:ca05c5e41f90493e0923a33ffd7a4ee7f4457f0e}}. Recently it has found many
applications, including Connes-Kreimer's {{cite:2359501ed72afd84d4899e568bdabd6b1c45beac}} algebraic
approach to the renormalization in perturbative quantum field
theory. There are close connections between Rota-Baxter operators and noncommutative
symmetric functions and Hopf algebras {{cite:4c785e337c60ea318d7d8601fc7c062672ebf455}}, {{cite:834bf3c783ddbda163e3cd3484fcf8654a5dcd1f}}, {{cite:740cb0c8ed572855166e609e5dae135479f6be83}}. Recently the relationship between Rota-Baxter operators and double Poisson algebras were studied in {{cite:42357ec2b5ed0ad3e4ae1d1a0fafdca34e77efba}}. For further details on
Rota-Baxter operators, see {{cite:a47bf83e121d2ce03e8a6470abab8336b10dd270}}, {{cite:3dd9c25b2cb2045eee1198e2c158bf72f67b5d82}}.
In the Lie algebra context, a Rota-Baxter operator was introduced independently in the 1980s as the
operator form of the classical Yang-Baxter equation that plays important roles in both mathematics and mathematical physics such as integrable
systems and quantum groups {{cite:486a41cf87bae13b4ae8a8a10db97f4222751a47}}, {{cite:5c4c8215321ef07576578abbaf5d52ce14370a32}}. B. A.
Kupershmidt introduced a more general notion, an {{formula:823f89d4-135b-4986-b8eb-e7354881a081}} -operator on a Lie algebra (later also called
a relative Rota-Baxter operator or a generalized Rota-Baxter operator) in his study of the classical Yang-Baxter equation and
related integrable systems {{cite:abd8ee49e2771267b4329acc4454d58950040e6d}}. Relative Rota-Baxter operators provide solutions of the classical Yang-Baxter equation in the semidirect product Lie algebra and give rise to pre-Lie algebras {{cite:ad8eec43ad1e51b2586add05a01df772cba6d799}}.
| i | 0669e5a9b59fb41cbf0fa7bbfcec7717 |
Our work extends the existing literature on sparsity and pruning. A very recent theoretical paper showed that simple linear sparse networks may be more robust to adversarial attacks {{cite:12a8fcf2fd62384bfc11255ebd16b5b07b2bc8f7}}. A number of papers have shown that it is possible to effectively introduce sparsity through pruning and retraining {{cite:8480be3039a439a683c88c447ab57b8ff41c288f}}, {{cite:4cee674bddcef9cc88d7771c6c2414497baee880}}, {{cite:3bf6fb0900c0a070869cce78c2ec3c26b9b8f3d5}}. The mechanisms introduced here can be seen as complementary to those techniques. Our network enforces sparse weights from the beginning by construction, and sparse weights are learned as part of the training process. In addition, we reduce the overall computational complexity by enforcing sparse activations, which in turn significantly reduces the number of overall non-zero products. This should produce significant power savings for optimized hardware implementations.
| d | 278b7bb092e1256fc90a489d775203c3 |
Figure REF shows the results obtained by V-Net {{cite:e98e0c97017af9346a5416df90115b62470261fc}}, UA-MT {{cite:08afd1bcea4b7133e54707ac26ffce660c4c1faf}}, SASSNet {{cite:facfda2618b078c76e4aebf7c2ea1fd2057e3a5a}}, our MTCTL, and the corresponding ground truth on the MICCAI STACOM 2018 Atrial Segmentation Challenge from left to right. The second row of the figure shows that all the three frameworks shows a portion of missing masks (red arrow) near Aorta (AO) region, whereas MTCTL generates more complete left atrium segmentation following the addition of multiple tasks (distance map, cross-tasks, and uncertainty guidance) as multiple decoders in either 3D or 2D view.
| r | 8525003fbe54a4778a62ec38343d26fd |
The Harris-Kesten theorem and exponential decay of correlations (see {{cite:14c805231982060b434888256a7f6406f720f81a}}) were also adapted to this setting, first for the case of the Bargmann-Fock field in {{cite:ba1e21db538c97e041fe0ca7bafb8cd3c61df895}}, and later, in an axiomatic setting, in {{cite:c3091201936de7bb7afc2395041b531368bfe97c}}. The setting was similar to the one detailed above except for the fact that the positivity condition, Condition (Weak) REF , was replaced by the strictly stronger Condition (Strong) REF . The proof used in {{cite:ba1e21db538c97e041fe0ca7bafb8cd3c61df895}} was inspired by {{cite:30ff541d127b8016f27a8648d46d9f76d1d9914d}}, and used an ad-hoc gaussian version superconcentration inequality for boolean functions called the KKL inequality (due to Kahn, Kalai and Linial, see {{cite:44bee72676633c123c4b0ad45b866ccff6afd6bd}}). However, the analogy was too tenuous to be generalized to an axiomatic setting. In contrast, {{cite:c3091201936de7bb7afc2395041b531368bfe97c}} used a randomized algorithm approach inspired by {{cite:a9e7767d698c3424c252cf9b5f8106f6e672b2c6}}, which was more robust but had its own limits, as we shall see in the next paragraph.
| r | 5b251292cd43f9d92414ebb8063b1e07 |
SampleHST leverages a Bag-of-Words (BoW) model {{cite:2ae081d96c497952193259504013810011ad6d7e}} as a count-based representation for each trace. By taking this representation as an input, we can generate a distribution of the mass values obtained from a forest of a tree-based classifier, namely Half Space Trees (HSTs) {{cite:a2409720489098f3c11523f4304a11f528b64cd6}}. This distribution is then used to perform an online clustering of the traces based on an algorithm we have developed which is part of the mean-shift clustering algorithm family {{cite:3f5134c20c4f50363dded61802258738d22a0f66}}. Once the clustering is complete, we decide to sample the trace based on its cluster association, i.e., a trace is more likely to be sampled if it is associated with a cluster with low mass values as such clusters represent rarely observed traces.
| i | 454ed23bb190c1f8d4cc130fabb12448 |
The most significant difference between proposed entropic herding and original point herding is that entropic herding represents the output distribution as a mixture of probability distributions. As for the applications of entropic herding, some of the desirable properties of density calculation and sampling, discussed in Section REF , are the results of using the distribution mixture for the output. There are also many probabilistic modeling methods that use the distribution mixture, such as the Gaussian mixture model and kernel density estimation {{cite:61f1098c6c7aee02fdf91dcfa0d465ed68b3d2d5}}. All of these methods, including entropic herding, share the above characteristics.
| d | fd50214b22a82d33f95bf8480cba3790 |
Deep learning models can learn a hierarchy of features, i.e., high-level features built upon low-level features. CNN {{cite:2e785cc700fdfa67b5147c85638d13116dfb9fb9}}, {{cite:a6564dd61e885af3fedfb5e9db92b74b4324b1e2}} is one popular type of deep learning models, in which trainable filters and local neighborhood pooling operations are applied in an alternating sequence starting with the raw input images. When trained with appropriate regularization, CNN can achieve superior performance on visual object recognition and image classification tasks {{cite:836d42e11888a94b711f50a0da2015017b55e60d}}. However, most of CNNs are designed for 2D natural images. They are not well suited for medical image analysis, since most of medical images are 3D volumetric images, such as MRI, CT and PET. Additionally, the output of a conventional CNN is a single target value, which means that for a full volume, it would be necessary to compute one output for every voxel. This framework has the obvious disadvantage of requiring a large computational time, but also is unable to preserve neighborhood information in the output space. The task of image synthesis can be seen as a regression problem, where for every voxel in the input, an estimated output is required. Typically an Euclidean loss function is used during training for regression networks, which could potentially generate blurry images.
| m | 433d2e8463332c1d8e36757f0d75ae3c |
Feature-based time-series analysis is a powerful computational tool for solving problems using sequential (e.g., time-ordered) data.
We have introduced theft, an open-source package for R which implements the extraction, processing, visualization, and statistical analysis of time-series features.
The value of time-series features stems from their interpretability and strong connection to theory that can be used to understand empirical dynamics.
theft provides a unified interface to extracting features from six open-source packages—catch22, feasts, tsfeatures, Kats, tsfresh, and TSFEL—along with a comprehensive range of analyses to leverage the combined contributions from all of these packages.
For the first time in the free and open-source software setting, theft provides a full workflow for conducting feature-based time-series analysis, taking the analyst from feature extraction through to generating interpretable insights about their data.
We demonstrated theft on the five-class Bonn EEG time-series classification problem {{cite:82a5278d38100fe3b4fc213046022baf3a680057}}, in which the full feature-based classification analysis pipeline—from feature extraction to normalization, classification, and interpretation of individual features—was achieved using a small number of key functions in theft.
theft can compare feature-set performance and leverage the combined set of features from all six packages, with in-built techniques like low-dimensional projections (plot_low_dimension) and feature–feature correlation matrices (compute_top_features) assisting in interpreting the patterns detected.
Analysts no longer need to construct complex workflows with multiple software libraries that were not designed to work together—theft provides a full suite of functionality, but also provides a blueprint for advanced users to alter and adapt as their research requires.
| d | dfbd429682dba5d7f6664f12c9867400 |
While the net magnetization energy current is always zero, its bulk and surface counterparts in magnetic materials and metamaterials can be very significant. To calculate the Poynting vector, the bulk magnetization energy flux, {{formula:8ed67d59-c4ea-4cd4-bd72-c09f2b017f18}} , should be added to the electromagnetic energy flux, {{formula:49983ef0-2f50-4ef0-8405-11d85ef1c085}} . Thus, the Poynting vector is given by {{formula:ccc76937-d54b-49c9-b40b-1ab422cd17e6}} (Eq. 33). We have shown that the term {{formula:6c68d3a7-2f8c-44e9-b971-1e4ad75ee5c9}} previously associated with the dissipated power (see Refs. {{cite:8075b5955c5107a9f2772dd88511b8c04e5878e2}}, {{cite:805c6429f475ea63fa200ed7ee585273a0540f76}}, {{cite:31320ecebc1a9d103ec885a7192f11280525686e}}) in fact, describes the energy redistribution between the surface and bulk energy currents (see Fig. 3). The new expression for the Poynting vector and dissipationless redistribution of the magnetization energy are critically important for understanding of the energy transfer in metamaterials.
| d | ebf914fac0e634852da465bcaa02c306 |
Given the (approximate) solution of (REF ), we again apply a line-search and follow the Armijo rule to verify the sufficient decrease, which is referred to as the damped- or relaxed Newton method.
We shall also mention that Newton's method is commonly combined with a so-called Wolfe condition, see {{cite:bde5bce9950f1511843826c3b7ca742b2eefeee0}}.
The above-explained damped Newton method can be summarized by alg:newtonsmethod.
| m | e61e9bedf4de40474c0428f5eac62863 |
{{cite:c58100a000768ac3d3c824e2eeba6349c8677297}} show that non-saturating GAN training approximately
minimizes an objective function.
The objective function derived there is expressed as {{formula:b0d3b751-c3ba-41cf-b828-5810c06720a5}} , which is a
rearrangement of the expression {{formula:01952052-0533-46de-a200-c9547cf3d0db}} derived in §REF .
The paper suggests the negative sign of the second term is “pushing for the
distributions to be different, which seems like a fault in the update”,
whereas writing the objective function as a divergence makes it clear this is not an issue.
| d | 02c1ea89447ceb9f88fdc913648ee205 |
Overall, we discovered that large label taxonomies tend to mean that the choice of method for ground-truth inference is redundant. This may be due to some relation to the class subset sample size, as it can be seen from the overall sample sizes that CT and EM both have some sensitivity to this. Keeping in mind that it is usually the goal to accrue as much data as possible, EM seems to be even more sensitive to the overall sample size, concluding that 500-1000 as a minimum sample size can increase the possibility that a particular method will help boost ground-truth inference. This is particularly curious as the example in Dawid & Skene{{cite:81fc259db3fc64e450e7427a8f8e9fca2cd48376}} base their work on a, albeit contrived, sample size of 45.
| d | 6e5d5fdc673914043def01cf04411531 |
OOD robustness.
Beyond uncertainty quantification, the superior accuracy and calibration of ensembles under dataset shift is also often attributed to ensemble diversity {{cite:7ac16eb284fbf8b35af9e1f63b1b699961058674}}, {{cite:abdfc36f6d55c0e4dfa5220d89b6782575110cc8}}.
However, our results show these qualities again are not unique to ensembles.
Prior work demonstrates a deterministic relationship between a (single) neural network's 0-1 accuracy on InD and OOD datasets {{cite:17c444133081fc65b635804713d79686b7306fe2}}, {{cite:6bfa2790280e1bdc1809c35a01c3acbe1e6749d2}},
whereby any two models with the same InD accuracy will achieve very similar accuracy on OOD or shifted datasets.
Our results demonstrate that deep ensembles also follow the same deterministic trend as single networks. In this sense, ensembles do not offer any “effective robustness” over individual models,
as an (InD) accuracy-matched ensemble and single model will also achieve the same OOD accuracy.
We extend these findings to probabilistic performance metrics (NLL, Brier score, and calibration error) where, based on prior work {{cite:abdfc36f6d55c0e4dfa5220d89b6782575110cc8}}, one might expect ensembles to be advantageous.
Even by these metrics, ensembles offer no effective robustness over single models.
| i | a1caa5636f62cfc82d452e0cf8f27801 |
Both VAEs and GANs are able to outperform Gaussian Noise on MNIST dataset (compare Figure REF a) with b) and c)).
VAEs are also able to obtain excellent results on the CelebA dataset, where some samples are arguably indistinguishable from real people. Together with the results of statistical tests this is enough to claim that principal components containing information about important image features can have nonlinear dependencies between each other. GANs also show an improvement over generation from Gaussians, producing more consistent images, however, their improvement is not as significant as that of VAEs. GANs also generate very similar samples, which is due to a phenomenon called the "mode-collapse". However, as argued by Ian Goodfellow {{cite:864896a2d45da69b672b9e1e292d570d84ee575a}}, this is a general tendency of GAN models and while it can be reduced, it cannot be completely avoided.
| d | 9ce5d11982ac1e2463ad6e951a863005 |
The systematic study of integrability in {{formula:5d2f2545-fd89-42c3-a7f6-e2b56aa0f406}} CFT has been initiated by Bazhanov, Lukyanov and Zamolodchikov in {{cite:11005e0869ac292bec0708fd191ff60d11d749ba}}, {{cite:eeec312dafcfc3fc8e08676292842f596c6dead6}}, {{cite:34dd7f5c61224cccc3a452ed43aaeadda29ea339}} (the so called BLZ approach). They considered the simplest example of integrable system which appears in CFT – the quantum KdV system. The most important outcome of {{cite:11005e0869ac292bec0708fd191ff60d11d749ba}}, {{cite:eeec312dafcfc3fc8e08676292842f596c6dead6}}, {{cite:34dd7f5c61224cccc3a452ed43aaeadda29ea339}} was the construction of generating functions for local and non-local Integrals of Motion (IM's). Later it has been generalized for other models {{cite:db5da5c3dd458ef75af8dceb9a363f50f9f6659f}}, {{cite:169e54f768d612359b73279b2edf11e7fa2903c8}} and, in particular, in {{cite:e3f0dddc1ca3fecd4522d753a149104bec12d911}}, {{cite:bd0fb22bf79c409740cf84186e11161f95515581}} for the quantum supersymmetric system ({{formula:ae6cc64a-643d-429a-8316-1877464ebe8e}} KdV).
| i | 732f6339dfa0144e55bd8482453da7eb |
We use numerical simulations to compare the performance of the proposed schemes. For reference, we also simulate another setup, called virtual MISO, where the spatial multiplexing gain at the receiver side is used only for achieving a beamforming gain. For this setup, we consider just one receive beamforming vector {{formula:8c629672-6232-4cc8-85cc-6cff049cca0b}} for user {{formula:1642fc51-822c-4070-8d68-1e26df2c6046}} , and set it as the eigenvector corresponding to the strongest eigenmode (i.e., the largest eigenvalue) of {{formula:e40ccc13-1347-41fc-bc85-430cfea7988c}} (the channel matrix of user {{formula:1b19c447-caf4-4b3e-abff-a91c3708461b}} ). The coded caching scheme is also set to be the MISO scheme in {{cite:087bf77889886d5d3f9c83fff375ba2c5c2bf063}}. The goal of simulating this virtual MISO setup is to analyze the real performance gains achieved by using the proposed MIMO-CC schemes. All the simulations are done for a network of {{formula:ed830471-2cc9-4ff4-936c-d14701008054}} users with coded caching gain {{formula:36b52733-3b7a-4ae9-a064-8d5265968434}} , and optimized beamformers are used for transmissions.
| r | b0498f6e1fdb3d26e6bd0c3a161ad3fd |
We have listed the 20 stars which contribute the most to the diffuse flux at {{formula:5e501207-9a57-4b0b-a063-593eb31a1d48}} in Table REF . The two stars which contribute the most flux at any value of {{formula:d5b4b615-8a4b-4c59-a628-3ecefed9054a}} are near the right edge of Fig. REF accounting for part of the rise in the UV fluxes to lower longitudes. However, there are enough stars contributing with a range of distances and positions that the dependence on {{formula:23fea158-e90c-45e6-87f6-caa0485c9ff1}} is washed out, as was found by {{cite:6b3b0f391f2a9f58a3cbd44ea478d717077b8fc5}} in the upper Scorpius region. We have adopted {{formula:d3b89aa6-c9e4-40bb-99df-6ceb99765f57}} which is consistent with most observations in the UV {{cite:8407e1521542298060170d8b6b9feefbef3d4eeb}}.
{{figure:72c56160-199a-4b7a-a411-e39519ec987f}}{{figure:d3a19c5e-ae5e-4836-ba49-0bf4284a2fec}}{{figure:1019b773-e24b-4bbc-83ca-514a7fea3b00}}{{figure:f7f35613-fb24-4f25-bf6d-405f39bc8a23}}{{figure:e8790f03-a8a0-4a7f-8527-ef7a1df01c19}}{{figure:fa5c1f32-b284-42be-bb5d-b2846b50f75e}}{{figure:0b9798ab-9e9d-43f0-95b8-e90510bf9d4a}} | r | e737862134bc4ca01cc2aa15a758b765 |
This perspective opened new doors to analysis but did not explain the effectiveness of training neural networks using the widely used gradient descent approach. {{cite:db4917ab40d4e403a82a3bf2b3e2e363909b40b2}} developed the solution to this by further generalizing infinite-width neural networks via a recursively defined kernel called the neural tangent kernel. The neural tangent kernel can be used to represent and analyze a given infinite-width neural network during training with a specific depth, activation, and variance initialization. Future works utilized this kernel and expanded on the 1989 single layer results by showing that wide neural networks trained under gradient descent work as linear models and that empirically, finite networks also share those attributes {{cite:6ec7c51671332c13fc81d242add8a545ba0fb5d8}}. In addition, further neural tangent kernel parameterizations were discovered for convolutional, recurrent, and graph neural network architectures {{cite:8cb5ca0c24d2e35f999bd36fef6f7f31c02f3090}}, {{cite:e36b97f7499a30c5d54f3e10b779563a7ecd65a0}}, {{cite:b76b31fd70994b46ce6737702fd4b1796c12ea5d}}. Furthermore, the neural tangent kernel was also shown to generalize with neural networks that allow for regularization and gradient noise during training {{cite:d2dda86acd78f821e6dedbe00b9326066cbca43b}}.
| i | 960d3e209555675c3ac0f61146fa6b76 |
Altogether, these results may be seen as a strong indication of the existence of an internal, non-trivial, microscopic black hole structure, which should represent the starting point for explaining the black hole macroscopic behavior. Unfortunately, owing to the classical no-hair theorems, it is almost impossible for a distant observer to have direct access to this internal microscopic information. The only direct window an asymptotic observer has on the microscopic black-hole structure is the way the hole responds to external perturbations. This response is codified in the quasi-normal modes (QNMs) spectrum {{cite:f3c2e23d7d984fa0bd0f98e92400e57e63418346}}, {{cite:63d8a13752462f357916a747ca270dcbf0d1f1ae}}, {{cite:f1cd132b78addadf84e610cfdc48c026b8284652}}. QNMs are the characteristic oscillations produced by a perturbed black hole and they decay exponentially in time. Their spectrum
can be experimentally detected, by observing the gravitational wave signal originated in the ringdown phase of two compact objects merging to form a black hole.
| i | 32818773048d0b43afc547c5d328ba9f |
First, we observe that our model significantly outperforms models that use extensive sets of hand-crafted features {{cite:80536def9e5fb6b9033103123dbf43c0b330c99b}}, {{cite:a6f55490b06db347f9fc402355387a16fdec88c9}} as well as the system of {{cite:81f0f33faf049fda83aad9ef1c687094c3bbfe79}} that uses NE and Entity Linking annotations to jointly optimize the performance on both tasks. Second, our model outperforms as well other NN models that only use standard word embeddings, which indicates that our lexical feature vector is complementary to standard word embeddings.
Third, our system matches state-of-the-art performances of models that use either more complex architectures or more elaborate features. tran2017named use three layers of stacked residual RNN (Bi-LSTM) with bias decoding. Our model is much simpler and faster. They report a performance of 90.43 when using an architecture similar to ours. The two systems that have slightly higher F1 scores on the CoNLL dataset both use embeddings obtained from a forward and a backward Language Model trained on the One Billion Word Benchmark {{cite:38144a4d8d8746258f7495f064087fa1a20c8290}}. They report gains between 0.8 and 1.2 points by using such LM embeddings, which suggests that LS vectors are indeed efficient. Unfortunately, due to time and resource constraints,LM embeddings are not publicly available, and according to jozefowicz2016exploring, they require three weeks to train on 32 GPUs. we were not able to measure whether both features complement each other. This is left for future investigations.
| r | fcecc12cde95a2982cb726f866568626 |
The use of synthetic datasets has recently gathered pace in deep learning and such datasets have proven their value either as a replacement or as an augmentation to existing training data {{cite:ffd4f70317e0e0e4d9232a4dc9d1f42cb2d92c46}}, {{cite:69c1923e1a0003773ea47e6ff066c31a8adea712}}. Indeed, in {{cite:b9bc4f249a23eae4e9dc0b22dfec3e3f5577c9f5}}, it is demonstrated that deep neural networks can achieve state-of-the-art results when trained on synthetic, yet realistic datasets. The domains of computer vision where synthetic datasets are widely used range from semantic image segmentation {{cite:d31a241559bcf5c91d67373daaf260670d5d4ffb}}, and object detection {{cite:08537fb0a4388da9daf67e4ef9e6eab8b3c663b5}} to pose estimation {{cite:86bd2b8b80bae2d1900bb6f58fe9756a44bd4e6f}}, and face recognition {{cite:c3c76b170c6c7c612c7282ce293243aa0764896a}}.
In {{cite:038185fe73ba50a391071f9b6524b271b0db6181}}, the authors trained scene-specific pedestrian detection models using only synthetic data. Surprisingly, those models managed to outperform models trained on real data. In {{cite:00efcf19041d995b4d515442516fa5dab7b7bc9e}}, the authors presented an automatic approach that generates synthetic data for human pose estimation. In {{cite:d13fd10e70df5efa8eb548b604519d645cac457f}}, a diverse, large and realistic synthetic dataset for human action recognition was generated containing a total of 39,982 videos and 35 action categories. Finally, synthetic datasets are also used for facial recognition. Such an example is {{cite:c3c76b170c6c7c612c7282ce293243aa0764896a}}, where the authors use 3D models of faces to modify existing images in order to generate novel poses and expressions.
| m | e9ec2c108e72199b35bbc7c8760757c3 |
Generate a referring expression from the knowledge acquired from step (1).
In step (1), most previous work falls into two categories. {{cite:c504066f6b3769ab2635c50960a3dfbce4ddc241}} and {{cite:1a38886a255216176829471905dfff388e566f7a}} assume the information about objects and their properties are known to the agent generating the expression. On the other hand, {{cite:84da6be12a1b750009283b90acc0d3a484759238}} and {{cite:1b7b5cb2f4556aec40db933495b6397eac8a1f7a}} use deep learning to obtain embeddings of the image and the targeted region. {{cite:20a33def47787fb4715dadf0170ccce1320eb128}} combine the embedding extraction step with the referring expression in one single model.
In step (1), we neither assume the availability of descriptive knowledge of the images like {{cite:c504066f6b3769ab2635c50960a3dfbce4ddc241}} nor do we use an image and region embedding like {{cite:84da6be12a1b750009283b90acc0d3a484759238}}. Instead, we generate both the utterance space and the literal semantics of the input image by applying Graph R-CNN to obtain objects' relations and Detectron2 to obtain objects' properties. This idea is motivated by the intractable problem that {{cite:84da6be12a1b750009283b90acc0d3a484759238}} face when considering a vast number of utterances at every step. By extracting the symbolic textual information from images, we vastly reduce the number of utterances per step since the number of objects, their relations, and properties are limited in each image. Specifically, Detectron2 outputs objects and the probability that some property is applicable to those objects. For example, a given object categorized as an elephant might have a high probability of having the property big and a lower probability of having the property pink. Graph R-CNN outputs pairs of objects and probabilities of how true some predefined relation is to some pair of objects.
One challenge in merging computer vision systems with datasets like RefCOCO is matching the target referent in the dataset to the right visually detected object (assuming it is found).
RefCOCO provides a bounding box around the target referent, and Detectron2 and Graph R-CNN may or may not identify an object with the same position and dimensions.
One simple approach is to use the most overlapped detected object with the target box as the subject for the generation algorithm. However, there is no guarantee that the most overlapped detected object is the target. We overcome this problem by combining feature extraction with target feature extraction from Detectron2. We first let Detectron2 identify all the objects it can in the image (call this the context). We then instruct Detectron2 to consider the target box an object and classify it. If there is an object in the context that overlaps at least 80% with the target box and is assigned the same class, then we leave the context as is; otherwise we add the target box to the context.
{{figure:da2a2ea7-7b96-4aaa-bb70-0d4363e748be}}To enrich object relations beyond binary relations in Graph R-CNN, we also implemented a simple algorithm to generate ordinal relations. We do so by sorting detected objects of the same category (e.g all dogs in an image) by the {{formula:15a83f94-0475-4cd1-9edc-cdc5c80f7452}} -axis and assign predefined ordinal relations such as left, right, or second from left.
The product of these image analysis methods are used in the literal semantics, which
are categorical, although they are based on the gradient output of Detectron2 and Graph R-CNN, which assigns objects to properties and relations with varying degrees of certainty.
Since Detectron2 and Graph-RCNN output likelihood values for attributes and types for each object as shown in Figure REF , the last step in the textual extraction process is using a cutoff threshold to decide what level of likelihood make one attribute belongs to a particular object. If the threshold is too low, then objects would contain many irrelevant attributes; if the threshold is too high, there may not be enough attributes to uniquely describe some objects. Currently, we use a hard-coded value that is slightly higher than the minimum value where most of the irrelevant attributes and types are, as examined by hand.
Thus, in the spirit of {{cite:455a712e1c47df8e51372a472df19f18bc8c5879}}, we assume a threshold {{formula:ec0d8eca-9c1b-468f-acc1-2fbf7b37b61e}} to decide whether a given type or attribute holds of a given object. Let {{formula:5fd19b8f-e19b-4978-9c35-56a14a9e48af}} be a function that assigns: to each attribute and type, a function from {{formula:fa84a29f-5813-4b78-8c97-28fd89cecebc}} to [0,1]; and to each relation, a function from {{formula:be22ba84-3ef7-434a-bfac-19065f7fc98d}} to [0,1], where {{formula:30c3faf7-a44d-4760-a680-a82ff8fe2548}} is the set of objects in the image. {{formula:5f1d4238-3499-4415-a532-b370109fbfef}} represents the output of the Detectron2 and Graph R-CNN. For each type, attribute, and relation symbol {{formula:fe1659c6-854a-47e8-a04b-ee42e782d4c5}} , {{formula:d12003f8-ad4e-43ad-8e3c-f209de1b2c8e}} is a threshold between 0 and 1 serving as the cutoff for the truthful application of the type, attribute, or relation to the object(s). Then {{formula:c4109c4b-15da-4221-9545-5a8b082ef22a}} iff {{formula:1f62ccf7-2a5d-4476-8b0e-627784e9334f}} , etc. Ultimately we plan to learn these thresholds from referring expression training datasets such as RefCOCO. Currently, they are fixed by hand: one uniform threshold for types/attributes and relations, respectively. Using categorical semantics rather than the gradient semantics that would be obtained directly from the Detectron2 avoids the well-known problems of modification in fuzzy semantics, a proper solution to which would require conditional probabilities that are unknown {{cite:bb4c95a1e79330007b5b59c18a9aa6b2db063537}}.
Our key contribution with respect to step (2) is at the speaker level. We introduce iterative RSA, described in the Algorithm REF below. Iterative RSA takes as input the domain of all objects {{formula:2f8d3fa8-065e-4729-9f10-0bac45631b05}} , a prior {{formula:796031c3-39e5-45fa-8820-423b0faf16dc}} over all objects {{formula:dd49b8e0-33fe-4f4f-8853-f68711338ced}} , the referent object {{formula:e3d7dd27-fa0c-4c44-8b5f-3f9ea9bad046}} and list of possible `utterances' {{formula:9df0dc27-4792-4c17-b417-16a09f1edaf8}} . Although an utterance may consist of multiple words, each `utterance' here is a single predicate (e.g. dog, second from left, wearing black polo). We will use the word `descriptor' instead of `utterance' in this setting, because the strings in question may be combined into a single output that the speaker pronounces once (a single utterance, in the proper sense of the word). Again, we take the prior over objects to be proportional to salience (which we define as object size). Our RSA speaker will iteratively generate one descriptor at a time and update the listener's prior over objects at every step until either (i) the entropy of the probability distribution over objects reaches some desirable threshold {{formula:c6e51487-a7a0-4d92-98fc-fbc21c930091}} , signifying that the listener has enough information to differentiate {{formula:8ff77375-f619-41f7-ad2e-17a3cc4159d2}} among objects in {{formula:0fb22b55-09d4-4a61-999d-d3d7f3dedd71}} , or (ii) the maximum utterance length {{formula:76de446b-e1b7-4461-afbd-b4c3fcc05aa9}} has been reached.
Inputinput
Outputoutput
initialization: {{formula:62e6ec80-3277-4774-a558-01f5abb771ae}}
{{formula:b0d9f9a1-a76d-4ccc-a0a9-e5478915b523}} & Entropy{{formula:573e352f-6c00-49be-a70f-d53dc31174a2}}
{{formula:ec2b04b1-8e8d-417a-b81e-f45a1cae1f12}} = sample(Speaker {{formula:b11ef3da-b970-4c40-90e1-e7d8778120ac}} )
{{formula:74d94234-344f-44f1-aa4c-4acd9a860c5a}} = Literal listener {{formula:0e2c14ae-74b1-4e09-a5f6-e0210d1c8dec}}
add {{formula:53bfd405-3bd2-4818-8427-c272e84eb904}} to {{formula:5b1dca50-8dd1-41f5-b873-ad49784e5d2f}}
{{formula:65736ad8-72d6-40e3-b91c-e21a9f49022e}}
Iterative RSA
In standard RSA, the utility function {{formula:c594e5e9-88a5-4aa3-84a7-b4501ddfacc3}} is defined as {{formula:656b05b8-efe3-484c-b785-9a50f547dbe5}} {{cite:7174fb2ad71ce639f3bd3fae967ea51bae4ef478}}. We define ours as:
{{formula:c0c5a2d0-5416-478b-aafc-c0a2ea20bfa1}}
where {{formula:2dad0308-8508-4bf0-8d8d-000e83c7ade4}} is the probability of {{formula:b6313763-4e50-414b-afbd-93e8f1394a33}} following the previous {{formula:85a2a89b-7fe3-49e0-8d63-3c004f1a37bb}} words in {{formula:e879ef0b-496d-4b10-b440-4ba64d40c4d1}} . Specifically, we use a 3-gram LSTM model ({{formula:2a4d86bd-284b-495d-aa53-514e46017304}} =3). Figure REF outlines our overall workflow.
Experiment and Result
The framework is implemented in Python and will be made publicly available. In the implementation of Algorithm REF , we set {{formula:c156b641-7caa-486c-ae9f-72e3574a6958}} . This value for maximum utterances per expressions come from the average length of the expressions from our target dataset, both RefCOCO and RefCOCO+ have average length less than 4 utterances per expression. We evaluate our framework on the test set of RefCOCO and RefCOCO+ datasets released by {{cite:7329a2553a529988f511871b59f0744317b45872}}. For these two datasets, each data point consists of one image, one bounding box for a referent (the target box) and some referring expressions for the referent.
We used pre-trained weights from the COCO dataset for Graph R-CNN and Detectron2. Additionally, we experiment separately with finetuning Detectron on RefCOCO referring expressions. Finally, we test the framework with RefCOCO Google split test set and RefCOCO+ UNC split test set.
We evaluate the generated expressions on the test dataset with both automatic overlap-based metrics (BLEU, ROUGE and METEOR) and accuracy (human evaluation) (Table REF ). Specifically, we run human evaluation through crowdsourcing site Prolific on the following scheme: our IterativeRSA, RecurrentRSA {{cite:1b7b5cb2f4556aec40db933495b6397eac8a1f7a}} and SLR {{cite:9f8f0eb75cdfae4d9ae023e6465246e76d484326}} trained on {{formula:2e23190c-8293-4d86-a033-15c1e614d236}} and {{formula:1802c47e-aa91-42b3-a0ca-0c5226b62355}} of the training sets of RefCOCO and RefCOCO+. For each scheme, we collected survey results for 1000 randomly selected instance from the RefCOCO test dataset from 20 participants and 3000 instances from RefCOCO+ test dataset from 60 participants. Each image is preprocessed by adding 6 bounding boxes on some objects in the image, one of which is the true target. The boxes are chosen from 5 random objects detected by Detectron2 an the true target object. Each participant is asked to find the matching object given expression for 50 images through multiple choice questions. In addition, we also manually insert 5 extra instances where the answer is fairly obvious and use those instances as a sanity check. Data from participants who failed more than half of the sanity checks (i.e {{formula:796fe7b8-5072-4ef3-86fc-e3b8c8e962b6}} ) was not included in the analysis. Since our referring expressions are generated based on extracted textual information about individual objects and not the raw image as a whole, there are cases where Detectron2 does not recognize the object in the target box or the suggested bounding box from Detectron2 is different in size compared to the target box. In such cases, our algorithm ended up generating an expression for a different observable object than the targeted one. To understand the different types of errors our model makes, we also included additional options in cases where the testers cannot identify a box that matched the expression. Specifically, we added three categories of error when no (unique) matching object is identified:
nothing in the picture matches the description
several things match this description equally well
the thing that matches the description best is not highlighted
Despite the simplicity of our proposed method, it achieves comparable performance in terms of METEOR score to the Speaker-Listener-Reinforcer(SLR) {{cite:9f8f0eb75cdfae4d9ae023e6465246e76d484326}}. More importantly, our method outperforms SLR in human comprehension under low training data scheme and RecurrentRSA with both RefCOCO and RefCOCO+.
{{table:aafbaf30-c696-4dce-9928-c08984185b94}}Beside raw accuracy, we also report the accuracy rate using the formula {{formula:21f6b9d4-37ac-4540-aa96-aa0f740eb201}} where Underinformative counts instances where the expressions correctly refer to the referent objects but are not distinctive enough. Our human evaluation accuracy is slightly less than that of MMI {{cite:7329a2553a529988f511871b59f0744317b45872}} and while our METEOR score is higher. However, our performance measures fall short when compared to the state-of-the-art extensively trained end-to-end deep neural network model by SLR {{cite:4dd7f7ba7fdcb454e32ee893c878fb337af4fb81}}. This is to be expected as our method was not trained and does not require training on the specific task of referring expression generation or comprehension. Further performance analysis will be given in the next sections.
{{table:96e8e345-335d-4564-b09f-0e1c52b6a393}}{{table:0d958dc6-e559-406f-846d-0371ec859943}}Comparison with Recurrent RSA and SLR trained with limited data
As discussed above, to see the advantages and drawbacks of Iterative RSA, we run human evaluation on generated expressions from RefCOCO and RefCOCO+ datasets and compare Iterative RSA with RecurrentRSA-another RSA approach as well as SLR. From Table REF , Iterative RSA outperforms RecurrentRSA with {{formula:d2e0e87c-dd15-41bc-a55f-1595fd9a4c37}} compared to {{formula:88cfd55c-0593-43e2-b1c1-08144dac6f6a}} . On the other hand, to make a fair comparison with a deep learning end-to-end approach like SLR, we decided to train SLR with limited training data as Iterative RSA does not require any direct training process. From Table REF , the Iterative RSA (no training) outperforms all SLR models trained with {{formula:c3f146cc-49c7-4139-a01f-a05ee97876fc}} and {{formula:2516486c-ecee-4fb4-90ce-44b5a03b446f}} training data for refCOCO+ dataset and outperform SLR model trained with highly limited training data ({{formula:b694fd32-69e5-4656-af73-6abcc4ed9150}} ) on RefCOCO. Furthermore, when examining the SLR-generated expressions, we observed that for the model trained and tested on RefCOCO dataset, a lot of the expressions contains positional property of objects such as left, right, which makes identifying the target easier when the expression is low quality and incomplete (as a result of training on limited data). Thus, we can see that SLR performs better on RefCOCO than RefCOCO+. On the other hand, IterativeRSA performs more consistently, especially when used without any training or observation of the data. Finetuning the Detectron2 model for object detection with RefCOCO expressions improve the performance on the corresponding dataset, however, using the same model on the RefCOCO+ dataset does not show any significant change in accuracy.
{{figure:07dcf74b-a496-4b34-a70d-f7c275ef75fa}}Figure REF is an example of referring expression generated with RSA compared to SLR trained with limited data. For the RSA expression, it clearly shows that the model explains Gricean maxim of quantity by generating the shortest possible word to describe the target which are the jeans, whereas SLR shows the overfitting behavior when generating unrelated expression to the target.
Analysis of the human evaluation
As mentioned above, in our study, aside from letting users choose one of the objects surrounded by bounding boxes given the generated expression, we also give additional options to handle the case where survey participants cannot find a sensible object to match the description. Overall, we observe that incorrect responses can be divided into the following categories: under-informative expression, not highlighted, no match and false.
These categories of error help in identifying the sources of deficiency in our approach. If the expression is under-informative,
there are two possibilities. The first is that the textual data extraction step (i.e., Detectron2) was able to identify multiple objects of the same type, but the algorithm is unable to differentiate between the target and the rest of the objects. In this case the problem is on the linguistic side of our model. Another possibility is that not all objects of the relevant type were detected, which is the deficiency of our visual system (Detectron2).
Another type of visual system deficiency happens when the described object is not the highlighted one or if there is no match. In these cases, the visual system (Detectron2) mis-classified the object in the bounding box. As shown in Table REF , about {{formula:8a0b6278-eb1a-4493-ad38-cd0dba504180}} of the recorded instances belong to these two categories.
Under-informative expressions
One type of error is when the generated expression is under-informative. This occurs when the expression correctly indicated the type of the target object but failed to differentiate between the target and other objects of the same type in the picture. For example, in Figure REF , the algorithm was able to correctly identify the type of object in the bounding box but the modifier (cooking) failed to differentiate the target from the other instance of that type.
{{figure:77d7c420-5567-4375-bbb3-435220153e33}}
Object not highlighted
Another type of errors revealed through human evaluation is when
the matching object is not highlighted as the target.
{{figure:5717cc47-4884-4fd1-a680-c1a9056a8d03}}This type of deficiency is due to the textual extraction component (Detectron2) not observing all objects of the same type. In Figure REF , Detectron2 can only observe four instances of the category man, which are all highlighted in this image with box {{formula:0021923b-c047-424f-9ea5-1ab6d4625c48}} . When comparing the available attributes for these mans, target man in box 2 (i.e., the light green box at the bottom left of the image) is assigned a distinctive attribute that others do not have: laying down (although he is sitting, not laying down). The use of this modifier increases the salience of the target relative to the other individuals that are detected. It is quite possible that participants assumed laying down man refers to the only person at the bottom center of the image who is actually laying down. However, that individual is not detected by Detectron2 and thus there is no highlighted box.
High quality expression
When the participants correctly identify the target object by choosing the right bounding box, we observe that the textual extraction step provides sufficient information for the algorithm to work correctly. Figure REF is an example where we observe that the system works well when the extracted textual information is accurate and sufficient. Specifically, Detectron2 found all the objects of the type train in box 4 and 5. Furthermore, the train objects have fairly sensible attributes, including the left and the right.
{{figure:8784b9d4-ac15-4336-a753-b3f959618fed}}
Discussion
The Iterative RSA introduced in this paper is able to generate multiple-modifier descriptions, which goes far beyond the vanilla RSA speaker described by {{cite:7174fb2ad71ce639f3bd3fae967ea51bae4ef478}} and {{cite:c504066f6b3769ab2635c50960a3dfbce4ddc241}}, and our RSA speaker has even gone past the two-word stage of {{cite:1a38886a255216176829471905dfff388e566f7a}}. While the result is not at the level of the state-of-the-art end-to-end model, Iterative RSA outperforms Recurrent RSA and SLR trained under limited data. We can clearly explain how our model comes up with the referring expressions it generates. The explainability of our model is a contrast feature when compare with RecurrentRSA. While RecurrentRSA also applies the RSA model to generate expressions, its expression generation by recursively generate characters makes it hard to explain why at each step, why one character is a feasible choice that helps identify a target object. Furthermore, to our knowledge, we are the first attempt to apply pure probabilistic RSA model without any neural network components in the expression generation step of the referring expression generation from image task. From the analysis of the human evaluation and concrete examples, it is clear that the performance of Iterative RSA is tightly coupled with the performance of the textual extraction model, particularly Detectron2. When Detectron2 detects enough information, including the objects in a given image as well as their probable attributes, we observe that our proposed Iterative RSA can create high quality expressions with distinctive modifiers.
Another key strength and also a weakness of our proposed iterative RSA is the size of the vocabulary of descriptors. Currently, this vocabulary is limited to the attributes and types vocabulary that Detectron2 possesses. While this vastly reduces the search space of all possible descriptors, it also limits the possible descriptors that RSA can choose from, given a target. The textual extraction step (Detectron2 in this case) can be analogized to the act of “observing” and the Iterative RSA algorithm to “reasoning”. One cannot reason about objects or aspects of objects that are not observed.
On the other hand, in terms of efficiency, our proposed method is fast because Iterative RSA does not require training data and can be applied directly on the fly with any given textual extraction system. In addition, our application of Detectron2 and Graph-RCNN also does not require training as it utilizes pre-trained weights. Experiments with fine-tuning Detectron2 with RefCOCO data does show better accuracy on the test set of RefCOCO dataset but does not show any major improvement when tested on RefCOCO+ as shown in Table REF . Thus, the base Iterative RSA is more generalized and consistent across different datasets.
Minimal reliance on training data has other advantages: That property makes our approach a promising one for low-resource languages where labeled data for training, especially for vision-language tasks such as referring expression generation/comprehension, are virtually non-existent {{cite:edeb46b770efc2a6ea3d8ee26613a47240b0f383}} for languages other than English.
Conclusion
In this paper, we have explored the possibility of decomposing referring expression generation into a two-component process of symbolic knowledge acquisition and expression generation, adapting the RSA framework to real world scenes where textual information is not available. We also introduce two promising innovations that help to address the intractability problem of applying RSA to real world scenes in previous work, which includes (1) constraining the utterance space using the output of object recognition and scene graph generation systems, and (2) proposing a simple yet intuitive and explainable model for referring expression generation called iterative RSA, which incrementally outputs referring expression one predicate at a time. Lastly, our method allows for easy analysis and understanding of each individual expression, and provides clear explanations as to why the system generates the expressions it does.
| m | 42e360606ec1eeebd81165509a9ae7b6 |
ML Applications and Datasets: LC-Checkpoint is evaluated on four typical ML applications: Multinomial Logistic Regression (MLR), LeNet-5 (Lenet) {{cite:4fa1ac1210f8c7f78cb1b116a3f3a67b01cd1693}}, AlexNet {{cite:e92ab0e1e643f1318ce8f2cd78a24cafef339844}} and Matrix Factorization (MF). The first three applications are trained on MNIST {{cite:4fa1ac1210f8c7f78cb1b116a3f3a67b01cd1693}} and FashionMNIST {{cite:1e91550066acc5ac4a41926bc83d9593bb92e66f}} datasets. The last one, MF is trained on Jester {{cite:4d5c0d2524364590f532489dbfaf26db92ae32b9}} and MovieLens10M {{cite:d3968994ce5cfddf2b911d0e2886583d71f92021}}.
| m | 19c5110eb5d8981cbd26e8263351d6e9 |
We implemented the aforementioned neutral-neutral reactions with a rate coefficient
of 10{{formula:e808de38-00d7-4dbb-bee7-fe2137a57843}} cm{{formula:52c9d058-4e5f-44a5-b4cd-8b47ad82b68c}} s{{formula:cc5aab18-1a17-49cf-a097-cc9edeff2c9f}} in a gas-phase chemical model, in which we adopted
typical physical conditions of cold dark clouds (see e.g. {{cite:9c338c6279d116489e115aa7cffae3f18b85986b}})
and used the chemical network UMIST RATE12 {{cite:d630db450e6600dcb851acebef2bae5d78ce02c8}}, revised
and expanded according to {{cite:e2f62bb07dccbceed64748c3f5b558fbb9ff094e}} and {{cite:86f51a1105c4a50c92af6d72145c8ccdb623f97a}}. The chemical model
reproduces the observed abundances of the O-bearing molecules HCOCCH
and HCOCN reasonably well. Moreover, the observed abundance ratio HCOCCH/HCOCN of {{formula:51583b28-e6bc-4b5a-a213-df93a2433aae}} 4 is of the
same order as the observed abundance ratios CCH/CN ({{formula:9ac630c3-61c0-4c6b-ad26-3de65a73a83c}} 10; {{cite:4292eac390ce26fe797f04568a8dd850a1b9aa0b}})
and CH{{formula:d53193d8-4892-4e55-9394-bd7ecad33b77}} CCH/CH{{formula:00f588ad-4cb2-45a9-956c-a58d58b0c90e}} CN ({{formula:e386f2d8-3688-4f65-9ddf-2a7470b01f87}} 6; {{cite:4730ff8f72bfacb8754c05813a9e70205af4c403}}; {{cite:c398ec85b760f2a25dc5894eb29214e5e4dbf6e6}}), which
is consistent with the chemical routes proposed. In the case of the S-bearing molecules
HCSCCH and HCSCN, the chemical model underestimates their abundances by two orders of
magnitude, which may be related to an excessively low abundance of atomic sulphur calculated by
the chemical model or to missing formation reactions, such as ion-neutral reactions.
| d | 7d193df4e8a168507cdf7fade6963d26 |
Our method determines two (pregrasp and grasp) 6D poses from a point cloud captured from a single RGB-D sensor. In this section, we summarise the important steps from data acquisition to the grasp pose generation.
Given a raw input point cloud, all unreachable structures are cropped. We then use Random Sample Consensus (RANSAC) {{cite:13adeb39ad4b97378a8baae85b3906276042877d}} to detect and fit the dominant plane in the remaining data. The outlying points, with respect to this plane, are assumed to constitute the object of interest.
{{figure:4f3e1ddc-d0d9-4e6d-8fa5-8288f8d77881}} | m | 5b257dbeb8d120738e6903a152e050b8 |
This study has some limitations. Firstly, we did not compare our approach to a variety of existing methods for ensemble generation, e.g. snapshot ensembles {{cite:cea5c06e11ab6cf0467b5e6aa61d00a1dd6f1733}}. However, these methods are heuristic, and as discussed in the related work, our method can be used in conjunction with them to make them more principled. The second limitation is that we did not explore different techniques of generating weighting distributions for the diversity term. However, even with our simple approximation, we obtained substantial improvements over DE. Another limitation is the lack of parallelization possibilities compared to DE. We note, however, that one should choose principled and mathematically understood methods in critical applications such as healthcare.
| d | 59883cf9e659dd68590c4812cbe47c03 |
We note that the SVGP framework for scaling Gaussian process is one
approach to build upon for our application — other frameworks for scaling
kernel methods could have been employed. One example is random (or
carefully selected) features for approximating the kernel
function {{cite:9c81caca56c19d8e5d43b62da7407526920be0cc}}, {{cite:5a7475de9823006aedd99e1c62f832377bc80b3e}}, {{cite:abd839943f50f73d8c0c8697a2fb4f7bc5a712d9}}.
While these approximate kernel methods could yield superior performance,
one reason we reach for the SVGP framework is extensibility.
The variational inference framework can incorporate more complex
probabilistic graphical model structure. For this application, additional
types of observations can be incorporated into a more sophisticated likelihood
model to help identify the spatial dust distribution and incorporate additional
sources of uncertainty.
{{figure:2a3599e8-eef6-4602-bd73-fb243c91aecd}} | m | 9bc19a4832bd9bfd8829fb9553789f57 |
Since Sn doping could effectively suppress the BHV ordering, it is natural to check its influence on superconductivity. The temperature-dependent resistivity down to 0.3 K is shown in Fig. REF a and their {{formula:20ddf500-5232-415c-977f-07eb11fe0ac5}} s are extracted in Fig. REF b. We can see that IrSb{{formula:cc92a235-1dbe-47a7-8b3d-d42c596026ba}} Sn{{formula:8cd89d9b-4164-4a3d-95be-28cd9656df22}} with apparent residual resistance sits at the boundary of bulk superconductivity, agreeing well with the disappearance of the superstructure peaks and the lattice collapse shown in Fig. REF . The phase diagram of Ir{{formula:5b60678f-07ec-4e6b-aa23-a436ab99697f}} Rh{{formula:7d267a03-009d-4521-a51e-3d3de405a006}} Sb has been included for comparison. The phase diagram of the Sn-doping case is quite different from that of Rh doping. Instead of a continuous {{formula:5b7647b4-977e-4068-bc04-f71ca61854f8}} evolution in Ir{{formula:27995e78-3b22-4dd0-9d49-34335d09ff1c}} Rh{{formula:0eb808e7-8473-4ec0-800e-8e04bc7e561c}} Sb (a broad ‘dome’ structure), the {{formula:b3e73bac-8957-41ce-b855-32da10e64cc8}} of IrSb{{formula:50fbe272-4c16-4be9-8c2e-031d96d6886d}} Sn{{formula:43d19cda-2f8c-45cf-87be-64fb373544aa}} remains almost constant at around 1.5 {{formula:573849a6-a664-47ba-aaed-06fa4ba02679}} 1.6 K. As demonstrated in Fig. REF b, the bulk superconducting region is quite small (less than 10%). These observations are reminiscent of the K{{formula:17127f78-5095-4b06-bf06-8e9d91e42af6}} Fe{{formula:dd73cb81-d534-4bb3-acdb-381a37418361}} Se{{formula:7d8b7827-c547-4159-8ba1-00355f9e6144}} where the {{formula:fcbbf581-6128-4826-b801-ced812d3ec25}} and the composition are barely tunable{{cite:c2b10c3467cbfc3373b228e976a132b36c738da7}}, {{cite:51f50551adfe0fec531a09d6af68551435dcf4f6}}, {{cite:b3ba0b7eb482dfec218063a3f4db93483866ee57}}, {{cite:6fb3b3d90b3fa9da8cb9d19f56c7eded22914448}}, {{cite:b8d58f4c01fec4ea352cf83b6a9301f843005678}}, {{cite:48db3b04769ffd7e41a3b628742bac00ba450ce6}}, {{cite:b6cb01a07342bb06c3a28e16d02c78d31b2f4f69}}.
| r | b6cc2291dbc394d4f1889ea53f062f9f |
The TSI is the integral over the entire solar radiation spectrum that ranges from X-rays to radio waves. The bulk of solar radiant energy is in the visible (Vis, 400–700 nm), followed by the infrared (IR, 700 nm–1 mm) and ultraviolet (UV, 100–400 nm) bands. Measurements of the SSI also started in the 1970s, but are less continuous and more uncertain than those of TSI. Until just less than 20 years ago, they mainly covered the UV band {{cite:edd762293308ccce94ebe3a093b429c8218f914f}}. Nevertheless, all present data clearly show that the form and amplitude of SSI variations are strongly wavelength dependent.
Although the various experiments produced different estimates of the magnitude of UV changes, all available data agree on that they are in phase with the solar cycle {{cite:c87193077f895ca328e47aa1558713926f730988}}, {{cite:e6b6cac6336c958322a971d27cb4f07f17ed6bfb}}. In contrast, SSI measurements at the IR and longer wavelengths show variations that are in anti-phase with the solar cycle.
In regard to Vis, conflicting results from two experiments make SSI variations at this spectral range still uncertain. In particular, measurements from the Spectral Irradiance Monitor (SIM) on-board the SOlar Radiation and Climate Experiment (SORCE) satellite show Vis changes that are in anti-phase relation with the solar cycle {{cite:3d8d6088663f0aa2d1f10f75179f91a6b65ad57e}}, while those from the Variability of solar IRadiance and Gravity Oscillations (VIRGO) experiment on-board the SOlar and Heliospheric Observatory (SOHO) display an in-phase variation {{cite:d59ebd7da16a23d3df8ad8fb5f20cc4c270f07a3}}.
However, it has been suggested that the SORCE/SIM data before 2010, which are the ones showing the anti-phase relation, are unreliable due to potential instrumental issues {{cite:907158aad6b64f746d6f8904fbd90a9d28bb5ce0}}, {{cite:c02c7eed6c748053d346f2356df92aa0b488db93}}, {{cite:0d5ff178f00e7c9a910f9b40ba786af28137c0dc}}.
{{figure:ae4b9a82-e856-4003-9319-efc628e6420d}} | i | 5ca0eac4d59bd580f3003c0a99cc3624 |
Approaches based on unsupervised learning are the most popular way for anomaly detection, because they do not require labeled anomalous instances to train anomaly detectors.
The simple strategy of unsupervised image anomaly detections relies on a training of reconstruction processes for normal images using a deep convolutional
autoencoder {{cite:a0834d5ed6d092b19595c36975016bfad2cf25c5}}. However, the autoencoder sometimes fails to reconstruct fine structures. Consequently, it outputs immoderate blurry structures.
Recently, generative adversarial networks (GAN) have been used for image anomaly detection to overcome this point. AnoGAN {{cite:13dd7997814d64bcd00cbce64743b42d6ed84c18}} firstly employed
GAN to image anomaly detection. In applications of medical image processing, AnoGAN and its extensions {{cite:114bc92bb26a0bb330feba47f9aeca095cc63271}}, {{cite:0e66513c68fcd7e4de7f322cceaac932cd19f782}} realized to detect
minute anomalies. More recently, the idea of AnoGAN was extended in terms of color reconstructability to realize sensitive detection of color anomalies {{cite:0d5533652db7ac7ef2087c816a44335d6b1df9ab}}.
It is a common procedure in unsupervised anomaly detection to define the difference between the original image and the reconstructed image
as Anomaly Score.
| i | fe5489c39ee43eaebf517b307561413e |
With the inferred properties of ISM and IGM as above, we can speculate the following astrophysical situation for the jets in NGC 5322. The jets in NGC 5322 are undergoing weak entrainment from the ISM within the galaxy and further even much weaker entrainment outside the galaxy in the IGM. The slow-down process of the jets on parsec-scale could also be very weak due to large deficit of stellar material in the inner environment of the jets. The likely scenario for the large collimated jets in NGC 5322 therefore appears to be lack of dense material (stars or gases) near the core and low density of ISM and IGM surrounding the jets throughout its progression. This result strengthens the views presented in earlier studies (e.g., {{cite:f8b126dea0c8531275259787094e90abb4ac3a58}} and {{cite:a2dc57ab60a2d7f316f65acff6099c731143f8ed}}) where the FR dichotomy is explained based upon jet interaction with the medium external to the central engine. Under an assumed theoretical scenario where the brightness evolution (re-acceleration) and the collimation of jets on kpc-scales are governed entirely by entrainment of material, the jets may remain well collimated over long distances due to lack of strong external instabilities and also become faint due to lack of particle (re)acceleration.
| d | 34ed108451743eed55f0cbb2ed68f027 |
Selection of explainable methods: As discussed above various methods under the three categories tell us different things about the basis of predictions and they compliment each other to further explain the model predictions. But attribute methods give the most information, followed by signal methods and function methods. We want to explore many attribution methods, some signal methods and at least one function method.
Based on above considerations we selected a function method ‘Gradients’ {{cite:c4433f80f7f59dd8fc6a60cfca5e46120472a703}}, two signal methods ‘Deconvnet’, ‘Guided Backpropagation’ {{cite:74995e19ca393645b9e6334014720fc0ea257b59}}{{cite:a2b1b3f01f9766575a2ff29363d35736efec64f6}}, and six attribution methods ‘input * Gradients’, ‘Deep Taylor’, ‘LRP-Epsilon’, ‘LRP-Z’, ‘LRP-PresetAFlat’, LRP-PresetBFlat’ {{cite:8116aa31672b486d9d3679740fc0e697f74d4910}}{{cite:1b100151d0b04b59ed18f6c9b2d1176dffd9312c}}{{cite:a072c6ab73ef9c53474e5c8aacbd81682823db14}}.
| m | fbb4bea0b8b61dc0b75d4703e6fc4c37 |
The nontrivial quadrupole moment of C{{formula:30e6975d-8f47-4242-b19f-f2f77be4adb4}} N can be understood from the symmetry properties and Wannier centers of the occupied states.
For a one-atom-thick 2D system, the entire two-dimensional plane is mirror-invariant, which means that all states in the plane can be classified into two groups: odd and even under the mirror operation M{{formula:51dbdbdc-34e8-4d3b-90b3-1e2880dd1b93}} . The p{{formula:0d89ca24-fa3a-464e-a2aa-1d662ceae2e0}} states are odd, whereas the s, p{{formula:723482c7-1a28-4489-92da-d5561862c26b}} and p{{formula:3028d5f3-99b2-4edc-9b49-1b138da4a2a9}} states are even. In other words, all p{{formula:91ef12e7-266b-4b20-8011-a99abc2955a5}} states form an independent subspace and the in-plane mirror symmetry M{{formula:92267e09-4a01-42f5-ad94-a0238a3a28ed}} can be utilized to differentiate p{{formula:bd8fedfb-b663-41c5-8c85-5a968f7cc09a}} states from s, p{{formula:bbb126e6-702a-4e4a-9c6a-315f16debc95}} and p{{formula:73d8dc9d-2252-42a7-bf0f-f13db228398a}} states. Therefore, it is sufficient to use the subgroup P6mm (No. 183) to investigate the p{{formula:d12e74ce-fd45-4544-b938-2252e745ac8a}} states, and this subgroup can be generated by the operations C{{formula:845b64c0-bd99-4932-a7c2-5a183057eaab}} , C{{formula:99ddfc19-a306-4c54-bd81-710ff4556a0d}} and M{{formula:de18c74d-8cd5-4932-9763-531a8fc79b14}} . There is a C{{formula:3d847e42-78ef-4ff4-9bd6-2739a9ef66e5}} rotation operation along z-axis. All Wyckoff positions of the space group are listed in Tab. S3. The C and N atoms of 2D C{{formula:9493fc6a-ce2a-4037-93ed-8562e9564dd4}} N locate at the Wyckoff positions of 12f and 6d with the local point group of E and C{{formula:9cbf74a6-baa5-489d-9ca5-9253e3251caa}} , respectively. The induced irreps from the {{formula:17e32727-f2eb-4b2b-8068-a1aa9064a884}} orbitals at the two positions can be obtained with the theory of elementary band representations (EBRs){{cite:9927f871195a38d57af3a034637df051fcfb3499}}, {{cite:f113fdf98ea3ddbc0a8b9ddeaae189dd658aab9d}}, {{cite:97af70a287c5076012f59566d69e237cdeea38e2}}, and the results are listed in Tab. S4 and Tab. S5. However, by summing the number of the valence electrons of C and N atoms, only half of the bands are occupied, which makes the centers of the Wannier functions of the occupied bands may not coincide with the positions of the ions. For the systems with C{{formula:4e79503e-d0f4-4056-a1c3-c6c60a49ccc6}} rotation symmetry, the Wyckoff positions of 1a, 2b, and 3c are the maximal, and we only consider the irreps of the wave functions at the high symmetry points of {{formula:5a0eb0ff-8214-4309-a905-bd4aa269c353}} , K, and M induced from them. The 1a and 3c Wyckoff positions are labeled with green dots and red pentagrams in REF (a), respectively. The EBRs induced by the Wannier functions on these Wyckoff positions can be found in the Bilbao Crystallographic Server{{cite:dc8da0faa8cd04415f866a7a4388d57914ae2d57}}, {{cite:358bae8b38b295b5e58039eb4e25d751fc1f5ffe}}. As demonstrated in the supplemental material's formula (1), we establish a series of linear equations using the EBRs at {{formula:9d9e13eb-f554-424a-b6c8-6dd9abbd04c5}} , K, and M as the basis set and all the irreps of C{{formula:8dbeee5b-c4c2-4175-ade0-ce5daec54884}} N's valence bands as the solutions. A set of coefficients represents a collection of possible EBRs for the valence bands. Certainly, the coefficients of these equations must be integers. After solving these equations, we discover that the nine valence bands can only be induced by the sum of the Wannier functions of A1{{formula:a0c9bacf-a713-4b9c-b2f2-36077eaa6c2b}} , A2{{formula:4e56dbef-562b-472b-9a04-f1dc96aa25a3}} , and B1{{formula:017ddb61-459e-41f2-9b3b-3bd6b8c79f6a}} .
The mappings between them are
{{formula:74c468d4-bb3e-4dbd-8d46-8f068b81a4e0}}
| r | 7847d3f35a1fbf85d1226ea207603701 |
Deep convolutional neural networks (CNNs) are state-of-the-art models for most computer vision tasks, such as semantic segmentation. A CNN typically stacks a large number of convolution operations to aggregate contextual information {{cite:20499403938a803573435c9f3e0050af39170ab2}}.
Each convolution is associated with a kernel that consists of a fixed number of learnable weights, which is proportional to the kernel size.
For many semantic segmentation tasks, especially in the biomedical domain, successful CNN architectures integrate both short-range and long-range information {{cite:e32596593ebca836db864e6c7d51258a9b1ab436}}, {{cite:9bc56ba85421e4a93cc60d9bce6579fda578b60f}}.
Because convolutions are local operations, successive convolutional layers, increased kernel size, and downsampling operations are often used to capture long-range information and increase capacity {{cite:84f0ca69a0da27842058a45ca5862aabaecbe0a0}}, {{cite:b92ea2378e0cd858e478cd34d58edff300e64f2d}}, {{cite:f812a1b0ff120f93c5d9f9bc3d1cded76f812f80}}.
{{figure:4458b4c5-8c66-4e1a-8c8a-7e885b1ba486}} | i | 16bdaa8d067d7fc98c8f5cf2d190f693 |
In this paper, we have not observed the formation of long tails in the collision models considered
in Section REF . However, when we described the results obtained in some collision models, such as
Tom and Rot, we mentioned that some spiral arms have been formed. It must be emphasized that these structures can
also be named tails, in the sense that they were formed in close encounters of the
galaxy model, because the mutual tidal force made particles of the disk and bulge to be ejected from
the central region. Thus, they can be named either tails or arms and these structures are small in
length. The reason for the lack of long tails in our simulations was already
explained by {{cite:b2de381ebf58aa98ae80c7491df1813befb9179c}}, so that the formation of long tails in interacting galaxies can be inhibited
by the presence of a massive dark-matter halo. Later, {{cite:ba1b834f01f5f802c9e2e2f0f1770d5e7ff28696}} demonstrated that a dark matter
halo with a large enough spin parameter led to the formation of long tidal tails, otherwise, no tails are observed.
| d | c8af53a9aa2d9609e5d10d18a54960ca |
consisting of a {{formula:41a94d86-9a63-4f6f-aa95-e10ed45ebc54}} edges connecting the vertex {{formula:ff37d37d-f6f5-4b4b-988d-bf502b6ca77a}} to vertex {{formula:60eacc53-6aee-48f9-b2b1-b8df3f6cd51c}} which itself has {{formula:d7eb64ab-b2a5-4763-957c-a6eedf4bc042}} -loops. If all finitely generated projective modules over {{formula:64bd0e2b-4c19-4652-b9b1-d8924e5ec671}} are free, then by Lemma REF , {{formula:f495510c-9b78-4936-b9b5-2ad4f87cef68}} in {{formula:995fb0d4-b3c6-4a74-8068-f351fc9734c6}} . Thus in {{formula:7305c1ad-8bff-450a-b72b-7bcd915ea622}} , {{formula:2cb613c0-d57b-491f-ad0e-2f107c107898}} , for some {{formula:69cb15e8-05b2-4de5-b2a8-8e58e09d39f6}} . Applying the Confluence Lemma REF to this equality in {{formula:0d080857-8b08-4b43-ad75-b3129471ab18}} , we obtain {{formula:7e66dfba-e7b6-45a0-b61b-078e79296711}} in the free monoid {{formula:eed27f0c-e8e3-4be6-a121-7bae45f62ec9}} , for some {{formula:8d8bb5f6-4a7c-4759-bb95-31381c118ef4}} . This gives that {{formula:7eb18977-ce54-46cf-862a-ee602b73ae4f}} . This immediately implies {{formula:424ae217-330d-41f9-bbfb-f347a4af59c4}} . Thus by {{cite:47e42cd6e6b4a3afbe8614c1020f8d4ddd6ecd79}}, {{formula:808d870d-1e92-412c-9097-788902846d75}} which could be considered as the first test of our Conjecture REF .
| r | 76919b1705dbc20e21c4961f4e402fe0 |
Memory consumption. Our training scheme significantly reduces memory consumption compared to the standard BP training. This is because Skip-Sideways is a temporal training scheme that forward-propagates all the information (activations and pseudo-gradients), without the need to store activations throughout the sequence length like in BPTT. To illustrate this behaviour, we have trained 3D VGG16 (with BP), Sideways, and Skip-Sideways, and we measured the maximal possible batch-size on a single Quadro P5000 (16GB) in all three settings, for the same sequence length. Table REF shows that Sideways and Skip-Sideways training allows for much larger batches, whereas BP training has resulted in out-of-memory error. This result opens the door to dealing with long videos, beyond the commonly used 2-3 second clips, or to methods that need very large batches such as contrastive methods {{cite:298d7b266a0d1d23b358533b029f08930b197216}}, or alternative and more expensive architectural designs such as Full-Res. Note that Skip-Sideways has a memory usage similar to Sideways even though, advantageously, the former has a temporal receptive field growing linearly with the number of Skip-Sideways units, whereas the Sideways's temporal receptive field is one.
| r | 02b7c6d659c68449fbe0137a5f892e22 |
H2 can in fact be available in large quantities when a planet has accreted primordial H/He envelopes. Hydrogen-dominated envelopes are likely shaping the radii of sub-Neptunes {{cite:86e8bfad46223111ca8c2a6eda6542b7eb7cb3f6}}, {{cite:baf01a852c9fc644c23fb1d88c1fa8dc06f328e7}}, although additional large water budgets are possible {{cite:13dcc3d8b3e7b5e56b961a73f9073a069fb0e708}}, {{cite:da9f9fa4c293b0c456d7298d19d7d609293cf082}}, {{cite:4e192d1b7f254f8a1006eb6d2efe07a0e8a3af1f}}. But what about deep water reservoirs in molten mantles of sub-Neptunes?
| d | 7d9e13f3b530138c522cae877e4bcda5 |
We recover that ensembling improves performances {{cite:992284d44c5b6952594e32f79087538c187945c9}}, as one single network (1-net) performs significantly worse than ensemble approaches with 4-branches ResNet-32. Members' disagreements decrease internal temperature and increase uncertainty estimation. DICE performs best even after TS, and reduces NLL from 8.13 to 7.98 and BS from 3.24 to 3.12 compared to independant learning. Calibration criteria benefit from diversity though they do not provide a consistent ranking as stated in {{cite:767c8ab13bbf4319d147ae19ae3a99fe2bd31fd2}}: for example, we notice that ECE highly depends on hyperparameters, especially {{formula:34f77c6a-fb71-4d22-8dbc-ae0b833c0115}} , as shown on Figure REF in Appendix REF .
| r | 1b856d7fd2e4c7ebd965eeac6d93d57d |
In this section, we comprehensively investigate BER and PAPR performance for the proposed SEFDM-IM systems. All investigated SEFDM-IM systems have been detailedly described in Section . The results of classical OFDM-IM and traditional SEFDM-IM-Tra systems are provided as benchmarks.
The performance comparisons of classical OFDM-IM and traditional SEFDM-IM-Tra with basic OFDM have been comprehensively investigated in existing research such as {{cite:4c1bd3bbcb7d3a763d7eec76419818865ce07b22}} and {{cite:42854eea91cc7125c66e9b33407e40536ee4634b}}. This work aims to improve pattern design in the IM domain. Therefore, we focus our performance comparisons in terms of IM-based schemes.
For convenience, the figure legend is specified by {{formula:29e75243-16a1-48c9-86cc-934aac5a043b}} , where the modulation scheme refers to that used in pattern-1, pattern-3 and pattern-4, i.e., {{formula:e4b28599-a2ab-4b2c-86ba-2053e9061877}} . The modulation schemes used in pattern-2 are not specified, which can be found in Section . Since we deploy two independent LDPC decoders, we can calculate BER from index bits and data bits separately. By counting the number of differences between the input index bits {{formula:108a4c1f-c130-47bf-ac6a-22b612660c6d}} and the output index bits {{formula:b85c97df-56bd-4f05-a5fb-91789abf6e57}} , the index BER is obtained. Similarly, the data BER is obtained by comparing {{formula:92afa073-8a16-45c7-b590-74d27a7ac417}} and {{formula:89619fc7-c0d5-421a-8ff5-5d5f7bbfced4}} . The average BER is obtained by comparing {{formula:fe6b2ecb-36aa-489f-9a79-7d652cfdba63}} and {{formula:219540b8-3d7d-4222-a814-f6f70d04456e}} , and it is referred to as BER unless otherwise specified. In all simulations, a coding rate of {{formula:c6409e46-eb69-4165-88e3-bfe9d905f7bf}} is used for LDPC encoding, and both LDPC decoders deploy the belief propagation algorithm with 50 decoding iterations. In addition, we assume an AWGN channel and the following system parameters: {{formula:173fe0ce-62f8-47d3-8848-8e658f7e80fc}} and {{formula:15a1aff6-173c-4b21-8863-d2e9dc212116}} .
{{figure:48221435-5605-4053-8779-9416b97160ba}}{{figure:381fdde9-b66a-4caa-9b79-00f00d72708d}}{{figure:396ba6db-fd4a-4aff-8f04-807bfe75c0e5}}{{figure:3ed5a509-19cd-47a2-8aa0-30f105ac6f21}} | r | 5a51f9d7f0e97daba03b64d81555c495 |
Polynomial Network (PolyNet) {{cite:247015db6e9b9f3b94a8ecb132386a4d1dac4ac7}} is a recently proposed method that utilizes polynomial kernel on all features. We compare the augmented PolyNet (which adds a constant one to the feature vector {{cite:b0b280159217b3b2454ef7cdfb6844b16c997ad0}}) with up to the second-order, and third-order kernel and denote them as PolyNet-2 and PolyNet-3.
| m | 254f9b3452577a6520581a0bb6354155 |
where p{{formula:a13144f9-401c-4f9f-806f-928c6e4db3c1}} and p{{formula:53b20c24-ab71-49d1-8fc2-4162f0d5a70d}} are the bulk dipole moments along the two reciprocal lattice directions and the term of {{formula:087b5a87-3b9e-4c0b-99d3-15500ec789d6}} denotes the C{{formula:62b24c8c-5449-4401-a3ec-62c03b11923e}} eigenvalues of the {{formula:d89b074f-5c09-4c42-828e-56591ed30a65}} th occupied band at {{formula:028f2ace-16df-4f28-b689-68836196d90d}} or M. As for p{{formula:a3c0fdf2-4e42-4f92-9380-e174977fb8d3}} states, the occupied number {{formula:db524634-2a50-4c52-8c74-5150a7245121}} is 9. The numbers of the negative C{{formula:c3e7523d-97fb-4f59-b1ee-c81864f933db}} eigenvalues for {{formula:26f75780-e963-4cfb-8674-b59e8b7903b8}} and M points are 6 and 4 (as listed in Tab. S2), respectively, resulting in vanishing bulk dipole moments{{cite:df4a0d0b92cf6fc520ebb39bd40988b09dd8642a}}. The bulk quadrupole moment of C{{formula:9d8cd402-d54b-4cb8-95f8-97c153f63a39}} N can be further calculated from the bulk dipole moments by{{cite:df4a0d0b92cf6fc520ebb39bd40988b09dd8642a}}
{{formula:9e2d7e2b-5bf7-4742-b333-fb32ede744ac}}
| r | 6d52bcc4caafb996cc1190f85857449a |
In the motivating example, the proposed diagnostic indicated that naively fusing data from the two ACTG trials may not be valid, which was expected due to known differences in CD4 cell counts. While the differences in eligibility by CD4 count are apparent in the inclusion criteria, data sources from different places or times may differ in ways not readily apparent in inclusion or exclusion criteria. The proposed diagnostics may be helpful in other bridged treatment comparisons since differences between populations unaccounted for in estimation can result in biased estimates of the parameter. The proposed graphical diagnostic and permutation test comparing the shared arms can be used to assess whether at least one of the data fusion assumptions (i.e., identification assumptions or models for nuisance parameters are correctly specified) does not hold. The proposed diagnostic is analogous to testable implications of assumptions proposed for generalizability and meta-analyses.{{cite:b2ebe5c5e0ed01ff882efdb2b60a3cbffa07d662}}, {{cite:04a393418a93854a5e04891978096fec6b6eb198}} It should be noted, however, that the lack of a difference between the shared arms is not sufficient to conclude that all assumptions hold true. As a counterexample, consider when the censoring models for the shared arms are correctly specified but at least one of the censoring models for one of the other treatment arms is incorrectly specified. In this case, the proposed diagnostics will fail to detect the model misspecification. Alternatively, if multiple variables requires for exchangeability of sampling were omitted from the sampling model, the impact of those missing variables could cancel or mask each other such that no difference between the shared arms is detected. These counterexamples are akin to limitations of other diagnostics, such as comparison of the g-formula under the natural course to the observed data,{{cite:d1c711fb78ab3cd259a681a52656a43c42ec6016}} or checking for imbalances in the pseudo-population when using inverse probability weighting.{{cite:f0ca0736dd9a4e2a961aff5dbaddae6ddb833ad6}}
| d | 10108e83d89058cb48a5a84b3d2804ce |
{{cite:15d405593973859caaf5cc303b972db1acc6da0b}} found that BAL QSOs on average have higher Eddington ratios and accretion rates than those of non-BAL QSOs in a small sample of BAL QSOs, and a similar conclusion has been corroborated by recent studies (e.g., {{cite:65830fcae904f8b38a49e8a1e6f8130649ff9721}}, {{cite:96fe5dbbfab4bbb2ffd982e5a177e78f9cded5b6}}).
Moreover, some studies suggest that BAL QSOs are redder and/or more luminous than other quasars {{cite:3a9deb7855e6ba86d49a2ebfaa0d19d7a8884d20}}, {{cite:7450b289e2899d26866b61d56d65a77c6dd68c5b}}, {{cite:cce4e586d1c999ab4b3c44e195615250e1b2794e}}.
The high Eddington ratio of the LoBAL QSO J0122+1216, in fact, fits into this scenario of violently accreting systems having stronger outflows.
Further, observational evidence to support the luminosity - outflow connection has been found between the blueshift and asymmetry of the C iv profile and the Eddington ratio (e.g.,{{cite:911113dc60cfd388dfbc1d2d61a2031fd33ddede}}, {{cite:69e9ef3a1145b67f0f2ed8f67c6622cc53a31e17}}).
It is possible that high Eddington ratios, even though not the main driver in the feedback processes of BAL QSOs, may control the formation of extreme outflows with sub-relativistic components under extreme circumnuclear conditions.
Though the variability of Ly{{formula:0b2bc5d0-0935-4797-87ef-5f63ce397294}} and Ly{{formula:23dbbbb2-47e9-4426-a810-e51f7facf7db}} emission lines has been detected, no corresponding pattern with the variability of C iv or Si iv absorption troughs has been found. Thus, due to the effects of low S/N spectra and a short time span of monitoring, we cannot establish a relation between the high-ionization broad emission/absorption lines to pin down the origin of circumnuclear outflows.
| d | 5b9d2305ec301230d67e29db12ce500e |
One of the most promising topics of modern research in cosmology is the accelerated expansion of the universe. Cosmologists argue that the accelerating expansion of the universe depends on dark energy and dark matter which retains negative pressure. As a substitute of {{formula:789aa0d5-2760-4446-8bf7-8ab391aa7b3f}} , different gravitational theories have been presented to unfold the mystery behind dark energy issues. These gravitational theories are recognized as modified theories of gravity. Some of these modified theories are {{formula:e8259c65-3e59-41c4-9543-b912c3851a1f}} Among these valuable theories, {{formula:cf7a4c20-c703-4c94-83b4-bfda5ecac6c7}} is one of the most simplest and popular theory, obtained as an arbitrary function of Ricci scalar. This theory was proposed by Buchdahl {{cite:34f3610d63de64a8a1d2501f16a2d585a5afe670}}. Later on, Nojiri and Odintsov {{cite:22c7ec0168709f31f90c5eef1751af38da517bd4}} demonstrated some models of {{formula:dbc92765-feb8-4696-b8c0-2c07578a3adf}} theory of gravity by placing curvature as a function of Ricci scalar and the outcomes of their considered models are quite viable and stable. Further, Starobinsky {{cite:5c8601b03f0e67684899ceffd5e0825ab330b1e9}} presented an interesting class of {{formula:27fbd65a-a9ee-4c8a-bb5a-52900940a222}} theory of gravity models that showed the physically acceptable results in laboratory testing of the solar structure. Some {{formula:e889d56c-2a23-4a7d-b82b-d087a3a78a66}} gravity model was proposed by Hu and Sawicki {{cite:018aa82824f4eeb59aad184f0836d244bf7b38e2}} by ignoring the cosmological constant and their study evident some interesting results in regard to accelerating expansion phenomena. The viability of physical attributes of compact stars by taking exponential type models of {{formula:88db20f1-7cb5-4542-bb53-4fd4c111fa3d}} theory of gravity was discussed by Cognola et al. {{cite:3e9b61aba0268a339dfb20a5ae35586b95af7f66}}. In modified theories of gravity beyond {{formula:3aa9c559-66f6-42f1-a1f9-8d301dc80b5a}} and its Hilbert-Einstein action, diffeomorphism invariance and the Bianchi identities violation has attracted a lot of interest. Hamity and Barraco {{cite:109adbcea30b4a18eab0fb3e5424435374de1068}} derived the generalized Bianchi identities for the non-linear {{formula:8fe77439-58dc-4cef-8dd4-d2f7ac014792}} gravity to throw some light on the issue that {{formula:eafaa2d4-1ff5-4738-a288-ee555cbd5ff2}} theory of gravity generates higher than second order equations of motion and violates Bianchi identities. Further, Wang et al. {{cite:8ff6d03388fd4eb86112a63a8e86c60b53c2c6f2}} confirmed the local energy-momentum conservation of Bianchi identities by establishing the equivalence relation between Palatini {{formula:b179c1f5-3417-4803-8318-eedc4e36a43e}} and the Brans-Dicke gravity. Moreover, Koivisto {{cite:9432e784462c0b364f6b71806b451181d62c3e63}} explored a composition of {{formula:7f2ed6ac-2ed2-474c-9da1-bed8ac0fb52e}} gravity and the generalized Brans-Dicke gravity and claimed covariant conservation from both the metric tensors and the Palatini variational techniques.
| i | 0d84a91cf299e034483a5869f026c910 |
Then, to infer a statistically significant ranking of the methods, we rely on the non-parametric Friedman test {{cite:4f4956b763a2c236b5cf3d9e806da50c65b5a78a}}. The null hypothesis {{formula:8b5b4492-4693-4ba5-b4fc-e548dfd18739}} of the Friedman test is that “The mean performance for each method is equal”, while the alternative hypothesis {{formula:2ad05db4-6a5f-4954-85b9-8b57ba1c49df}} states exactly the opposite. With p-values 0.004, 0.003, 0.001 and 0.003 of Friedman test for Hits@1, Hits@10, MR and MRR, respectively, we can reject the null hypothesis {{formula:0323cf0d-c337-4297-84c1-782a59156122}} at a {{formula:e9227e3a-657c-48bc-ab59-d365d0e4fcbc}} confidence-level {{formula:b7913df6-d06a-4cad-b7ee-cfdc9f4920cb}} . In the sequel, we conduct the Nemenyi post-hoc test to compare the methods pairwise. This test reports as significance the average ranks of two methods if they differ by a critical distance (CD) given by {{formula:271a1e69-5b8a-4714-9dda-6faf857cc65c}} , where {{formula:8b21e190-9a2e-4afd-be6d-9632ef62b8d3}} is the number of the datasets, {{formula:9f3a5a01-36cb-4f1e-8e25-f6edde2e41e0}} is a constant based on {{formula:3362fc23-efee-4cc1-8876-00e52ee47672}} , and {{formula:1285807e-434d-4a53-b528-6bdfe9ee0ee0}} is the number of methods in total. For 8 EA methods, 8 datasets and {{formula:4a02f781-7e92-45e8-8cfd-67e87731717a}} , the value of {{formula:fd7b5af3-70f6-4f3e-9772-23c093898f95}} is 3.40.
| m | 7eb7134f387b799d8bea2644d1f2c27e |
With the CBCT and MR segmenters extracted from APA2Seg-Nets, we integrate the segmenters into our anatomy-guided multimodal registration pipeline for registering MR to CBCT. The CBCT and MR liver segmentation from segmenters are inputted into RPM to generate the transformation parameters. For qualitative studies, we first compared our registration results with classical previous works of intensity-based affine registration and intensity-based B-spline registration {{cite:5c76d099afbf677c2f640425a82d79138f2c09ea}}, {{cite:91606f9ff45b20355c126ff2cfec08be28a70b41}}. We also compared our registration results with intensity-based affine/B-spline registration based on CT images translated from CBCT and MR using APA-Net - similar to the idea in {{cite:8ed78714a47878601b7440f43191b216fb8ea8b3}}. Two examples are illustrated in Figure REF . The ground truth (GT) CBCT liver mask (green) and the transformed GT MR liver mask (blue) are overlaid on the CBCT image to qualitatively evaluate the registration performance. As we can observe, neither intensity-based registration methods can correctly estimate the MR transformation, while our anatomy-guided registration, as demonstrated in the last column of Figure REF , can more accurately map the MR to CBCT images. Compared to the RPM registration based on ground truth liver segmentations, our anatomy-guided registration based on APA2Seg-Net's segmenter provides similar registration performance. Additional registration results using our method are shown in Figure REF .
| r | 584a2f45d5b0c26095268a09fbf7248e |
Lemma 3 Let {{formula:31e0f7c6-c38f-4a8b-936a-da233d5c6e18}} be a nonempty set (possibly uncountably infinite). Let {{formula:1a20d63b-bad9-446b-9427-5501beea144f}} and
{{formula:a8585ae7-3965-41c6-9f8c-f6c03b09b560}} for {{formula:f511d342-91e4-4f1a-8add-1cc5b5a233de}} be measurable spaces.
Then [see similar Lemmas 1.7, 1.8 in {{cite:df041b6e6bb740b8429516f04bfbc1b7588e8ca4}}]:
| r | 13926eb3e55ecf3548e8e47c975b2b38 |
Figure REF (a) shows a fine-structure split Gd{{formula:a977d1c6-8d47-4557-83fe-5cd5bdd627f0}} ESR spectrum at {{formula:280a5a8d-9f3a-407c-82c9-fd53d361fb83}} = 4 K for Sm{{formula:57cf5803-ea68-400f-92a2-1c3af869ca36}} Gd{{formula:698a9e23-bc4f-4bfd-9eb6-6281cb68668e}} B{{formula:b9195f53-4e59-47ed-ba26-a1ffde6e4c01}} ({{formula:0cb0f6f0-38e7-4693-8efc-db3d09d05559}} = 0.0004) with applied magnetic field {{formula:3d1174ef-28cc-467a-ae8f-6f957a32bc73}} parallel to the [100] direction. The well-resolved fine structure is characteristic of spin probes immersed in the insulating sample bulk allowing the weak crystalline electric field (CEF) of the Gd{{formula:8b466c96-7812-4c2c-9dd9-48fe7747048f}} ions to split the line {{cite:46b273ab1355e5bdd5b32f19966e2ff9539af787}}, {{cite:aaadaf2d01dee8eb5a33f12b83933de62d96d90f}}. Gd{{formula:bfbbc5ea-86bc-4a67-bf8c-4b3a83b5f133}} substitute Sm ions, which have a cubic local symmetry. As such, a cubic CEF effect is expected for Gd{{formula:19699722-0223-4341-b5af-72dc1f19cc9e}} ions. In fact, the red solid line is a simulation with seven resonances considering a cubic CEF spin Hamiltonian with a Gd{{formula:81056924-4446-45d3-9394-3794c68c0035}} crystal field parameter {{formula:dbdc5232-e41a-49ff-919a-d7e65f967cdd}} = -9.5(3) Oe {{cite:68861b70c43f0f01beb4ae4dfc6aeb715b9054c7}}. Two pairs of fine-structure transitions are close in energy, which results in weak shoulders. In order to analyze our ESR line without the fine-structure influence, we turned the sample by 30 degrees away from the [001] towards the [110] direction until the Gd{{formula:6ff9a9c2-234b-4f40-a306-e04aaee2cd75}} ESR spectrum is collapsed into one Gd{{formula:429f1444-43a3-4356-b325-234e6f423d9d}} resonance line {{cite:aaadaf2d01dee8eb5a33f12b83933de62d96d90f}}, {{cite:46b273ab1355e5bdd5b32f19966e2ff9539af787}} as shown in Figure REF (b). The red solid line is the best fit with a Lorentzian line shape, which is expected for an insulator.
| r | dd0bd14a3a62bb6859acd6f4461c6576 |
We provide a Gaussian approximation technique for an expectation of smooth functions via the Stein's identity.
The technique has been developed by several studies {{cite:eb87f92fe94f71cd0e8471aebf55f6be1ed4abd4}}, {{cite:7b62cbf48958b7090b47d5d8d213767958ad5f97}}.
The following lemma is a straightforward application of the result by {{cite:ce05f4c0332a4c60c2eda43c46f3ef4b83e349fb}}.
| r | fca69dfed3f243c4f29743f3a90e1683 |
The coincidence between quantum probability and the degree of belief with coherence should be distinguished from other major interpretations of classical probability.
For example, in the logical interpretation of classical probability, (conditional) probability is equivalent to the measure of the plausibility of a logical statement under incomplete information {{cite:4cf1fbd71e8a95e69dd7294e8789f325b4480488}}, {{cite:eceff1bfcda81e1a1fe028326a8f2155f2c84d19}}, {{cite:ed3a0ef1a241d7e93a797cb61eb73d411f04b237}}, {{cite:5ceee14690f3e870b904644a6842fbf3cd4d0254}}, {{cite:018282be4c68bffd7a61e072e719fda7195fadae}}, which obeys natural inference rules. In contrast, quantum conditional probability does not obey the rules in the case of non-commuting projectors {{cite:263b2a9e967a9a1d2b01a13f1eaf91f2f5b00f5a}}.
| d | 29fe497ec7ce0deb4eb4832d1469d9bd |
Our NIR spectroscopic observations have revealed that in addition to dust-formation, dLHdC and RCB stars can in most cases be distinguished based on their values of {{formula:5ce90188-2226-4e54-9f43-5c3f3392338d}} O/{{formula:cd5262f4-8d8c-406e-aec9-c9ce80998159}} O. dLHdC stars in general have a lower {{formula:dc6bb9b0-b890-42cd-b8df-7ead47886cba}} O/{{formula:e0786b84-5616-46e3-8476-e372c95f5825}} O than RCB stars. It is not surprising that the oxygen isotope ratios are an important factor in the study of dLHdC and RCB stars. Anomalously low {{formula:0a12c445-e108-49c1-9a0f-86eb4346e085}} O/{{formula:66c5d80d-2f3c-489d-a61e-ee6a3e5fdc1a}} O in dLHdC and RCB stars was key to identifying the merger of a He-core and a CO-core white dwarf as their formation channel. {{formula:bea0b432-b23e-4ee4-8749-88f3dc8b5257}} O is synthesized by the partial helium burning reaction {{formula:c02fd783-e191-4ae7-8c74-8f255984a60b}} N({{formula:f2cba0d8-4efb-4a0c-9001-cb379776a93c}} ,{{formula:b73ceabf-862f-4c2e-a8c3-2b7a353c7a20}} ) F{{formula:af188d58-fa56-4728-8d7a-a1f7c8eb4e9f}} ({{formula:e8ac7539-c3c4-4591-a5af-e0c153d5762f}} ){{formula:a12fc151-3fa4-47f6-82dd-431f9eb078e9}} O. This reaction is efficient at temperatures of {{formula:c8b266b9-6181-4f7f-a3de-f413aa3a5b66}} K {{cite:5bbdc612dc973a1e14898281ec06c8cd17b63fce}}, {{cite:dcc96c2daf4bd8be91f2b483d0c9f74eccb48a41}}. At higher temperatures, {{formula:882481ab-209b-447b-9b7b-bbd315eafc3a}} O is burnt to {{formula:ba74e9b1-9481-4728-b6f7-ebd2eaf1f7ee}} Ne. These conditions can be achieved in a thin helium burning shell around the merger remnant of a He-core and a CO-core white dwarf {{cite:5bbdc612dc973a1e14898281ec06c8cd17b63fce}}. The {{formula:107401a2-4dca-4ed0-9686-708b4c96c0f9}} O is convectively dredged up to the surface of the star within the first few hundred years after merger {{cite:e69c7911ab2fecce1949394043d109e3ea4c4275}}, {{cite:e2958d40f6e59ffa78d5e1aa29971887c1de4581}}, {{cite:77d00b458f72ee3324a12ebf3f8cd6fe96d732dc}}. The photospheric value of {{formula:623adc83-7880-4193-b68f-aa31d63262ff}} O/{{formula:70c22c3d-c790-4925-a7ae-d85c531bb403}} O in dLHdC and RCB stars is thus set within the first hundred years and remains constant for the rest of their lifetimes ({{formula:78655273-20bb-44ab-b736-229217b3ef31}} years). Here, we explore the properties of the merging white dwarfs that set the values of {{formula:e6fd126a-205d-45ce-833d-226c589f4d1d}} O/{{formula:1657a884-dbf7-478b-9daf-9fc99af0aa64}} O in the remnant supergiants. We also discuss the implications of our observations on the dLHdC-RCB connection.
| d | caf438d6740224b0b1b671d45fdd453b |
The problem in a class of radially symmetric bodies was first stated and solved by Newton himself in 1687 in {{cite:ea905813a60842268a5583ba347468d6a382d8f1}}. The more general version of the problem was posed by Buttazzo and Kawohl in 1993 in {{cite:e16e022527b5b5a5843a34d61e3f16032f10cda7}}. This general problem can be formulated in the functional form as follows:
| i | 686dc17442671d80b1181c342e36af30 |
Moreover, {{formula:c2ecd187-cce2-4a0f-bc7d-b53e81c781da}} does satisfy the Hörmander's rank condition {{cite:23a5c9704d19e52d8164200f09a32484d43f94c7}}
{{formula:2b29ac7a-5ee1-4066-b42d-defbcbca7fb7}}
| i | efbffb3f2d22a8411e9040e94046dc83 |
Decomposing data into disjoint independent factors of variations, i.e., learning disentangled representations, is essential for interpretable and controllable machine learning {{cite:d08fed4457020fa388d455bc84170bfae0e71497}}.
Recent works have shown that disentangled representation is useful for abstract reasoning {{cite:4923dcd7a954041a721ef78428a0e7aca38264b0}}, fairness {{cite:675bcafe0bf945d5fe9be7f87202c3aaacdcb5e6}}, {{cite:9cde50d952bcdd167caa7ffd9ad47e918a674dcb}}, reinforcement learning {{cite:f1aea7385e9d28b90b07b2dc8a73add3b3ce9b6d}} and general predictive performance {{cite:b3b91be1a7a0ee9edb469add3d1d3858efba6485}}.
While there is no consensus on the definition of disentanglement, existing works define it as learning to separate all factors of variation in the data {{cite:d08fed4457020fa388d455bc84170bfae0e71497}}.
According to this definition, altering a single underlying factor of variation should only affect a single factor in the learned representation. However, works in learning disentangled representations higgins2016beta,ChenLGD18,locatello2019challenging have shown that this setting comes with a trade-off between the precision of the representation and the fidelity of the samples.
Therefore, learning precise representations for finer factors, i.e., each factor of variation, may not be practical or desirable.
We deviate from this stringent assumption to learn group-disentangled representations, in which a group might include several factors of variation that can co-variate. For instance, groups of interest may be content, style, or background. As a result, a change in one component might affect other variables in a group but not on other groups.
| i | 1542a84fa0313939c834da7570dab58b |
Therefore, this paper aims to add the influence of the laser field during electron-nucleon scattering when {{formula:85a3fe4c-eae1-40ae-94e3-f9ea7ff1761b}} is comparable to the nucleon radius. In order to analyze the influence of the laser field on the electric form factor, the nucleon will be treated as a spinless particle during this scattering process. The laser field's impact will be examined only for charged electrons using the Volkov formalism {{cite:1ce4cbdc6002ab86cc3e54237ef0a22b5eb945a1}} for unpolarized electrons. Plane-wave functions will be used to represent initial and final electrons. In the second section, we construct a theoretical analytical calculation of the differential cross section of electron-nucleon scattering in the laboratory reference system in both absence and presence of a laser field. We assume that, in the first Born approximation, the electron exchanges a virtual photon {{formula:20443c7e-7fa0-4207-83a6-d6ab4daab9c2}} or a {{formula:27777451-b14a-43a6-8cfa-5ad1c1126b94}} boson with the nucleon during the scattering process (Electroweak interaction). This theoretical approach can also be examined when the target is a system of protons and neutrons. In the third section, we present the different obtained results. Finally, a brief conclusion is given in the last section.
| i | e5f3ffd3688aacf5539d3edfc18024ce |
Parton showers are a cornerstone of computer simulations for high-energy
collider physics {{cite:fb9bcd38a41e743993a9b6d404d59381f137df76}}, {{cite:5bb2e6710c314b6ecfb64a9e221d6de8202957f7}}. They implement
the evolution of QCD from the hard scales to be probed by experiments,
to the low scale of hadronization, where the transition of quasi-free partons
(the quarks and gluons of perturbative QCD) to observable hadrons occurs.
In this process, a number of additional partons are generated according to
evolution equations that are based on the factorization properties
of QCD amplitudes in the soft and collinear limits.
The most commonly used parton showers can be thought of as numerical
implementations of the DGLAP equations {{cite:877308869143f2ec247d2d2bb0cb8f417453d953}}, {{cite:3de2f958e7d3a046f57fee204667b3d4b1427174}}, {{cite:022e72eb2de447abaee0f95c8460597d42d8c6ef}}, {{cite:22771957cfbdc214b14b1c9015d591f6b1ad3e6e}}, but various other approaches
exist {{cite:4c2ef1003a80fb4757472aca2eff4cd3b3e5a726}}, {{cite:c3fb8edd0ce1fa142116f1929b90522c262175ae}}, {{cite:ef23123609a6dd174ed8539942c84173f3fd53b1}}.
| i | ef3a8ee02a2574874a6fd09c8b274c43 |
Fourthly, what the previous sections prove is that Alice is capable to steer Bob state in Paris by choosing different measurements at Tokio. This is possible due to the spreading over large distances of the entangled wavefunction, i.e. the spreading of the single-particle entangled wavefunction. To produce the steering she ask Bob about the kind of state he wants, then after turning on the SGE by using a classical control protocol (capable of sending a single atom or {{formula:891615db-2434-4029-85e9-05a3cbbf8bea}} atoms, as she wish), she could be able to steer Bob quantum states in such a way that this process rules out the existence of local hidden state models {{cite:06ad3bee21f7db6b799a2bd6a84178ad2b9e32b7}} (using some Bob's protocol if he does not trust Alice). In concrete terms, by the use of {{formula:bab40097-bbd5-4c69-822a-7f8ed059bff4}} atoms Alice, by means of measuring the position observable, she will obtain {{formula:27bc6b76-60f7-47ef-bf2e-44145217402b}} times the eigenvalue {{formula:de32c807-af19-4786-8842-fca3307e4a5b}} at Tokio, whereas Bob is going to obtain {{formula:eec31d63-5d04-4de4-8fa1-dfe07cab9351}} times the eigenvalue {{formula:a91dfca7-9864-421f-8e98-836300df3873}} at Paris. On the other hand, by the use of {{formula:6ee52c53-4954-4af2-a719-400dad897608}} atoms Alice, by means of measuring the spin {{formula:7814e529-4cdf-4ccf-b3c3-2ad13fd0bb6e}} , she will obtain {{formula:9625ce55-65af-4651-b3ba-12b54ead2aa3}} times the eigenvalue {{formula:f35bd99e-41fc-46df-bd09-90c1eed88a26}} at Tokio, whereas Bob is going to obtain {{formula:8cace5fc-f239-4960-a9c5-681966924b7f}} times the eigenvalue {{formula:2a977691-e595-49b1-b8d6-9c08f0750abe}} at Paris. Complex correlations could arise by measuring {{formula:bb3104ec-6f7b-47d1-8eb8-9680da99cbdf}} or by measuring {{formula:3d989a8c-d1d1-4e99-ae7f-68022bffe0e6}} .
| d | 968586ea1df62ce88bda53512c7beeb4 |
Whenever the statistics of a measurement on a composite quantum state contradict the assumptions of local realism, thus violating a Bell-type inequality, the correlations are referred to as nonlocal {{cite:6020cd4d7d98c04ee04300fb7af43beea177de95}}.
These nonlocal correlations are used to certify private randomness in device-independent quantum key distribution (DIQKD) {{cite:690c6bd36bf0bfab0bc138a0694751b20c6562f3}}, {{cite:b65730bdc8d5a7df0a6de500bcfe2c651f109552}}, {{cite:8e242f0168f6eb65d2fada3a61801f58a64b4b94}}, {{cite:cac0233aec8f794b4d148c85a3298599e5a4bdfe}}, {{cite:d11f82f9c47e91c540f266caedc154cf3da17366}}, {{cite:719caa2a8c48274896635744506dbb1f8dcbb1ad}}, {{cite:ce94c50a420555de66a0c8fe3d12ced8e007e16b}}, {{cite:7042e5eebcf56410f070d7f85d82d035618b9556}}, {{cite:8e54dba1985ba16817a2328c2caea2b0af03eafa}}, {{cite:4a1d2ac8b8df3a4d79a50b0002d080ee4454d07c}}, {{cite:43d0c538d01ea5da756e0571ff4f318002936278}}, {{cite:d038d51c03ac2cd62cb78a6503fb8ffbaf1ae553}} and device-independent randomness generation (DIRNG) {{cite:097378ffe6f4a2e5cfeb68c4b741c4cc830d682f}}, {{cite:79bd3e672524bdde150fed73bc1a3e9034f00484}}, {{cite:2ab84ba2b63c309f31c3a68021cda91410cce816}}, {{cite:79eb6134b7c74fe6970b8f878d04668a00788f85}}, {{cite:8e9043eefdb86041cdb26c7cb12dd7bd4d523674}}, {{cite:21e8ff712a0b720b4b8365f6fcd76e77d3a62356}}, {{cite:3a73a84dcf0e4ae253cbe0472e81f3a4c2e44adc}}, {{cite:beaa7623a04e1e1d3189bc82112837c7c22d842b}}, {{cite:9f93ca8b3db9cec24b07a26a45ec7b8fbb9bed66}}. For quantifying randomness, estimating the guessing probability is often an important task. The guessing probability is the probability with which an adversary can guess an outcome of another party's measurement.
If the guessing probability is less than 1, the adversary cannot predict the outcome with certainty. This implies the presence of intrinsic randomness in the system. However, bounding the guessing probability is not an easy task. Typically it is not possible to explicitly compute the guessing probability, but one can only provide an upper bound by solving a semi-definite optimization problem. Usually, one bounds the guessing probability from a given Bell inequality, and the corresponding quantum violation {{cite:719caa2a8c48274896635744506dbb1f8dcbb1ad}}, {{cite:097378ffe6f4a2e5cfeb68c4b741c4cc830d682f}}. Here, one needs to use the hierarchical structure of the quantum correlations {{cite:3d2ca99e2f5236c66fe3c01a012eb250b64ffbb4}}, {{cite:928965e5bb0d08c5e7a5cd5339892d931dff9f6f}} to solve the semi-definite optimization problem.
The complexity of this optimization problem is increasing and becoming computationally demanding with the number of settings and outcomes.
| i | 63d29710e568da8137259e714a649eac |
where the parameter {{formula:a2f503dd-ce2e-4999-86fe-834329815feb}} can be further reparameterized as {{formula:73e6f545-df99-49f7-8313-cb25d27e0e37}} with {{formula:911ed88b-794d-43d6-bff7-f8fdd5e9b333}} and {{formula:4263f0bb-cefc-483c-aa64-096ff3ba726e}} is the mass of the exchanged meson. The model parameter {{formula:51c84ed9-6f20-44ee-848b-fb71042795fb}} should be of order of unity {{cite:8bc6a7162d56f317315511eb7d4a3eaee0fb0474}}, {{cite:0e598976a6ca33c25b5d5dd7e7fee60397f2a9ed}}, {{cite:9954d4049d6355e092b3f48fb84a94bf6e203089}}, {{cite:4d66da1eadd778b37e0622ee515b8b174974f27b}}, but its concrete value cannot be estimated by the first principle. In practice, the value of {{formula:b1eb7349-b5f2-489c-a4c2-db9353b13cfd}} is usually determined by comparing theoretical estimates with the corresponding experimental measurements.
{{figure:defe0e6e-898d-43e5-9162-3d2174222410}} | r | 0ba351417f272782673c47f162099987 |
This modulation is then generated a number of times ({{formula:ed8d7cd9-bacc-4878-9cbd-fa5ee45570dd}} ), saved, and fit to a gaussian corresponding to the probability of observing a given modulation amplitude for either the background only or signal+background case. These distributions are then compared to assess the ability of the detector to distinguish between the two models.
Samples of these can be seen in Fig. REF , where {{formula:b264abfc-70f1-4d7a-97e6-dcd1ced58d3a}} and {{formula:bbe7d4e6-fe2f-4033-94ff-303bb3e49633}} are DAMA observations from Ref. {{cite:5c9fd12567b2f43be2b988137097051b8447f201}}.
{{figure:43a4e170-ff40-415a-9fbe-d6d81e10554a}} | m | bce78d4a798563177b7231892534aa59 |
The framework proposed in {{cite:90034a70c5bf01faf6936becdbd4126ade1f4c0c}}, {{cite:5ab058f198366ee9546c877cc63a23e3a0a9795f}}, {{cite:06e4ab27247eb092cb5140c0a2dbd19f431c93b0}} relies on a systematic study of bouncing junctions at geometric and fluid interfaces. For regular junction hypersurfaces, one can use Israel's junction conditions {{cite:b1478c78f7befb8986c265402a96347b574b5708}},
about which we refer the reader to Marc and Senovilla {{cite:3e08a110dd9f305f76950d86955bdfc1c440ccce}}.
To deal with singularity hypersurfaces, we begin by analyzing the degrees of freedom and constraints.
In the regime of
“quiescent” cosmology (cf. Barrow {{cite:77f2e121b8dc5f6a9e2c5c16f77e0141ae491e35}} and Andersson and Rendall {{cite:57f8aeb03097011107aff46086aac5663a383e7f}}),
spacetimes have a monotone behavior (as opposed to BKL oscillations identified by Belinsky, Khalatnikov, Lifshitz)
and asymptotic expansions of Fuchsian type can be established.
The quiescent behavior on gravitational singularities is observed for large classes of matter models as well as for the vacuum Einstein equations in high dimensions, or for spacetimes admitting certain symmetries (for instance {{formula:a2cca8df-ee4b-4325-b625-f1a656484ddd}} symmetry).
| m | 74b93b83bc3ea40f5c2e13c9e4dbc123 |
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